Cursed Units 2: Curseder Units

The long awaited sequel. See the original here:

Corrections: the force F in Ampere's law should be force per unit of length, and the denominator factor should be 2 instead of 4.

Maxwell's "A Dynamical Theory of the Electromagnetic Field is available on the Royal Society's website
Other videos briefly mentioned at 18:50 which you should check out:

[mekafinchi]

how could people complain about the music??? it's literally the best part with how much character and emotional weight it gives every part of the videos!

[dalitas]

Friendly reminder that the pH of the sun is approximately -3.

[owenyoshida]

chemist here. we love our cursed units! one of my favourites is the rate constant of a chemical reaction, whose units depend on the order of the reaction. For a 0th order reaction it is mol/L/s, for 1st order it is just s^-1, for 2nd order it is L/mol/s, for 3rd order it is L^2/mol^2/s, and so on. The real fun comes in because some chemists prefer to use dm^3 instead of L, which gives you beautiful units like dm^6/mol^2/s

[PretzelBS]

I put milk powder in my milk to get more milk per milk

[large_bean]

my favorite cursed unit from engineering school was the refrigeration ton, which is neither a unit of mass nor weight, but of power.
it's the rate of energy consumption that would result in the melting of a 1-ton block of ice in exactly 24 hours at 0°C - probably real useful back when buildings' cooling systems involved big blocks of ice, not so much these days - but it still gets some use
nowadays one ton of refrigeration is defined as 12, 000 BTU/hr, or about 3.5kW
good old industrial inertia. kilowatts are right there

[Subcontrabassoon]

I could write a big effusive textwall, but I'll keep it simple and just say that everything about these videos is sublime and the 40 minutes we've gotten are an absolute gift. Thank you.

[jeremymcginnis]

Materials science: "We will not cancel the cm."
Electricity: "resistivity is totally measured in ohm*meters, just trust me."

[itwasntme]

As everywhere I see cursed units, I have to add:
The ounce.
As a thickness.
In PCB-manufacturing, the thickness of the copper layers will be gives as ounces (of copper per square foot).
So if you are working in imperial units you will have to look up the density of copper.
If you are working in SI and planning to do anything useful, say calculate the max current, you will need to get the density of copper, and also what a foot and an ounce are in SI.

[kono]

I cant believe people complained about the music, its so good and really rare to have videos that have music to go along exactly with the video. I especially love when you say something cursed and play some dissonant thing on the piano, it works so perfectly!

[__dm__]

dB as used by industry is pretty cursed.
1. the base unit is Bel, but for some reason society has agreed 1/10th of a Bel is a more convenient unit to use.
2. dB was originally used to compute ratios between electrical power. However, since power is proportional to voltage squared, if you want to express the ratio of voltages, it kind of makes sense to multiply the dB value by two. The problem here is that they extended this "2x" idea to everything that is "voltage-like", which includes stuff like pressure, displacement, etc etc and you kind of need some background knowledge to know what counts as "voltage-like" quantities.
3. dB was originally used to compute ratios, but it turns out it's useful to have a logarithmically increasing quantity to express single values, not as a ratio. So they made a bunch of units where instead of measuring a ratio between two things, one of the things to compare is fixed, and is noted at the end of the unit to express what it is. dBm is a quantity of power, not quantity of a ratio of powers, as measured against dB against 1mW.
3.1. Except this combines with 2, and sometimes people measure voltages with respect to 1mW, but voltage and power are not interchageable, so it's widely understood as dB with respect to 1mW in a 50 ohm system.
4. The final boss to the insanity extends 3, where a bunch of customized units exist where the reference level and the measurement technique are... exotic and requires domain knowledge. A good example is dBA, or dB A-weighted audio levels. Since the human ear perceives different frequencies at a different level of sensitivity, it kind of makes sense to have a weighting scale to accurately understand how loud it is, rather than how much real power it carries (that said, A-weighting isn't even accurate). But not only that, you still need a reference sound level, but since A-weighting is not flat in frequency, you need to know that the reference level is 20 micropascals RMS at 1 kHz. Oh yeah, the sound industry just uses "dB" all the time even though it should be called dBA.

More examples:
EIN noise: input referred noise of an audio amplifier with (usually) a 150 ohm input load, expressed usually as dBm, as equivalent input referred noise power on the input load. This one's particularly annoying because you need to do quite a bit of math to convert this into input referred dB SPL given a certain microphone.
Radar cross section: equivalent radar reflectivity, expressed as dBsm, or decibel square meter, where the reference level is how much a square meter of a square ideal reflector would reflect
(fun exercise: do you think radar cross section is a "power" like quantity or voltage like quantity, i.e. is it 10log(area) or 20log(area)?)
Microphone sensitivity: how much volts the microphone outputs for a given pressure wave. I've seen various units but it's usually given as dBV at 1Pa, but sometimes people write dBV/P which if you think about it is extremely cursed (and arguably wrong)

[crimsondragon]

Chemistry is best described as “Dimensional Analysis: the game”.

[calyodelphi]

I've got a fun one for you that comes out of meteorology:

CAPE, or Convective Available Potential Energy, is a measure of the amount of convective energy that a _hypothetical_ lifted parcel of air has available to it once it is able to convect adiabatically through the column of air above it. This is expressed in J/kg, as in joules of energy per kilogram of air. That's pretty sensible, you might think, except that joules are expressed as So the unit is actually

Now, here's where the accursedness comes in: You can get a crude estimate of the theoretical updraft velocity within a supercell by _square-rooting the CAPE value._ The updraft velocity is in meters per second after you do this, which suddenly makes sense when the dimensional analysis is done.

[junkice]

As an engineering student, I absolutely LOVE these videos. In high school, my physics teacher always let us use a unit reference table on every test. When someone asked why, he spent a whole class explaining how you could technically use some advanced physics to express just about every unit in terms of any other unit using universal constants. The "standard" units we choose, at the end of the day, are just a point at which someone decided that we should just abbreviate, and aren't always the best/most practical way of understanding things (he brought up mpg expressed as cm^2 as an example). We aren't taking physics to memorize all of these standards, we're taking it to gain a further understanding of how the world works and so shouldn't have memorizing the standards as an obstacle.

[maraganina]

I love how this is not just a list of ugly units. The explanations make sense and there's a nice story overall. Thanks for the video

[NestorCustodio]

The fact that *a Mole is just a number but somehow gets a unit* confused the heck out of me through the entirety of both my chemistry courses. I could never get past the feeling that I was screwing something up whenever I would simplify equations and a unit would magically appear or disappear seemingly arbitrarily.

[aura]

I'm an optometry student and i remember when our teacher told us about the barrier units that we use in a contactology class and said that it was a complete mess that he wasn't going to explain to us the mathematical meaning. Now i understood why, it had blown my mind hahaha 😂

[dannygabel]

The thing with pH is that it isn't actually the negative log of H+ concentration. Its technically the negative log of the activity of H+ of a solution, which is the concentration of H+ in a solution multiplied by a constant that depends on the different ions in solution and their concentrations. The unit of the activity coefficient is liters per mole, which is why the units for concentration cancel. The reason why it's never mentioned is because it's a pain to calculate and it's really close to 1 for relatively dilute solutions. The same thing applies for equilibrium constants.

Acidity in general is kinda weird. pH depends on concentration and is only really used for aqueous solutions, so its kinda useless for determining how "strong" an acid really is. pKa is a more useful measure of the "strength" of an acid since it doesn't depend on the solution's concentration. But even that depends on the solvent you are putting the acid into. It also can't be used to describe superacids and highly concentrated acids. What an acid even is depends on the context, as well. Theres three commonly used definitions and various other obscure ones used in specific subfields of chemistry.

[Bit_]

From the Torr article on Wikipedia: "Historically, one torr was intended to be the same as one "millimeter of mercury", but subsequent redefinitions of the two units made them slightly different (by less than 0.000015%)."

Why.

[barrupa]

Love the piano music. It sounds like an old-timey cartoon, with the twist of being filled with science and mathematics. An odd choice, but surprisingly fitting.

[Audey]

IN DEFENSE OF kWh/1000h:
It's probably been said, but it makes sense for a consumer facing unit. The "kWh", to most people, is not a unit in the same way something like km/h is. It's a chunked known quantity, handled mentally the same way a "dozen" is. It's a thing you buy, like a carton of eggs or a jug of milk. We consume energy in kWh sized chunks, and at the end of the month the power company sends us a bill based on the current value of a kWh and how many we used. That makes sense and allows us to think of something abstract like electricity/energy in concrete terms, similar to gallons of gasoline.

Now, if our goal is to give a consumers the ability to calculate the energy cost of using a product, we need to factor in usage. For some products, like a fridge, that usage is the same for everyone, so we can just use per year and be done. Other products we might want to use something else, kWh per load or 10 loads with a dryer or dishwasher for example. For electronics, I think 'per 1000 hours' is a perfectly reasonable choice. Firstly, it's large enough that it gets you away from awkward fractions of a cent in the final cost. Second, it hits a nice middle ground where both low and high use consumers can meaningfully estimate their costs on a monthly/annual basis.

So in the end we're left with a goofy unit that accomplishes it's intended goals: 1) Give a standard basis to compare two products, and 2) Allow all consumers (even less scientifically literate ones) to easily estimate how much they can expect a given product to cost them in energy; and all they need is their phone calculator and electricity bill.

ps. In the US I think we mostly just give a cost per month/year on all products, with a little fine print stating its based on median energy prices and usage. Its definitely simpler but it also obfuscates things to the point of being potentially misleading.