Agreed on all points! I'll be mentioning this article in my newsletter Zero Retries 0204 - https://www.zeroretries.org/p/zero-retries-0204 which will autopublish on 2025-05-30 at 15:30 Pacific.
Yes, it makes little sense mathematically, but if you get used to particular use (for example in RF power) the units are so convenient to work with. For example you can have a box of attenuators labelled in dB and you know at a glance what they do. No need to count zeroes etc.
Lets not forget VU units where 0 VU are +4dBu if you are in a studio but are -10 dBu if that's in your home hifi...but...but...if you are in a digital environment then 0 dBs is whatever DAC you're using full scale...headache coming.
The classical reason for the log dB scale is the 1860 Weber-Fechner Psychophysical Law that the subjective sense of intensity is proportional to the log of the physical intensity of a stimulus .
Like the Richter scale for earthquakes , log scales are very useful for covering many orders of magnitude and related to the relevant phenomenon .
Wait until you hear about the „base“ units mole and candela. Mole being just some number of particles, and candela depending on the human light perception.
There's a bunch of "unitless" units like that. The radian is a unit of... nothing. The coulomb is a bit more than that - a unit of charge - but it's essentially just a count too. But I'm don't think these are nearly as messed up. Their semantics are predicable and reasonably well-specified.
Sure, but that's a property of exponent notation, not some brilliant aspect of decibels specifically. An amplifier with a gain of 1e4 followed by 1e2 has a total gain of 1e6. You don't need any of the dB weirdness on top of that.
> In principle, we have several types of shorthand notations; for example, instead of “300,000” we can write “3e5”. That said, I don’t know how to pronounce “3e5”, so it’s not unreasonable to come up with a name for the exponent.
I'm working to promote "magnitude notation". In this, 3e5 would become ^5.5, and pronounced "mag 5.5". Closer to the Richter scale than decibels, but universally applicable.
Yeah, that one is a bit of a mess. As some comments point out, within a given application where one of its permutations is used consistently, it's a handy way to compare relative values, but trying to wrap one's head around all its applications is frustratingly illogical.
Yes, the bel and decibel seem contrived, but mastering them can make some mathematics and electrical engineering less daunting. In my 40+ years career in electronics engineering (the latter half in failure analysis) I've found the decibel very handy! It also makes many mathematics equations easier to evaluate, so I've gotten very comfortable with them.
I can see an xkcd-style cartoon in showing how all the conventional dB scales relate to each other, and maybe a nursery rhyme style "the dB's related to the dB...".
PS: Your formula for Power doesn't seem to be rendering properly for me. It shows up as P = V^2 . R rather than P = V^2 / R.
PS: if you're after fodder for the backlog then I'd love to hear about when to use pressure and when to use vacuum when doing resin for the CNC mould making stuff. It seems some people like to squash the bubbles away and some like to ease them out, but I'm never clear whether these are interchangeable techniques or there is more methodology behind the decisions.
The big difference is that you don't let the resin cure under vacuum. Offgassing under vacuum continues for a very long time, and you don't want new bubbles popping into existence while the resin is curing. If that happens, they might end up being "frozen solid".
So, vacuum degassing is a better way to get rid of bubbles in the freshly-mixed resin before you pour it (or right after). It's preferable to just crushing the bubbles with pressure, because large bubbles might not fully dissolve back into the liquid.
But *during the curing process*, you want pressure instead, to nuke any stragglers and suppress the formation of new bubbles instead of encouraging it. And at that point, the main potential source of new bubbles are side reactions between isocyanates and water (which may be present in the resin, may be on your mold or tools, might be in the air, etc). These reactions evolve carbon dioxide.
Anyway: vacuum rigs are generally cheaper, safer, and take up less space, so for basic casting, you can often get away just with the first part. That said, pressure casting is a lifesaver if you're making water-clear parts, both because these resins tend to be more moisture-sensitive and because even tiny defects show up right away.
"the unit of loudness on a scale beginning at zero for the faintest audible sound and corresponding to the decibel scale of sound intensity, with the number of phons of a given sound being equal to the decibels of a pure 1000-hertz tone judged by the average listener to be equal in loudness to the given sound"
Decibels are a way of measuring perceived loudness. Perception is key here as humans aren't good at quantifying what amounts to a feeling. It's why a logarithmic scale makes sense for human experiences. We can tell that one sound is much louder than another, but people are hard pressed to say how much louder with any degree of specificity.
Like I'm going to be really unreasonably picky here... but perceived loudness is measured (by telecommunications technicians) using a psophometer, which is a very slightly bent voltmeter working with respect to dBm as before. Psophometers are also frequency dependent.
Still, the psophometric measurement is almost exactly the same as the dB measurement - like I said I'm being really picky.
Decibels are useful because they make it easy to keep track of the gains and losses in a system. With dB you only need to add or subtract, but multiplying and dividing gains and losses would soon get old.
I'm an electronics engineer with over 16 years at university and 40 years experience. Electronics classes are very heavy in mathematics, so together with my work experience I'm very comfortable with logarithms (and decibels). For sure there are hurdles to mastering these concepts, but they become easy after that - and they make complex circuit analysis significantly less daunting.
Agreed on all points! I'll be mentioning this article in my newsletter Zero Retries 0204 - https://www.zeroretries.org/p/zero-retries-0204 which will autopublish on 2025-05-30 at 15:30 Pacific.
Yes, it makes little sense mathematically, but if you get used to particular use (for example in RF power) the units are so convenient to work with. For example you can have a box of attenuators labelled in dB and you know at a glance what they do. No need to count zeroes etc.
Lets not forget VU units where 0 VU are +4dBu if you are in a studio but are -10 dBu if that's in your home hifi...but...but...if you are in a digital environment then 0 dBs is whatever DAC you're using full scale...headache coming.
The classical reason for the log dB scale is the 1860 Weber-Fechner Psychophysical Law that the subjective sense of intensity is proportional to the log of the physical intensity of a stimulus .
Like the Richter scale for earthquakes , log scales are very useful for covering many orders of magnitude and related to the relevant phenomenon .
Wait until you hear about the „base“ units mole and candela. Mole being just some number of particles, and candela depending on the human light perception.
There's a bunch of "unitless" units like that. The radian is a unit of... nothing. The coulomb is a bit more than that - a unit of charge - but it's essentially just a count too. But I'm don't think these are nearly as messed up. Their semantics are predicable and reasonably well-specified.
You only mention the bad; decibels convert multiplications into additions, simplifying the calculation of cascaded gains and losses.
Sure, but that's a property of exponent notation, not some brilliant aspect of decibels specifically. An amplifier with a gain of 1e4 followed by 1e2 has a total gain of 1e6. You don't need any of the dB weirdness on top of that.
> In principle, we have several types of shorthand notations; for example, instead of “300,000” we can write “3e5”. That said, I don’t know how to pronounce “3e5”, so it’s not unreasonable to come up with a name for the exponent.
I'm working to promote "magnitude notation". In this, 3e5 would become ^5.5, and pronounced "mag 5.5". Closer to the Richter scale than decibels, but universally applicable.
https://saul.pw/mag
Yeah, that one is a bit of a mess. As some comments point out, within a given application where one of its permutations is used consistently, it's a handy way to compare relative values, but trying to wrap one's head around all its applications is frustratingly illogical.
Yes, the bel and decibel seem contrived, but mastering them can make some mathematics and electrical engineering less daunting. In my 40+ years career in electronics engineering (the latter half in failure analysis) I've found the decibel very handy! It also makes many mathematics equations easier to evaluate, so I've gotten very comfortable with them.
You are missing the annoying language thing in at least electronics education where 3dB is used to mean exactly, not approximately, 2.
Another great writeup!
I can see an xkcd-style cartoon in showing how all the conventional dB scales relate to each other, and maybe a nursery rhyme style "the dB's related to the dB...".
PS: Your formula for Power doesn't seem to be rendering properly for me. It shows up as P = V^2 . R rather than P = V^2 / R.
Oops, fixed! Thanks.
I see it now!
PS: if you're after fodder for the backlog then I'd love to hear about when to use pressure and when to use vacuum when doing resin for the CNC mould making stuff. It seems some people like to squash the bubbles away and some like to ease them out, but I'm never clear whether these are interchangeable techniques or there is more methodology behind the decisions.
The big difference is that you don't let the resin cure under vacuum. Offgassing under vacuum continues for a very long time, and you don't want new bubbles popping into existence while the resin is curing. If that happens, they might end up being "frozen solid".
So, vacuum degassing is a better way to get rid of bubbles in the freshly-mixed resin before you pour it (or right after). It's preferable to just crushing the bubbles with pressure, because large bubbles might not fully dissolve back into the liquid.
But *during the curing process*, you want pressure instead, to nuke any stragglers and suppress the formation of new bubbles instead of encouraging it. And at that point, the main potential source of new bubbles are side reactions between isocyanates and water (which may be present in the resin, may be on your mold or tools, might be in the air, etc). These reactions evolve carbon dioxide.
Anyway: vacuum rigs are generally cheaper, safer, and take up less space, so for basic casting, you can often get away just with the first part. That said, pressure casting is a lifesaver if you're making water-clear parts, both because these resins tend to be more moisture-sensitive and because even tiny defects show up right away.
Wow, thanks for the detailed reply.
In Switzerland (https://www.fedlex.admin.ch/eli/cc/1994/3109_3109_3109/de) and Austria Decibel is actually a unit.
In Switzerland it is normalized against the "standard pressure" of 20 µPa.
Thank you for scratching that itch.
With dB (decibel), the difference of 10 in dB is factor of 10x in the original unit (e.g. power).
So what's the actual unit to measure "loudness", if there is one?
It's the phon:
"the unit of loudness on a scale beginning at zero for the faintest audible sound and corresponding to the decibel scale of sound intensity, with the number of phons of a given sound being equal to the decibels of a pure 1000-hertz tone judged by the average listener to be equal in loudness to the given sound"
Have fun with https://en.wikipedia.org/wiki/Sone and https://en.wikipedia.org/wiki/Phon :)
Decibels are a way of measuring perceived loudness. Perception is key here as humans aren't good at quantifying what amounts to a feeling. It's why a logarithmic scale makes sense for human experiences. We can tell that one sound is much louder than another, but people are hard pressed to say how much louder with any degree of specificity.
Like I'm going to be really unreasonably picky here... but perceived loudness is measured (by telecommunications technicians) using a psophometer, which is a very slightly bent voltmeter working with respect to dBm as before. Psophometers are also frequency dependent.
Still, the psophometric measurement is almost exactly the same as the dB measurement - like I said I'm being really picky.
Decibels are useful because they make it easy to keep track of the gains and losses in a system. With dB you only need to add or subtract, but multiplying and dividing gains and losses would soon get old.
The numerous problems the poster described with the unit and its uses are not about using a log scale...
I'm an electronics engineer with over 16 years at university and 40 years experience. Electronics classes are very heavy in mathematics, so together with my work experience I'm very comfortable with logarithms (and decibels). For sure there are hurdles to mastering these concepts, but they become easy after that - and they make complex circuit analysis significantly less daunting.
I'd say the OP gripes are more with rationality and consistency about how the decibels are defined and used - as opposed with utility and ease of use.