The scientific “unit” we call the decibel
lcamtuf.substack.com618 points by Ariarule 2 days ago
618 points by Ariarule 2 days ago
The only thing you should know is that any use of bel and thus decibel should ideally have the reference level suffixed (usually in parentheses or subscript), not implied. The absolute sound pressure level is dB(SPL). The human-perceived loudness level is dB(A) and similar. The RMS voltage expressed in power is dB(u) (formerly dB(v), not same as capital dB(V)). And so on. And then each different instance of dB unit is simply distinct, only connected by the fact that it represents some ratio in the logarithmic fashion. Treat any new dB unit you haven't seen as an alien.
> The human-perceived loudness level is dB(A) and similar.
But db(A) doesn't really measure that for anything but sounds that could cause hearing damage, or test tones. You've essentially taken a newcomer's problem of underspecification and carried it into the given domain.
I feel like it'd be better to say dB(A) measures flaunkis, which is defined by the human frequency response. Then the newcomer's next question will be something like, "how do I use flaunkis to compute the loudness of a music recording?" And that's the right question to ask, because the answer is: it's complicated. :)
This is exactly it. The people who get confused by decibels are treating it a unit in it's own right when it's really just a ratio of some unit.
Disagree.
The people who get confused by decibels, are exposed to other people treating it like it's a unit in its own right.
I agree that what the parent described, should be done. If it was what was done, this article wouldn't exist.
As I've said in the other comment, I believe this should be ultimately addressed by the SI.
It's SI that caused some of this weirdness in the first place by discouraging "same unit" ratio units like m/m or kg/kg and then intentionally disallowing those derived units to be individually named. On the one hand, there is a sort of "clean sense" that km/km cancels out and disappears, but on the other hand there are too many "unitless quantities" in SI that are very formula-specific that a ratio unit would better explain and help save the wrong thing from being plugged into the formula. It's enough of a need that scientists found themselves using worse tools like deciBels for some of these "same unit" ratio formulas just to have "some unit at all" to avoid accidental unit-less mistakes.
Some Scientists and Mathematicians would rather use random log_10(x) functions than allow units like km/km in their formulas. It's wild, and SI has been a part of those decisions all along.
I would agree.
Right now what we've got is basically "millis", and you just have to know whether the speaker is talking about length or mass. I like your proposal.
I actually want those suffixes mandatory, because there may be multiple plausible suffixes for each use. For example the loudness might be dB(A), dB(B), dB(C), dB(D) depending on the exact curve or even dB(SPL) if the sound pressure level is used as a proxy. So it is much more confusable than, say, "millis" when suffixes are implied.
There is a legitimate use of dB without a reference point. An attenuator attenuates by -20dB, not by -20dBm.
This is right and all... But this usage still leads to confusion about what you are measuring your filter by.
There are filters we measure on power, there are filters we measure on signal amplitude, and "signal amplitude" can be ambiguous on some contexts too. There should be a way to specify this one better.
Well, dB is fully specified in that regard. It's always power. You can calculate the voltage gain from it under certain assumptions, and under normal assumptions you get that factor 2. But a -20dB attenuator will always reduce the power by a factor of 100.
people are often confused by decibels because the necessary disambiguation is more often than not absent (see: spec sheets of some kind of appliance talking about noise)
That is of course not true. dB without reference is perfectly fine to use for gain and attenuation. dBm or any of the variants would be flat out wrong.
Even then, you'll get different results if it's 10 dB of voltage gain or 10 dB of power gain. You need to know what the actual units are.
No, dB are always power gain.
Exactly, and that's why a voltage gain of factor 10 is 20dB, because it's a power gain of factor 100.
...unless we're talking about a unitless ratio, like "this has 10dB less power than that". Which happens a lot.
But we used to use the same unit for the absolute measure and the relative measure, like degrees Celcius/Fahrenheit. (Okay, % vs. %p is different but is probably an exception.) I see no particular reason to avoid suffixes in such situations.
It's correct to use dB without a suffix to indicate a pure ratio. (It's ok if some people don't see why that's correct. That's acceptable.)
Nobody (I hope) says that 100mW is "10 dBm" more than 10mW. That would be wrong. Readers would be confused. Most people would cross their fingers and correct it to "10 dB", but who knows what it might mean?
When I worked on a radar project, my fellow radar engineers (I'm software) used dB a lot. A lot of them would actually agree with the article, but historical sometimes wins even when you're aware of its shortcomings. Aren't we the same in software anyway? The email protocol, terminal escape sequences, the UX of git command line, etc... Each of those could have an "X is ridiculous" blog post (and I would enjoy every single one).
One upside of dB not touched in the article is that it changes multiplication into addition. So you can do math of gains and attenuations in your head a bit more conveniently. Why this would be useful in the age of computers is confusing, but on some radio projects both gains and losses are actually enormous exponents when expressed linearly, so I sort of see why you would switch to logs (aka decibels). Kinda like how you switch to adding logs instead of multiplying a lot of small floats for numerical computing.
> A lot of them would actually agree with the article, but historical sometimes wins
Indeed – as evidenced by some parts of the world still using non-metric units in daily life or even engineering :)
As a European if somebody tells me the diagonal size of a display in cm or meter, I'm simply not able to "grasp" it. I need to whip out the calculator and divide by 2.54, turning it into inches. It's just how monitors are measured in my head at this point.
When the Euro was introduced, I've heard people say things like "older generations will never adapt to the new currency, they'll always refer to the old denominations in their head" – which turned out to be completely untrue.
Adapting to new units is very possible, but it needs a concerted effort. Absent a good inherent reason or anybody capable of artificially creating one, it won't happen on its own.
Wasn't arguing otherwise. If anything, I was illustrating so: I used inch so much, that despite it not being the native unit of length measurement over here, for the specific purpose I used it for it managed to stick incredibly hard.
While I thoroughly enjoyed reading this piece of internet-rant, I've to argue that dB is still probably the best we have on this!
In RF engineering, expressing signal levels in dBm or gains in dB means you can add values instead of multiplying, which definitely appeared like a huge convenience for my college assignments! A filter with -3 dB loss and an amplifier with +20 dB gain? Just add. You can also use this short notation to represent a variety of things, such as power, gain, attenuation, SPL, etc.
I guess, engineers don’t use dB because they’re masochists (though many of them surely are). They use it because in the messy world of signals, it works. And because nobody knows anything that might work better!
There's nothing wrong with using a logarithmic system, that's not the complaint here. The complaint is that using decibels instead of bels is weird, and also that it's a scale and not a unit but people use it as if it was a unit without specifying a reference point, and also that the scale changes for different base units. Crazy how many people here are missing the point.
dBm is fully defined. Its reference is 1 mW into 50 ohms. I agree that using dB as a unit and not as a comparison (10 dB more power) is confusing, though.
A pet peeve I share! An expanded version of this article should become the article on decibels on Wikipedia.
I've read that article many times over my life and for the first couple times came back thinking I was too dim to understand.
Transparently leading it with "Here's something ridiculously overcomplicated that makes no sense whatsoever..." wouldn't fit Wikipedia's serious voice but actually be pedagogically very helpful.
There's often a Criticism of... section in Wikipedia pages.
Maybe this blog post could work as a source, although it would be better to find something more established.
Here's another related one that always bothers me: When you say something's loudness in decibels, you also need to specify a measurement distance.
The author of this article even accidentally makes this omission:
> It’s 94 dB, roughly the loudness of a gas-powered lawnmower
And that distance is very important; the actual sound pressure measured is proportional to distance^2. So for a lawnmower measuring 94dB, let's say we assume that we're measuring at 1m. At 2m away, the sound is actually 91dB.
And don't get me started about the fact that a halving in power is 3dB, that's just wacky. I wish we used base 2.
> And that distance is very important; the actual sound pressure measured is proportional to distance^2.
While we're sniping nerds, the inverse square law only applies in the far field (which is tautologically "far enough away for the source to behave as a point source and follow the inverse square law"). That's probably a good bit further than 1m for a lawnmower in the physical world. For loudpseakers you have to be about 2m away before the inverse square law kicks in, unless they've been designed to operate as line sources which decay linearly for a very long distance. For loud sound sources near barriers like the ground they behave like half point sources, which will eventually act like point sources but there's a good bit of distance before it is really measurable.
"The bel is named in the honor of Alexander Bell; this is in the same tradition that prompted us to name the “wat” in honor of James Watt."
This line killed me. I literally laughed out loud.
Do a deep dive into audio vu Meters and how they got calibrated. Without being 100% sure, it's basically a totally subjective model, where back in the 1920s the BBC and some US company decided to assert "like us" and two models persist which have been retconned into some BIPM acceptable ground truth but it basically was "test it against the one we made which works"
The hysteresis in the coil-magnet meter response turned out to be a feature, not a bug.
I worked in RF (radar) for a while and the dB/dBm is an incredibly useful tool there. It makes reasoning about amplifier chains and insertion loss so much more straightforward. It also means you can talk about transmitters and receivers in a comparable unit - in reality the signals are many many orders of magnitude apart.
Generally speaking, the db scale is very useful for many practical situations, and this is overlooked in this critique.
As have been pointed out, it's just a power ratio on a logarithmic scale, but this has many benefits, the main one being that chaining gain/attenuation in a system is just a case of adding the db values together. 'We're loosing 4db in this cable, and the gain through this amp is 6db, so the output is 2db hotter than the input'. Talk to any sound engineer and you'll do this sort of thing successfully without necessarily understanding the science, so that's a massive win.
I didn't get that reading the article. The author acknowledge that ratios are useful, but that there are specific problems in how we use this unit and how we picked and express the reference scales.
> On the face of it, the idea makes sense.
Your specific example is a pure ratio so there's no problem with it (there is no reference). Apart from the fact that I have to guess whether you are measuring volts or watts through your cables, of course...
So what I learned today, via another comment and confirmed with a dictionary, is that decibels (unspecified reference) is NOT pure ratio - it's a _power_ ratio. So it will be Watts, not Volts.
But that's why it's so confusing. Did they purposefully leave off the reference to indicate Watts, or did they mean volts (as I'd guess audio engineers typically do when talking about amplifiers).
No, it isn't Watts if there's no reference. It's a ratio of powers. i.e. amplification or attenuation.
To have an actual amount of power, you need to reference it to some particular amount of power, like dBm for power-ratio-relative-to-milliwatt.
> this has many benefits, the main one being that chaining gain/attenuation in a system is just a case of adding the db values together. 'We're loosing 4db in this cable, and the gain through this amp is 6db, so the output is 2db hotter than the input'.
I'm not a sound engineer, so to check my understanding: would this not be the case for any other scale indicator?
If you have a cable that loses 4m and you're sending 6m into it, you'd not get 2m out?
(The m being milli here, as in millivolts or whatever unit would be useful here — leaving it unspecified to keep the comparison to dB as close as possible)
No, because db is logarithmic. That's the key property that allows you to do addition instead of multiplication. Remember these are ratios here as well.
So the original example in linear units would be: We're reducing the signal by 63% in the this cable, and the gain through this amp is 199.5%, so the output is...
0.63 * 1.995 = 1.26
126% which is 20log10(1.26) db or around 2db.
-4 + 6 = 2 is a little easier to do.
It's a ratio, not a fixed amount. The amount you lose depends on the amount you send.
Abbreviation confusability is relative to { in fact one might say measured by ;-) - number? entropy? etc. } the listener/reader's knowledge/exposure, much as sound levels need a reference distance.
I have heard "bare K" refer to a great many different things, not just kilobits (transmission) or kilobytes (storage) or kilograms (drug trade) or kilometers (foot races) and on & on, but pages or items or etc.
The fundamental problem is that some humans like to abbreviate while others get caught and annoyed by the necessary ambiguity of such abbreviation. Sometimes this can be the very same human in different contexts. ;-)
In fact, there even seems to be some effect where "in the know people" do this intentionally - like kids with their slang - as a token of in-group membership. And yes, this membership is at direct odds with broader communication, by definition/construction. To me this article seems to be just complaining about "how people are". So it goes!
This is the primary complaint. The secondary one about voltage and power and the ambiguity of the prefix itself was addressed in another comment (https://news.ycombinator.com/item?id=44059611).
> I have heard "bare K" refer to a great many different things
The worst of the worst is when it refers to kilometres. Like, "I'm selling my car on the used market and its odometer is 150k", where they mean "150k km", but stacked prefixes are not allowed in metric, so the correct notation is "150 Mm" or "150 megametres".
I get immense pushback whenever I point this out - the response is usually along the lines of "but you know what I meant", and it inherently assumes that km is the universal unit for talking about distance traveled by car.
I point out that this is as ridiculous as saying "the hard drive is 4k GB" because they grew up with gigabytes; no, the correct notation is either "4000 GB" or "4 TB".
Also regarding bare k or kilo (especially キロ in Japanese), you can say something ridiculously ambiguous like "My scooter goes up to 30k for 90k and weighs 20k" (respectively km/h, km, and kg).
Great post, the fusion of scale with unit is a mess.
When using it as a factor, for example when describing attenuation or amplification it is fine and can be used similar to percent. Though the author is right - it would be even more elegant to use scientific notation like 1e-4 in this case.
For using it as a unit it would really help to have a common notation for the reference quantity (e.g. 1mW).
But I guess there is no way to change it now that they are established since decades in the way the author describes.
Scientific notation would be worse, because you can't add them to get the combined gain. That's where dB's really shine.
This seems exceedingly ignorant of the work decibels do in telecommunications, RF and fibre engineering. The voltage vs power relationship is something that exists and is a core memory of beginner blunders in the field, but it boils down to a simple 10 vs 20 division operation. Besides that, the decibel simplifies a lot of multiplying very small and very big numbers to summing of two-digit numbers that you can do in your head, and still preserve a big degree of accuracy.
Whining about it makes me really doubt that the OP has any practical experience about the things they're talking about.
> makes me really doubt that the OP has any practical experience about the things they're talking about.
Maybe not, but you can get used to many odd things given enough experience.
I totally share the authors view. I don't usually have trouble grasping the definition of a unit, but dBs are just hilariously overloaded.
The same symbol can literally mean one of two dimensionless numbers, or one of who knows how many physical units.
That's not normal, something as basic as units is usually very cleanly defined in physics.
Someone in this comment section said it's not a problem because there's usually going to be a suffix that is unambiguous. If that were actually the case, you wouldn't see these types of complaints.
This like arguing that aspect ratios are stupid and wrong because sometimes they apply to a screen which is really big and sometimes it's really small and sometimes they apply to a physical print or a photo or a billboard or a vintage TV and sometimes it's a jpg or a PNG.
Aspect ratio is a ratio. It can be a ratio between pixel counts, or between print dimensions, or physical display dimensions.
All of which are useful in their own way, none of which are directly comparable, all of which are understandable in context.
dB is the same. It's a ratio split into convenient steps - more convenient than Bels would be - that compares two quantities. The quantities can be measured in different units. The units are implied by the context.
The only mild confusion is the relationship between voltage and power ratios. But that's a minor wrinkle, not a showstopping intellectual challenge.
> Aspect ratio is a ratio.
Right, but in this case they only give you one of the two numbers. Imagine being told that your TV had an aspect ration of ":16", and you just have to magically know what the other number means in the context. And sometimes ":16" actually means ":4", because quadratic mumble mumble, and sometimes the number is scaled according to some other "how big it seems to humans" factor; all of which you also just have to know in context.
Imagine being told that your TV had an aspect ration of ":16"
We kind of have that with people talking about a screen or image being "2k" and then expect you to infer what the actual resolution and aspect ratio is from context.
The real absurdity of 2k/4k/etc is that those refer to approximate horizontal pixel counts, when "lines" (vertical pixel count) such as 480/525/1080/etc has been the typical dimension for such a long time. Why the switch? In the 16:9 world, ~2k horizontal is close enough to ~1k (1080) vertical, and ~4k horizontal is close enough to ~2k (2160) vertical, etc. so it can't be that the horizontal numbers round to the nearest k better than the vertical numbers.
I think the difference is that if you write a blog post complaining about the silliness of these labels, you don't get people telling you that no, you don't get it, it's totally fine, these are just aspect ratios.
I remember a recent post about the ambiguous nature of a pixel, and extended to aspect rations, that garnered VERY similar responses to what you described.
Yeah, it did get similar responses. https://www.nayuki.io/page/pixel-is-a-unit-of-length-and-are... , https://news.ycombinator.com/item?id=43769478
4:3 only makes sense to you because you know which is length and width a priori. I for example, always have to recheck that. So if it was written as 1.33 or 4/3 it makes the same difference to me, and is similar in that way to dB
Ratio is just a single number. 4:3 can be expressed as 1.3333~ and it just says how much bigger one number is compared to another.
RE: Yes, I was able to read and understand the article. I also have 8 years of EE. Ratio is still a single number in the end. You can have an actual size of a monitor 1600 x 1200 and the ratio of sides is 1600/1200, which is just a single number. You can express it in multiple ways. You still need at least one size + understanding of what the aspect ratio is used to describe in a particular situation (units (mm, px, ...), ...) to be able to calculate the complete dimensions of a monitor screen.
Same issue with % or ppm, or whatever.
You always need a defintition to understand what the numbers are abstracting in any particular situation.
Sure, and 10db means "10x more power". But:
1. 10x more power than what? It changes, and you Just Have to Know.
2. It's 10x more power; so if you're measuring power, like pascals, then 10db means 10x more pascals. But if you're measuring something like voltage, then it's not 10x more voltage, it's something else.
3. And if you're talking about sound, you may be talking about objective power; or you might be talking about how much more powerful it seems to humans.
> Sure, and 10db means "10x more power". But: 1. 10x more power than what? It changes, and you Just Have to Know.
That gives me an idea - explicitly state the basis and multiply. So the current notation "3 dBm" should instead be "1 mW × 3 dB".
Furthermore, any addition in the logarithmic domain must be grouped, like: "3 dBm + 5 dB" --> "1 mW × (3 dB + 5 dB)".
So my display aspect ratio is 2.5dB. Or is it 5dB because it's not measuring power?
Why, you're right: aspect ratios are stupid because people often don't bother distinguishing between SAR, PAR and DAR, leading to lots of confusion. And sometimes even mistake the ratio of pixel densities for the pixel aspect ratio:
Nothing better than spending hours encoding something, only to discover you got one of those wrong.
Respectfully, I'm not sure you fully understand how dB is used. The analogy to aspect ratios only works for one of multiple uses of decibel.
dB SPL and dB(A) are not ratios, they're absolute. You can derive them from a ratio and a reference level, but the former can be expressed in Pascal and the latter relates to Pascals after applying a perceptual correction function.
Similarly, dBm can be expressed as an absolute potential in Volt.
And then you've got the cases where it really just is a ratio (one of two possibilities).
You'll see all of these called "decibels".
You see why people are irritated?
Yep you have dB for a ratio, and dB SPL as a physical unit. Just as the article says.
And yeah, the issue is when people forget to use physical units, like if they say it's 30 degrees outside amd not saying C F or K or latitude.
The historical context is a bit meaningless as well since the main application for the OG dB is 101 classes.
Stop saying "one of two possibilities". It isn't. A dB is a power ratio. The fact that you can describe that in terms of voltage ratio is a simple reflection of the fact that power ratios can be described as a voltage ratio squared. When talking about voltage ratios directly from dB you're just short circuiting the necessary square root.
> The units are implied by the context.
This is the absurd part. There do exist other ratios that masquerade as units, e.g. specific gravity, and its meaning also changes depending on what you’re using it for - liquids are compared to pure water at 4 C, gases are compared to air at 20 C. As the parent comment points out, you can get used to things with experience. That doesn’t make them any less absurd. Look at Fahrenheit, for example. I’m American, and I still think it’s absurd, but because I’m extremely used to it, it feels natural.
Coulomb? In a discussion about units, leaving out the degree word or symbol made me initially try to parse it as that you must mean it literally, though context quickly makes clear that isn't the case ^^'
> Look at Fahrenheit, for example. I’m American, and I still think it’s absurd, but because I’m extremely used to it, it feels natural.
What do you find absurd about Fahrenheit?
If it is that its 0 point is not absolute 0 then I think you can make a good case, at least for scientific work. It's a bit harder to make the case for absolute 0 being the 0 point a scale for ordinary day to day use since all temperatures most people deal with will be 3 digit numbers (and making you degree large won't help because people will still need 3 digit number--they just won't be integers any more).
If you find it absurd compared to Celsius then I think it is hard to make a convincing case. They are both scales with a 0 point way above absolute 0, differing only on where they put their 0 point and the size of the degree. (They originally differed on direction, with Celsius putting 0 at the boiling point of water and setting the degree size so that water froze at 100, but Celsius soon came to his sense and flipped so the numbers went up as it got hotter).
Fahrenheit set 0 at the coldest temperature he could make in his lab and tried to set 100 at body temperature. Celsius (once he got the direction fixed) set 0 at water freezing and 100 at water boiling.
That gives Fahrenheit a smaller degree and puts the range of temperatures most people deal with most of the time above 0.
Celsius made it easier to memorize two temperatures that are very significant in many human activities, namely the freezing point of water and the boiling point of water (although the latter is probably less important...generally most people only deal with boiling water when they are trying to boil water and don't need to care about the temperature. It's not like freezing which can happen naturally and so people often need to monitor temperature to find out if there is danger of freezing).
But that 0 point in Celsius means that a lot of people have to regularly deal with negative temperature which is a little annoying.
The metric system chose Celsius, but I've not been able to find any compelling technical reason for that. A metric system with Fahrenheit would have fine too.
Note that unlike mass, length, area, and volume units pre-metric systems generally only had one temperature unit. There was nothing in temperature like miles, yards, inches, feet, furlongs, etc. for length and gallons, pints, cups, etc. for volume. A system that went with one single length unit (the meter) and one single volume unit (the liter) and then derived larger and smaller units from those using consistent ratios and prefixes that were the same across different types of units was a massive simplification.
I asked an LLM why metric went with Celsius and got a lot of circular reasons. For example it cited that various thermodynamic forumals would not work with F degrees because the Boltzman constant is defined in the SI system using K. But the Boltzman constant is defined that way because SI uses the metric system. In an F based metric system the Boltzman constant would be defined in R and everything would work fine.
The non-circular reasons it suggested were also not satisfactory. One was that C was more common than F in Europe at the time the metric system was created, which technically does answer the question I asked but then raises the question of why C became more common pre-metric.
It also suggested that having water freeze at 0 and boil at 100 fits in better with a decimal system which doesn't really make a lot of sense.
As for why C became more popular than F pre-metric it suggests that the 0 and 100 points were easier to reproduce. Fahrenheit's choice of body temperature for the 100 point was definitely a mistake as it is too fuzzy (it was even dumber than metric's initial choice for the meter as 1/10000000th of the distance from the distance from the North Pole to the equator along the meridian passing through Paris).
Freezing and boiling of water do take some care to use (you need to control pressure and contaminants) but are going to be more consistent that body temperature.
But there is no reason I can see that the fuzziness in Fahrenheit's 100 point couldn't have been fixed by simply changing the defining points from 0 and 100 to water freezes at 32 and boils at 212. Yes, it is not as easy to memorize as 0 and 100 but does let us have a scale where most temperatures dealt with by most people most of the time are 2 or 3 digit positive integers.
For the same reason that every other Imperial measurement is absurd – they’re completely arbitrary. 1 inch is 3 barleycorns, which can have very different sizes. 12 inches to a foot, because a human foot is a decent measurement, I guess? 3 feet to a yard, 5280 feet to a mile… these make sense for their time, but we are no longer in that time.
I understand the argument for Fahrenheit having better granularity with whole numbers in the human range of the scale. I don’t think that justifies everything else about it, especially considering the rest of the world somehow manages with Celsius.
As compared to to what? where C and K are 273.15 apart.
But joking aside, While you do point out some of the worst offences, 5280 foot in mile is a special sort of stupid. I do wish we would have metriced around base 12 like a lot of the old measurements were instead of base 10.
Base 10 sort sucks for quantities. I mean, we are all used to it and it works well enough, and having a proper base system is far far better than the alternative coughs roman numbers. but base 10 is a quirk of chance, we very nearly ended up with base 12, and I think we would have been slightly richer for it.
And before you give me the tired ol "BuT yOu HaVe TeN FiNgErS", no, you have 8 fingers and 3 bones per finger, a very common early way of counting for them who had to actually count large numbers(sheep herders) was to use your thumb to mark the spot and count on your finger bones, 12 on one hand, and 12 on the other, this is why 144 (a gross) is so common.
Update: I take back what I said about the mile.
/usr/games/factor 5280
5280: 2 2 2 2 2 3 5 11
> I do wish we would have metriced around base 12
Please clarify what you mean by this. Let me call your system altmetric for clarity.
Surely, you want altmetric to use prefixes that are powers of 12 - okay, fair enough. I see the analogy with the fact that 1 foot = 12 inches, and how base-60 is used in minutes and seconds (also arcminutes and arcseconds). (But why no thirds and fourths?)
But do you want altmetric to require all numbers to be expressed in base-12? If no, then your system does not allow easy conversion. In real metric, the fact that 1.234 kg = 1234 g is a trivial conversion, and it turns a calculation problem into a mere syntactical transformation. If yes and you require base-12, then you've basically alienated everyone. It would be about as weird as telling construction workers and doctors and drivers to use hexadecimal. But at least it makes unit conversions as trivial as base-10 metric.
Let's say you have your altmetric utopia with prefixes based on powers of 12, regardless of whether you require numbers to be expressed in base-12 or not. What do you do about the rest of the world which uses base-10?
You're the head chef for a cruise ship, and the upcoming voyage has 572 people for 14 days. (Imaginary) guidelines say that to keep people happy, you need to provision an average of 800 g of food per person per day. In metric: 572×14×800 g = 6406400 g ≈ 6406 kg ≈ 6.4 Mg (tonne), a simple calculation.
In altmetric, you still get 6406400 g, but now you need to start dividing by 12 repeatedly to form larger groups. Let's just say alpha = 12^3 and beta = 12^6. So 6406400 g ≈ 3707 alphagrams ≈ 2.15 betagrams. That doesn't make life any easier.
Or let's take a somewhat different example. When buying stocks on the market, you specify how many shares you want to buy and the price you want to buy at. But you can't say "I have $X, buy as many shares as possible without exceeding $X". So say you just received a $30000 bonus (after tax) and your favorite stock has an asking price of $68.49 per share for an unlimited quantity. In decimal math, this is easy to figure out - $30000/($68.49/share) = 438.02 shares, so you round down to 438 shares and place your order.
But suppose you're in some F'd up world where you have to specify your stock order in stones, pounds, and shares ("ounces"), where 1 stone = 14 pounds, 1 pound = 16 shares. So your order of 438 shares becomes 1 stone + 13 pounds + 6 shares. You had to do an excessive amount of busywork just to fit into that non-decimal system. And along the way, you might have to think about things like the fact that it's also $15341.76/stone, $1095.84/pound.
You're not the first person I've come across who wants measurements to be grouped/divided into units by some factor other than 10, usually 12. I did a lot of thinking about this, and my conclusion is that if you make an altmetric system where prefixes are not powers of 10, then you lose a huge benefit of the metric system. (The other huge benefit is coherent derived units, like 1 joule = 1 newton × 1 metre.)
> I take back what I said about the mile.
It looks like the derivation of the English statute mile is this: 1 mile = 8 furlongs, 1 furlong = 10 chains, 1 chain = 4 rods, 1 rod = 5.5 yards, 1 yard = 3 feet. You can confirm that 8 × 10 × 4 × 5.5 × 3 = 5280.
https://en.wikipedia.org/wiki/Mile#Statute , https://en.wikipedia.org/wiki/Furlong , https://en.wikipedia.org/wiki/Chain_(unit) , https://en.wikipedia.org/wiki/Rod_(unit)
This mythical altMetric utopia requires everyone to actually count in base C (to use dc notation) as well. the main advantage is that thirds and quarters(the useful fractions) tend toward whole numbers. In base 10 all you get are halfs and fifths(and nobody wants to use fifths)
everything would still be metric, the calculations would be as simple, every one would learn their baseC times tables and how to do baseC long division.
$3000 / $(68.49/share) = 54.59B1 shares 54 shares = total cost of $2B88.B6 take your remaining 33.07 and have a nice lunch
1000 Cgrams(1728Agrams) = 1kiloCgram 1000kiloCgrams = 1 Cton
but going smaller a third of a Cgram is 0.4 Cgrams a quarter is 0.3 Cgrams
Does this actually makes any ones life better... Probably not. but it has every advantage of using baseA and the minor(very minor) advantage that thirds and quarters are easier.
But this assumes that baseC won over baseA 1500 years ago, and if there is one truly global success story it is baseA, many languages, cultures, writing systems, but everyone(statisticly) uses baseA with arabic style numbers
footnote: I am using the slightly obnoxious prose of using baseA and baseC to avoid the confusing ambiguity that saying base 10 in base twelve means there are twelve numbers in a digit(where the word digit, coming from the way we count on fingers would also mean twelve.)
It's likely as simple as Celsius befriending/visiting France, while Fahrenheit - England...
Ratios are numbers. They are literally just fractions. No one argues that the numbers don't make sense because you can have different units. But that's what units are for – to know what does the preceding number refer to. Why have a unit that doesn't give you full information?
this
if a TV seller went bonkers and only said "it's 10:16", can you guess the actual size of that TV?
But that's not what is being expressed. You might as well complain that the ratio doesn't give you information on the price, weight, or power usage of the TV.
Consider the signal chain of a live audio system, from a singer to a PA.
The singer produces sound pressure waves into a mic. These pressure waves are measured in dB SPL, and the microphone's specifications will tell you its sensitivity, maximum sound pressure level, frequency response, on- and off-axis response, and so on. An engineer can look at all these specs to choose a mic based on the environment, how much background noise there is and where it's coming from, the quality and character of the singer's voice, etc.
The microphone will produce a voltage, which is measured in dBV or dBu. This voltage travels to a preamplifier, which boosts the signal to a nominal level by applying a gain (in dB, with no units since it's just a dimensionless ratio between input level and output level) and converts it to a digital signal -- measured in dBFS ("decibels full-scale", signal level relative to the maximum level that can fit in the bit-width of the digital signal).
Note that all the different signals going into the preamps have wildly different voltage levels -- a kick drum produces much more sound energy than a singer. And the ratio between SPL and voltage is not fixed; different mics have different sensitivities, and an active guitar amp will generate a signal many orders of magnitude stronger than a passive microphone. For some instruments like synthesizers, "SPL" isn't even a concept that makes sense because the sound is produced entirely electronically, rather than by capturing a mechanical wave. So, the preamps are configured to normalize all the incoming signals to one nominal level for processing.
After the preamp, the signal goes through a digital signal processing chain. Most of these processing steps will affect the level of the signal, and the amount is measured in dB (without units, since this is a dimensionless ratio between input level and output level. Remember, we're dealing with a fully digital waveform, so there is not even a physical measure of "loudness" or "signal strength" that can apply to the signal at this point.)
The signals from all the different sound sources are mixed together, and the mixer's per-channel volume faders are marked in decibels -- usually from +10 to -infinity, with 0 corresponding to "unity gain" (which means the output signal should have the same intensity as the input signal). Again, no units because we aren't measuring a physical quantity, just how much the mixer should change the intensity of the signal.
Finally, the signal is converted back to an analog voltage (measured in dBu) and sent to a power amplifier. The power amplifier applies an adjustable gain, and outputs a signal measured in watts (dBm) for sending to the PA system. You might then walk around the room with an SPL meter to ensure the sound is at a safe level; the value you measure will depend on the frequency and directional response of the speakers, as well as how far away from the speaker you're measuring.
Throughout this process we had signals in the form of sound pressure, voltage, digital samples, and wattage, at power levels ranging from microwatts to kilowatts. Even a simple physical quantity like sound pressure for a single signal is not straightforward -- how far are you measuring it from, and are you talking about SPL before the microphone or after the speaker?
The fact that a single unit is used for all of these different purposes is a feature, not a bug. If my preamp is close to clipping and I turn it down by 3 dB, how much do I need to turn up the gain at my compressor to compensate? Easy -- 3 dB. If we used more "appropriate" physical units at each step of the signal chain, it would be impossible to determine this number quickly or in your head; and would involve taking into account even more factors I haven't mentioned (like input impedances). The fact that decibels are scaled differently depending on whether you're working with voltage or power means that 1 dB corresponds to the same change in loudness everywhere without having to remember whether it's 1 dB of voltage or power.
dB for sound in particular aligns with human experience. The (10 -) 1-10 on a volume knob typically aligns with a logarithmic scale because we hear differences in loudness at an order of magnitude.
A linear volume knob would be frustratingly useless as you would have to crank it many many many times the higher up you want to go. Presumably hundreds of times. A traditional pot couldn’t do that of course but maybe you could satisfy your curiosity with a rotary encoder?
Nothing in the article and nobody in the comments takes issue with the fact that it's logarithmic. It's everything else that's the problem. (It's a ratio where the base value is situation dependent, and the base of the logarithm varies.)
But the base value is well defined, qualitatively (“a quiet room”), which is fine for what we are talking about which is “experienced loudness”. Once you go past log(3) it really doesn’t matter what the noise was at log(0).
I'm sorry, but did you read the article? This is not the complaint.
If decibels were used only to measure sound relative to "experienced loudness" there would be no complaint.
The complaint is that it is used in many other ways, often without distinguishing what the base unit is.
The issue is that it’s not “well defined” that it’s somehow subjective. But the whole point with a logarithmic scale is the small values don’t matter.
Does that also work for showers, with mixing hot and cold water. I feel that a 1% change in the knob/balance goes from too cold to too hot.
Nothing to do with decibels but the thermostat on the water heater might be set too high. If one lowers the overall temperature the ratio of cold to hot will balance.
You are bounded by a minimum floor for the hot water. Below a certain point you can get legionnaires.
To me it seems like one of two things: external pressure between hot and cold is mismatched so a small change to one side overwhelms the weaker flow.
Alternatively it might just be a broken or poor quality mixer that isn’t providing the appropriate ‘nuance’ of control, and that may indeed be expressed as some sort of non-linear relationship.
> Below a certain point you can get legionnaires.
I know you mean legionnaires' disease, but the idea of a bunch of soldiers getting to your house because you turned your boiler too low made me chuckle. Good thing the US have the third amendment to protect against this.
The thermostat could still be set too high. I think you might be overstating the dangers of legionnaires.
It also a simple thing to check and would be the first step in my troubleshooting routine for this complaint.
Here is a link describing the dangers.
https://www.heatgeek.com/hot-water-temperature-scalding-and-...
You could have log Watts or something, it doesn't have to be dB to be logarithmic.
We have a unit for that. It's dBm and very easy to grasp. 0 dBm is 1 mW, every 10 dBm is an order of magnitude more (10 dBm = 10 mW).
dB is only confusing if people omit which quantities they are relating. If it's clear like in the case of dBm which relate to 1 mW, it's an awesome tool.
Unfortunately, people omit the quantities all the time. Domain experts assume it when talking to each other, and non-experts repeat it without knowing that it refers to anything at all. (I still don't really know what it means for a sound to have "decibels".)
When referring to sound in the physical world, "decibel" mean dB SPL (sound pressure level). Which is defined as the ratio to the smallest perceivable sound pressure level. Unfortunately that is still a bit underspecified, it may be measured with a frequency weighting like A weighting. And then there is the integration time or other temporal aggregation, but that is separate from decibel/log.
When in analog audio, it usually means dbV, relative to a reference voltage.
And in digital audio, usually dBFS - relative to the maximum amplitude that can be represented.
You can't take the log of a quantity with units like watts. It would be log of some ratio of powers, and then it doesn't matter what unit of power you use because they cancel out. Instead, it matters what the denominator in the ratio is so we're back at needing something confusing like dB :(
That would be dishonest. You don’t adjust input power - you adjust attenuation
EDIT if you did let’s say approximate power, or measure and present the consumed power (as some systems do) you would still be in a situation about how to present this data. Do you present your users with a simple 1-10 (logarithmic) or a 10 digit display which sweeps over vast ranges of uninteresting values.
If you opted for a more compact scientific notation … well guess what that’s also logarithmic but in two parts LOL
Sure, but a. IME, volume controls with 1-10 are nowhere near log b. many manufacturers don’t even do this. A lot of car manufacturers seem to use 0-40 for the stereo volume, which seems completely arbitrary. I’m assuming they decided that’s a good balance between granularity and annoyance, but c’mon… couldn’t have at least capped it at 50? Halfway to 100 feels vaguely more intuitive.
This also doesn’t even begin to touch on frequency response curves.
Ever have a cheap set of external speakers that got super loud in the first quarter turn of the volume knob but were pretty much the same loudness after that? Yeah, linear pot for the volume knob.
No need for an encoder and software, though, logarithmic pots are readily available for precisely this reason. :)
This doesn't make any sense to me. Isn't this completely backwards? Wouldn't this behavior be expected from a logarithmic knob, and not a linear knob? I know what a logarithmic curve looks like, it rises quickly and then it tapers off, exactly the behavior you describe. But then you attribute that to a lineae knob! The parent comment confuses the hell out of me too, I am just really not putting 2 and 2 together here.
You're missing a critical piece of information. Human hearing (and vision) are logarithmic sensors.
Ears can register sounds from maybe 20-30 dB upwards of 120ish which isn't a factor of 4-6 in terms of power but rather a factor of 120-30=90 decibels or 9 bels or 10^9 or one billion.
Because your ears have absolutely enormous range you need the potentiometer (pot) to have a logarithmic taper to it. The amplifier has an essentially fixed amount of amplification so that's a fixed sound dB output. Your ears can hear a vast range. A linear pot essentially locks the entire output into the same 10 decibels as the amplifier maximum output through its linearity. Once you've turned it to 10% of the range it has precisely 10 decibels worth of range left. If you want to turn the volume down by 40 decibels you have to do that within the 0-10% part of the pot's range.
A logarithmic pot will give you maybe 40-60 decibels worth of adjustment by dividing things up differently. Every 20% of the range increases the output not by 20% but by a factor of 10 let's say. That gives you a pot with a range of 50 decibels which is enough that it roughly matches the absolutely miraculous range of the ear.
"logarithmic" here refers to the number on the scale being logarithmic in the sound pressure level. Restated, power is exponential in the knob value, which roughly matches human perception of a linear increase. An actual linear function is far too slow.
Got it, so the sound pressure is logarithmic, but the sound power is exponential, and you can control both at once with one knob, and they, align, quite well I guess.
The point is that sound perception is logarithmic. You perceive a 10 times stronger air vibration as twice as loud. So if you have a knob that increases the power that produces the vibrations linearly, you hear a logarithmic increase.
You need a knob that increases power exponentially to hear a linear increase in loudness.
No I’ve never had one of those LOL
Pots do log and lin scales but they only have a limited angular range.
I've actually noticed this two days ago with some bluetooth headphones and my phone.
The volume control on my android phone was acting just like this when my headphones were connected. When changing the volume with the phone only a small section of the bottom quarter of the volume control actually made a difference, but the volume controls on the headphone themselves were acting "normally".
Usually the phone volume is fine, it only screws up on bluetooth devices (my speakers + my headphones). I have to use the volume control on the device itself to have any good control.
This explains the weird behaviour, the phone volume changes are being sent linearly, but the headphone/speaker settings are correct and being set logarithmically.
i.e. somewhere a developer working on the bluetooth integration didn't understand the difference, screwed up and never tested it. That it's happening to both my Edifier speakers and my cheapo headphones probably means it's on the stock Android end (it's a pixel phone).
I've had the same issues as you, and here are some things I've done or tried as a remedy.
Try going into Android "Developer options" and enable the option "Disable Absolute Volume". Some devices cannot handle the way Android maps the "master" volume of the system to Bluetooth. With the option enabled you will have a separate slider to adjust the Bluetooth volume, and the volume buttons will instead only control the "Media" volume.
An alternate thing to do is under the same Developer Options is instead of disabling Absolute control is to change the Bluetooth AVRCP version to at least v1.5. v1.5 AVRCP introduces the Absolute Volume control functionality.
But, it could also be what you may have are Bluetooth devices that do not support Absolute Volume, or lack AVRCP v1.5 compatibility. If none of this works, I suggest purchasing the "Precise Volume 2.0 + Equalizer" app. I use this as it gives you more fine-grained control over the number of steps in the volume slider (for example, I now have 100 steps). It also allows you to calibrate the number of steps to a specific device, so you can literally change how many steps from quiet to loud. It's worth all of the $10 it costs, and has other nice quality of life features as well.
Logarithmic scale aligns with human experience.
OP isn't criticizing logarithmic scale in general but dB in particular.
If dB in particular aligned well with human experience - volume knobs would be labeled with dB values instead of 1-11.
A properly designed volume control affects the sound power output logarithmically, but is labeled linearly (with 1-11 or 0-1 or something like that) to reflect how humans perceive the effect.
People in the field get this wrong all the time — for instance, the volume control on ChromeOS appears to be a linear multiplier, yielding a control with huge perceived steps in the output between 0 and 3, and negligible perceived change in the output between 7 and 10.
I suspect that the confusing design of the dB contributes towards how often such mistakes get made.
Decibels in gain, those are fine. Though they use a silly base. dBm makes a decent amount of sense, given the RF background. The fact that decibels work differently for voltage and power is very weird, but understandable in isolation.
But audio decibels are horribly underspecified. And any other use of a decibel as a dimensionful unit is horrible. I think the RF people know, and that's why they use dBm. Any system that uses decibels as dimensional units needs to make their baseline clear.
I recently saw a fan advertising a low decibel noise "at 3 meters". And it's nice that they advertise (part of) the baseline, but it sweeps a ~10db difference in pressure under the rug, comparee to the standard 1m reference.
Decibels aren't units... they are ratios. The ratio could be gain, or loss, or compared to the noise floor, or the signal of interest, or a standard unit, such as Watts, milliWatts, or microVolts into 50 ohms.
>The fact that decibels work differently for voltage and power is very weird, but understandable in isolation.
If you have a given load, increasing the voltage by a ratio of 10:1 (20 dB) is exactly the same as increasing the power by a ratio of 100:1 (20 dB) (because increasing the voltage ALSO increases the current, and the power is the product of the two)
> If you have a given load, increasing the voltage by a ratio of 10:1 (20 dB) is exactly the same as increasing the power by a ratio of 100:1 (20 dB) (because increasing the voltage ALSO increases the current, and the power is the product of the two)
It's not that we don't understand this. We do understand this, and simply think it's ludicrous that the same nominal "unit" is used to refer to both, rather than calling the voltage one, say, "hemidecibels". Because we're not talking about power always, we're talking about, as you say, ratios.
> Decibels aren't units... they are ratios.
Until they are a ratio to a specific arcane reference level as mentioned in the article.
It's not that arcane, it's referenced to a sound pressure level of 1 pascal. Which, yes, is still arbitrary in that it all ends up back at the arbitrary values of things like metres, seconds, kilograms, etc.
Volts per pascal might make sense in some contexts (like your input buffer power supply), but log volts per pascal makes sense in others, particularly for audio applications where you stack gains and attenuations onto an already-logarithmic domain.
dB SPL is referenced to 20 µPa, not 1 Pa. You might be confused by the fact that the 94 dB SPL (1 Pa) is the default for microphone calibrators and specifying microphone sensitivity.
I was referring to the latter, which is why volts are involved at all. But I suppose if they'd chosen to follow the SPL zero point for the voltage-pressure scale as well as the absolute pressure scale that's would be equally arbitrary in its own way, even if more consistent in another.
I work in a related field (lots of signal processing, but not necessarily RF-y or audio-y), and it's a constant source of confusion. I actively avoid using them in technical communication because they will be misinterpreted by someone, and when we have customers who use them they usually don't actually know enough context to disambiguate them.
You haven't addressed any of the points the author made. You only show habituation and status quo bias.
I think the "whining" is just a stylistic choice and an excuse to talk about the things he finds worth noting. I didn't perceive the tone of the article as negative.
Having a logarithmic scale is a very different feature than having this one symbol to express all logarithmic scales with contextual meanings that sometimes need to be incorporated as two or three separate variations in a conversation.
Why wouldn't this work better broken out as half a dozen different units, with objective zero points and mathematical convertibility?
The fact that the numbers on the scale align with intuition at a few points does not mean that the scale is a good one. dBs are jargon encoded with false rigor. No other "unit" has flexible meaning based on the background of the speaker, but jargon does.
Decibels are completely ridiculous. They are only useful if you are a cable monkey just adding and subtracting amplification/dampening factors. As soon as you need to do any kind of non-trivial conversion or computation, dB* is more of a hindrance to understanding and simplicity, because you will always need to look up in some strange table of dB weirdness. Integrate over a spectral power density in dB/Hz? You better convert that to real metric first... Need to solder in a capacitor/resistor/coil as a filter? Better convert to real metric first, because only some pre-made filters are specified in dB (and there are quite a few weird conventions, so you better convert to real metric and check first...).
I do see needs for something like decibels. It is a useful way to communicate an inherently logarithmic quantity. The real and IMHO only mistake is that it was described as a typical unit, while it should have been a unit constructor and specially treated in the SI unlike others. (Not in the SI, but the [milli]meter in mmHg etc. and `p` in pH---really p[H+] [1]---are other popular examples of unit constructor.)
[1] To be clear, I'm aware that pH and p[H+] are technically different. But that's orthogonal here.
I'd say the engineers I knew building satellites at companies like SS/L and Boeing deserved a better title than than "cable monkeys".
"It's weird and blunder prone but useful" is not actually a counterargument to the author, who is not arguing that it is not a useful thing.
Yeah that was my thought as well. Decibels make it much easier to do link budgets as you can just add or subtract instead of multiplying or dividing.
That's an excellent application of Decibels (or really any other logarithmic unit). TFA's gripes are with the many not so great ones.
Yeah, I'm not really familiar with sound engineering, so I don't know how valid his points are. But I'm fully on board with the complaints about notation, there must be a better way to do it than the current way.
As someone who teaches this concept to.. art students I have to say that this complaint sounds a lot like the typical misconceptions and confusions a beginner would have.
Yes, dB is a weird and unintuitive concept and it takes a moment to understand it, but it is also extremely useful once you get it. The fact that people don't write out the reference values does not help either, people will bounce out that audio mix at -20dB when in fact they mean -20dBFS which is referenced to the digital maximum (Full Scale) value. Above 0dBFS you clip the waveform.
People leaving out the reference part is the mean reason for the confusion IMO.
So one thing I always wondered about with audio mixing is that clipping should be random? Like if the sine waves somehow all line up the momentary amplitude could be much greater than the typical amplitude.
And this would mean that there isn't a fixed volume above which you get clipping and below which you don't get clipping. Playing tricks with phases could prevent/cause clipping.
Is -20 db then simply a rule of thumb for preventing occasional clipping?
You're talking about the difference between Average amplitude and Peak amplitude. Yes, the peaks will be higher than the average, but not by a constant amount unless you're working with a pure constant sine wave. It will depend on the sound you're working with. The phase is part of that sound so generally you can't mess with it.
-20 db would just be a starting point, you could adjust up or down from there.
Doesn't OP addres that multiple times in the article? He constantly reminds that the unit means vastly different things based on the domain, and focuses on acoustics after that, which is what every laymen would think about given the mention of decibels.
The same can be said of any unit. "If you just learn to work with it regardless of its weirdness, it's completely normal" doesn't mean the standard isn't ridiculous.
I don't think anyone has stated that a logarithmic scale is bad. The type of logarithmic scale changing depending on the field it's being used in, and the non-standard notation (dBm being used instead of dBmW for instance), is just inconsistent for no reason.
For a unit of immense scale, I rarely see it used outside of the -100 to 100 range, though. That puts its daily use square in the middle of SIs giga/nano range. I'm sure the formulae are a bit easier by not having to include exponents, but I don't see a practical reason why dB's normal use can't have been covered by normal prefixes.
What sets the dB* aside from other American units is that this one is very close to following standard units. If it weren't for the deci- prefix and the usage of standard units like Watts and Volts ("Bell-horsepowers"), the inconsistencies in practical use would probably have been expected, making learning about the weird intricacies of each field a lot less infuriating.
> I don't see a practical reason why dB's normal use can't have been covered by normal prefixes
Because instead of numbers going like 1, 10, 100, 1k, 10k, 100k, 1M, 10M, 100M, 1G, and so on when using prefixes, we get a much more smoother numbers of 0 dB, 10 dB, 20 dB, 30 dB, 40 dB, 50 dB, 60 dB, 70 dB, 80 dB, 90 dB. You can see the the number for the dB get bigger, while when using prefixes the numbers get bigger two times in a row and then go back to smaller. With dB you usually just see a number from 0 to around +/- 100 or so. You can plot dB nicely as an axis of a chart and then see the slope of a curve in so many dB per decade.
> You can see the the number for the dB get bigger, while when using prefixes the numbers get bigger two times in a row and then go back to smaller
Interesting, I don't have any issues with that, and I see the numbers getting bigger and bigger no problemo. Perhaps it's an issue of metric/imperial, as I grew up in a metric country: I have a mental visual model of decades, while dB feels linear. The opposite is likely true e.g. in the US.
> You can plot dB nicely as an axis of a chart
Nothing prevents you from putting the decimal scale on a chart. As a matter of fact, many engineering fields do precisely that. One example that comes to mind are components datasheets: a lot is in log scales, but explicitly so, by putting the 1-10-100 numbers with naught-k-M-G. It's explicitly logarithmic.
Sure, log scales are done quite often with SI prefixes for absolute (non-ratio) data that doesn't have a standard reference (which is the case for component datasheets). But dB can be more convenient when you want to present logarithmically-varying ratios, particularly for gain or attenuation (which are relative to unity) or when you have a commonly-accepted reference of your absolute data that is a useful standard to compare against. This gives your 0-point typically at the top or bottom of the axis a standard meaning across all graphs in a particular domain, and then datapoints typically have about a couple significant digits above the "." of the dB datapoint that you generally are interested in.
I grew up in a metric country too, but still it is much easier to speak of 0 to 100 or so of decibels with decades of power being in increments of 10 rather than having to say 10, 100, 1k, 10k, 100k, 1M, 10M, 100M, 1G, 10G, etc of gain or 100m, 10m, 1m, 100u, 10u, 1u, 100n, 10n, 1n, 100p, etc of attenuation. Especially when gains or attenuations would be multiplied, then decibel makes it really easy to just add and or subtract in decibels. For an example, a signal with 10M of gain (or that is 10M times some reference) that gets passed through 100m attenuation would result in a 1M signal (which takes my brain some fiddling with those letters and numbers), but in decibel we are just dealing with simple addition & subtraction: 70 dB minus 10 dB equals 60 dB.
Logarithmic axes exist outside of dB and are just fine. They work for any unit too, so log(bytes) for example is ok. We don't specifically need dB for it.
> I don't see a practical reason why dB's normal use can't have been covered by normal prefixes
Because you can easily add dB values that are on greatly different scales in your head, especially when the values aren't exactly powers of ten. If I have 86 dBW of Effective Isotropic Radiated Power and -162 dB of free space loss to some distance, the power flux density at that distance is -76 dBW/m^2.
You can use logarithmic scale without making it a pseudo-unit that changes the factors depending on the application.
Additionally - attacking people you don't know for ignorance because they have different opinions is very narrowminded.
> and is a core memory of beginner blunders in the field
Are you into creating artificial issues to make understanding things harder? If not... what's your point?
> doubt that the OP has any practical experience
One quick search would save you from writing a very silly thing.
You are completely missing the point, which is that decibels are opaque and carry hidden field specific meaning that is not possible to know from the "unit".
This is not a criticism of how useful they are in calculations.
sound IS funny, db does work, and for people building the things that produce or record sound. Useing db is just another unit used in engineering. Now if someone wants to get into the (very facinating), psychoacoustic side of sound, where another unit has been tried, "phons", prounounced fonz ;) , then it becomes clear that determining sound pressure levels is a tricky thing, as at the low end of perceptable sound the real world power of the actual sound is miniscule when converted into heat or mechanical power, and at the othete end a amp/speaker set up that was 100% efficient would only need 5 or 10 watts of electricity to power a stadium concert. we work with what we have, in a past lifeI got a degree in sound engineering, but barely practiced it, found myself way more into enjoying the products that have been built to be used, but am always greatfull to the people who make it possible, who on occasion are entertained by the sometimes exotic ways that I abuse the equipment, as the good ones take pride in having thought of and planed for such things, but do like confermation from the field. STC ratings anyone?
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However you must concede that the perspective of an outsider can be refreshingly eye opening sometimes, even to experts. Especially when it reveals the arcane practices that make a field difficult to learn - for example here the point about the base being too implicit is very valid. The article is perhaps ignorant of a few things, but its criticism shouldn't be dismissed outright IMO. Accepting constructive criticism from someone less experienced at something is a good exercise in humility, and can often help you improve. It's far from a "curse in any field".
That would assume that the entire world hasn't already tried this a thousand times over.
Measurements are standardised communication tools. If you start changing the definitions, things fall out of the sky and on your head.
No, changing definitions was exactly how we ended up with SI units. That was a very good (and necessary) thing and definitely not the sky falling down.
This mindset is why the US is still using barley seeds as a standardized unit of measure.
Glad we never changed them and still drink in hogshead, use the original foot reference, and never resolved what base is a megabyte. ;)
You haven't addressed any points the author has made, we don't need to have "experience" in a field to know that ambiguous units are ridiculous and bad.
When I'm buying a piece of string for my garden, I don't need to find an agricultural textbook to know whether "10 meters" in agriculture is the same as "10 meters" in engineering, and whether the definition of "meters" depends on whether the string is made out of cotton or polyester. The same is not true for "decibels". People seem to assume that we're too stupid to understand logarithms, we're not.
Well 10 millimetres of rain is different that 10 millimetres thickness for say branch...
At first I was going to contradict you but then I realised 10 mm of rain is actually a measure of volume or mass, corresponding to 10 kg, right?
And of course, people use it mainly as a rate, i.e. 10 kg per hour, or per four hours, or six hours, or 24 hours.
And it gets worse when we start talking about snow, the density of which can vary a lot!
Well depending on area you are counting it on. So yes per square meter it would be 10 kg. Your rain gauge might for example not have 10mm spaced markings...
Could you elaborate on this?
If 10mm rain falls, and you have an open collection container, then the depth of the water in that container would be more, less, or the same as the thickness of the branch?
...as long as the container has straight sides. The area of the opening needs to be the same as the area of the container all the way down, otherwise the two areas don't cancel out.
Sure you can do that, and now you're measuring something different. The volume of an exotic container is measured in different units than the depth of rain falling from the sky evenly.
I have no idea what you mean here. Exotic containers? I'm talking about something like a measuring cylinder or a straight-sided glass or mug.
This StackOverflow answer probably does the subject more justice than I can: https://earthscience.stackexchange.com/questions/14587/what-...
but I'll try and explain it succinctly:
What you're measuring is the volume of rain falling per unit area in a given time (usually 24 hours). If you're collecting rain in a vessel, you divide the volume collected by the area of the vessel's mouth to get the volume collected per unit area. And in order to measure the volume in the container, you measure the height of the water and multiply by the area of the vessel's bottom.
If the bottom and mouth have the same area, those cancel out and you can just specify the rain height regardless of the size of the container. That is, if you have 1ml of rain falling per square mm over 24 hours, it will produce the same height of water if you set out a big container or a small container, as long as the containers have straight walls.
If they don't have the same area, then you can't use the handy mm unit.
I couldn't have explained it better myself. Glad you understand!
Aside from the last bit. The rainfall per unit area is not relevant to the shape of a particular container. 5mm of rain falls regardless of your container shape. Whether that 5mm of rain falling, also means that the water in your container is 5mm deep, is a function of your container shape.
It's not a unit problem. If you're trying to measure rainfall in a conical vessel, you can do that, and the conversion from collected volume to fallen rain will still yield the same 5mm out of the sky.
It's like telling a chemist that moles are a useless complication. They'll swear up and down how important they but have no reasons except that everyone in the field uses them so they must be important. Sometimes conventions live on past the original need they met and experts are blind to that because they're only experts in using the convention, not evaluating conventions. Moles might have made sense when we didn't even know atoms existed and perhaps dB are similar, though I wouldn't know about that one.
> Moles might have made sense when we didn't even know atoms existed and perhaps dB are similar, though I wouldn't know about that one.
Moles make sense because atoms exist.
Moles still work without knowing that atoms exist. The quantity being called "amount of substance" not "number of things" reflects that. However, they are still a redundant over-complicated legacy that doesn't need to exist.
Moles are used because they are useful abstraction. When you want to get from reaction equation to actual real word having some fixed weight is useful. It becomes useful to have fixed relatively usable quantity to work with.
They are relatively decent size for actually weighing out things.
And honestly mapping number of elementary particles directly to grams is not unreasonable. Even if because physics of world are tad weird there is still possibility for some sanity checks.
They're not necessary, just a complicated way of doing what SI prefixes already do. Chemists don't notice this because they're intertwined with a whole network of conventions that would all have to be discarded at the same time. That's the legacy effect - it's too hard to untangle all at once.
Inches are a relatively decent size for measuring lengths too, but people manage without.
The idea that helped make decibels click for me is that they're a way to quickly do both dimensional analysis and gain/attenuation calculations at the same time.
"Plain" decibels are simply (power) ratios. These can describe multiplicative changes in power. These are positive for gains (like in a power amplifier) or negative for attenuations (like path loss). They are unitless quantities.
Decibels add. A ten 10 dB gain (x10) followed by a 20 dB loss (x0.01) is -10 dB (x0.1).
"Flavored" decibels are in reference to some power quantity. For example, dBm uses one milliwatt as its reference. So 2 mW / 1 mW = 2 = 10^(3/10) = 3 dBm. These quantities have associated units, but they're still technically dimensionless.
Here's the key insight. You can only have one "flavored" decibel value per computation. Say you have some 3 dBm signal (2 mW). You can add as many regular decibel values as you want, but the unit is still dBm. 3dBm + 4 dB - 7 dB = 0 dBm. In linear units, 2 mW * 2.5 * 0.2 = 1 mW
If you were to do something like 3 dBm + 0 dBm, the linear units would be 2 mW * 1 mW = 2 mW^2, which is probably not what you want.
dBs are confusing. Different fields have slightly different conventions. People talk about any factor of 2 as a 3 dB change, when technically it should only be relative to power-like quantities. It's weird that some of these "units" can be added together, while others can't. The factors of 10 and 20 can be confusing.
But if you consider the units from a dimensional analysis standpoint, decibels are much more sane and intuitive than they appear.
> "Plain" decibels are simply (power) ratios. / "Flavored" decibels are in reference to some power quantity.
I think this is analogous to https://en.wikipedia.org/wiki/Affine_space . If I understand correctly, an affine space has absolute points and relative vectors.
In terms of types: point ± vector = point; point + point = illegal; point - point = vector; vector ± vector = vector.
Similar with datetimes - you have absolute datetimes (e.g. 2025-05-23T05:16:35Z) and relative offsets (+1 minute, -1 day, etc.). You cannot add two datetimes together.
A plain decibel would be a vector, and a flavored decibel would be a point.
> 2 mW / 1 mW = 2 = 10^(3/10) = 3 dBm
It's worth noting that this is wrong, in exactly the way that makes decibels confusing. 3 dBm is an absolute power figure (about 2 mW). 2 mW / 1 mW is a ratio of 2 (about 3 dB).
2 mW / 1 mW = 2 = 10^(3/10) = 3 dB.
2 mW = 2 * 1 mW = 10^(3/10) * 1 mW = 3 dB (1 mW) = 3 dBm.
Similarly, but in a very different context:
I have to teach non-engineers C programming for an undergrad course, which is basically trying to teach very explicit attention to punctuation (among many other things). "Watch those double quotes!", "single quotes, not double!", "where's your semi-colon??", and so on.
Then, three weeks into the course, we're passing values by reference with &, and I get the question, "isn't that scanf missing the and-sign in front of the string name?", and I'm forced to answer, "that punctuation doesn't matter, this time," because the C standard makes & do nothing in front of a string specifically because so many people were confused about that fact that a string's variable name is already passing by reference.
Yeah, that's a better way of thinking about it. That way you don't have any phantom bookkeeping like the way I was taught. The units are still right there.
While the author is technically right, I must argue that in the area of sound work, decibels make sense. Zero is base level, -3db is half loudness, +3dB is double. There may be a better way to describe loudness, but decibel is good enough.
But, no! -3dB is half power, not half loudness. -3dB down is just slightly less loud.
Exactly. There's no way +3dB is perceptibly twice as loud. That's easy to test for yourself. +10dB is roughly twice as loud.
For practical day to day use in very narrow context, yes.
But, what you're saying is only approximately correct (the factor is a bit less than 2) and there are many related fields, even in areas that would be relevant to the physics of sound reproduction, in which the same notation "dB" means something different.
> -3db is half loudness
Sure, perfect sense.
That's great, but only if 'Base level' is clear to everyone involved. Besides the base level, you also need to define what exactly you are measuring. Including the frequency weighting.
This makes a spec sheet that says "this machine produces X dB of sound" effectively useless.
Any reasonable spec sheet would not say that. I say reasonable, because in the audio world, people pay extra money for oxygen-free copper cables.
I'm looking at quite a few consumer level workshop machines. All of them have horrible spec sheets already. But on sound, even if they do mention it, it is still useless.
> -3db is half loudness, +3dB is double
It isn't tho. It's close but not exactly. And there's nothing about -3 behing half that makes sense except for familiarity (and it's not even wide-spread familiarity - most people wouldn't know how much louder +3dB is).
It's just an unnecesarilly confusing definition that stuck for historic reasons.
> It isn't tho. It's close but not exactly.
It isn't tho :-). It's not close to double loudness. It's double power, which is 1.41 higher sound pressure, which is only slightly louder.
So on my amplifier, 0db is the loudest and -50db, where I usually listen is what?
-47db is definitely not twice as loud as -50db, of course.
I'm not confident in what I'm saying here, so please correct me if I'm wrong as I'd like to learn:
Human hearing isn't linear in terms of loudness. So a 3db increase in loudness sounds like "an increase", but the pressure is actually double. Hence, it makes sense to use db to describe loudness even in the context of perceived loudness to human-hearing.
This is similar to brightness. In photography, "stops" are used to measure brightness. One stop brighter is technically twice the light, but to the human eye, it just looks "somewhat brighter", as human brightness appreciation is logarithmic, just like "stops" and "db".
3dB is “twice as loud” in that it’s twice (or half) as much power.
Part of the reason why the bel is used is that human perception is closer to logarithmic than linear (weber-fechner law), so a logarithmic scale is a better approximation of “loudness” than a linear one.
Again, technically, it is. But ear isn't scientific device, neither is your amplifier. What I was describing is more than an agreement than some precise measurement. 3dB is more or less double the volume but different frequencies have different responses so I really wouldn't want to have some "perfect" way of measuring loudness as it would be so needlessly complicated that it would be useless.
As someone else alluded to, 3dB is a doubling in power, not perceived loudness. 10dB will be perceived as a doubling in loudness. This is the original unit (the Bel, rather than deciBel) which was I believe derived by testing on human subjects to measure this.
TBH I don't agree with a lot of the article - yes, dB on its own only indicates a ratio, but certainly in the field I work with this is known, and there are qualifiers (dBA, dbFS dbU) which tie the ratio to a known value so you're talking about an absolute, known quantity - even the dBa which is mentioned as if it comes out of nowhere is something which most audio engineers know about and use regularly because it's important to know the difference betweent he signal present and perception of it by the listener.
I mean, it should be, unless your amplifier is taking its own liberties with the definition of dB.
You should have a legitimate question as to what dB’s the amp is referring to. What brand and model is it?
First, is it actually specified as dB’s? Most amps I’ve seen display volume on an arbitrary scale, no units specified.
Second, the amp has no way to know dB sound pressure, as that depends on the rest of signal chain.
So is the displayed figure referring to dBu, dB mV, something else, or something totally bunk?
If 0 dB is its maximum, then -50dB is 50 dB down in power from its maximum (so 10^-5). No m V or other post-fix needed.
Human hearing perception response is logarithmic. This is part of the reason we use the unit. Our senses naturally work in that domain.
> Human hearing perception response is logarithmic.
It is, but -50db to -47db (+3db) is not double perceived loudness. It's double power. About +6 or even +10db would be double perceived loudness.
Going from -50dB to -44dB is a much louder change than going from -6dB to 0dB.
Human hearing is logarithmic. The dB is measuring ratio of sound pressure level and it's accurate that +/-3dB is almost doubling/halving of the SPL.
That doesn't make sense. -50dB to -44dB and -6dB to 0dB is the same change in power, as a factor. If human hearing is logarithmic, the same factor produces the same increase in loudness.
The problem with using decibels is that since it is a relative unit you need to know what it is relative to, and that is often not just the unit but also the quantity. Unfortunately, this part is (as expressed) at times omitted or put in the wrong place. And its often also the engineers in the respective fields that keep using this incorrect notation spreading the confusion for those outside the domain.
E.g., acoustic engineers often write db(A) for A-weighted sound pressure levels. Yes, it is often noted this way, but it is incorrect. The correct way is to specify the quantity and that the quantity is A-weighted, `L_{p, A} = 80 dB` for example to express an A-weighted sound pressure level of 80 dB.
Regarding sound pressure and sound power. Sound power is not expressed using A-weighting because it does not make sense. Sound power is a property of the source. A-weighting is a property of the receiver, that is, the human listener.
> The problem with using decibels is that since it is a relative unit you need to know what it is relative to
Ye but that is also the point. The author seem to prefer to memorize dozens of absolute values.
I see dB scale units used without contextual issues in near uniformity. Unfortunately, I have to agree with the OP, that microphone capsule manufactures seem to be an edge case. I'm not sure where dBV/Pa became the standard. I can understand why given 94dBSPL@1000Hz calibration standards, and the measurement equipment of the time, but I've run into my own fair share of datasheets with lines such as 'Sensitivity -45dB' with no units or other call outs for the standard in use. Thankfully, it seems like most modern datasheets use mV/Pa which seems like a much better unit in my book.
"This is nuts: it’s akin to saying that the milli- prefix should have different meanings depending on whether we’re talking about meters or liters."
Were were here recently with "mega": Sometimes mega is squared as in megapixels. Sometime not as in megabytes.
No biggie.
Db in audio is a relative scale and that makes perfect sense. If you mixer goes + or - 6db that makes sense but can't be measured as power, your mixer might not be plugged in to any speakers so relation to real power is moot in the digital realm.
3 eq bands with -+6db makes sense too. Doesn't need to be precisly specified to be of immediate value, +-12db is clearly something else and users know what.
> Sometimes mega is squared as in megapixels. Sometime not as in megabytes.
Even worse is Mega in Megabytes could be 1,000,000 or 1,048,576 and it's more or less up to you to know what's what
(Yeah, there are formally megabytes/mebiibytes/MiB/MB, but I honestly cannot recall the last time I heard anyone use anything other than just "megabyte" for 2^20 bytes... Or even wanted to refer to exactly 1,000,000 bytes. Other than decades ago when disk manufacturers wanted to make their hardware seem higher capacity than it really was)
I think the biggest issue by far is that many of the different contextual uses for dB are all in the same domain, or very close.
When you're talking about the loudness of sound, in the same exact context you might care about SPL, perceived loudness, AND gain.
If it was just a matter of "in electrical engineering / physics, dB implies this unit + baseline, when dealing with acoustics, it implies this other unit + baseline", it would be less problematic.
Megapixels aren’t ‘squared’ though?
Ah, unless you’re trying to make ‘pixels’ the same unit as in ‘pixels per inch’…
The problem there isn’t how ‘mega’ is applied but how ‘pixel’ means both an area pixel as well as the linear size of a pixel.
> Sometimes mega is squared as in megapixels.
Is that right? A pixel is a 2D object already. It's not like e.g. with centimeters, where it's a 1D unit, so it becomes centimeters squared to form a 2D unit.
it's (cm)^2, not c(m^2). If there would be the one-dimensional equivalent to pixels, say pix, then 1pixel = 1pix^2, and then 1 megapixel = (kpix)^2
After putting significantly more effort than perhaps socially acceptable into this, I completely agree so far, but I'm still horribly confused about GP's point about "mega" being a "squared unit in megapixels".
That to me implies that "mega" in "megapixels" is a planar ("[pre?-]squared") scaling factor, but it's... not really? Are those even a thing?
I think this is what the debate is about at least. Mega does line up with kilo squared, but that's not because mega becomes a planar scaling factor, but because it just so happens that 1000 times 1000 is 1 million. It's kind of a coincidence? Like it's literally 1 million pixels, that's what's being meant. Just like with cm squared, the ohhhhhhhhhhhhhhhhhhhhhhhhh
I believe the point is that in "centimeters squared" you also square the cm. So it's 1/100 of a meter, then squared. While the mega in megapixels applies to the area. So presumably there are two length multiplied to be a pixel, and then you have a million of those.
I don't think it's a very deep point, and I would say the mega is not squared, but the centi is squared.
What finally clicked it into place for me was trying to perform a unit conversion. It's kind of annoying cause we don't really use mega with anything squared usually (I don't recall anything at the moment at least), which added to the confusion.
When one converts from square kilometers (km2) to square meters (m2), one needs to undo the kilo (x1000) not once, but twice, accounting for both dimensions. So as you say, it's actually here where the scaling factor is secretly squared, it's k2, just not written out. Hence despite kilo being a 1000x bump, you need to divide by 1 million, because it's actually squared in kilometers squared.
So if mega in megapixels was behaving "normally", that would imply similar semantics, so to convert into kilopixels, you'd divide by 1000 not just once, but twice. But no, 1 megapixels is 1000 kilopixels. I guess the idea is that instead of being "secretly" squared it's "explicitly" already "square" as a result? So instead of resolving to mega2 pixels2, it's just mega pixels, since pixels is 2D, and so squaring it is unnecessary.
I think I get it now at least, but yeah, I agree with your sentiment. It actually reminds me, when I first learned converting between units of area in primary school, I had quite the troubles with wrapping my head around it exactly because of this.
Yes, and I think it just depends where how you read the square. For cm^2, we mean that we square a centimeter, not that we have a centi of a meter^2. But a hectare is really a hect of ares, so 100 ares. Here the square "is baked in" into what comes after the modifier.
It's a bit like "percent". A shorthand for dealing with ratios, often with hidden assumptions.
Sure, but you never say "the production is at 50%". 50% of what? Peak possible output? Typical output? That's what the author's complaint is: dB, while arguably useful, is annoying because people leave out the part that it's relative to. And then people, when talking about dB, assume the other party has knowledge of what their ratio is relative to. dBm, dbSPL, etc.
In every communication, the sender assumes that the other party has some knowledge. For example, I assume that you can read my badly worded English text. There is rarely confusion with the people in the fields that use dB a lot. That other people often get confused by dB is not a failure of dB, not even of its common use, the same way I can't blame English for not being Chinese, or for Americans use F instead of C, or K, for temperatures.
Insert mandatory complaint about percentages being misused : their point is the approximation : 1.02×1.03~1.05 <=> +2%+3%~+5%, which only holds up to low tens +/-%.
There is a solution for you - log points! https://en.wikipedia.org/wiki/Relative_change#Logarithmic_ch... , http://a-loonie-saved.blogspot.com/2008/08/log-points.html
An example of deceptive arithmetic: A mutual fund's 5-year history of annual returns is −70%, +30%, +50%, +20%, +40%. Naively, the total return for the 5-year period looks like +70%. But in fact it's −1.72%, because the reciprocal function makes the −70% very “heavyweight” compared to the positive changes.
Using log points instead, the 5-year sequence is approximately −120.4, +26.2, +40.5, +18.2, +33.6. The sum of these rounded numbers is −1.9 (nowhere near +60.0), which agrees well with the correct result of about −1.735 log points (i.e. −1.72%).
Not surprisingly, Tom Scott has an interesting video on this:
Another surprising place decibels pop up, pretty far from loudness related things, is in image comparison metrics. Peak signal-to-noise ratio is mean squared error normalized by a certain peak intensity and it is generally expressed in dB, i.e. as 10 log10(normalized mse). https://en.m.wikipedia.org/wiki/Peak_signal-to-noise_ratio
Edit: typo
Decibels make a lot of sense for ratios in any kind of signal processing.
They are not that suited to sound, but sound is generally hard to quantify.
I'll summarize: It's annoying that dB is often used as a physical unit without the necessary suffix. It's annoying that the suffix seems quite random for most units It's annoying that the factor for power differs from the factor for voltage, etc. It's slightly annoying that it's usually decibel instead of Bel.
However, we all agree that dBs are really useful.
> However, we all agree that dBs are really useful.
Which part of the article was that again? I was surprised to see that conclusion as summary because it's not what the takeaway seemed like to me, so went back to the article and I don't see this mentioned, perhaps I'm overlooking it because I didn't do a careful read a second time
Yes, dB is a mess and if we could do it again we ought to use something more explicit like just annotating the units with log10 such as log10(W). Then it's easy to use other convenient units like log2(W) or if you want to reproduce dBV: 20log10(V). dB is fine shorthand, but it gets used all the time in places where things should be explicit.
The writing style is antagonistic like a clickbait title. I find it bothersome. I would have much preferred an organized breakdown of all the different ways dB are used and what they mean instead of a random rant. It complains about how unscientific 'the' unit is, knowing that it's not a single unit then adds little to sort it out.
If you're specifying decibels in written form you always include the basis or you're simply being incomplete with your units. I don't understand the complaint there.
In casual conversation, the context implies the basis.
Dealing with decibels is also another shorthand to know the domain has a wide enough value gamut such that logarithmic values (where addition is multiplication) makes sense. See also, the Richter scale.
> If you're specifying decibels in written form you always include the basis or you're simply being incomplete with your units. I don't understand the complaint there.
It seems that a lot of people who are specifying decibels in written form aren't aware of what you just said
Did you ever see someone use p as a unit and expect anyone to understand it means pico? Because I've seen that with dB. In this very thread. You really don't have to look far for the tendency for dB to be used as incomplete unit
> See also, the Richter scale
Looking at the article and trying to substitute Richter, I can't imagine what you'd plug in the different positions:
- it's not a derivative of another relative unit (no decirichter)
- it was not originally meant for something else (dB was originally meant for power, leading to difference in meaning of dB in dB(V) vs. dB(W), if I'm understanding the article correctly)
- it's not trying to indicate the magnitude of the actual unit (you don't specify Richter-Volts or something, just Richter, so you can't forget to specify the actual unit)
- there aren't different meanings depending on the field you're in (a –45dB microphone is mentioned in the article as referring to Volts whereas an acoustic 10dB loudness difference is apparently in Pascals; Richters are always Richters)
The article criticises a lot of dB's aspects but I'm not sure the exponentialness is one of them
Exactly! I have seen temperatures specified as degrees, without specifying Fahrenheit or Celsius. It's a bit like that.
My exposure to dB is mainly the RF field, and it's simple. dB is gain/loss (power ratio, just like the dictionary says!) and dBm is relative to a milliwatt. In software defined radio, you've got dBFS - relative to maximum representable. And they're all labeled correctly.
> I don't understand the complaint there.
The problem is that almost nobody does. I can't remember the last time outside of HN comments here that I've seen dB(A) or similar in real world.
I guess I'm biased from my Electrical Engineering background as we use different decibels all the time so the basis is essential.
It would be akin to saying 'kilo', but not specifying a 'gram', or 'meter'.
That's fine for bakers as they don't work with kilometers routinely, but not for physicists or antenna engineering.
The one thing that really resonates with me from this article is also the silliest thing: Why decibels instead of bels? Everyone has multiplied in scientific notation before, and making a power ratio of 10^4 = 4 B would be so much more intuitive for conversion to absolute figures. It's a completely silly complaint, given that it's literally just a decimal point instead of a d, but it would make mental math of absolute conversions that much faster, especially for people who don't live and breathe amplifier chains all day.
I want to live in a world where a radio can be specified as a -10.2 Bm sensitivity. -9 is three SI prefixes down from 1 mW, so less than 0.1 pW.
I think dB is a good way to represent certain user interfaces. I've always preferred to operate my audio equipment using a logarithmic scale. Changing the volume is much more intuitive to me this way than with some linear 0-100 mapping.
One way to illustrate some of the weirdness of dB is to look at the documentation of unit libraries, e.g.:
The nice thing about dBs is that they are logarithms: successive applications of gain/attenuation are easily computed by just adding up the dBs. (but yes, I agree that there should be more consistency in their definition)
I appreciate the sentiment, but I've found this resource [0] much more direct and comprehensive. It explains all of the nuance regarding dB and related terminology from audio engineering to perception (voltage, power, intensity, volume, loudness, etc.)
The format is a bit circular; just enjoy getting lost in it for half an hour.
The author gives the downsides but not the upside of why it is like that.
It's basically so it describes sound levels on an understandable scale with 0db being just audible and 100dB being very loud.
It also corresponds to the energy carried by the sound - 0 dB is 1 pW per square meter so it is kind of a scientific unit. It's probably easier to have a measure that is understandable by the public and let engineers do conversion calculations for signal levels in networks than the other way around.
I assume you mean dB(A) here, because the sound level at dB(SPL) depends on the reference pressure chosen (20 mPa for db(A) with a calibrated microphone) and the constants for dB(A) are applicable to a large part of human sound perception. Though, if you use human perception as a reference, you'll also need to take dB(B) and dB(C) into account, depending on the sound you're playing and where you're playing that sound.
You can't use "dB" standalone. You need to specify what kind of dB you're talking about, because every field has different dBs that measure different units or are adjusted to different constants.
10dB is like 10k. 10dB is a tiny number if you're talking about volume, but blows your audio equipment if we're talking dB(u) or dB(v) (not to be confused with dB(V). In the same sense, 10k is a low number if it's the price for a new electric car, or an election changing amount of voters when talking about a population.
Ah - it's complicated I guess. I was looking at this stuff https://en.wikipedia.org/wiki/Sound_intensity#Sound_intensit...
Yeah. And don't get me started on the folks who think "6dB/octave" is a reasonable thing to say. Which is, apparently, everyone who works with audio filters except me.
How else would you describe what occurs other than 6dB/octave?
For a 6dB/octave lowpass filter, I would say power gain is inversely proportional to frequency squared (1/f^2). There's precedent for this notation, for example pink noise is known as both 3dB/octave and as 1/f.
Notice how both dB and octave are ratios, but for some reason for frequency ratios we don't use bels or decibels. An octave is a ratio of 2, a bel is a ratio of 10.
For frequency, a decade is a ratio of 10, akin to a bel. And in photography, a stop or an EV is a factor of 2, akin to an octave. https://en.wikipedia.org/wiki/Logarithmic_scale#Common_uses
Speaking of which. Does anyone know why, in Physics, we only use the operators +, * and exponentiation? And why higher operators in the hyperoperation sequence are never used?
You would use it if it was useful or convenient
It was more of a question about the nature of our universe, similar to: why are there only n spatial dimensions?
The power vs voltage thing I think comes from the historical connection of dB to sensing waves. Because you can change impedance to match any sensor, but power is conserved, power was just more often more important to discuss than voltage. I still have to look it up every time whether 10x is 10 or 20 dB.
The author seems confused. Decibels aren’t units. They’re a way to express a ratio between a reference value and some other value.
They’re used where they are useful.
dBs are so often used as units. That's 80% of the complaint in the article.
The fact that dBs aren't units, but are used like units, is the point being made.
They are units too. When you have regulations relating to sound they will say how many dB the limit is.
No. dB is not a unit. If it's quoted as a unit, then the person using it doesn't know what they are doing. dBx where x is some reference value is a unit and that means dB relative to the reference unit. So dBm/dBv etc are units. dB is not.
Mathematically, dB is the ratio between two unit values and for example if you divide metres by metres you cancel the units.
Exactly. If someone says that "this plane is about 130dB" what they mean is in reference to 0dB given 0dB is the threshold of human hearing. It seems most people are confused by dB because they don't understand it provides a logarithmically scaled unit compared to a reference which happens to be quite useful for something like audio where our perceptual models are stacked with these types of curves.
No they will specify something like dB SPL, A-weighted with Fast time integration. Sometimes referred to as dB(A) SPL. And measured with a particular method, which specifies things like distance from sources, environmental conditions, etc.
I've never seen dB being used like that in anything remotely official.
Maybe the reference is implied though?
That's hilarious, though they do seem to get it right on the other, more in-depth pages.
Yep, the NIOSH meter app they recommend uses dB(A).
Though that's still incomplete, because (more of the context stuff that you just have to know already) the "A" here refers to the frequency-weighting scheme used in the measurement, and not to the reference level (which is SPL).
It should probably be given as: dB(A) SPL, or dB SPL (A-weighted).
Though that's still incomplete, because (more of the context stuff that you just have to know already) the "SPL" here refers to the reference level in air (20 µPa) and not water or oil (1 µPa).
It should probably be given as: dB(A) SPL (1=20 µPa).
Though that's still incomplete, because (more of the context stuff that you just have to know already) the 20 µPa only applies at the standard temperature and pressure.
It should probably be given as: dB(A) SPL (1=20 µPa, T=293 K, P=101.3 kPa, in standard air).
Though that's still incomplete, because (more of the context stuff that you just have to know already) the (A) here is actually the A-weighting curve specified in IEC 61672:2003.
It should probably be given as: dB A-weighted (IEC 61672:2003) SPL (1=20 µPa, T=293 K, P=101.3 kPa, in standard air).
Though that's still incomplete, because (more of the context stuff that you just have to know already) ...
...
The point of communication is to transport information, not pointless pedantry (except for a small subset of the population). Nobody is confused as to what 85 dBA refers to.
Granted, I should have been clearer about my intended point, which is just the hazard of assuming that the letter(s) after the dB tell you the reference, because sometimes they don't.
Gosh, I didn't know it was that bad - I didn't know it was used for so many different things.
The confusing thing about decibels is not the Watts versus Volts thing.
It is the following.
If you mix two identical signals (same shape and amplitude) which are in phase, you double the voltage, and so quadruple the power, which is +6 dB.
But if you mix two unrelated signals which are about the same in amplitude, their power levels merely add, doubling the power: +3 dB.
That has nothing to do with decibels at all, that's the fundamental physics (or mathematics if you want) of adding waves, i.e. interference.
Sure, but people who are confused by the voltage vs power thing (also fundamental physics) will likely be quadruply confused by this.
If they're identical and in phase, the addition is obviously a multiplication by 2 -> 6dB.
If they're unrelated the signals can also cancel out. So not 6bB. If not 6 dB then what is it? An integral that has already been solved for us :D
> This means that if you’re talking about watts, +1 bel is an increase of 10×; but if you’re talking about volts, it’s an increase of √10×. This is nuts: it’s akin to saying that the milli- prefix should have different meanings depending on whether we’re talking about meters or liters.
Well no, because even if you are focusing on a signal measured in volts, the bel continues to be related to power and not voltage. As soon as you mention bels or decibels, you're talking about the power aspect of the signal.
If volume were measured in meters, which were understood to be the length of one edge of a cube whose volume is being given, then one millimeter (1/1000th of distance) would have to be interpreted as one billionth (1/1,000,000,000) of the volume.
When you use voltage to convey the amplitude of a signal, it's like giving an area in meters, where it is understood that 100x more meters is 10,000x the area.
There could exist a logarithmic scale in which +3 units represents a doubling of voltage. We just wouldn't be able to call those units decibels.
The Bel is a unitless quantity. Yes, by convention, in certain fields, it applies to the logarithm of the ratio of powers. But in other fields (for example, quantifying a change in the degree of evidence for a hypothesis, as in Bayesian probability theory) it is applied to a ratio of different quantities (in the Bayesian case, a ratio of probabilities). There is no reason why dB can't be used for any unit, and its meaning is incomplete until the denominator of the ratio within the logarithm is known.
This is the gripe that is being conveyed in this article. Mathematically, the Bel is unitless. It is only by additional context that one can understand the value of the denominator in the logarithm.
Mathematically, the Bel is unitless because it is a function applied to a ratio of measurements. Whatever units those measurements have disappear due to the cancelation.
If that measurement is linked to another one in a nonlinear way, that nonlinearity doesn't disappear: the fact that if the unitless fraction in which certain units canceled out is 2, then the corresponding unitless fraction obtained via different units is 4.
Just because the units disappeared in a fraction doesn't mean they are not relevant.
The denominator isn't the issue. The context-dependent base of the logarithm is, which makes 1 Bel = 10x for some things and 1 Bel = 3.16x for others.
I've never heard of decibels used in probability theory. Did they adopt it with the same baked-in bastardizations? Please tell me +10dB(stdev) = +10dB(variance) isn't a thing.
The problem stated in the article is that the unitless quantity of 1 Bel is effectively applied only to power ratios. It is of course true that one can transfer a scaling of powers into the base of the logarithm when we are trying to figure out what effective scaling of voltages corresponds to 1 Bel of power scaling, but it is ultimately more meaningful to state that a Bel is "only a scaling of power", which is a statement about the units of the two variables in the logarithm (but ultimately, once we know the denominator that belongs to the definition, the numerator is also known, so we only need to know the reference denominator).
In Bayesian probability theory, there is a quantity known as the "evidence". It is defined as e(D|H) = 10 * log_10 (O(D|H)), where O(D|H) is the odds of some data, D, given the hypothesis, H.
The odds are the ratio of the probability of the data given that the hypothesis H is true, over the probability of the data given that the hypothesis is false, or: O(D|H) = P(D|H)/P(D|NOT(H)).
Taking the logarithm of the odds allows us to add up terms instead of multiplying the probability ratios when we are dividing D into subsets; so we can construct systems that reason through additive increases or decreases in evidence, as new data "arrives" in some sequence.
The advantage of representing the evidence in dB is that we often deal with changes to odds that are difficult to represent in decimal, such as the difference between 1000:1 (probability of 0.999, or an evidence of 30dB) and 10000:1 (probability of 0.9999, or evidence of 40dB).
This use of evidence has been around at least since the 60s. For example, you can find it in Chapter 4 of "Probability Theory - The Logic of Science" by E.T. Jaynes.
The puzzling thing is why they chose to adopt a term used to describe "only a scaling of power" to talk about log10 values. If 1 Bel simply meant 10x, I'd get it, but Bel has baggage and also means sqrt(10)x.
Is odds a power-like or amplitude-like quantity? If you can't tell, dB isn't the most fortunate choice. It's not like mathematicians need fake units to talk about unitless ratios and their logarithms.
The useage of dB in the case of probability is exactly as the 1 Bel -> 10x meaning, but that is the technical meaning, without further context of the unit in the logarithm. There is no need to conceptualise this further as involving power or amplitude (which does not apply in probability).
I think that the unit having been popularised in the telecommunications industry just meant that every other instance of a log_10 ratio in physics lead to a realisation that it was a Bel. For Bayesian odds, this was probably because even the development of Bayesian probability was largely advanced by physicists (E.T. Jaynes being a famous example), who also were trained, and often worked, in signal processing of some kind or another. But I doubt they would have thought about this "power-ratios-only" adherence that is more the conception of telecommunications engineers, as opposed to physicists.
(Funny you should mention that because while writing my grandparent comment above I vaguely ruminated about some kind of example involving standard deviation and variance, due to those being linked by squaring.)
Even if there isn't a +10dB(stddev), logarithmic graphs are a thing, in many disciplines. You just refer to the axes as "log <whatever>". Any time you are dealing with data which has a wide dynamic range, especially with scale-invariant patterns.
Back in the realm of electronics and signal processing, we commonly apply logarithm to the frequency domain, for Bode plots and whatnot. I've not heard of a word being assigned to the log f axis; it's just log f.
Decibels aren't actually that ridiculous if you just accept them as plain logarithmic ratios, between your signal and the noise floor or some other signal. (Or between anything else, really.)
3dB is roughly double, 10dB is 10x, but only sounds about twice as loud because our ears are weird.
Tangential question: Are there any sound meters that can actually measure down to 0 dB? The best I’ve seen specify 20 dB, which to me is still very audible.
(Note that, as the article mentions, 0 dB doesn’t mean “zero sound pressure”, but just “threshold of hearing”.)
Some laboratory-grade equipment probably.
> 0 dB doesn’t mean “zero sound pressure”
From the decibel definition, zero of anything is -∞ in dB_suffix scale.
> Some laboratory-grade equipment probably.
I wasn’t able to find any listings, that’s why I’m asking.
His first equation is wrong. It should be P=V^2/R, not P=V^2R.
Horsepower is a unit of measurement. There's hp and bhp and hpE and...
"Other names for the metric horsepower are the Italian cavallo vapore (cv), Dutch paardenkracht (pk), the French cheval-vapeur (ch), the Spanish caballo de vapor and Portuguese cavalo-vapor (cv), the Russian лошадиная сила (л. с.), the Swedish hästkraft (hk), the Finnish hevosvoima (hv), the Estonian hobujõud (hj), the Norwegian and Danish hestekraft (hk), the Hungarian lóerő (LE), the Czech koňská síla and Slovak konská sila (k or ks), the Serbo-Croatian konjska snaga (KS), the Bulgarian конска сила, the Macedonian коњска сила (KC), the Polish koń mechaniczny (KM) (lit. 'mechanical horse'), Slovenian konjska moč (KM), the Ukrainian кінська сила (к. с.), the Romanian cal-putere (CP), and the German Pferdestärke (PS)." [1]
Decibel is not a unit of measurement. Decibels are a relative measurement. It tells you how much louder or powerful something is relative to something else. And frankly far less ridiculous than horsepower, which has a hilarious Wiki article if you read it with a critical mindset.
Deriving some of the constants without Googling is a fun exercise to verify that you're not as smart as you think you are. "Hydraulic horsepower = pressure (pounds per square inch) * flow rate (gallons per minute) / 1714"
Yes, those are the reasons why nobody uses horsepower in an engineering context.
> "Other names for the metric horsepower are [...]"
I'm not clear on what point you think you're making. Is it interesting that the same thing might have different names in different languages?
That subsection of the article, by the way, is obviously lying:
> The various units used to indicate this definition (PS, KM, cv, hk, pk, k, ks and ch) all translate to horse power in English.
cv and ch translate to steam horse, which isn't hard to see even if you only speak English. What does "vapor" mean to you?
The opening of the article does suggest some problems, though not problems that wouldn't apply to the word "ounce". But you seem to have pulled an extended quote describing a completely expected state of affairs, while ignoring this:
> There are many different standards and types of horsepower. Two common definitions used today are the imperial horsepower as in "hp" or "bhp" which is about 745.7 watts, and the metric horsepower as in "cv" or "PS" which is approximately 735.5 watts. The electric horsepower "hpE" is exactly 746 watts, while the boiler horsepower is 9809.5 or 9811 watts, depending on the exact year.
I don't get it.
That a unit of power has a dozen metric abbreviations and converts to watts at different values depending on what it is measuring (and when) is precisely the point.
Decibels aren't ridicluous or a unit of measure. Horsepower, however...
> That a unit of power has a dozen metric abbreviations and converts to watts at different values depending on what it is measuring (and when) is precisely the point.
How is that point illustrated by an extended digression on the words for the unit in various different languages?
> For some reason, the bel — again, what started as a sensible 10× increment — was soon deemed too big to use. I don’t quite know why: in other aspects of life, decimal notation suits us just fine.
Decimal notation can be a tad cumbersome to write and speak. Meanwhile, decibel usage commonly results in nice simple numbers that range between 0 and 100, with the fractional digits often being too insignificant to say out loud. For instance, the dynamic range of 16-bit audio (which is generally all the range that our ears care about) is 96 dB, while volume increments smaller than 1 dB aren't really noticeable, so decibel makes it easy to communicate volume levels without saying "point" or writing a "." or breaking out exponential notation. Even in fields other than audio the common ranges also conveniently will be around 1 dB for being on the verge of significance to around 100 dB or 200 dB for the upper range. (Also the whole power vs root-power caveat is simply something users of dB have to be cognizant of because we need to stick with one or the other to make consistent comparisons, and at the end of the day physical things hapen with power.) So while decibels may seem ridiculous, they actually are quite convenient for dealing with logarithmically-varying numbers in convient range from 1 dB to around 100 dB or so in many engineering fields.
Its like why we use percent from 0% to 100% instead of speaking of ratios from 0 point something to 1.
I have a vague report that "root-power" or voltage-like quantities (20 dB per order of magnitude) are signed or vector-like, while power-like quantities are unsigned scalars?
Weird that the author makes no mention of Sones: https://en.wikipedia.org/wiki/Sone
Nor phons!
“The phon is a logarithmic unit of loudness level for tones and complex sounds.”
Fahrenheit on the other hand makes sense...
Love this kind of articles but I wished the author suggested solutions.
I go even further than this author : sometimes decibels are computed using logarithms and what we put inside the logarithm has a physical unit. But I can prove mathematically that this is wrong and that whats given to a log function has to be dimensionless. Hence a lot of dB calculus is mathematically wrong and physically meaningless
If decibels in acoustics confuse you, try learning decibels in optical communication. That's a witchcraft.
This is an armchair rant with a very narrow complaint. The decibel unit has objective utility in both analog and digital signal processing and the field of audio engineering. It is far from meaningless in filter design and a useful reference for software and hardware interfaces that employ them.
> this is in the same tradition that prompted us to name the “wat” in honor of James Watt.
The unit is Watt, not Wat.
I'm sorry, that you missed the hilarious joke!
For reference: https://www.destroyallsoftware.com/talks/wat
Ahh, I get the joke now. Good one :)
As for the reason, if I have to guess, is because "decibel" looks better than "decibell".
(Keep in mind decibel was actually renamed from the previous unit called "Transmission Unit" and was meant to be used as the main unit even at the beginning. "bel" was simply derived/implied from it, not the other way around).
This is an incredibly valuable article for anyone who's trying to make sense of decibels in some context. Michał clearly explains almost all of the gotchas you have to understand.
I realized recently, after years of doing it for signal powers, that dB are a pretty convenient way to do mental logarithmic estimates for things that have nothing to do with power or signals, with only a small amount of memorization. Logarithms are great because they allow you to do multiplication with just addition, and mental addition isn't that hard. For example, if you want to know how many pixels are in a 3840×2160 4K display, well, log₁₀(3840) ≈ 3.58 (35.8dB-pixel) and log₁₀(2160) ≈ 3.33 (33.3dB-pixel), and 3.58 + 3.33 = 6.91 (69.1 dB-square-pixel), and 10⁶·⁹¹ ≈ 8.13 million. The correct number is 8.29 million, so the result is off by about 2%, which is precise enough for many purposes. (To be fair, though, 4000 × 2000 = 8000, which is only off by 3.5%.)
The great difficulty with logarithms is that you need a table of logarithms to use them, and a mental table of logarithms is a lot of rote memorization. You can get pretty decent results linearly interpolating between entries in a table of logarithms, so you can use a lot more logarithms than you know, but you have to know some.
It's pretty commonplace in EE work to make casual use of the fact that a factor of 2× [in power] is about 3 dB, which is a surprisingly good approximation (3.0103dB is a more precise number). This is related to the hacker commonplace that 2¹⁰ = 1024 ≈ 1000 = 10³; 1024× is 30.103dB, while 1000× is precisely 30dB.
To the extent that you're willing to accept this approximation, it allows you to easily derive several other numbers. 4× is 6dB, 8× is 9dB, 16× is 12dB, and therefore 1.6× is 2dB. ½× is -3dB, so 5× is 7dB (10-3). So with just 2× = 3.01dB we already know the base-10 logarithms of 1, 2, 4, 5, and 8, to fairly good precision. That's half of the most basic logarithm table. (The most imprecise of these is 8: 10⁰·⁹ is about 7.94, which is an error of about -0.7% when the right answer was 8.)
If we're willing to add a second magic number to our memorization, 3× ≈ 4.77dB. This allows us to derive 6× ≈ 7.78dB and 9× ≈ 9.54dB. So, with two magic numbers, we have fairly precise logarithms for 1, 2, 3, 4, 5, 6, 8, and 9.
The only multiplier digit we're missing is 7. (Shades of the Pentium's ×3 circuit: http://www.righto.com/2025/03/pentium-multiplier-adder-rever....) So a third magic number to memorize is that 7× ≈ 8.45dB. And now we can mentally approximate products and quotients with mentally interpolated logarithms.
You can do my example above of 3840×2160 as follows. 3.8 is 80% of the way from 3 (4.8dB) to 4 (6.0dB), so it's about 5.8dB. 2.2 is 20% of the way from 2 (3.0dB) to 3 (4.8dB), so about 3.4dB. 35.8dB + 33.4dB = 69.2dB, which is between 8 million (69.0dB) and 9 million (69.5dB), about 40% of the way, so our linear interpolation gives us 8.4 million. This result is high by 1.2%, which is much better than you'd expect from the crudity of the estimation process.
For a more difficult problem, what's the diameter of a round cable with 1.5 square centimeters of cross-sectional area? That's 150mm², half of 300mm², so 24.77 dB-square-millimeters minus 3.01, 21.76dB. A = πr². Divide by π by subtracting 5dB (okay, I guess that's a fourth magic number: log₁₀(π) ≈ 4.97dB) and you're at 16.76dB. Take the square root to get the radius by dividing that by 2: 8.38dB-millimeters. That's less than 7× ≈ 8.45dB by only 0.07dB, so 7-millimeter radius is a pretty decent approximation, 14mm diameter. The precise answer is closer to 13.82mm.
For approximating small corrections like that, it can be useful to keep in mind that ln(10) ≈ 2.303 (a fifth magic number to memorize), so every 1% of a dB (10¹·⁰⁰¹) is a change of about 0.23%. So that leftover 0.07dB meant that 7mm was high by a couple percent.
More crudely: 150mm² is 22dB, ÷π is 17dB, √ is 8½ (pace Fellini), 7×.
It's pretty common in engineering and scientific calculations like this to have a lot of factors to multiply and divide, increasing the number of additions and subtractions relative to the number of logarithmic conversions; this is why slide rules were so popular. Maybe you derived the 1.5cm² number from copper's conductivity and a resistance bound, or from the yield strength of a steel and a load, say. 3840×2160 pixels × 4 bytes/pixel / (10.8 gigabytes/second), as I was calculating last night in https://news.ycombinator.com/item?id=44056923? That's just 35.8 dB + 33.3dB + 6dB - 100.3dB = -25.2dB-seconds, which is 3.0 milliseconds to memcpy that 4K framebuffer. (I didn't do that mentally, though.) Even 36 + 33 + 6 - 100 = -25, so π ms, is a fine approximation if what you want to know is mostly whether it's more or less than 16.7 ms.
So here's a full list of the seven magic numbers to memorize for these purposes:
2× ≈ 3.01dB (∴ 4×, 8×, 5×)
3× ≈ 4.77dB (∴ 6×, 9×, 1.5×)
7× ≈ 8.45dB
π× ≈ 4.97dB
ln(10) ≈ 2.303 (∴ 0.01dB ≈ 0.23%, etc.)
1.259× ≈ 1dB (+1dB ≈ +25.9%)
(1 - .206)× ≈ -1dB (-1dB ≈ -20.6%)
It occurs to me that 100 is 2% more than 7×7×2, so you could reasonably approximate 7× (if you didn't know it) as follows. Since 1dB is about 23%, 2% is about 0.09dB, so 98× is about 19.91dB, 49× is about 16.90dB, and so 7× has to be half that: 8.45dB. And so it is.
I've been using decibels as a scale for log-odds for a while when reporting results. It works pretty well, since the relevant part of the scale is wide, unlike using nepers, which I had never heard of until I started noodling around with this.
Like, how many decibels of evidence does this observation provide for this hypothesis? That seems potentially pretty workable, as long as you can ensure conditional independence.
I wrote:
> So with just 2× = 3.01dB we already know (...) 8, to fairly good precision. (...) (The most imprecise of these is 8: 10⁰·⁹ is about 7.94, which is an error of about -0.7% when the right answer was 8.)
This is slightly mixed up. It's true that approximating 8× as 9dB gives you an 0.7% error. But I was talking about 3.01dB, and approximating 8× as 9.03dB gives 7.998×, only about 0.02% low.
The errors for the logarithms of the 10 digits thus approximated are:
>>> print('\n'.join([f' {10*p:.2f}: {100*(10**p-i-1)/(i+1):+.3f}%' for i, p in enumerate([0, .301, .477, .602, .699, .778, .845, .903, .954])]))
0.00: +0.000%
3.01: -0.007%
4.77: -0.028%
6.02: -0.014%
6.99: +0.007%
7.78: -0.035%
8.45: -0.023%
9.03: -0.021%
9.54: -0.056%Does this have anything to do with decibels specifically or is it just general log-space arithmetic?
I just can't understand why "[specialized domain] uses these stupid wrong units, it should be [unit that no educated smart SMEs use]" types don't do their researches to understand why those are used at all. This type of weird non-SI units appear when means of measurement and unit is related to one another and has downstream dependencies.
Just look at aviation. An airplane's:
- speed is measured in knots, or minute of angle of latitude per hour, which is measured by ratio of static and dynamic pressure as a proxy.
- vertical speed or rate of climb is measured in feet per minute, which is a leaky pressure gauge, probably all designed in inches.
- altitude is measured in feet, through pressure, which scale is corrected by local barometric pressures advertised on radio, with the fallback default of 29.92 inHg. When they say "1000ft" vertical separation, it's more like 1 inHg or 30 hPa of separation.
- engine power is often measured in "N1 RPM %" in jet engines, which obviously has nothing to do with anything. It's an rev/minutes figure of a windmilling shaft in an engine. Sometimes it's EPR or Engine Pressure Ratio or pressure ratio between intake and exhaust. They could install a force sensor on the engine mount but they don't.
- tire pressure is psi or pound per square inch, screw tightening torques MAY be N-m, ft-lbs, or in-lbs, even within a same machine.
I mean, just type in "use of decibels[dB] considered harmful" at the box at chatgpt.com. It'll generate basically this article with an armchair version of the top comment here as the conclusion.
Wait until you hear about unit conversions in aeronautical mental math. 1 NM across ground corresponds to 1000 or 100 feet of altitude in many conversion formulas. For small angles, sines and tangents are approximated by degrees of azimuth × distance in NM = 60.
this is one of the best videos to understand what a dB is and when it is used, and how to interpret them. what's unique about this unit is it relies a lot on the context.
This difference in mindset makes me comfortable as an EE that all the laid-off SWEs aren't going to take my job. Granted, demand side of the job market isn't rosy due to macro conditions, but at least supply isn't.
still doesn't answer what 0.3 Sone is in dBA
Almost as annoying as Euler angles, which force you to choose an arbitrary ordering (XYZ, ZYX, ZXZ, …), while each choice is equally valid yet mutually incompatible, so there is no canonical “true” yaw-pitch-roll.
Not to mention gimbal-lock singularities, wrapping discontinuously at +/-PI, mapping one orientation to many triples, and forcing you to juggle trig identities just to compose two spins.
To pure mathematicians obsessed with elegant unambiguous coordinate-free clarity, Euler’s pick-any-order gimmick is like hammering tacky street signs onto the cosmos: a slapdash, brittle hack that smothers the true geometry while quaternions and rotation matrices sail by in elegant, unambiguous splendor.
You use a unit that maps well between the thing you want to measure and the thing you want to know about it. If you do this enough with the same until you give it a name. I don’t get the author’s complaint.
When you want to measure a related but different quantity, don't use the same name as the first one because that leads to confusion. This rule is not followed by Decibel and that is complaint.
But dB is not a unit, it is a multiplier. dB on its own is unitless and if we say "X is reduced by 6 dB" you know that the value of X is half of what it was before (×0.5) if something is amplified by 6 dB it is double of what it was before (×2.0)¹
Note that the unit only starts to play a role when you reference your dB value to some absolute maximum, e.g.:
dBV which is referenced to 1V RMS
dBu which is referenced to 0.775V RMS (1mW into a typical audio system impedance of 600 Ohms)
dBFS which is referenced to a digital audio maximum level (0dBFS) beyond which your numeric range would clip (meaning all practical values will be negative)
dBSPL which is refrenced to the Sound Pressure Level that is at the lower edge of hearing (0 dBSPL), this is what people mean when they say the engine of a starting airplane is 120dB loud
When we think about the connection between analog and digital audio dB is useful because despite you having volts on the one side and bits on the other side a 6dB change on one side translates to a 6dB change on the other, the reference has just changed. If we had no dB we would have to do conversions constantly.
Going from multiplier x to dB: 20×log₁₀(x)
Going from dB to multiplier x: 10^(x/20)
If you use dB to describe the power of a signal that is slightly different (you use 10 instead of 20 as multiplier/divisor)
But you can see, dB is just a way to describe a unreferenced size change in a uniform way or to describe a referenced ratio. And then it would be good to know what that reference is. So if someone says a thing has 40dB you they forgot to tell you the unit.
¹ this is true for the amplitude of a signal and differs when we talk about the power of a signal, where 3dB is a doubling/halving.
> But dB is not a unit, it is a multiplier. dB on its own is unitless.
The point of the article is exactly that this should be the case. But it ends up not being the case. Mostly because people use dB with reference to some assumed baseline. But also because a 20db change could be a 10x change conpared to baseline, or a 100x change compared to baseline, depending on what unit you are measuring in.
20 dB is always the same, actually. If you multiply voltage (and thus current as well) by 10:1 (20 db) the power is multiplied by 100:1 (also 20 dB)
That's the point that's confusing. Especially in contexts where it's not obvious whether it's power-like or amplitude-like. It should be 40dB of power gain or 20dB of amplitude gain, with the context made explicit.
I don't see how it's confusing. Thanks to the scaling of voltage dB, you never have to worry, 10 dB of voltage gain is the same as 10 dB of power gain.
Yes but my conclusion would not be that Decibels are ridiculous, but that "People don't understand Decibels".
Decibels are okay. They are useful. They work. The problem is that people use referenced decibel values without adding anything that would allow us to understand which reference was used.
Maybe one could have come up with a better numeric way of doing the same thing (I am missing a proposal for this in the blog post), but then you'd have the XKCD-yet-another-standard problem. Everything uses dB for ages now, so dB it is or you need to convert between one and another all the time.
As an audio engineer I have no issue with dB as a unit. It is much better than using raw amplitude numbers.
> If you use dB to describe the power of a signal that is slightly different (you use 10 instead of 20 as multiplier/divisor)
This is the part I don't get. This is the part where "dB is just a multiplier" falls short. It's there to "so that the related power and root-power levels change by the same value in linear systems" (that's how Wikipedia formulates it). Why is that even something you would want? Isn't it much more logical, intuitive, consistent and useful to reflect the fact of power being proportional to the square of the signal in it having double the dB value?
Decibels make sense and it’s usually only laymen who use only „dB“. I’d be surprised if you’d find „-45 dB“ as the specification for a microphone. Here’s two random examples:
Sensitivity at 1 kHz into 1 kohm: 23 mV/Pa ≙ –32.5 dBV ± 1 dB
Sensitivity: -56 dBV/Pa (1.85 mV)
Except finding '-45 dB' is frustratingly common. Have a look at this random microphone datasheet from DigiKey: https://www.sameskydevices.com/product/resource/cmm-3125at-4...
They do state the test conditions "at 94 dB SPL, 1 kHz", but don't specify the units attacked to the actually measurement. It's given as a ratio to an unspecified quantity.
Thanks, it's a good example for this bad practice. Especially because this could reasonably be both dBu and dBV, so it's actually ambiguous. (On the other hand with that tolerance the difference between the two is not that significant)
Decibels are not anywhere near as ridiculous as Marketing Kilobytes introduced in the 1990s. Pot, meet kettle.
This is one of those cases where marketing is correct.
Oh tell me, if your CPU processes 1 byte in 1 cycle, and it runs at 800 MHz, how many bytes does it process in 1 second?
The answer is 800 million bytes, or 800 (real) megabytes. It cannot be 800 mebibytes. (Equal to 763 mebibytes.)
Similarly, let's say we have a 1-bit Boolean attribute for each person in the world, and the world population is 8 062 000 000 billion people. How many bits do we need in our database? It's 8.062 gigabits, not 8.062 gibibits. (Equal to 7.508 gibibits.)
The telecom industry has always used power-of-1000 prefixes on bits and bits per second. You have a gigabit Ethernet LAN, and assume no protocol overhead. How long does it take to transmit a 4.7 GB (real gigabytes) DVD image? Multiply by 8 to convert from bytes to bits, so that's 37.6 Gb, so that will take 37.6 seconds to transmit. But how long does it take to transmit a "700 MB" (actually MiB) CD image? Well, it's 734 MB (real megabytes), so 5872 Mb, which is 5.872 seconds.
The problem with the abusively overloaded definition that 1 kilobyte = 1024 bytes, 1 megabyte = 1048576 bytes, etc. is that it fails to align with the rest of the metric system, or even how we group decimal numbers into thousands and millions. The computer industry is wrong here.
And now you have the problem that you can't fit a memory dump of "16 GB" of RAM onto a "16 GB" flash memory card, because the former is actually GiB but the latter is real GB.
> Oh tell me, if your CPU processes 1 byte in 1 cycle, and it runs at 800 MHz, how many bytes does it process in 1 second?
An interesting metric, used by noone in the Universe except you for the sake of this discussion. But let's entertain this: if the actual CPU speed is 838,860,800Hz, how many bytes does it process in 1 second?
> Similarly, let's say we have a 1-bit Boolean attribute for each person in the world
I have no problem with definition of bits.
> And now you have the problem that you can't fit a memory dump of "16 GB" of RAM onto a "16 GB" flash memory card, because the former is actually GiB but the latter is real GB.
Remarkable circular reasoning, since the Marketing Kilobyte was defined in the 1990s precisely to inflate actual storage sizes without getting class action suits.
> it fails to align with the rest of the metric system
Look, byte is not derived from fundamental units. It is thus not a part of metric system so SI has zero business regulating information storage. On the other hand you can't buy a computer that does not address memory in anything other than powers of two. Nor you could ever buy a 1000 million bytes RAM chip, because they don't ever exist for basic reason that binary computers use 2^n addressable space.
> An interesting metric, used by noone in the Universe except you for the sake of this discussion.
The speed of cryptographic function such as ciphers and hashes are quoted in cycles per byte. This is because in the pure numeric code, without worrying about memory transfer speed, the speed of the crypto algorithm is directly proportional to the CPU clock speed. https://en.wikipedia.org/wiki/Encryption_software#Performanc... . Random example: https://bench.cr.yp.to/results-hash/amd64-hertz.html
> if the actual CPU speed is 838,860,800Hz, how many bytes does it process in 1 second?
If the CPU is 800 MiHz (never heard of that term, lol), then it processes 800 MiB in 1 second. Stated differently, 839 MHz --> 839 MB.
> Remarkable circular reasoning
No, I'm pointed out that the industry has already splintered into two. Your "16 GB" of RAM is a different measure than "16 GB" of HDD or SSD.
> It is thus not a part of metric system so SI has zero business regulating information storage.
If a byte is not derived from fundamental SI units, then it should not take on SI prefixes.
Otherwise, if it takes on prefixes, it should respect the SI definition and not abusively have its own contradictory definition.
> On the other hand you can't buy a computer that does not address memory in anything other than powers of two.
So what? I can use that same logic to argue that all RAM sizes should be quoted in base-2, so I'm buying 1_0000_0000_0000_0000 (base-2) bytes of RAM, right? Clearly base-10 notation is a poor fit, so why not go all the way to base-2?
> Nor you could ever buy a 1000 million bytes RAM chip
It is certainly feasible. You can just cut a bunch of rows at the end. I know how binary decoder gates work.
Also, if you have a computer and put in a 4 GiB stick of RAM and a 2 GiB stick, then you have 6 GiB of addressable memory, which is clearly not a power of 2.
> The speed of cryptographic function such as ciphers and hashes are quoted in cycles per byte.
That's called throughput, and denomination for it absolutely doesn't matter. You can measure it in megabytes as well as in MarketingMegabytes.
> If the CPU is 800 MiHz (never heard of that term, lol), then it processes 800 MiB in 1 second.
Plot twist, your 800MHz CPU oscillator would never run at 800,000,000Hz sharp for any substantial stretch of time. And clock specs are typically rounded numbers. That's why this whole example is ridiculous.
> No, I'm pointed out that the industry has already splintered into two.
No shit it did. My point is that it did it for no advantage at all. You could measure storage megabytes in same normal sane megabytes as before, just couldn't lie about it to the customers.
> If a byte is not derived from fundamental SI units, then it should not take on SI prefixes.
Kilo is a Greek prefix, not SI prefix. You can split hairs that it should mean sharp thosuand but it does not exist in terms of computer architecture. Kibi however is completely made up shit used by noone else and it sounds like a wannabe cartoon character.
> It is certainly feasible.
It is not feasible, that's why they aren't ever gonna be made.
> Also, if you have a computer and put in a 4 GiB stick of RAM and a 2 GiB stick, then you have 6 GiB of addressable memory, which is clearly not a power of 2.
It is not a power of 10 either, you should really think this through.
Decibels are not ridiculous, but very frequently the notations for quantities expressed in decibels are ridiculous.
The decibel is an arbitrary unit for the quantity named "logarithmic ratio".
Logarithmic ratio, plane angle and solid angle are 3 quantities for which arbitrary units must be chosen by a mathematical convention and these 3 units are base units, i.e. units that cannot be derived from other units. For a complete system of base units for the physical quantities, there are other 3 base units for dynamic quantities that must be chosen arbitrarily by choosing some physical object characterized by those quantities, i.e. a physical standard (originally the 3 dynamic quantities were length, time and mass, but in the present SI the reality is that mass has been replaced by electric voltage, despite the fact that the text of the SI specification hides this fact, for the purpose of backward compatibility), and there also are other 2 base units for discrete quantities (amount of substance and electric charge) which must be established by convention.
Like for the plane angle one may choose various arbitrary units, e.g. right angles, cycles, degrees, centesimal degrees, radians, or any other plane angles, for the logarithmic ratio one may choose various arbitrary units, e.g. octave, neper, bel, decibel.
So if we choose decibel all is OK. Decibels have the advantage that for those used to them it is very easy to convert in mind between a logarithmic ratio expressed in decibels and the corresponding linear ratio, so it is very easy to make very approximate computations in mind, but good enough for many engineering debugging tasks, in order to replace multiplications, divisions and exponentiations with additions, subtractions and rare simple multiplications, for a quick estimate of what should be seen in a measurement in a lab or in the field.
The problem is that whenever a logarithmic ratio is specified in decibels, it must be accompanied by 2 quantities, what kind of physical quantities have been divided and which is the reference value. Humans are lazy, so they usually do not bother to write these things, assuming that the reader will guess them from the context, but frequently the context is lost and guessing becomes difficult or impossible.
An additional complication is that one never uses logarithmic ratios for electric voltages or currents, but only for powers. When it is said that a logarithmic ratio refers to a voltage or a current, what is meant is that the logarithmic ratio refers to the power that would be generated by that voltage or current into an 1 ohm resistor. A similar problem exists for sound pressures, because logarithmic ratios are used only for sound intensities, so where sound pressure is mentioned, actually the corresponding sound intensity is meant.
This complication has appeared because voltages, currents and sound pressures are what are actually measured, but powers and sound intensities are frequently needed and using logarithmic ratios with different values for related quantities, while omitting frequently to mention the reference value, would have caused even more confusion than the current practice.
It's a bit like hating numbers, and saying "What do you mean by 'three'; what is it - three volts, three amps, three metres? Clearly 'three' is meaningless, and we should stop using it and all the other numbers besides."
decibels are simply a dimensionless ratio, used as a multiplier for some known value of some known quantity.
In every context where decibels are used, either the unit they qualify is explicitly specified, or the unit is implicity known from the context. For instance, in the case of loudness of noise to human ears in air, the unit can be taken to be dBA (in all but rare cases which will be specified) measured with an appropriate A-weighted sensor, relative to the standard reference power level.
And similar (but different) principles apply to every other thing measured in dB; either theres an implicit convention, or the 0 dB point and measurement basis are specified.
People who assume that everyone is an idiot but themselves are rarely correct.
I look forward to the author discovering about (for example) the measurement of light, or colorimetry, and the many and various subtleties involved. The apparent excessive complexity is necessary, not invented to create confusion.
> In every context where decibels are used, either the unit they qualify is explicitly specified, or the unit is implicity known from the context.
The author's whole point is that this is not true.
To adapt your analogy, it's not like being mad at the number three, it's like being mad about people not attaching any units to the number three, arguing that it's clear in context. It isn't!
Just because the author is ignorant of the context doesn’t mean that the engineers working in those fields are. They use it because it all makes sense in context.
Yeah hence his comment “If you know you know.” The author is far from ignorant on the subject, he’s pointing out the unit is often used without context.
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You may have missed the short article explaining how it could mean 3 different things in an audio context, or 3 other different things in a radio context. Or how it doesn't actually mean anything by itself and yet people insist on using it that way.
The point of units is to indicate both what dimension, and relative magnitude in that dimension, is being talked about clearly.
In virtually any other situation, leaving off units and counting on context to fill them in would be considered to be at the extreme end of unacceptable.
The unit problems in question, are only accepted because they are an historically created anomaly. Not because they are a good idea, or anyone wanted that outcome.
This is literally the same as saying that you don't need to explicitly specify units in any field because "it all makes sense in context" to "engineers working in those fields".
No. We've painstakingly figured out the right answer to this through the generations of doing science and engineering: You always specify units.
But obviously we don’t. So, there’s your counter proof.
Except the various disasters caused by assuming the wrong units (Mars Climate Orbiter, for example).
The team that wrote their code in English units instead of Metric defied specifications, that has nothing to do with this.
> The Software Interface Specification (SIS), used to define the format of the AMD file, specifies the units associated with the impulse bit to be Newton-seconds (N-s). Newton seconds are the proper units for impulse (Force x Time) for metric units. The AMD software installed on the spacecraft used metric units for the computation and was correct. In the case of the ground software, the impulse bit reported to the AMD file was in English units of pounds (force)-seconds (lbf-s) rather than the metric units specified.
From https://llis.nasa.gov/llis_lib/pdf/1009464main1_0641-mr.pdf
Hey don't blame the English for that. I would be prepared to wager you couldn't find a single English engineer who uses lbfs or anything similar. Everyone in physics or engineering uses metric for everything to do with forces even those who might use mph for a speed informally.
Nobody is blaming the english for anything, those are simply the units they used.
Which proves what? That misunderstandings happen? Yes they do. Get over it. But most amplifiers and recordings don’t crash and burn, so there’s your counter proof. Use units when they might be ambiguous. But in many fields they aren’t.
> But in many fields they aren’t.
I am lost. What fields you are talking about?
1. I am unaware of any field operating within its own echo/context chamber using unit-less numeric notation for anything but actual unit-less quantities. Except for informal slap-dash arithmetic, on trivial calculations.
2. Units indicate the dimension being measured, not just the relative magnitude within that dimension. Nobody is going to know from any shared context, except in person, what a bare number measures.
3. Virtually every measurable quantity has multiple possible units of different relative magnitude, depending on micro context, so even people within a field, who agree on the dimension measured, still need units. Meters, light years, AU, angstroms?
4. You cannot apply standard formulas of physics, or anything else, without specific units. Formulas operate on dimensions, but to interpret and calculate any numbers, you need to know the specific unit being used for each dimension.
(In any context, but a late night napkin argument between two well acquainted colleagues in a bar, units are universally used. And in that case, the opportunity for serious misunderstandings is more likely to be from missing units, than the quantity of scotch each has imbibed, or how much they have spilled on the napkin.)
Sure, but the author is wrong.
“How old is your son?” “He’s 3.”
Clear in context. People write things like dB SPL (A-weighted) in spec sheets because spec sheets benefit from being unambiguous. Most of the time it’s really clear, like you’re talking about insertion loss or amplifier gain and there’s only one reasonable way to interpret it.
But for insertion loss and amplifier gain it is "just" dB, it's the ratio of the input to the output. The amplifier has a gain of 35 dB means its output is 35 dB higher than the input. If the input is -30 dBm the output is +5 dBm, etc. The reference for an amplifier, or insertion loss is clear in context since you're talking about the gain / loss of a device, and isn't referenced to any fixed scale like db relative to 1 mW, SPL (A-weighted), or 1 volt.
On detailed spec sheets they list the gain of amplifiers as xxx dB.
That depends, the dropped unit could be either a year or a month.
It’s understood in context, that’s the point.
no it's not - it's assumed by maybe taking the most likely unit (year). But if the conversation is in hospital with your kid having emergency I guess doctor would appreciate to know if they will have to do surgery on 3 months child or 3 years kid.
If the doctor has trouble figuring out the difference between 3 months and years, there are bigger problems than specificity.
There are places specificity is necessary, and there are places the implicit assumptions people make are specific, and only need additional specification if the implication is violated. That's how language works - shortcuts everywhere, even with really important things, because people figure it out. There are also lots of examples of this biting people in the ass - it doesn't always work, even if most of the time, it does.
A 3 month old kid looks very different to a 3 year old kid.
and thats the exact point - you assume doctor see the kid instead of you calling doctor or doctor is getting briefed by emergency stuff.