The scientific “unit” we call the decibel
lcamtuf.substack.com
lcamtuf.substack.com
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.
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.
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.
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.
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. :)
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?
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.
Indeed – as evidenced by some parts of the world still using non-metric units in daily life or even engineering :)
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.
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!
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.
Maybe this blog post could work as a source, although it would be better to find something more established.
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).
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).
I have nightmares of 150km meaning kilo-miles instead of kilo-metre. And when I say that my car has 260 mega-meter on the odometer, even people born metric look at me funny.
And don't get me started on MB vs MiB. I have seen so many stupid production outages because of people miss-allocating resources by confusing SI and IEC bytes.
/rant
Oh dear. I haven't looked into 3D printer specifications, but I definitely understand how it is a problem now that you mentioned it.
Relatedly, most pocket-sized power banks have their charge capacity quoted in milliamp-hours, like 10,000 mAh. There is a high temptation for the layman to call it "10k mAh" instead of the proper and shorter "10 A⋅h". I'm disappointed that people don't think critically when applying the metric system, and just blindly follow certain patterns.
> I have nightmares of 150km meaning kilo-miles instead of kilo-metre.
Yeah, that would be bad. On the other hand, if you bought a used car in America with "150k" on the odometer, I don't have a problem with that meaning "150,000 miles" because rules don't apply to imperial, and "150k" isn't legal metric notation anyway.
> when I say that my car has 260 mega-meter on the odometer, even people born metric look at me funny
I understand your frustration, and I educate people on the existence of the megametre even to an ostensibly metric audience in Canada. (Our road distances are quoted in kilometres, speeds in kilometres per hour, car maintenance intervals in kilometres.)
I pitch megametres as a way to reduce words, imply less accuracy, and all around improve efficiency. For example, if your car calls for an oil change every 8000 km, I just say 8 Mm (megametres) because it's not like the engine will destroy itself if you wait until 9 Mm. And "eight thousand kilometres" is more syllables than "eight megametres".
Similarly, I talk about my yearly bicycling distance as 3 megametres, not 3000 kilometres or "3k k". I mention that chain waxing can support a chain lifetime of over 10 Mm rather than the more verbose 10,000 km.
> And don't get me started on MB vs MiB.
Agreed. And in online debates, I see way too many people who defend the abusive notation where 1 KB = 1024 bytes, and they think that HDD marketers screwed everyone over by using the smaller unit so that their capacities look bigger, and they think that RAM manufacturers have the true claim to prefixes. All of that is nonsense and doesn't hold up to the slightest scrutiny. e.g. https://news.ycombinator.com/item?id=44060099
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.
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 hysteresis in the coil-magnet meter response turned out to be a feature, not a bug.
This line killed me. I literally laughed out loud.
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.
> 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...
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.
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)
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.
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.
Whining about it makes me really doubt that the OP has any practical experience about the things they're talking about.
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.
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?
-20 db would just be a starting point, you could adjust up or down from there.
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.
>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)
Until they are a ratio to a specific arcane reference level as mentioned in the article.
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.
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.
[1] To be clear, I'm aware that pH and p[H+] are technically different. But that's orthogonal here.
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.
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?
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
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.
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.
No need for an encoder and software, though, logarithmic pots are readily available for precisely this reason. :)
Pots do log and lin scales but they only have a limited angular range.
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).
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.
You need a knob that increases power exponentially to hear a linear increase in loudness.
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.
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.
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-...
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.
... hot water baths ..."
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.
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.
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.
This also doesn’t even begin to touch on frequency response curves.
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.
if a TV seller went bonkers and only said "it's 10:16", can you guess the actual size of that TV?
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.
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.
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.
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)".
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.
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?
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.
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.
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.
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.
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
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)
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.)
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.
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.
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.
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.
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.
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.
Additionally - attacking people you don't know for ignorance because they have different opinions is very narrowminded.
This is not a criticism of how useful they are in calculations.
Why wouldn't this work better broken out as half a dozen different units, with objective zero points and mathematical convertibility?
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.
"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.
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.
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.
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.
-47db is definitely not twice as loud as -50db, of course.
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".
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.
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.
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.
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?
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.
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.
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 not close to double loudness. It's double power, which is 1.41 higher sound pressure, which is only slightly louder.
If +10dB is absolutely twice as loud, it means that 110 dB is 32 times as loud as 60 dB. We are then essentially denying that perception of loudness is logarithmic!
Sure, perfect sense.
That's the math of it.
This makes a spec sheet that says "this machine produces X dB of sound" effectively useless.
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.
Ye but that is also the point. The author seem to prefer to memorize dozens of absolute values.
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.
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.
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 don't think it's a very deep point, and I would say the mega is not squared, but the centi is squared.
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.
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)
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.
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.
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%).
Edit: typo
They are not that suited to sound, but sound is generally hard to quantify.
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.
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
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.
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.
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.
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
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.
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.
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.
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?
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.
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.
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.
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.
The format is a bit circular; just enjoy getting lost in it for half an hour.
They’re used where they are useful.
Maybe the reference is implied though?
It should probably be given as: dB(A) SPL, or dB SPL (A-weighted).
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.
Mathematically, dB is the ratio between two unit values and for example if you divide metres by metres you cancel the units.
The fact that dBs aren't units, but are used like units, is the point being made.
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.
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
3dB is roughly double, 10dB is 10x, but only sounds about twice as loud because our ears are weird.
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.
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.
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.
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.
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.
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.
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.
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.
(Note that, as the article mentions, 0 dB doesn’t mean “zero sound pressure”, but just “threshold of hearing”.)
> 0 dB doesn’t mean “zero sound pressure”
From the decibel definition, zero of anything is -∞ in dB_suffix scale.
I wasn’t able to find any listings, that’s why I’m asking.
Sensitivity at 1 kHz into 1 kohm: 23 mV/Pa ≙ –32.5 dBV ± 1 dB
Sensitivity: -56 dBV/Pa (1.85 mV)
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.
"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"
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.
Decibels aren't ridicluous or a unit of measure. Horsepower, however...
How is that point illustrated by an extended digression on the words for the unit in various different languages?
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.
“The phon is a logarithmic unit of loudness level for tones and complex sounds.”
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
The unit is Watt, not Wat.
For reference: https://www.destroyallsoftware.com/talks/wat
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).
Or mine does.
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%)
> 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%It's the same math as logits, but the scale's a bit nicer.
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.
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.
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.
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.
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.
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.
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.
Except they are not. 1 dB can sometimes mean a ratio of ~ 1.26 and other times it can mean a ratio of ~ 1.12.
"In every context where decibels are used, either the unit they qualify is explicitly specified, or the unit is implicity known from the context."
Maybe in university, but certainly not in the real world.
Our senses are all like this - for the same reason we have dozens of systems to describe color. And why perfume and wine makers can never agree descriptions.
That only indicates that you haven't found the many angry blog posts yet, not that they don't exist :)
The SI way to write `10 dBm` is to write `10 dB (1mW)`, clearly communicating both the power level and the reference point and unit. This ensures that you do not have to just memorize a bunch of decibell suffixes and their magical reference values.
But this is not arcane knowledge only known by a priesthood. Since you are clearly confused about what a decibel is and how and why it is used, you can read
https://en.wikipedia.org/wiki/Decibel
and all will be revealed.
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!
“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.
dB for anyone not already knowing the answer is like going to another planet and hearing "he's 3". Of course it's on a logarithmic scale, offset to -5 as starting point, counting the skin shedding events - clear in context and you should've known that.
I just don’t remember encountering the problem you’re describing, and it’s unfamiliar to me. There’s something about your experience that I don’t understand, but I don’t know what it is.
The voltage / power example doesn’t make sense. It’s always power or voltage squared, which are equivalent when the load is resistive.
But this comment doesn’t illustrate your point, and I still don’t really understand where you’re seeing this.
But these are totally different. I'm used to and thus comfortable with lots of things that are nonetheless terrible!
For instance, I've heard loudness of sounds described in decibels for my whole life, and first saw the actual units people are describing when I read this article and thread today.
I don't think either of your parent's paths say that:
> There are two paths: "it was weird but then I got used to it, you're just ignorant" or "it was weird, I got used to it, but we should improve the situation". I know which side I want to be on. Even if it takes decades like the data SI prefixes.
I believe that they're saying that, yes, experts get used to it, after which it makes complete sense (as would any arbitrary but consistent convention, once you got used to it), but, in any living field, there will constantly be non-experts looking to become experts. If there is a way to make the process easier for them while not introducing any lack of precision that would hamper experts, then why not?
If you every find an "official" written document that uses dB not as attenuation/gain and is not specifying the reference (at least in a footnote), it's written either by idiots or for idiots, or both.
A-weighting describes how different frequencies are summed up. It’s like saying “RMS”. RMS is not units, A-weighting is not units. You can apply A weighting to voltage, digital signals, or audio. They all have different units but can all be A-weighted.
You could invent a new unit for A-weighted audio, but you would need several.
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.
3 days, weeks, months or years are ironically all common units when someone is "3".
On detailed spec sheets they list the gain of amplifiers as xxx dB.
No. We've painstakingly figured out the right answer to this through the generations of doing science and engineering: You always specify units.
> 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
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.)
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.
How about velocity? What's 0 m/s? What does it mean to be absolutely still? All motion is relative, and being still is entirely a matter of perspective. You might be sitting still on a train, but traveling very quickly relative to a cow standing still while you blow by.
Bels are a relative measure that confuse some because they pop up in different contexts that seem unrelated. However, they are useful when dealing with quantities for which most pertinent relationships are exponential. e.g. They work for sound because humans perceive exponential increases in volume in a linear fashion. Something that is 3dB louder is twice as loud in terms of pressure levels, but we only perceive it as a little bit louder. Sound pressure levels are both relative measures and an attempt to reflect human perception . That makes them, necessarily, a bit odd.
Kid: "Thirty."
Interviewer" "Thirty what?"
Kid: "Umm..."
Kid: "Speed."
You see the same in HN threads where people complain that eg Git or Rust are needlessly complex, there's a swath of people who are so emotionally invested in how well they understand the ins and outs of Git resp Rust that any suggestion that maybe things could be better makes them angry.
It's possible for decibels to be usable and generally fine and also for them to needlessly complex, ie for there to exist better alternatives in each place they're used.
As an example, it makes no sense to me that eg in audio software, volume sliders start at 0 dB and then go down to negative $MUCHO, until complete silence at -Infinity. And then this same unit is also used to measure how loud my coffee machine is, somehow, but then it's suddenly positive and not a relative number at all? That's just weird shit, it's like expressing the luminosity of a pixel (in HSL terms) in lumen instead of a unitless percentage.
In the audio software context, it would be much more intuitive for "no sound" to be 0, and "full volume" to be 100, a bit like percentages. The "but volume needs to be logarithmic because that's how we hear it!" argument doesn't disallow that at all. Just because a slider goes from 0 to 100 doesn't mean that a 10 must mean 10% of the power output. Decibels are ridiculous.
This one doesn’t bother me. Those sliders, and especially the real analog sliders they’re modeled after, don’t have an absolute scale — they are attenuators that reduce voltage. So 0dB is the same as no slider at all, -20dB reduces voltage by a factor of 10, etc.
A major reason decibels are used is to make it easy to assess the overall gain or loss of an entire chain of processing stages: you simply add the numbers. The equipment's output can only go down from 0 dB, so the rest of the scale is negative.
As for sound pressure levels in dB, those are given relative to a 0-dB point that corresponded originally to the faintest sound people were generally considered capable of perceiving. These days "0 dB" refers to a specific amount of acoustic power, which I don't know off the top of my head, and that might or might not be near the threshold of perception for a given listener. But the reasoning still applies: amplification or attenuation of power levels is a simple matter of addition when expressed in dB. Arbitrarily defining a system's reference level to be 100 dB instead of 0 dB would be of no use to anyone.
Maybe they're all in a conspiracy to make things needlessly complex. But that's not the only possibility.
You're just projecting your ideas here. I've not made that choice, it's just the only option in a lot of software - I'd like my % slider back.
They are still some kind of faux-logarithmic*
*behavior depends on drivers/hardware.**
**for some hardware 50 in Windows will be neutral and 100 will be something like a +30 dB digital gain, that's probably in part because Windows is mapping the 0-100 range in some way to the USB audio control range, which is at most +-127 dB or something like that.***
***with some audio interfaces (the non-USB-Audio-class kind) the 0-100 actually becomes a linear factor of 0-1, making the windows controls very useless indeed, as 70% of the slider range does approximately nothing.
Ultimately people who use this a lot would choose to become familiar with dB, as they always have. But there's no rush.
Surely constant unchanging air pressure has zero volume?
Volume is the range of variation in air pressure, right? That can surely go down to zero.
It can also only meaningfully go up to about double the absolute mean air pressure, before what you are talking about becomes shockwaves of overpressure.
Volume can be a statistical property, like temperature.
Zero volume is when a speaker's diaphragm is still. On an 8-bit PCM audio file, it corresponds to a value of zero.
In the context of a signal, full volume corresponds to the 127 value in an 8-but PCM audio file (or arguably -128). In the context of a speaker, those values should push the diaphragm no further than how far it can travel linearly without distortion. Obviously the user may want to turn down the volume from this full volume.
I hope you understand that even when using an audio editor that displays values in dB, the underlying values are integers (or floats) that absolutely have zero and "full volume" meanings, and conventionally map respectively to -∞ dB and 0 dB.
“0 dB SPL” is 20 micro pascals which is roughly the threshold of hearing. A loud rock concert at 120 dB SPL is 20 pascals (no micro). The dB figures are a lot more convenient to work with.
It’s intuitive for 0 to be silent and 100 to be full, but if you work with audio you learn that dB are more convenient. Long-term convenience for experts tends to win out over short-term intuition for non-experts. This is why musicians continue to use sheet music and all of its seemingly ridiculous conventions—and likewise, decibels only seem ridiculous to people who don’t work in audio.
I don’t know what more usable alternative there would be, to decibels.
They're not the same unit, at all.
The audio software is a skeuomorphism from an analogue mixing console that is applying a change to a signal. 0 is unity gain and deviation from this describes an amplitude variation. This is important, as it means you are either discarding information by lowering the level and reducing dynamic range, or interpolating new information (/ decreasing SNR) by applying gain. This is less important today with floating point, but has strong historical reasons for existence across both analogue and digital domains.
If you look at an audio power amp, you will likely have some form of positive number as this is applying gain. Depending on the context this may have some specific meaning or it may be a screen print of a Spinal Tap logo and the numbers 1..11. These are all just UI decisions and part of doing that well is presenting coherent information for the target user group.
When you're talking about an acoustic noise source this is dB SPL which is a quantifier against a physical reference. That reference level quantifier is omitted a lot, which leads us to a lot of the angst in this post and the comments here. These are precise measurements, with very specific meaning. Their expression is often sloppy, but the units aren't to blame.
(excuse me while I got "full HN" here - I appreciate the irony in this response noting your first few sentences)
The reason people respond strongly to comments like this (or those about Git, or Rust) is because details matter. When you immerse in a domain, you learn the reason for those details. That does not mean things can't be improved, but this also does not imply those details can be removed or are wrong. A lot of the world, particularly when working outside of the bounds of a computer, depends on necessary complexity.
Exactly, so why label two different things using the exact same letters in a potentially ambiguous context.
If I pay for something in Australia and the bill comes to $50 this has meaning within that context.
I receive a bill in Zimbabwe for $50 this also has meaning within that context.
These values are not equivalent.
Ditto if I were to say it’s 30 degrees out. You may interpret that as either a good day for the beach, nice weather for ice skating, or we need to bear north-northeast depending on what context we share.
Language is messy.
Your argument that it isn't so bad in practice doesn't change the fact that it has no benefits whatsoever.
It's just ambiguity for the sake of it, because way back when people started measuring sound stuff, nobody bothered to go "but wait is this actually handy?" and then we got stuck with whatever the first guy came up with. It's just like the whole kilobyte/kibibyte crap and the whole Wh vs mAh vs kilojoule soup. It's all downside.
And then put two in series. Is there a simple formula to calculate the total attenuation?
This works flawlessly with dB. Just add. And it doesn't matter how you break it: -20dB and -20 dB in series is the same as -40dB and 0dB.
Print this, frame this, put this up on walls in schools, offices, heck even outdoor on large billboards!
Many buildings don't have a 13th floor because superstitious people think it's unlucky.
Some people lose their shit at 8647 because paranoid delusional people think it's out to kill them.
No, it’s a bit like saying “for chocolate M&Ms, 3 obviously means 9, to compensate for the fact that they’re much smaller than the peanut ones”.
https://en.wikipedia.org/wiki/Mel-frequency_cepstrum
>Mel-frequency cepstral coefficients (MFCCs) are coefficients that collectively make up an MFC. They are derived from a type of cepstral representation of the audio clip (a nonlinear "spectrum-of-a-spectrum"). The difference between the cepstrum and the mel-frequency cepstrum is that in the MFC, the frequency bands are equally spaced on the mel scale, which approximates the human auditory system's response more closely than the linearly-spaced frequency bands used in the normal spectrum. This frequency warping can allow for better representation of sound, for example, in audio compression that might potentially reduce the transmission bandwidth and the storage requirements of audio signals.
https://en.wikipedia.org/wiki/Psychoacoustics
>Psychoacoustics is the branch of psychophysics involving the scientific study of the perception of sound by the human auditory system. It is the branch of science studying the psychological responses associated with sound including noise, speech, and music. Psychoacoustics is an interdisciplinary field including psychology, acoustics, electronic engineering, physics, biology, physiology, and computer science.
This was covered in the article. But also it was discussed why things aren't this simple.
> People who assume that everyone is an idiot but themselves are rarely correct.
Indeed.
Of course, unless it's a multiplier for an unknown value of a known quantity, like every amplifier, filter, and sensor specified in dB.
> For instance, in the case of loudness of noise to human ears in air, the unit can be taken to be dBA
Unless you're using dBB or dBC, but of course we all know exactly why you'd use dBC (more suitable for figuring out safety of high impulse, short events) or dBB (it's somewhere in between - you'll know it when you see it).
> The apparent excessive complexity is necessary, not invented to create confusion.
Wait, so writing dB instead of dBA is now necessary, not just convenient?
The complexity absolutely is not necessary. Maybe you mean to say it’s understandable or it’s coherent if you know the rules.
Physics doesn’t require us to create ambiguity by assigning DB to mean multiple possible ratios. If it needs to be disambiguated, then they both didn’t need to be DB in the first place.
This is an off-by-one error.
Like you have to describe relative intensity of waves in some way and these were experimental scientists, not commerce merchants looking for absolute interchangeability like weights and measures.
Computer blog people like standards and languageisms but science isn’t determined by big tech sponsored committee. It’s the best tool put forward so far and db is a physics concept and with a reference denominator you can calculate the absolute value. It’s fine. If you dabble with physics and expect the universe to make intuitive sense then you need an education.
Read books not blogs.
It can be used to express and calculate relative change in power, amplitude ratios, and absolute change. All of these are different units and should always use different notation, but sometimes it's skipped.
"Three to the exponent of five." Or "Three Exponent Five." Or "Three Exp Five."
> Seeing this, some madman decided that 1 bel should always describe a 10× increase in power, even if it’s applied to another base unit. 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 power vs. amplitude. This is the specific reason the dB is so useful in these systems.
> the value is meaningless unless we know the base unit and the reference point
No you just need to know if you have a power or a root-power quantity. Which should generally be obvious.
https://en.wikipedia.org/wiki/Power,_root-power,_and_field_q...
There has to be a Yogi Berra witticism about obvious things. Suffice to say fools like me work unadvisedly in spaces where this kind of axiom isn't obvious, because we're simpletons.
> "Three to the exponent of five." Or "Three Exponent Five." Or "Three Exp Five."
Somehow, you need to distinguish between 3^5 (=243), 3 x e^5 (=~445.24), and 3 x 10^5 (=300,000).
I'd pronounce "3e5" and "three times ten to the 5" in most cases.
Three to the power of five.
> 3 x e^5
Three times the fifth power of e. Or Three times e's fifth power.
> 3 x 10^5 (=300,000).
Three to the exponent of five.
A calculator user once suggested "decapower." I think exponent and "EXP" are comfortable and easy to say and are ingrained to most old school calculator users. Which is also why I think "e's fifth power" can be a more natural sequence.
I think that's still ambiguous. The base of the exponent is implied, and there are decent arguments or fields in which the assumed base of 10 isn't universal. In your "Three times e's fifth power." version, you needed so specify e. I think for accuracy it's also needed to specify 10 in that "Three to the exponent of five." case.
(Having said that, there are certainly cases where the 10 as the base of the exponent will be clear/unambiguous from the context. )