I mean even basic UV meters with their lambert-beer law make their cuvets 1 cm. So E = epsilon*consentration*distance becomes E extinction = Extinction coefficient (epsilon)*concentration c (mol).
Also while one Watt=Amper*Volt, it's totally different than a VoltAmper or VoltAmperReactance edit: To be honest Ohm*meter generally seems like a useful for things like cables and other ways of electrical connections over a distance
@@ImieNazwiskoOKI thought that at first, but actually that's already included in the resistance in Ohms. resistivity is a property of a material, not an object. Copper has a resistivity of around 1.7x10^-8 Ωm. Looking it up, it seems to me that a more natural way to describe resistivity would be Ω m^2 / m, where Ω would represent the resistance of a cable made out of some material, m^2 is the cross-sectional area of that wire, and m is the length of the wire. The reason it's weird is that resistance has a proportional relationship with the length of the resistor, but an inverse relationship with the width and height.
@@FatedHandJonathon Well, (Ω*m²)/m=Ω/m . But ye that would be more of "full" unit that is self explanatory like the example of gas permeability in the video. Also I think an easier way to word it is it being inversely proportional to the cross section.
Well within the spirit of "don't cancel the units if it obscures where the unit came from" it should probably be Ω * mm^2 / m or something along those lines, after all you probably don't measure wire's cross-sectional area in m^2
You can s#it on imperial units all you want. Keep your metric system: it has some pretty cursed units of its own. Take for example... >Height via length: something like 99.97% of all humans who've ever lived land between 1½ m and 2 m tall. Good god, that is a catastrophic failure in quantifying human height. >Temperature: a fairly average temporate climate will vary year-round by approximately 30 degrees Fahrenheit, 55°F - 85°F. The comparable Celcius span shrinks to less than 17 degrees, 12.7°C - 29.4°C. >Length in millimeters: standard materials used in the production of most rulers aren't precise enough to accurately measure millimeters. So then why on earth do they always appear on there as subdivisions of centimeters??
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
he mentions it in 5:56 also, I don't understand why chemistry teachers decided that teaching this in first year hs chemistry classes (which includes people who studied physics where you think about the units and understand when they're dimensionless) is a good idea
@@not_vinkami no that is for first order. You have r = k[A]^n where [A] is the concentration of the reactant and n the order. This gives you units as mol^(1-n) L^(n-1) s^-1
I remember doing an intro to rates in high school and I kid you not, this one thing was probably like half the reason I went to study Physics and Uni instead of chemistry (Actually that's a joke I just liked Physics better even though I was probably better at chemistry according to my test scores at least)
I think this is the most cursed unit because milk and milk powder aren't exactly identical. Not in taste, not in nutrition, not in mass, etc. It's like if you had an equation with _7pi/22_ in it.
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
Similar to the horsepower, which is actually 1/3 of the power of a horse... Because a 3 horsepower steam engine could replace a stable of three horses operating around the clock in 8-hour shifts. Also, i was surprised the other day to find that 1 refrigeration ton ~ 3.5 kW and 1 kW ~ 3500 btu/hr.
My understanding was that it's the PRACTICAL net refrigerant effect of a daily shipment of 1 ton of ice... is that not right? Is it indeed the calculated energy consumption of melting a ton of ice?
And since its a plasma its H+ anyway so it fits perfectly to use pH Mass of sun×%(Hydrogen)/1g/mole Then use the Volume of the sun to get H+ concentration and then pH=-log([H+])
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.
@@Bit125_ well, the reasonable measurement would be a standard unit of length in the first place. Eg. mm, or at this point fractions of an inch. But the original is a relict of the manufacturing process of the copper foil
@@itwasntme967and what's the standard fraction of an inch used in pcb design? A thousandth in an inch, called a "mil". Not to be confused with the SI unit used, the millimeter, which everyone in SI using countries casually contracts to "a mill" (as in "it's two mills off"). I'm sure that's never caused issues.
@@SimonBuchanNz Standart thickness is 1oz, which comes out to 0.0348mm or 1.37mils. In cases of high currents 2oz may be used, and in high density, multilayer PCBs 0.5oz will be used for inner layers
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!
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.
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.
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.
Because many old units have been redefined in terms of a fixed number of SI units, at a time when their value, as originally defined, was imperfectly known. In the case of the torr, I suppose the difference is because the density of mercury or the sea-level gravitational acceleration of the Earth were still known to only so many figures when the unit was redefined, but became known more precisely after that. The mole was recently redefined as a fixed number of atoms, so that now one mole of carbon-12 atoms is no longer *exactly* 12 grams, as it used to be. Now it is 12 grams plus or minus some nanograms, and we may already know that the error is more than some X. And the standards organizations that define the imperial units have agreed to redefine the inch as 25.4 millimetres, *exactly* . So technically the length of one inch, too, has changed by some small amount.
Because torr is based on mmHg but defined exactly as 1/760 atm (101325/760 Pa) and will therefore differ from mmHg. It's like how an inch was redefined among the countries using it to be exactly 25400 μm, but this causes the old units of inch, such as US survey inch, to differ slightly.
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 kilogram-meters-squared-per-second-squared. So the unit is actually meters-squared-per-second-squared. 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.
Fun fact, CAPE isn't the only convective parameter in units of m²/s². SRH (storm relative helicity) is taken by integrating the dot product of storm-relative winds and the curl of the (absolute) winds over height*, which ends up with units of (m/s) (/s) (m) -> m²/s². This is used to help with looking at supercell and tornado development. CAPE is also fun in how it's calculated; it's another integral, but of TEMPERATURE. Specifically, it's how much warmer a parcel raised "moist adiabatically" (adiabatic except for the latent heat of vaporisation released on condensation of water vapor) from a specified level (usually either the surface or the mixed layer average) is compared to the temperature of the atmosphere, divided by the temperature of the atmosphere to make it unitless. All that is multiplied by gravity and then integrated by height* over the portion of the atmosphere that the parcel is warmer than. Now, you might be wondering why I put an asterisk after both heights. That's because meteorology doesn't use actual (aka geometric) heights; rather, they use a coordinate called geopotential height, which is gotten by taking geopotential and dividing it by standard gravity of 9.81 m/s². Which means that since geopotential height is in meters, then geopotential is yet another meteorology unit in m²/s². And it's obtained by yet another integral, this time from sea level to the geometric height... of /gravity/ (because gravity varies based off of both height and latitude, using geopotential height rather than actual height means we can ignore the variations of gravity and treat it as a constant). Oh and also there's EHI (energy helicity index), which literally is you multiply both CAPE and SRH together and divide by 160,000. Why 160,000? It just scales the numbers down to something close to observed frequency: EHI values less than one rarely had tornadoes and supercells, while values greater than three have strong tornadoes likely. It's said to be unitless, but technically it has units of m⁴/s⁴.
In the same vein: As Randall Munroe (author of xkcd) points out in e.g. What If 86, "Units are weird: The maximum speed the edge of a cylinder of a given material can rotate is equal to the square root of its specific tensile strength (tensile strength over density)."
@@secretpandalord Meteorologists also have one of the most cursed data plots you might ever encounter, called the "Skew-T, Log-P Plot". Why does it have this name? Well, the horizontal axis of the graph plots temperature, but the "isotherms" (lines of constant temperature, the grid lines associated with this axis) are _skewed_ 45° just to make the temperature plots easier to read, otherwise the data plot would be EXTRA WIDE as temperature drops precipitously up through the troposphere right up until the tropopause where it then stops dropping or even starts rising slightly again up through the stratosphere (this change in lapse rate is literally what defines the boundaries of atmospheric layers). So the skew distorts the temperature plot so that everything fits more vertically and is easier to publish and read as sounding charts. The "Log-P" part comes on the vertical axis, as atmospheric pressure drops off logarithmically with altitude. This is actually the most sensible axis plotted on the chart, especially since atmospheric conditions don't actually care about our arbitrary systems of measuring altitude. Instead it's the air pressure that matters, so a lot of meteorology deals in "isobars" (lines of constant pressure), and the altitude above the surface is merely an afterthought marked on the same vertical axis with secondary labels. These plots sometimes have a whole bunch of other bits of information plotted on them such as mixing ratio lines (lines of equal moisture content in the atmosphere), dry adiabats (the temperature a dry parcel forced to rise would have at any given elevation), and moist adiabats (the temperature a saturated 100% humid air parcel forced to rise would have at any elevation) and so on. It's a heck of a lot of visual noise, but they are incredibly important for weather forecasting.
@@calyodelphi124 With the exception of the Log-P part which makes perfect sense to me, I hate everything you've just written. Thank you for introducing it to my life.
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!
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)
Another random thought: the dBA thing made me think about Sun Protection Factor, which is used for stuff like sunscreens, since that is also weighted for human skin damage potential wrt. the radiation wavelength spectrum. SPF of 30 is defined as 1/30th the damage potential with respect to not being on, which seems like it would work really well as a decibel unit. A SPF 30 would be about -15 dB SPF, and SPF 120 would be -21 dB SPF. This is particularly nice since every 3dB step in SPF means you're getting sunburnt half the amount. A common criticism of SPF is that people find the high SPF products to not be a big benefit compared to the low SPF products (e.g. 30 SPF vs 50 SPF) and using decibels would make it more intuitive.
@@la.zanmal. There are more weightings and they all adjust depending on frequency. To my knowledge(and I only had 1 class about acoustics and noise) the A weighting is used frequently when you’re considering the human ear, especially for hearing damage as the laws are written in regard to A weighting(even if it’s not strictly accurate). In OSHA regulations, there is a maximum equivalent exposure to sound, so something that’s extremely loud for a short time and something that’s just quite loud for a much longer time can be considered similarly to one another. The baseline for that is 90 dBA for 8 hours and there’s some sort of equation that will give how long at 100 dBA is equivalent to that.
And then when decibels get involved in digital calculations, you end up with all sorts of weird variants like dBVU, dBFS and dBTP which don't even measure anything in real life
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.
I find it astonishing how all the pedagogical research indicates that direct, lecture style, instruction like that is the least effective form of instruction, and yet everyone I talk to can remember at least a half dozen such direct lectures, sometimes from as early as 8 years old, with distinction and clarity.
Check out Jan Misali and his various number videos. The CCC video and a few others helped keep me sane through DE, if you can call an engineer sane. PS: the whole point of the CCC video is using universal standards to define an absurdist units system
Electronic engineer here, i had a good dose of cursed units when i was learning why Inductances and Capacitances behave like resistances in complex variable
it's even more fun when you're taking a course on electrodynamics while also taking a course on 3phase power systems modeling and both subjects use the same symbols to mean completely different things
@@Jacobschannel18802 Also a massive issue in mathematics. People run out of symbols for operators and then use whatever. Also different fields using very different terms for essentially the same objects. Gnnnnnnnnh!
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.
I remember having very ambitious (and very good, so it wasn't a problem) professor of Chemistry in Highschool. We did learn all about calculating pH as well as some things that I don't know if they aren't technically wrong (for super strong acids, I don't even remember if me measured it in fractions or negatives, because chem teacher might have been ambitious, but math teacher didn't teach us logarithms yet back then ;) - it was a bit nebulous). Not to mention learning that you can exceed "standard" scale of pH (1-14) - so while in highschool it was wacky (and there was so much of it, I'm now not sure which exact model was correct, because teacher was ambitious so he had to show us also all the "wrong" ways in which pH can be measured and misapplied) - it really helped in Uni, where for a time I did study Chemistry. Because back then I remembered all the possible pitfalls of measuring and calculating pH and how to avoid them. Sadly I don't remember now, because I haven't done this in 20+ years.
The reason why the equilibrium constant and reaction quotient are unitless is also the same: the ‘concentration’/‘partial pressure’ values that you substitute into the reaction quotient are actually thermodynamic activities. This also plays into why solids and liquids don’t contribute to the equilibrium expression or reaction quotient because their activities are close to if not exactly 1.
Ah yes, throwback to the time when there were 3 different acid theories and we learnt all of them. From the super narrow hydrogen ion producing idea of Arrhenius to Lewis going, "Fuck it, if it can accept a lone pair it's an acid." I mean, it did bring the definition of acid to a lot of things like transition metal complexes and all of that, so I guess that's kind of cool.
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.
@@cshairydude The only issue with that is the majority of products vary in how often they're used from person to person. In August, someone in Montana might run a window AC unit for 4 hours a day, meanwhile someone in an identical apartment in Phoenix might have theirs running for 18 hours. Then you get into having labels with fine print (*based off the median home with blah blah blah...), and different companies choosing different standards for comparison. Its just a whole confusing mess. kWh per n hours is imo just a very clear and consumer friendly way of conveying the relevant information.
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 😂
Tbh i have just looked at my notes and we actually use it in mmHg and not in cmHg as you pointed out. Just for u to know we normally use it to figure out the quantity of oxygen that is going to get to the cornea throw the contact lens and is a very useful way to known if it's going to cause corneal edema for the hypoxia during the use of the contact lenses. Also in reality we normally write it as DK/t where DK is the part that's only dependent on the material and t the thickness but the barrier is an actual unit that we study hahahah
3:18 I think a reason as to why torque has the same unit as joules is that torque is the cross product between force and length while work is the dot product, so they're still describing different things
ugh. I still remember college physics and having to deal with figuring out the angle between two vector quantities, and how that would be the hardest part of the problem, because angles in 3d are nightmarishly problematic to deal with - especially when the coordinate system is at an unrelated angle to either vector for literally no reason, but that's how the problem in the ****ing textbook is.
Good ol' quaternions pretending to be arrows. At least we aren't talking about the 6-dimensional entity that I've seen called "forque" (that's effectively just the direct sum of force and torque, hence the portmanteau).
18:51 given that there's now just shy of 500k views on this video, I'm convinced there's just 500,000 of us dutifully watching all the measurement naming convention videos
As someone with a PhD in theoretical chemistry, I have a big gripe with people using the term unitless when they mean dimensionless, and the concept of units completely cancelling each other out. Just because two units have the same dimension, does not mean that they can completely cancel each other out, the actual thing that they are referring to remains, it is just the dimension part that cancels out. For the radians example, the units of 1 m arc length / 1 m radius = 1 radian, the dimension of the two units cancel (each being meter), but the units do not cancel, and we are instead left with a radian = arc length/arc radius. This may seem pedantic, but it is important to remember that these dimensionless quantities are still referring to ratios of actual things. Otherwise these numbers would have lost all of their meaning.
Important for what purpose? Angles ARE numbers. Trigonometric functions, for example, can be defined geometrically, but also analytically, with no reference to circles or angles or anything like that. Pi can be defined as a certain ratio of lengths, or n-dimensional volumes, or as the square of the Gaussian integral, or as a sum of many interesting series, or in infinitely many other ways. By fixating on one particular "meaning" of these concepts you're losing the flexibility that comes with understanding all "meanings" at once.
19:00 Hol' up. you can rewrite the pressure as force/area, which cancels with the other area in the denominator. Mol, can be replaced with 1, if you scale everything down by the avogadro number. You end up with cm/(second*force). Now, Force is just mass×distance/timesquared. So it is distance/(time×(mass×distance/timesquared)). It simplifies to mass/time. In the end it really just tells how much stuff get's trough over time.
@@tamassoos5915 really it's so you can use known tables of material properties without doing unit conversions all the time. So, e.g., while "mass/time" is fun, it doesn't really allow you to predict the membrane properties based on its dimensions and material properties.
@@tamassoos5915 Depends what you want to calculate and what formula is for. For example, such "complex" formula can show and educate people new to this particular field how many things have to be factored in. Then you introduce simplified formula for everyday (so like 99%) use, but full formula can still be useful to remember if you're dealing with cases that are.... very abnormal. In such situations some people legitimately might have problems operating with simplified formula, because they would have to take into account too many things at once. Full formula allows you to change every single parameter one at the time, without juggling dependencies between various units and assumptions. Which can create errors. In the end of course most people will be using "simplified" formula and as they gain experience with it, they will have to go to basics less and less. Also importantly, when you do dimensional analysis of new problem and write new formulas - I personally found most useful to write the most "full" formula possible, run it few times through few examples and then try to simplify it, after getting some experience with full formula. With that experience you start to know best what you can simplify. Because generally speaking simplifying formula by cancelling "everything" results in stuff like in first video where you had "fuel efficiency" in milliliters (? - would have to double check it, but it was mentioned in this video). And that to people who are only beginning work in the field is "so simplified that it doesn't make sense". Not to mention - such formulas are great educational tool in dimensional analysis ;)
I recently had to deal with the standard cubic meter (Nm^3), which is similar to the cm^3_STP. The issues is that "standard temperature and pressure" are different standards for literally every single industry!!! You have DIN 1343 using 273.15 K and 101325 Pa for compressors and natural gas, unless your gas is American in which case you use 288.15 K (API). This standard is also used in gas turbines, though not pneumatic equipement. That uses 293.15 K at 1013 mbar instead. Nevermind that nearly all chemical properties can either be measured at 293.15 K or 298.15 K and the worst part is: surprisingly often people don't specify which standard they are using! I just want to know your actual energy usage per amount of substance produced via electrolysis! Are joules per mol too much to ask for?!
It´s funny that you complain about different standards being used for standard cubic meters and then use Nm³, which refers to normal cubic meters. In europe, people use normal cubic meters, which are cubic meters at normalized conditions of 0°C (273,15 K) and 1 atm (= 101325 Pa). Standard cubic meters may be used as well, but more common are standard cubic feet, with standard conditions being 298K (apparantly Californian room temperature) and I forgot the standard pressure. However, americans also often use local standard conditions based on local weather, which can be really annoying, when those conditions are given in PSI and °F.
@@AndreasPeters-r3e Well can you blame me for getting confused? 😅 And sure, while Nm3 is the most common in Europe, I have still come across manuals using Sm3 when compressors are involved
@@2001Pieps I do not blame you. I make little mistakes myself. Especially in you tube comments I very really re-check what I just wrote - it´s not science usually.
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.
11:30 I'm very proud of myself for immediately guessing c. While I don't know WHY it's there, it only makes sense to me that these stupid units must involve it somehow. It's the only constant that makes sense to me.
I was wondering if there was a meaningful ratio before he asked that question, and as soon as he implied it should be guessable, c was the obvious guess. Especially as I remembered the fact that the two main numbers describing the electical and magnetic properties of empty space can combine to give you a speed was one of the first hints that we needed Special Relativity.
The music is the main reason I liked the original video, when I first saw the thumbnail I was like "Ooh, a generic science trivia video, will this have a rantsona or not?" But to my surprise it was very well made and had an excellent post-production way beyond most YT videos. Great job! ❤
So I've taught classes on international economics. Something I've done that seems to help my students is take about 20 minutes to explain dimensional analysis at the beginning of the semester. We don't use it much, but when we get to the part where I'm trying to explain how the expected interest rates of European bonds affects the current exchange rate of USD and EUR, those units get quite handy to keep the model straight. And everything cancels nicely when trying to model expected rates of return: Expected rate of return on european bonds (measured in future value USD/current value USD) = current exchange rate * rate of return * expected future exchange rate = (EUR_{now}/USD_{now}) (EUR_{later}/EUR_{now}) E(USD_{later}/EUR_{later})
My favorite cursed unit lurks at the heart of electrical wire gauge: the circular mil, or cmil. One cmil is defined as the area of a circle 1 thousandth of an inch in diameter. The equation for the area of a circle in cmils becomes A(cmil)=D(mil)^2. This unit is used in the form of kcmils for sizes of wire larger than #0000 AWG, and ampacity of wire is calculated by cmils instead of squaremils.
Your music is absolutely incredible. The "Chad" theme, the music being used as exclamations, excitation, suspense, and so much more through just background music. Masterpiece.
@Simon-ps3oj > the speed of almost anything is defined by how easy it is to get through the medium. Light being electromagnetic means that the ease with which the electric AND the magnetic parts get through the medium are both relevant in a vector-sum way (square root of the product of the two quantities). The two quantities are the permittivity of space (electric side) and the permeability of space (magnetic side). The lower these quantities, the faster light goes; the higher these quantities, the slower light goes. Hence an inverse relationship.
@@justinhadley3927 The speed of light is actually just the speed of causality, so I think one of those variables is actually set, and the other is based on that and c. I'm not sure what might be more fundamental, electrical or magnetic propogation.
the music is actually the best part of these. Now that I know you play it yourself it makes a lot of sense. It acts as a laughing track, but where a laughing track emphasizes humor, the music emphasizes cursedness.
As an upper year chemistry student, the mole example perfectly sums up why "cursed" ≠ "useless". We need some easy way of relating the mass of atoms to the mass of their constutient molecules. Being able to do this fast and reliably is a foundation of modern chemistry that you really can't get around. Chemistry has a lot of these cursed units though, our math is far from beautiful!
It's also important historically - we had the mole before we had any good estimate of the Avogadro constant. The best estimate of the constant fluctuated while we improved our measurement capability, and now (as of 2019) we actually locked it in and use it to define the units that previously defined it!
I just wanna add that as a radiation therapy student (graduating soon though), you did a good job explaining the subtle differences of radiation units and why its important to have 2 units with the same expansion but very different contexts. also wanted to add that you are actually correct about the centigray (shortened cGy)! The Rad came first in history before the Gray, so all of our machines are still calibrated to the Rad/cGy, mostly as a tradition/backwards compatibility measure, but as the world shifted to SI units for consistency, it was decided that we will exclusively only refer to it as a centigray and the math to find the accurate dose for a patient is based on SI units. Radiation is another weird world of units for sure! edit to add: i completely forgot about the electron-volt! a unit of energy that by forcing the speed of light to simplify to 1 with clever number manipulation, is also used to measure the mass of atomic particles as well.
in my first year of physics i took a class heavy on chemistry that was advertised as just as doable whether or whether not you did advanced chemistry in high school, and as someone in the latter camp i was curious to see how they would equalise it like that. turned out it was by subjecting us all to reaction quotients and making us watch our collective understanding of units get slowly murdered in real time
materials guy here. lol. Everyone failed and complained about physics. It seemed you had to be a savant to even understand the basic concept of Anything in there. However, chemistry was like full understanding of anything was impossible. Maybe like static shocks vs sunburn
You gotta make a full section on radioactivity units. There's at least 7, and it's painful. (Becquerel, Curie, Gray, Sievert, Ren, Rad, Roentgen, etc.) Also explain why we have so many measurements for pressure (bar, torr, psi, pascal, inHg, cmHg, mmHg, ATM, technical ATM (?), inH2O, kg/cm², the list goes on and on.)
In fairness to pressure, it depends widely on the ranges you are looking at. Like in oil and gas, I have only really seen psi and bar be used because the range and accuracy is more reliable/readable than say kPa.
Apparently I'm so familiar with electromagnetism that as soon as you said "this constant must have units of centimeters per second" that I instantly knew it was c. Shoutout to James Clerk Maxwell, dude contributed SO MUCH to our basic understanding of physics but is very rarely actually mentioned unless you're discussing entropy.
You'll get some more cursed units if you move to engineering and industrial efficiency metrics. Long ago I worked at a milk packaging plant. The goal at the for adequate efficiency was to use less water in plant operations (cleaning, cooling, break room drinks, staff toilet, etc.) than milk packaged and shipped. Efficiency was thus measurable in gallons/gallon or liters/liter. Or in large water system management, the Imperial unit is the acre-foot. Since the acre is a chain by a furlong, an intermediate step before getting to cubic feet is chains x furlongs x feet.
5:54 Physics student here, I'm feeling very relieved right now because I felt like I was going mildly insane learning reaction coefficients for my biophysics course. Also, I'd like to nominate Specific Impulse as a cursed unit. Not because it's that bad to use, it's just inexplicable. It's the measurement for the efficiency of rocket engines, which is measured in seconds. Why? Well, if you do the calculations, you find that the amount of velocity change you can get from your ship is proportional to the velocity of the exhaust gases, in m/s. Except, for some reason, it is then divided by the earths surface gravity of 9.81m/s², giving m/s/(m/s²)=s. For a unit that is pretty much never used on the surface of the earth. And whenever you use it, you need to multiply by 9.81 again.
To defend seconds as unit of impulse, after a while it gets quite convenient to have reference point in starting a rocket time, but i would more like a unit that is based on first escape velocity of earth as making an orbit is something that impulse is more used to than getting the ship to high altitude
It makes way more sense as kg*s thrust per kg fuel. Or pound seconds per pound of fuel. In fact, the fact that you get the same numbers in both metric and us customary was quite useful in the early days and definitely part of the reason that seconds became the standard.
The story (not really sure if true) is that the original unit was (pound of force produced)×(second)/(pound of fuel used), which is the same dimension as Ns/kg or m/s, but then people just canceled the pounds
The division by gravity was a trick used back when NASA hadn't standardized on SI units, so by dividing by gravity it didn't matter if you were working in imperial or metric units, you'd get the same value for rocket engine efficiency.
I would vastly prefer a m/s expression of rocket efficiency because that's what's going on, it's the force you get out of some expelled mass of propellant, which is proportional to the exit velocity of the propellant. Or, the most applicable, which is acceleration (or force, simplifying the mass of the rocket out) per mass of propellant, which is what'll be concerning anyone doing anything with different rockets. But it's still proportional to exit velocity.
These are absolutely excellent, I nearly spit out my coffee with the cmHg reveal. My personal favourite is the charging speed of an electric car. You get a certain amount of charge that gives you more range over time. Range is measured in km, and most EVs charge slow enough that hours is a good unit for the charge time. Which means your charge speed can be measure in km/h, which yes is also speed. It's fantastic because you can compare the charge speed directly to your average speed for a journey, to get an idea of how much longer a journey is going to take if you have to stop and charge.
That works on gas cars too, just need to convert the nozzle throughput to the L/100km value, and you are done. Though that's usually fast enough where it's not worth measuring.
16:37 In defense for kWh/1000h: The point for this rating is devices that operate on some (variable) duty cycle like a fridge. Giving it a fixed and aimplified rating like '50W' is pointless when, most of the time; it's 0W, but sometimes 300W. kWh/1000h describes the average power draw of a device over 1000 hours.
Makes sense, though I wonder why they didn’t go with kWh/year, as shown in another example in this video 1000h feels a bit weird to reason about in your head, even considering it’s roughly 6 weeks
@@vladyslavsmirnov1875 My guess is that it is a long enough period to get a useful average over, while still producing small enough values to make sense on these labels (typically 20-1000 kWh/1000h)
@@vladyslavsmirnov1875 Easy to convert to watts is probably the main reason. It was mentioned in the video why Watts can't be used (people use that as a measure of brightness instead of lumens).
It's actually dangerous (well kind of) to ignore that electrical devices may not use the same amount of energy (or have the same efficiency) at all times. The EU not only rates energy efficiency of TVs, they also rate vacuum cleaners. That is they did until the General Court of the European Union told them to stop (the way they did), because they only measured at the start of the vacuum cycle. But everybody easily realizes that the efficiency (in the unit ' "suck" per Watt') of a "normal" vacuum (that is one with a filter bag) obviously goes down the more stuff you vacuum in, while that of a "cyclonic" vacuum doesn't (more or less). It also differs between different filter vacuums.
One great thing about Planck units is that a velocity is always expressed as a proportion of the speed of light, which is basically β, making the Lorentz factor an elegant 1 / √(1 - v²).
The thing about the chemistry units is, that it is only cursed because we made it this way. We are actually talking about activity (which is dimensionless), but for small concentrations, activity is proportional to concentration / partial pressure / whatever is easier to use. And since activity can't be measured directly but concentrations can... We ended up with often messed up units.
A nitty-gritty detail: A mole _used_ to be defined based on carbon atoms, but since 2018 it isn't. Nowadays the SI-unit system is based on seven defining constants and Avogadros number is simply one of those defining constants: * The caesium frequency ∆v_Cs = 9 192 631 770 Hz (i.e 1/s), the unperturbed ground- state hyperfine transition frequency of the caesium 133 atom * The speed of light in vacuum= c 299 792 458 m/s * The Planck constant h = 6.626 070 15·10^−34 J s (i.e. kg m^2 s^−1 * The elementary charge e = 1.602 176 634 ·10^−19 C (i.e A s) * The Boltzmann constant k = 1.380 649·10^−23 J K^−1 = kg m^2 s^−2 K^−1 * The Avogadro number N_A = 6.022 140 76 ·10^23 mol^−1 number of elementary entities per mole * The luminous efficacy K_cd = 683 lm/W (i.e. cd sr W^−1 =cd sr kg^−1 m^−2 s^3) The luminous efficacy of monochromatic radiation of frequency 540·10^12 Hz
I liked the Avogadro proposal where they got a dude to grind a silicon sphere so precise that you could count the number of atoms in it to sufficient precision for the definition of Avogadro's number.
Yes, 1/12 mole of carbon-12 atoms happens to be 1 gram, but that is _not_ the _definition_ of mole nor of gram, just as little as 1/14 mole of carbon-14 atoms being 1 gram is not the definition of gram nor mole. The new SI-system is a fundamental philosophical shift on how we define units. Nowadays, the Avogadro number is by definition _exactly_ 6.022 140 76 ·10^23 mol^−1 and the connection to carbon is simply just historical, nothing else. In the hypothetical case that 1/12 mole of carbon-12 atoms would happen to be found to be 0.999999999999 gram, the definition of the Avogadro number would not be affected. In the old SI-system, the Avogadro number was an approximate number, not an exact number and the Avogadro number would then change if new measurements came up with new results
The build up and reveal at 11:36 to "The speed of light!" was perfect, its feels so out of nowhere but perfect at the same time. That some perfect alingment stuff and i bursted laughing. Great video man! LOVED the piano!❤
As an Astronomer, cursed units are everywhere in our field. CGS and SI are used interchangeably in some equations, especially involving electromagnetism or telescope detectors. At the same time we have several different ways to describe mass and length. And don't even get me started on Janskys or anything to do with radiative transfer theory.
@@Roxor128 Most of them exist because they are "handy" and relatable. Every field does this. In materials science we use electron-volts for energy. Typical values might be 1.4 eV. Why in the world would anyone in their right mind want to use 2.24305e-19 Joules instead? You could measure a planetary mass in Kg, but "Earth Masses" or "Jupiter Masses" are generally going to be much more handy units. Just like Proxima Centauri being 4.2 light years away is a lot more useful than 4.132 × 10^16 meters (41.32 petameters)
cant believe people didn't like the music! i loved it! when i watched the first video, i thought it was so amazing, i was so impressed when you timed the dramatic stings / dissonant notes / pauses in the music with key points in the script! it really gives the videos a bunch of unique character
2:10 how have you already hurt my soul this much with writing 2pi as 6.3 this is a video about cursed units, not cursed rounding! also omg the esu-emu conversion problem! we spent a long time on that in my history of science class! it’s so cool, i’m glad you gave it a huge microphone with your channel!
I'm soooooo glad you decided to keep the music. It's just a beautiful combination. I love both vids and am hyped for part 3. As an engineer student I find this both educative and funny asf. Thank you for making this.
One is a vector and the other is a scalar. You can consider the direction of a vector as part of its unit of measure. A newton-meter of work and a meter-newton north of torque are very different quantities.
I once in an exam stumbled upon the unit of energy density, or J/m³. Well, as Joule is also Nm, you can cancel the m and get N/m², which is the unit of pressure, also known as Pascals. So I wrote that in the exam, just as a joke. The teacher was a little confused and wrote a "?" and when he gave back the exam he asked me how I arrived at Pascals. He just stood there, looked at my derivation and went like "Huh. That's...odd." and had a little chuckle.
@@JanB1605 I would argue that energy density and pressure are much closer than torque and energy. Torque is a vector, gotten by the cross product of force and length, while energy is a scalar, gotten by the scalar product of the two. Totally different. On the other hand, pressure is the "movement part" of the total energy density. For an ideal mono-atomic gas, energy density is literally 3/2 of the pressure (the factor comes from 3 axis of movement, 2 directions each).
@@entcraft44 Nm ist also the unit for energy when you apply a force to an object and move it a certain distance. Torque is the same concept, just in a rotation. Instead of moving the object linearly, we turn an axel.
Avogadro's "number" is a constant with units mol^-1. If you divide a number of things (usually atoms or compounds or molecules) for the Avogadro's constant you get its number of moles, with units mol. In the reaction quotient the concentrations are approximations for the activities, so they are each multiplied by a conventional activity coefficient of 1dm^3/mol and the result is dimensionless. Anyway very funny video and I love the music, especially because it's made to match the tension of the talk!
The foe isn't a cursed unit dimensionally, but it's cursed in scale: ten to the ifty ne rgs. It's used to measure the yield of supernovae. Astronomy and astrophysics are full of non-SI units that exist because SI units just don't have the right scale, or because relevant physical constants either once were or still aren't well enough constrained to convert precisely to SI. The gravitational constant is still poorly enough constrained that we have a much better idea of the mass of the Earth in solar masses than in kg.
Similarly with the AU and Parsec. They let you measure things relative to the size of the Earth's orbit without needing to know exactly what that is. (Though I expect we have a very good idea now.)
@@SimonClarkstone The additional wrinkle I learnt is that general relativity throws another spanner in the works. I hazily remember that metres are only defined when special relativity is a Good Enough approximation, so while astronomical distances at the scale where space noticeably expands have a nominal conversion to SI units whether or not that conversion has any meaning can be questioned. (Of course, now that au is redefined to be just some fixed number of m, that changes a bit of a status.)
Same with particle physics and materials science. Can you imaging measuring band-gaps in semi-conductors in Joules instead of electron-volts. Everything would be in the 10 to the -19th power.
@@isoraqathedh The AU isn't anywhere near the scale where expansion is relevant. But yes, at the largest scales, the only observable we have to measure distance is redshift, and the value of the Hubble constant is poorly constrained, so distances in any units other than Hubble lengths are somewhat uncertain.
ICU doctor here. If you want a cursed unit for part 3, Systemic Vascular Resistance Index is measured in dyne.s.cm-5.m-2 Also keep the music, it reminds me of Untitled Goose Game!
It is a bit more complicated than that because the use of the pH assumes that you are in a water solution and while HCl is strong enough to protonate water to very low pH, at pH=0, water begging to act as a base and you have to add so much HCl that you leave the solution model and approach the mix model where pH doesn’t make sense anymore.
The music honestly adds so much to this video. This might sound weird, but it has a very similar energy to the music in Untitled Goose Game, or a Scruffy video. It creates a lighthearted atmosphere that I really like.
Color dispersion is a cursed unit. It's "demensionless" (according to literature) but isn't a multiplicative factor. 4:37 A mole is also a unit for integrated light output (different from optical W·s) that counts the number of photons. A typical 10W LED outputs about 1 mol/day, a unit called DLI. 7:33 This is similar to the triad [µmol/s, mW, lumen] for light intensity, depending on the usage (photochemical reactions, energy, brightness). 19:14 They could have introduced an intermediate unit, like "permeability resistance", that depends only on the material and area-divided-by-thickness, to greatly simplify the formula.. Just like ohms-per-cube. Did you know there's also ohms-per-square? (used in semiconductor design)
Interesting thing to note here, is that after the 2019 Redefinition of the SI Units, Vacuum Permeability/Permittivity (u0/e0) are no based upon the Fine Structure Constant, so while the overall system works a lot better, the "Constants" now have some amount of error within them. More interestingly however, the relation between the 2 aforementioned Units and the Speed of Light still hold, even as Vacuum Impedance, ie Impedance of Free Space, also has some error inbuilt to it
My favorite cursed unit is the snail (also called a slinch), which is a lbf s^2 / in, a unit of mass in American engineering units that's pretty common in structural analysis. Another great one from aerodynamics is air density, measured in slugs/ft^3 = lbf s^2 / ft^4
If you make a part 3, consider looking up degree Baume! Its _supposed_ to represent concentration of a solution, but in reality its a huge mess. On wikipedia they talk about it in terms of specific gravity, which itself is a dimensionless number derived from dividing 2 _densities_ together (density and concentration of course being different). The definition of this unit is /different/ if you're measuring solutions less or more concentrated than distilled water. To make matters worse, in practice, when you use it in practice to measure the concentration of various solutions, it's just a calibrated weight that bobs up and down in a cylinder. If you've looked at the scale, it /pretends/ to be a linear scale over small distances (it really isn't) ; ergo it feels like you're measuring a length ala mmHg. Historically, that callibration has been so incredibly inconsistent, that when this unit was adopted, there was extreme variation in what the same unit meant. Eventually it evolved into a family of equally stupid concentration units used in hyper specific places like Brix or specific gravity * 1000
Fluid mechanics also has a ton of dimensionless numbers to describe different characteristics of flow, like the Grashof number, Reynold's number. Then you also have the Rayleigh number which is a product of the Grashof number and the Reynolds number, or the Richardson number which is a ratio of the Grashof number and the Reynolds number.
An important note on CGS: There're different versions of that system, some commonly used today in theoretical electromagnetics because it cancels all the coefficients and even most of the units. Speed is measured in quantities of speed of light (so it can never exceed 1), charge is measured in numbers of electrons, vacuum permitivity = 1, etc.
3:41 THANK YOU for saying that. I hate how people pretend that radians are demsionless. Similar to meter, which usually indicates that the thing you measure is some sort of vector, the radian indicates that it is a bivector, that it works in some plane. THIS is the difference between joule and newton-meter (which should be more like newton-meter-rad). Joule is a scalar, but a torque needs a plane to rotate in, and it gets information about which plane, from radian. And if you multiply torqe by radian, you'll get actual joule. Also thanks for mentioning angles in revolutions, I also never understood when people say that unlike degrees, radians are the most natural unit for angles. Like, no, revolutions are! But nobody just seems to notice it.
I think we consider radian angle measure the most natural because of how it works with calculus. For example the derivative of sin(x) is only cos(x) if x is measured in radians. If you use another measure of angle, the derivative of sin(x) is A cos(x) where A is the ratio between an angle measured in the units of x and the same angle measured in radians. For example, if x is measured in degrees, the derivative of sin(x) is 180/pi * cos(x). If x is measured in revolutions, the derivative of sin(x) is 1/2pi cos(x).
The radian is still dimensionless. An equation only involving quantities and not units (think PV=nRT) should remain true regardless of the units. The equation defining angle is s=r theta where s is the signed arc length, r is the radius of the circle, and theta is the angle. 1) theta has to be dimensionless as changing from radians to cycles makes the equation wrong 2) theta has to be dimensionless as mentioned in the video: m/m=1
@@maxthexpfarmer3957 well that's like saying that newtons can't be vectors because meters already are. Torque is basically a rotating force, it makes sense that it has angle in it somewhere.
0:26 i love the slow piano buildup to the gigachad music in the background. it’s all the little details that make the whole video feel all the more special.
The absolute kicker about the barrer is the fact that, since cmHg is a pressure, the units can be reduced to volume/force. Considering the barrer is commonly used for describing material permeability, the simplified units actually *are* intuitive: what volume of the chosen fluid will pass into the given material under 1 unit of force?
I once saw the ideal gas constant R (8.314… Joules per mole Kelvin) expressed in: Inches of water cubic feet per pound-mole Rankine ((inH2O*ft^3)/(lbmol*Ra). I have absolutely no idea what use case this particular representation of that constant could ever have…
As an X-ray physicist, my favourite cursed unit is the Crab, a unit of flux (W/m^2). 1 Crab is the flux of X-rays from the Crab Nebula in the measured energy range. Of course, the Crab Nebula is one of the brighter X-ray sources on the sky, so it makes sense to measure most fluxes is mCrabs, or milliCrabs. Maybe a candidate for your next video? :)))
Materials science: "We will not cancel the cm."
Electricity: "resistivity is totally measured in ohm*meters, just trust me."
I mean even basic UV meters with their lambert-beer law make their cuvets 1 cm. So E = epsilon*consentration*distance becomes E extinction = Extinction coefficient (epsilon)*concentration c (mol).
Also while one Watt=Amper*Volt, it's totally different than a VoltAmper or VoltAmperReactance
edit: To be honest Ohm*meter generally seems like a useful for things like cables and other ways of electrical connections over a distance
@@ImieNazwiskoOKI thought that at first, but actually that's already included in the resistance in Ohms. resistivity is a property of a material, not an object. Copper has a resistivity of around 1.7x10^-8 Ωm.
Looking it up, it seems to me that a more natural way to describe resistivity would be Ω m^2 / m, where Ω would represent the resistance of a cable made out of some material, m^2 is the cross-sectional area of that wire, and m is the length of the wire. The reason it's weird is that resistance has a proportional relationship with the length of the resistor, but an inverse relationship with the width and height.
@@FatedHandJonathon Well, (Ω*m²)/m=Ω/m . But ye that would be more of "full" unit that is self explanatory like the example of gas permeability in the video.
Also I think an easier way to word it is it being inversely proportional to the cross section.
Well within the spirit of "don't cancel the units if it obscures where the unit came from" it should probably be Ω * mm^2 / m or something along those lines, after all you probably don't measure wire's cross-sectional area in m^2
Chemistry is best described as “Dimensional Analysis: the game”.
Electricity is best described as "Blueprints: the game"
@@mrpojsomnoj3313 you are far more correct than you could ever know.
Until you get to organic chemistry, which is more like "follow the electron pairs"...
Crap. I just lost The Game.
You can s#it on imperial units all you want. Keep your metric system: it has some pretty cursed units of its own. Take for example...
>Height via length: something like 99.97% of all humans who've ever lived land between 1½ m and 2 m tall. Good god, that is a catastrophic failure in quantifying human height.
>Temperature: a fairly average temporate climate will vary year-round by approximately 30 degrees Fahrenheit, 55°F - 85°F. The comparable Celcius span shrinks to less than 17 degrees, 12.7°C - 29.4°C.
>Length in millimeters: standard materials used in the production of most rulers aren't precise enough to accurately measure millimeters. So then why on earth do they always appear on there as subdivisions of centimeters??
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
Isn't the 0th order unit just inverse seconds?
he mentions it in 5:56 also, I don't understand why chemistry teachers decided that teaching this in first year hs chemistry classes (which includes people who studied physics where you think about the units and understand when they're dimensionless) is a good idea
@@not_vinkami no that is for first order. You have r = k[A]^n where [A] is the concentration of the reactant and n the order. This gives you units as mol^(1-n) L^(n-1) s^-1
I remember doing an intro to rates in high school and I kid you not, this one thing was probably like half the reason I went to study Physics and Uni instead of chemistry
(Actually that's a joke I just liked Physics better even though I was probably better at chemistry according to my test scores at least)
your feelings are irrational
I put milk powder in my milk to get more milk per milk
milk/milk > 1
*D I M E N S I O N L E S S*
*D A I R Y P R O D U C T*
Wouldn't that just be nutrition volume per capacity?
I think this is the most cursed unit because milk and milk powder aren't exactly identical. Not in taste, not in nutrition, not in mass, etc. It's like if you had an equation with _7pi/22_ in it.
Milk is approximately 87 percent water, so by adding milk powder you reduce the percentage and therefore get indeed more milk/milk
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
Similar to the horsepower, which is actually 1/3 of the power of a horse... Because a 3 horsepower steam engine could replace a stable of three horses operating around the clock in 8-hour shifts.
Also, i was surprised the other day to find that 1 refrigeration ton ~ 3.5 kW and 1 kW ~ 3500 btu/hr.
My understanding was that it's the PRACTICAL net refrigerant effect of a daily shipment of 1 ton of ice... is that not right? Is it indeed the calculated energy consumption of melting a ton of ice?
Everyone measures AC in Tons (my house has a 5 ton unit) but I never knew where it came from.
Thinking of inverse. So 3,5kW running a day could freeze ton of ice a day? Ignoring getting the stuff there and then stopping at 0C...
I propose that this is 1 Fusepower
Friendly reminder that the pH of the sun is approximately -3.
How does that work? I thought pH only applied to aqueous solutions
@@Plancksized its just very very concentrated
And since its a plasma its H+ anyway so it fits perfectly to use pH
Mass of sun×%(Hydrogen)/1g/mole
Then use the Volume of the sun to get H+ concentration and then pH=-log([H+])
lmao what
@@dalitas The sun isn't homogenous, it's much denser at the core
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.
i mean the looking up feels unavoidable unless you completely change how you measure it
@@Bit125_ well, the reasonable measurement would be a standard unit of length in the first place.
Eg. mm, or at this point fractions of an inch.
But the original is a relict of the manufacturing process of the copper foil
@@itwasntme967and what's the standard fraction of an inch used in pcb design? A thousandth in an inch, called a "mil". Not to be confused with the SI unit used, the millimeter, which everyone in SI using countries casually contracts to "a mill" (as in "it's two mills off"). I'm sure that's never caused issues.
@@SimonBuchanNz Standart thickness is 1oz, which comes out to 0.0348mm or 1.37mils.
In cases of high currents 2oz may be used, and in high density, multilayer PCBs 0.5oz will be used for inner layers
@@itwasntme967 sure, just complaining about naming!
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!
Hard agree
The "Hertz?!" sting from the first video gets me laughing every rewatch
the piano turning into can you feel my heart caught me off-guard
The music is great it's just very loud.
I love it as well. It reminds me of untitled goose game
5:54 As my prof always says: „The reaction quotient has some unit, but since no one knows what it is we just treat it as dimensionless”
Nah, it is dimensionless. Chemical activity is (for solutions) Concentration devided by Standard concentration (wich is 1 mol/L)
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.
Thank you !!!
I think of it as similar to pi. Pi is used as a unit all the time but it does mean something.It is a number.
@@santumi2298 no it’s not actually . Pi unit has no dimension
I'm gonna be a little controversial and argue that amount should be its own dimension anyway
@@fisch37 you mean, « amount » in general?
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.
Thank you so much! I remember finding your channel many years ago, so seeing you comment here is wild.
lazy
Why say many word when few word do trick
"If I had more time, i would have written a shorter letter"
Same
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.
Because many old units have been redefined in terms of a fixed number of SI units, at a time when their value, as originally defined, was imperfectly known. In the case of the torr, I suppose the difference is because the density of mercury or the sea-level gravitational acceleration of the Earth were still known to only so many figures when the unit was redefined, but became known more precisely after that.
The mole was recently redefined as a fixed number of atoms, so that now one mole of carbon-12 atoms is no longer *exactly* 12 grams, as it used to be. Now it is 12 grams plus or minus some nanograms, and we may already know that the error is more than some X.
And the standards organizations that define the imperial units have agreed to redefine the inch as 25.4 millimetres, *exactly* . So technically the length of one inch, too, has changed by some small amount.
Because torr is based on mmHg but defined exactly as 1/760 atm (101325/760 Pa) and will therefore differ from mmHg. It's like how an inch was redefined among the countries using it to be exactly 25400 μm, but this causes the old units of inch, such as US survey inch, to differ slightly.
@@Liggliluff why would inches be defined in micrometers and not cm
@@yann_ma It's actually defined as 1/36 of a yard and a yard is defined as exactly 0,9144 m. But it's the same. An inch is exactly 25400000 nm.
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 kilogram-meters-squared-per-second-squared. So the unit is actually meters-squared-per-second-squared.
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.
Fun fact, CAPE isn't the only convective parameter in units of m²/s². SRH (storm relative helicity) is taken by integrating the dot product of storm-relative winds and the curl of the (absolute) winds over height*, which ends up with units of (m/s) (/s) (m) -> m²/s². This is used to help with looking at supercell and tornado development.
CAPE is also fun in how it's calculated; it's another integral, but of TEMPERATURE. Specifically, it's how much warmer a parcel raised "moist adiabatically" (adiabatic except for the latent heat of vaporisation released on condensation of water vapor) from a specified level (usually either the surface or the mixed layer average) is compared to the temperature of the atmosphere, divided by the temperature of the atmosphere to make it unitless. All that is multiplied by gravity and then integrated by height* over the portion of the atmosphere that the parcel is warmer than.
Now, you might be wondering why I put an asterisk after both heights. That's because meteorology doesn't use actual (aka geometric) heights; rather, they use a coordinate called geopotential height, which is gotten by taking geopotential and dividing it by standard gravity of 9.81 m/s². Which means that since geopotential height is in meters, then geopotential is yet another meteorology unit in m²/s². And it's obtained by yet another integral, this time from sea level to the geometric height... of /gravity/ (because gravity varies based off of both height and latitude, using geopotential height rather than actual height means we can ignore the variations of gravity and treat it as a constant).
Oh and also there's EHI (energy helicity index), which literally is you multiply both CAPE and SRH together and divide by 160,000. Why 160,000? It just scales the numbers down to something close to observed frequency: EHI values less than one rarely had tornadoes and supercells, while values greater than three have strong tornadoes likely. It's said to be unitless, but technically it has units of m⁴/s⁴.
In the same vein: As Randall Munroe (author of xkcd) points out in e.g. What If 86, "Units are weird: The maximum speed the edge of a cylinder of a given material can rotate is equal to the square root of its specific tensile strength (tensile strength over density)."
@@Kieiros TIL meteorologists have the most cursedest units.
@@secretpandalord Meteorologists also have one of the most cursed data plots you might ever encounter, called the "Skew-T, Log-P Plot".
Why does it have this name?
Well, the horizontal axis of the graph plots temperature, but the "isotherms" (lines of constant temperature, the grid lines associated with this axis) are _skewed_ 45° just to make the temperature plots easier to read, otherwise the data plot would be EXTRA WIDE as temperature drops precipitously up through the troposphere right up until the tropopause where it then stops dropping or even starts rising slightly again up through the stratosphere (this change in lapse rate is literally what defines the boundaries of atmospheric layers). So the skew distorts the temperature plot so that everything fits more vertically and is easier to publish and read as sounding charts.
The "Log-P" part comes on the vertical axis, as atmospheric pressure drops off logarithmically with altitude. This is actually the most sensible axis plotted on the chart, especially since atmospheric conditions don't actually care about our arbitrary systems of measuring altitude. Instead it's the air pressure that matters, so a lot of meteorology deals in "isobars" (lines of constant pressure), and the altitude above the surface is merely an afterthought marked on the same vertical axis with secondary labels.
These plots sometimes have a whole bunch of other bits of information plotted on them such as mixing ratio lines (lines of equal moisture content in the atmosphere), dry adiabats (the temperature a dry parcel forced to rise would have at any given elevation), and moist adiabats (the temperature a saturated 100% humid air parcel forced to rise would have at any elevation) and so on. It's a heck of a lot of visual noise, but they are incredibly important for weather forecasting.
@@calyodelphi124 With the exception of the Log-P part which makes perfect sense to me, I hate everything you've just written. Thank you for introducing it to my life.
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!
Yeah I love the music but it's kinda loud, I can't hear well the man talking
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)
Another random thought: the dBA thing made me think about Sun Protection Factor, which is used for stuff like sunscreens, since that is also weighted for human skin damage potential wrt. the radiation wavelength spectrum. SPF of 30 is defined as 1/30th the damage potential with respect to not being on, which seems like it would work really well as a decibel unit. A SPF 30 would be about -15 dB SPF, and SPF 120 would be -21 dB SPF. This is particularly nice since every 3dB step in SPF means you're getting sunburnt half the amount. A common criticism of SPF is that people find the high SPF products to not be a big benefit compared to the low SPF products (e.g. 30 SPF vs 50 SPF) and using decibels would make it more intuitive.
Is there another weighting according to the potential for hearing damage? (Does that also depend on frequency?)
1. The base unit is not Bel, deci here stands for the base of logarithm.
@@la.zanmal. There are more weightings and they all adjust depending on frequency. To my knowledge(and I only had 1 class about acoustics and noise) the A weighting is used frequently when you’re considering the human ear, especially for hearing damage as the laws are written in regard to A weighting(even if it’s not strictly accurate). In OSHA regulations, there is a maximum equivalent exposure to sound, so something that’s extremely loud for a short time and something that’s just quite loud for a much longer time can be considered similarly to one another. The baseline for that is 90 dBA for 8 hours and there’s some sort of equation that will give how long at 100 dBA is equivalent to that.
And then when decibels get involved in digital calculations, you end up with all sorts of weird variants like dBVU, dBFS and dBTP which don't even measure anything in real life
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.
I wish my teachers could discuss with yours 😅.
Reminds me of a chemistry professor I had that gave me a unit for temperature as a function of acceleration
I find it astonishing how all the pedagogical research indicates that direct, lecture style, instruction like that is the least effective form of instruction, and yet everyone I talk to can remember at least a half dozen such direct lectures, sometimes from as early as 8 years old, with distinction and clarity.
@@joncooke158we surround ourselves with the intelligent ;)
Check out Jan Misali and his various number videos. The CCC video and a few others helped keep me sane through DE, if you can call an engineer sane.
PS: the whole point of the CCC video is using universal standards to define an absurdist units system
Electronic engineer here, i had a good dose of cursed units when i was learning why Inductances and Capacitances behave like resistances in complex variable
Treating d/dt, jω, or Laplace s like just another quantity.
it's even more fun when you're taking a course on electrodynamics while also taking a course on 3phase power systems modeling and both subjects use the same symbols to mean completely different things
@@Jacobschannel18802 Also a massive issue in mathematics. People run out of symbols for operators and then use whatever. Also different fields using very different terms for essentially the same objects. Gnnnnnnnnh!
@depressugar I believe that we have the same channel banner of the wan chai skyline from Victoria harbor in Hong Kong
I feel like this is the opposite of cursed -- complex impedance + linalg is a way nicer way to deal with analog systems than diff eq IMO
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.
I remember having very ambitious (and very good, so it wasn't a problem) professor of Chemistry in Highschool. We did learn all about calculating pH as well as some things that I don't know if they aren't technically wrong (for super strong acids, I don't even remember if me measured it in fractions or negatives, because chem teacher might have been ambitious, but math teacher didn't teach us logarithms yet back then ;) - it was a bit nebulous). Not to mention learning that you can exceed "standard" scale of pH (1-14) - so while in highschool it was wacky (and there was so much of it, I'm now not sure which exact model was correct, because teacher was ambitious so he had to show us also all the "wrong" ways in which pH can be measured and misapplied) - it really helped in Uni, where for a time I did study Chemistry. Because back then I remembered all the possible pitfalls of measuring and calculating pH and how to avoid them. Sadly I don't remember now, because I haven't done this in 20+ years.
The reason why the equilibrium constant and reaction quotient are unitless is also the same: the ‘concentration’/‘partial pressure’ values that you substitute into the reaction quotient are actually thermodynamic activities.
This also plays into why solids and liquids don’t contribute to the equilibrium expression or reaction quotient because their activities are close to if not exactly 1.
I was about to comment the same about activity. When I learned about it in college everything made much more sense.
Ah yes, throwback to the time when there were 3 different acid theories and we learnt all of them. From the super narrow hydrogen ion producing idea of Arrhenius to Lewis going, "Fuck it, if it can accept a lone pair it's an acid."
I mean, it did bring the definition of acid to a lot of things like transition metal complexes and all of that, so I guess that's kind of cool.
pKa relies on solvent? What?
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.
its..... just...a..WATTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT
Many people say KW instand of. KWH
So what we really want is kWh per calendar month, if we pay bills monthly.
@@cshairydude The only issue with that is the majority of products vary in how often they're used from person to person. In August, someone in Montana might run a window AC unit for 4 hours a day, meanwhile someone in an identical apartment in Phoenix might have theirs running for 18 hours. Then you get into having labels with fine print (*based off the median home with blah blah blah...), and different companies choosing different standards for comparison. Its just a whole confusing mess. kWh per n hours is imo just a very clear and consumer friendly way of conveying the relevant information.
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
When the world needed him the most
he came BACKKKKKKK
He vanished
…he cancelled himself from the equation. Jk, he didn't, because he wanted to maximise clarity and minimise ambiguity.
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 😂
Tbh i have just looked at my notes and we actually use it in mmHg and not in cmHg as you pointed out.
Just for u to know we normally use it to figure out the quantity of oxygen that is going to get to the cornea throw the contact lens and is a very useful way to known if it's going to cause corneal edema for the hypoxia during the use of the contact lenses.
Also in reality we normally write it as DK/t where DK is the part that's only dependent on the material and t the thickness but the barrier is an actual unit that we study hahahah
3:18
I think a reason as to why torque has the same unit as joules is that torque is the cross product between force and length while work is the dot product, so they're still describing different things
ugh. I still remember college physics and having to deal with figuring out the angle between two vector quantities, and how that would be the hardest part of the problem, because angles in 3d are nightmarishly problematic to deal with - especially when the coordinate system is at an unrelated angle to either vector for literally no reason, but that's how the problem in the ****ing textbook is.
@@comparatorclock dot em, divide by both lengths, then inv cosine
Coincidentally same units, but still different dimensions because one is a scalar and the other a vector.
@@comparatorclock you should try looking into geometric algebra, it's way more intuitive
Good ol' quaternions pretending to be arrows.
At least we aren't talking about the 6-dimensional entity that I've seen called "forque" (that's effectively just the direct sum of force and torque, hence the portmanteau).
0:19 the transition to the gigachad theme was so good
18:51 given that there's now just shy of 500k views on this video, I'm convinced there's just 500,000 of us dutifully watching all the measurement naming convention videos
As someone with a PhD in theoretical chemistry, I have a big gripe with people using the term unitless when they mean dimensionless, and the concept of units completely cancelling each other out. Just because two units have the same dimension, does not mean that they can completely cancel each other out, the actual thing that they are referring to remains, it is just the dimension part that cancels out.
For the radians example, the units of 1 m arc length / 1 m radius = 1 radian, the dimension of the two units cancel (each being meter), but the units do not cancel, and we are instead left with a radian = arc length/arc radius.
This may seem pedantic, but it is important to remember that these dimensionless quantities are still referring to ratios of actual things. Otherwise these numbers would have lost all of their meaning.
Combine that with people ignoring the difference between scalar and vector quantities and teaching dimensional analysis gets really hard.
What would an actual unitless constant be then?
@@entcraft44I don’t think those really exist in science maybe you could say Euler’s constant since it comes from mathematics.
@@entcraft44 Those are called “numbers”
Important for what purpose? Angles ARE numbers. Trigonometric functions, for example, can be defined geometrically, but also analytically, with no reference to circles or angles or anything like that. Pi can be defined as a certain ratio of lengths, or n-dimensional volumes, or as the square of the Gaussian integral, or as a sum of many interesting series, or in infinitely many other ways. By fixating on one particular "meaning" of these concepts you're losing the flexibility that comes with understanding all "meanings" at once.
19:00 Hol' up.
you can rewrite the pressure as force/area, which cancels with the other area in the denominator. Mol, can be replaced with 1, if you scale everything down by the avogadro number.
You end up with cm/(second*force). Now, Force is just mass×distance/timesquared. So it is distance/(time×(mass×distance/timesquared)). It simplifies to mass/time. In the end it really just tells how much stuff get's trough over time.
dimensional analysis at it's best
Yup - that is why it is useful unit in it's use. It's just cursed, not useless. And it does make sense.
Isn't it redundant trying to put all this information in the units? What's the point of the formula then? I'm in the simplifier camp for sure.
@@tamassoos5915 really it's so you can use known tables of material properties without doing unit conversions all the time. So, e.g., while "mass/time" is fun, it doesn't really allow you to predict the membrane properties based on its dimensions and material properties.
@@tamassoos5915 Depends what you want to calculate and what formula is for.
For example, such "complex" formula can show and educate people new to this particular field how many things have to be factored in. Then you introduce simplified formula for everyday (so like 99%) use, but full formula can still be useful to remember if you're dealing with cases that are.... very abnormal. In such situations some people legitimately might have problems operating with simplified formula, because they would have to take into account too many things at once. Full formula allows you to change every single parameter one at the time, without juggling dependencies between various units and assumptions. Which can create errors. In the end of course most people will be using "simplified" formula and as they gain experience with it, they will have to go to basics less and less.
Also importantly, when you do dimensional analysis of new problem and write new formulas - I personally found most useful to write the most "full" formula possible, run it few times through few examples and then try to simplify it, after getting some experience with full formula. With that experience you start to know best what you can simplify. Because generally speaking simplifying formula by cancelling "everything" results in stuff like in first video where you had "fuel efficiency" in milliliters (? - would have to double check it, but it was mentioned in this video). And that to people who are only beginning work in the field is "so simplified that it doesn't make sense".
Not to mention - such formulas are great educational tool in dimensional analysis ;)
I recently had to deal with the standard cubic meter (Nm^3), which is similar to the cm^3_STP. The issues is that "standard temperature and pressure" are different standards for literally every single industry!!! You have DIN 1343 using 273.15 K and 101325 Pa for compressors and natural gas, unless your gas is American in which case you use 288.15 K (API). This standard is also used in gas turbines, though not pneumatic equipement. That uses 293.15 K at 1013 mbar instead. Nevermind that nearly all chemical properties can either be measured at 293.15 K or 298.15 K and the worst part is: surprisingly often people don't specify which standard they are using! I just want to know your actual energy usage per amount of substance produced via electrolysis! Are joules per mol too much to ask for?!
It´s funny that you complain about different standards being used for standard cubic meters and then use Nm³, which refers to normal cubic meters.
In europe, people use normal cubic meters, which are cubic meters at normalized conditions of 0°C (273,15 K) and 1 atm (= 101325 Pa). Standard cubic meters may be used as well, but more common are standard cubic feet, with standard conditions being 298K (apparantly Californian room temperature) and I forgot the standard pressure. However, americans also often use local standard conditions based on local weather, which can be really annoying, when those conditions are given in PSI and °F.
@@AndreasPeters-r3e Well can you blame me for getting confused? 😅 And sure, while Nm3 is the most common in Europe, I have still come across manuals using Sm3 when compressors are involved
@@2001Pieps I do not blame you. I make little mistakes myself. Especially in you tube comments I very really re-check what I just wrote - it´s not science usually.
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.
11:30 I'm very proud of myself for immediately guessing c. While I don't know WHY it's there, it only makes sense to me that these stupid units must involve it somehow. It's the only constant that makes sense to me.
I was wondering if there was a meaningful ratio before he asked that question, and as soon as he implied it should be guessable, c was the obvious guess. Especially as I remembered the fact that the two main numbers describing the electical and magnetic properties of empty space can combine to give you a speed was one of the first hints that we needed Special Relativity.
My brain went right to static charge speed = 0. Energy speed in wire = c. Well done!
worth mentioning that the constants in the SI equations (permeability & permittivity of free space) multiply to c^-2; not just a quirk of CGS
I'm glad I'm in a field where people use sane units to build insane things rather than the other way around
What insane things do you build?
P.s. sorry for my bad English.
The music is the main reason I liked the original video, when I first saw the thumbnail I was like "Ooh, a generic science trivia video, will this have a rantsona or not?"
But to my surprise it was very well made and had an excellent post-production way beyond most YT videos. Great job! ❤
So I've taught classes on international economics. Something I've done that seems to help my students is take about 20 minutes to explain dimensional analysis at the beginning of the semester. We don't use it much, but when we get to the part where I'm trying to explain how the expected interest rates of European bonds affects the current exchange rate of USD and EUR, those units get quite handy to keep the model straight. And everything cancels nicely when trying to model expected rates of return:
Expected rate of return on european bonds (measured in future value USD/current value USD) = current exchange rate * rate of return * expected future exchange rate = (EUR_{now}/USD_{now}) (EUR_{later}/EUR_{now}) E(USD_{later}/EUR_{later})
My favorite cursed unit lurks at the heart of electrical wire gauge: the circular mil, or cmil. One cmil is defined as the area of a circle 1 thousandth of an inch in diameter. The equation for the area of a circle in cmils becomes A(cmil)=D(mil)^2. This unit is used in the form of kcmils for sizes of wire larger than #0000 AWG, and ampacity of wire is calculated by cmils instead of squaremils.
Your music is absolutely incredible. The "Chad" theme, the music being used as exclamations, excitation, suspense, and so much more through just background music. Masterpiece.
The speed of light being the constant for conversion between the electromagnetic units was a twist I was NOT prepared for
The speed of light being equivalent to 1/sqrt(permittivity of free space x the permeability of free space) gets my noodle scratching
@@justinhadley3927I'm sorry, it's equivalent to _what?_
@Simon-ps3oj > the speed of almost anything is defined by how easy it is to get through the medium. Light being electromagnetic means that the ease with which the electric AND the magnetic parts get through the medium are both relevant in a vector-sum way (square root of the product of the two quantities). The two quantities are the permittivity of space (electric side) and the permeability of space (magnetic side). The lower these quantities, the faster light goes; the higher these quantities, the slower light goes. Hence an inverse relationship.
@@justinhadley3927 The speed of light is actually just the speed of causality, so I think one of those variables is actually set, and the other is based on that and c. I'm not sure what might be more fundamental, electrical or magnetic propogation.
@kindlin could you please elaborate? I doubt a lot of people are in the same page
the music is actually the best part of these. Now that I know you play it yourself it makes a lot of sense. It acts as a laughing track, but where a laughing track emphasizes humor, the music emphasizes cursedness.
As an upper year chemistry student, the mole example perfectly sums up why "cursed" ≠ "useless". We need some easy way of relating the mass of atoms to the mass of their constutient molecules. Being able to do this fast and reliably is a foundation of modern chemistry that you really can't get around. Chemistry has a lot of these cursed units though, our math is far from beautiful!
It's also important historically - we had the mole before we had any good estimate of the Avogadro constant. The best estimate of the constant fluctuated while we improved our measurement capability, and now (as of 2019) we actually locked it in and use it to define the units that previously defined it!
that “CGS on Piano” is absolutely wonderful.
I totally feel you on the improvisation bloopers at 20:02
I just wanna add that as a radiation therapy student (graduating soon though), you did a good job explaining the subtle differences of radiation units and why its important to have 2 units with the same expansion but very different contexts. also wanted to add that you are actually correct about the centigray (shortened cGy)! The Rad came first in history before the Gray, so all of our machines are still calibrated to the Rad/cGy, mostly as a tradition/backwards compatibility measure, but as the world shifted to SI units for consistency, it was decided that we will exclusively only refer to it as a centigray and the math to find the accurate dose for a patient is based on SI units. Radiation is another weird world of units for sure!
edit to add: i completely forgot about the electron-volt! a unit of energy that by forcing the speed of light to simplify to 1 with clever number manipulation, is also used to measure the mass of atomic particles as well.
Room temperature is 25 milli-electron-volts.
in my first year of physics i took a class heavy on chemistry that was advertised as just as doable whether or whether not you did advanced chemistry in high school, and as someone in the latter camp i was curious to see how they would equalise it like that. turned out it was by subjecting us all to reaction quotients and making us watch our collective understanding of units get slowly murdered in real time
materials guy here. lol. Everyone failed and complained about physics. It seemed you had to be a savant to even understand the basic concept of Anything in there. However, chemistry was like full understanding of anything was impossible. Maybe like static shocks vs sunburn
You gotta make a full section on radioactivity units. There's at least 7, and it's painful. (Becquerel, Curie, Gray, Sievert, Ren, Rad, Roentgen, etc.) Also explain why we have so many measurements for pressure (bar, torr, psi, pascal, inHg, cmHg, mmHg, ATM, technical ATM (?), inH2O, kg/cm², the list goes on and on.)
As a Fallout Fan I'll stick to Rad.
In fairness to pressure, it depends widely on the ranges you are looking at. Like in oil and gas, I have only really seen psi and bar be used because the range and accuracy is more reliable/readable than say kPa.
ATM? You mean All the mods? I'd recommend 8th, it's not as hardware hungry as 9th, but still as convoluted as ATM modpack should be
@@paradoxcorporated2906no, atmospheres.
Isn't it Atm if you mean atmospheres?
Wait, so the Hubble Constant is only in Hz in a cyclical cosmology, otherwise it's becquerels?
Hi Robert Miles
Apparently I'm so familiar with electromagnetism that as soon as you said "this constant must have units of centimeters per second" that I instantly knew it was c. Shoutout to James Clerk Maxwell, dude contributed SO MUCH to our basic understanding of physics but is very rarely actually mentioned unless you're discussing entropy.
You'll get some more cursed units if you move to engineering and industrial efficiency metrics. Long ago I worked at a milk packaging plant. The goal at the for adequate efficiency was to use less water in plant operations (cleaning, cooling, break room drinks, staff toilet, etc.) than milk packaged and shipped. Efficiency was thus measurable in gallons/gallon or liters/liter. Or in large water system management, the Imperial unit is the acre-foot. Since the acre is a chain by a furlong, an intermediate step before getting to cubic feet is chains x furlongs x feet.
Agree with your point at the beginning. Cursed units can still be fun. Useful, even!
5:54 Physics student here, I'm feeling very relieved right now because I felt like I was going mildly insane learning reaction coefficients for my biophysics course.
Also, I'd like to nominate Specific Impulse as a cursed unit. Not because it's that bad to use, it's just inexplicable. It's the measurement for the efficiency of rocket engines, which is measured in seconds. Why? Well, if you do the calculations, you find that the amount of velocity change you can get from your ship is proportional to the velocity of the exhaust gases, in m/s. Except, for some reason, it is then divided by the earths surface gravity of 9.81m/s², giving m/s/(m/s²)=s. For a unit that is pretty much never used on the surface of the earth. And whenever you use it, you need to multiply by 9.81 again.
To defend seconds as unit of impulse, after a while it gets quite convenient to have reference point in starting a rocket time, but i would more like a unit that is based on first escape velocity of earth as making an orbit is something that impulse is more used to than getting the ship to high altitude
It makes way more sense as kg*s thrust per kg fuel. Or pound seconds per pound of fuel. In fact, the fact that you get the same numbers in both metric and us customary was quite useful in the early days and definitely part of the reason that seconds became the standard.
The story (not really sure if true) is that the original unit was (pound of force produced)×(second)/(pound of fuel used), which is the same dimension as Ns/kg or m/s, but then people just canceled the pounds
The division by gravity was a trick used back when NASA hadn't standardized on SI units, so by dividing by gravity it didn't matter if you were working in imperial or metric units, you'd get the same value for rocket engine efficiency.
I would vastly prefer a m/s expression of rocket efficiency because that's what's going on, it's the force you get out of some expelled mass of propellant, which is proportional to the exit velocity of the propellant.
Or, the most applicable, which is acceleration (or force, simplifying the mass of the rocket out) per mass of propellant, which is what'll be concerning anyone doing anything with different rockets. But it's still proportional to exit velocity.
The music is perfect and accurately represents the emotions of the watcher: the relaxation turned into confusion and shock turned into wary trust
absolutely love this charming series. the piano just makes it sooooo much better, thank you
These are absolutely excellent, I nearly spit out my coffee with the cmHg reveal. My personal favourite is the charging speed of an electric car. You get a certain amount of charge that gives you more range over time. Range is measured in km, and most EVs charge slow enough that hours is a good unit for the charge time. Which means your charge speed can be measure in km/h, which yes is also speed. It's fantastic because you can compare the charge speed directly to your average speed for a journey, to get an idea of how much longer a journey is going to take if you have to stop and charge.
That works on gas cars too, just need to convert the nozzle throughput to the L/100km value, and you are done.
Though that's usually fast enough where it's not worth measuring.
16:37 In defense for kWh/1000h: The point for this rating is devices that operate on some (variable) duty cycle like a fridge. Giving it a fixed and aimplified rating like '50W' is pointless when, most of the time; it's 0W, but sometimes 300W. kWh/1000h describes the average power draw of a device over 1000 hours.
Makes sense, though I wonder why they didn’t go with kWh/year, as shown in another example in this video
1000h feels a bit weird to reason about in your head, even considering it’s roughly 6 weeks
@@vladyslavsmirnov1875 My guess is that it is a long enough period to get a useful average over, while still producing small enough values to make sense on these labels (typically 20-1000 kWh/1000h)
@@vladyslavsmirnov1875 well if we say it's an average the Unit of the average is W which makes perfect sens.
@@vladyslavsmirnov1875 Easy to convert to watts is probably the main reason.
It was mentioned in the video why Watts can't be used (people use that as a measure of brightness instead of lumens).
It's actually dangerous (well kind of) to ignore that electrical devices may not use the same amount of energy (or have the same efficiency) at all times. The EU not only rates energy efficiency of TVs, they also rate vacuum cleaners. That is they did until the General Court of the European Union told them to stop (the way they did), because they only measured at the start of the vacuum cycle. But everybody easily realizes that the efficiency (in the unit ' "suck" per Watt') of a "normal" vacuum (that is one with a filter bag) obviously goes down the more stuff you vacuum in, while that of a "cyclonic" vacuum doesn't (more or less). It also differs between different filter vacuums.
One great thing about Planck units is that a velocity is always expressed as a proportion of the speed of light, which is basically β, making the Lorentz factor an elegant 1 / √(1 - v²).
Funfact the integral of the factor is arctan(v)+c; Very beautiful indeed!!!
The thing about the chemistry units is, that it is only cursed because we made it this way. We are actually talking about activity (which is dimensionless), but for small concentrations, activity is proportional to concentration / partial pressure / whatever is easier to use. And since activity can't be measured directly but concentrations can... We ended up with often messed up units.
This is by the way the case both pH and kinetic factors.
The piano score is exquisite, I honestly love it. It adds to the atmosphere, drama and suspense of it all
A nitty-gritty detail: A mole _used_ to be defined based on carbon atoms, but since 2018 it isn't. Nowadays the SI-unit system is based on seven defining constants and Avogadros number is simply one of those defining constants:
* The caesium frequency ∆v_Cs = 9 192 631 770 Hz (i.e 1/s), the unperturbed ground- state hyperfine transition frequency of the caesium 133 atom
* The speed of light in vacuum= c 299 792 458 m/s
* The Planck constant h = 6.626 070 15·10^−34 J s (i.e. kg m^2 s^−1
* The elementary charge e = 1.602 176 634 ·10^−19 C (i.e A s)
* The Boltzmann constant k = 1.380 649·10^−23 J K^−1 = kg m^2 s^−2 K^−1
* The Avogadro number N_A = 6.022 140 76 ·10^23 mol^−1 number of elementary entities per mole
* The luminous efficacy K_cd = 683 lm/W (i.e. cd sr W^−1 =cd sr kg^−1 m^−2 s^3) The luminous efficacy of monochromatic radiation of frequency 540·10^12 Hz
Yes ! But the Avogadro number (number so no unit) is now the Avogadro constant (mol^-1).
and not just carbon, but all
I liked the Avogadro proposal where they got a dude to grind a silicon sphere so precise that you could count the number of atoms in it to sufficient precision for the definition of Avogadro's number.
Tried that, got up to 1710 before giving up
Yes, 1/12 mole of carbon-12 atoms happens to be 1 gram, but that is _not_ the _definition_ of mole nor of gram, just as little as 1/14 mole of carbon-14 atoms being 1 gram is not the definition of gram nor mole. The new SI-system is a fundamental philosophical shift on how we define units. Nowadays, the Avogadro number is by definition _exactly_ 6.022 140 76 ·10^23 mol^−1 and the connection to carbon is simply just historical, nothing else. In the hypothetical case that 1/12 mole of carbon-12 atoms would happen to be found to be 0.999999999999 gram, the definition of the Avogadro number would not be affected.
In the old SI-system, the Avogadro number was an approximate number, not an exact number and the Avogadro number would then change if new measurements came up with new results
The build up and reveal at 11:36 to "The speed of light!" was perfect, its feels so out of nowhere but perfect at the same time. That some perfect alingment stuff and i bursted laughing.
Great video man! LOVED the piano!❤
I thought to myself, "of course it will be the speed of light", but the presentation was still amazing.
As an Astronomer, cursed units are everywhere in our field. CGS and SI are used interchangeably in some equations, especially involving electromagnetism or telescope detectors. At the same time we have several different ways to describe mass and length. And don't even get me started on Janskys or anything to do with radiative transfer theory.
That sounds painful. I wonder how many of them exist because SI doesn't have enough prefixes to cover astronomical use-cases?
@@Roxor128 Most of them exist because they are "handy" and relatable. Every field does this. In materials science we use electron-volts for energy. Typical values might be 1.4 eV. Why in the world would anyone in their right mind want to use 2.24305e-19 Joules instead?
You could measure a planetary mass in Kg, but "Earth Masses" or "Jupiter Masses" are generally going to be much more handy units. Just like Proxima Centauri being 4.2 light years away is a lot more useful than 4.132 × 10^16 meters (41.32 petameters)
cant believe people didn't like the music! i loved it! when i watched the first video, i thought it was so amazing, i was so impressed when you timed the dramatic stings / dissonant notes / pauses in the music with key points in the script! it really gives the videos a bunch of unique character
The piano is perfect! The fact that you play it yourself just makes the video better. Well done!
A sequel to one of the best videos on the internet!
2:10 how have you already hurt my soul this much with writing 2pi as 6.3
this is a video about cursed units, not cursed rounding!
also omg the esu-emu conversion problem! we spent a long time on that in my history of science class! it’s so cool, i’m glad you gave it a huge microphone with your channel!
Just be happy you get a single decimal place. -Pi as 3 and a bit user reporting in
@@christopherpepin6059 No Pi=3 is fine because I know he’d be trying to piss me off. But I genuinely can’t tell with 2Pi=6.3
Musuc is undoubtedly my favorite part of these videos, never change
I'm soooooo glad you decided to keep the music. It's just a beautiful combination. I love both vids and am hyped for part 3. As an engineer student I find this both educative and funny asf. Thank you for making this.
I always liked making jokes about how N*m for torque is the same as Joules. Glad someone else pointed it out.
If you throw in a radian-per-second, you get the equation for the power transferred by a rotating shaft.
One is a vector and the other is a scalar. You can consider the direction of a vector as part of its unit of measure. A newton-meter of work and a meter-newton north of torque are very different quantities.
I once in an exam stumbled upon the unit of energy density, or J/m³. Well, as Joule is also Nm, you can cancel the m and get N/m², which is the unit of pressure, also known as Pascals. So I wrote that in the exam, just as a joke. The teacher was a little confused and wrote a "?" and when he gave back the exam he asked me how I arrived at Pascals. He just stood there, looked at my derivation and went like "Huh. That's...odd." and had a little chuckle.
@@JanB1605 I would argue that energy density and pressure are much closer than torque and energy. Torque is a vector, gotten by the cross product of force and length, while energy is a scalar, gotten by the scalar product of the two. Totally different. On the other hand, pressure is the "movement part" of the total energy density. For an ideal mono-atomic gas, energy density is literally 3/2 of the pressure (the factor comes from 3 axis of movement, 2 directions each).
@@entcraft44 Nm ist also the unit for energy when you apply a force to an object and move it a certain distance. Torque is the same concept, just in a rotation. Instead of moving the object linearly, we turn an axel.
Avogadro's "number" is a constant with units mol^-1. If you divide a number of things (usually atoms or compounds or molecules) for the Avogadro's constant you get its number of moles, with units mol.
In the reaction quotient the concentrations are approximations for the activities, so they are each multiplied by a conventional activity coefficient of 1dm^3/mol and the result is dimensionless.
Anyway very funny video and I love the music, especially because it's made to match the tension of the talk!
The foe isn't a cursed unit dimensionally, but it's cursed in scale: ten to the ifty ne rgs. It's used to measure the yield of supernovae.
Astronomy and astrophysics are full of non-SI units that exist because SI units just don't have the right scale, or because relevant physical constants either once were or still aren't well enough constrained to convert precisely to SI. The gravitational constant is still poorly enough constrained that we have a much better idea of the mass of the Earth in solar masses than in kg.
Similarly with the AU and Parsec. They let you measure things relative to the size of the Earth's orbit without needing to know exactly what that is. (Though I expect we have a very good idea now.)
@@SimonClarkstone The additional wrinkle I learnt is that general relativity throws another spanner in the works. I hazily remember that metres are only defined when special relativity is a Good Enough approximation, so while astronomical distances at the scale where space noticeably expands have a nominal conversion to SI units whether or not that conversion has any meaning can be questioned.
(Of course, now that au is redefined to be just some fixed number of m, that changes a bit of a status.)
Same with particle physics and materials science. Can you imaging measuring band-gaps in semi-conductors in Joules instead of electron-volts. Everything would be in the 10 to the -19th power.
@@Rocketsong SI prefixes can deal with a lot of that: you could measure band gaps in attojoules.
@@isoraqathedh The AU isn't anywhere near the scale where expansion is relevant. But yes, at the largest scales, the only observable we have to measure distance is redshift, and the value of the Hubble constant is poorly constrained, so distances in any units other than Hubble lengths are somewhat uncertain.
1:15 Love the "Nestlé Crunch!" melody in the background there XD
ICU doctor here. If you want a cursed unit for part 3, Systemic Vascular Resistance Index is measured in dyne.s.cm-5.m-2
Also keep the music, it reminds me of Untitled Goose Game!
How were people complaining about the music?? Its very good and I feel that it gives a unique identity to your content
I know right? And it adapts to what he's saying! It's so good
too loud and kinda distracting
Probably because it was mediocre, no offense.
@@Sohlstyce was it? i'd like to see you try. so come on, give us an awe inspiring performance.
@@shadowsimp697so if you don’t like something, you must be able to do it much better… okay
It felt like forbidden knowledge when I learned that concentrated HCl can have a pH of -1
It is a bit more complicated than that because the use of the pH assumes that you are in a water solution and while HCl is strong enough to protonate water to very low pH, at pH=0, water begging to act as a base and you have to add so much HCl that you leave the solution model and approach the mix model where pH doesn’t make sense anymore.
Is no one gonna talk about how epic the music transition was in 0:25
Was not expecting to have it switch up to the Gigachad song theme lmao
It was amazing
I was just about to
i love how the piano busted out the gigachad theme at some point lol
as someone who loves science (or tries to) as well as music, this is pure gold
The music honestly adds so much to this video. This might sound weird, but it has a very similar energy to the music in Untitled Goose Game, or a Scruffy video. It creates a lighthearted atmosphere that I really like.
Color dispersion is a cursed unit. It's "demensionless" (according to literature) but isn't a multiplicative factor.
4:37 A mole is also a unit for integrated light output (different from optical W·s) that counts the number of photons. A typical 10W LED outputs about 1 mol/day, a unit called DLI.
7:33 This is similar to the triad [µmol/s, mW, lumen] for light intensity, depending on the usage (photochemical reactions, energy, brightness).
19:14 They could have introduced an intermediate unit, like "permeability resistance", that depends only on the material and area-divided-by-thickness, to greatly simplify the formula.. Just like ohms-per-cube. Did you know there's also ohms-per-square? (used in semiconductor design)
Interesting thing to note here, is that after the 2019 Redefinition of the SI Units, Vacuum Permeability/Permittivity (u0/e0) are no based upon the Fine Structure Constant, so while the overall system works a lot better, the "Constants" now have some amount of error within them. More interestingly however, the relation between the 2 aforementioned Units and the Speed of Light still hold, even as Vacuum Impedance, ie Impedance of Free Space, also has some error inbuilt to it
Babe wake up, cursed units 2 just dropped
The Chad music and the Nestle Quik theme under the flashbang are absolute gold. Thank you for what you do
1:50 the right page of shame
My favorite cursed unit is the snail (also called a slinch), which is a lbf s^2 / in, a unit of mass in American engineering units that's pretty common in structural analysis. Another great one from aerodynamics is air density, measured in slugs/ft^3 = lbf s^2 / ft^4
Ewwwww... I didn't need to be reminded this existed. 🤢
AYOOOO????? This is something I waited a long time for
15:58
I just love that this secret loss edit is just living on semi hidden in plain sight
OH MY GOD YOU'RE RIGHT
I dont see it, can someone tell me where it is?
@@sebas31415 the entire thing is a loss edit, look carefully
@@mrtomithy I see it now, I was sleep deprived from celebrating pride the say before.
You were doing what?
THANK YOU! This finally explained to me why moles never made sense to me despite having to use them all the time!
OH MY GOD THE MAXWELL EQUATIONS COME FROM THE FUCKING CGS SYSTEM?! WHAT THE HELL?!?!?
I love improvised background piano. It's absolutely brilliant in both of your cursed units video, especially when you merge in the meme music.
If you make a part 3, consider looking up degree Baume! Its _supposed_ to represent concentration of a solution, but in reality its a huge mess. On wikipedia they talk about it in terms of specific gravity, which itself is a dimensionless number derived from dividing 2 _densities_ together (density and concentration of course being different). The definition of this unit is /different/ if you're measuring solutions less or more concentrated than distilled water.
To make matters worse, in practice, when you use it in practice to measure the concentration of various solutions, it's just a calibrated weight that bobs up and down in a cylinder. If you've looked at the scale, it /pretends/ to be a linear scale over small distances (it really isn't) ; ergo it feels like you're measuring a length ala mmHg.
Historically, that callibration has been so incredibly inconsistent, that when this unit was adopted, there was extreme variation in what the same unit meant. Eventually it evolved into a family of equally stupid concentration units used in hyper specific places like Brix or specific gravity * 1000
what does the integral on your pfp mean?
LET'S GO, been so excited to see any other stuff you've been working on
3:50
radian makes perfect sense when you use trigonometric functions for differnetial equations too though
Fluid mechanics also has a ton of dimensionless numbers to describe different characteristics of flow, like the Grashof number, Reynold's number.
Then you also have the Rayleigh number which is a product of the Grashof number and the Reynolds number, or the Richardson number which is a ratio of the Grashof number and the Reynolds number.
Just watched part 1 and the random walk music convinced me to subscribe for your production value.
An important note on CGS: There're different versions of that system, some commonly used today in theoretical electromagnetics because it cancels all the coefficients and even most of the units. Speed is measured in quantities of speed of light (so it can never exceed 1), charge is measured in numbers of electrons, vacuum permitivity = 1, etc.
3:41 THANK YOU for saying that. I hate how people pretend that radians are demsionless.
Similar to meter, which usually indicates that the thing you measure is some sort of vector, the radian indicates that it is a bivector, that it works in some plane.
THIS is the difference between joule and newton-meter (which should be more like newton-meter-rad). Joule is a scalar, but a torque needs a plane to rotate in, and it gets information about which plane, from radian. And if you multiply torqe by radian, you'll get actual joule.
Also thanks for mentioning angles in revolutions, I also never understood when people say that unlike degrees, radians are the most natural unit for angles. Like, no, revolutions are! But nobody just seems to notice it.
physical bivectors are measured in square meters
bivectors arent angles
fwiw, exp(it) only works when t is a scalar and equal to the value of an angle when measured in radians...
I think we consider radian angle measure the most natural because of how it works with calculus. For example the derivative of sin(x) is only cos(x) if x is measured in radians. If you use another measure of angle, the derivative of sin(x) is A cos(x) where A is the ratio between an angle measured in the units of x and the same angle measured in radians.
For example, if x is measured in degrees, the derivative of sin(x) is 180/pi * cos(x). If x is measured in revolutions, the derivative of sin(x) is 1/2pi cos(x).
The radian is still dimensionless. An equation only involving quantities and not units (think PV=nRT) should remain true regardless of the units. The equation defining angle is s=r theta where s is the signed arc length, r is the radius of the circle, and theta is the angle.
1) theta has to be dimensionless as changing from radians to cycles makes the equation wrong
2) theta has to be dimensionless as mentioned in the video: m/m=1
@@maxthexpfarmer3957 well that's like saying that newtons can't be vectors because meters already are.
Torque is basically a rotating force, it makes sense that it has angle in it somewhere.
love the video inserts of piano playing! makes the video feel more human imo, like there's a closer connection between the creator and the viewer.
Omg the first video is one of my favorite UA-cam videos and you managed to make this one actually better. I hope you can make a third part
0:26 i love the slow piano buildup to the gigachad music in the background. it’s all the little details that make the whole video feel all the more special.
YES! THE RETURN!
The absolute kicker about the barrer is the fact that, since cmHg is a pressure, the units can be reduced to volume/force. Considering the barrer is commonly used for describing material permeability, the simplified units actually *are* intuitive: what volume of the chosen fluid will pass into the given material under 1 unit of force?
I once saw the ideal gas constant R (8.314… Joules per mole Kelvin) expressed in: Inches of water cubic feet per pound-mole Rankine ((inH2O*ft^3)/(lbmol*Ra). I have absolutely no idea what use case this particular representation of that constant could ever have…
As an X-ray physicist, my favourite cursed unit is the Crab, a unit of flux (W/m^2). 1 Crab is the flux of X-rays from the Crab Nebula in the measured energy range. Of course, the Crab Nebula is one of the brighter X-ray sources on the sky, so it makes sense to measure most fluxes is mCrabs, or milliCrabs. Maybe a candidate for your next video? :)))
This is the series that got me interested in dimensional analysis
I can't wait for part 3!
Oh I hope there is a part 3.