2520: Symbols

Explain xkcd: It's 'cause you're dumb.
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Symbols
"röntgen" and "rem" are 20th-century physics terms that mean "no trespassing."
Title text: "röntgen" and "rem" are 20th-century physics terms that mean "no trespassing."

Explanation

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This comic refers to notation commonly used in various fields of math and science.

d/dx and ∂/∂x are both used to represent derivatives in calculus and related fields. d/dx is most commonly used in introductory and basic calculus, while ∂/∂x is the symbol for a partial derivative, indicating a problem involving multivariable calculus, which is a level of difficulty above single-variable calculus.

ħ (pronounced 'h-bar') is a symbol used for Planck's constant, a universal constant in quantum physics equal to the energy of a photon divided by its frequency.

NA is Avogadro's number, which is used in chemistry for calculating the number of molecules in a mass of substance. Its use implies a chemistry problem where relative concentrations and orders of magnitude are important; if a mistake is made the concentration of a potentially dangerous chemical could be far too strong or too weak.

μm and mK (micrometers and millikelvin) are very small units of length and temperature respectively. Any equipment that is operating in these units will be incredibly finely calibrated and thus very expensive. Millikelvins would measure temperatures barely above absolute zero, suggesting sensitive experiments probing quantum mechanical behavior that would likely only exist in an advanced lab.

nm and eV (nanometers and electronvolts) are also small units of length and energy. Nanometres in particular are commonly used to refer to wavelengths of light, and therefore might be seen when working with lasers, which you should definitely not shine in your eye. Electron volts are a measure of energy in particle physics; particle accelerators produce intense radiation which should definitely not be directed toward your eye.

mSv (millisieverts) are a unit of radiation exposure. Randall's comment may be referring to this chart.

mg/kg and μg/kg (milligrams per kilogram and micrograms per kilogram) are units used to count the proportion of a substance that contains a certain chemical; they are equivalent to 'parts per million' and 'parts per billion' respectively. These might be found when working with particularly dangerous chemicals, where even slight exposure could lead to severe health risks.

Finally, the comic references pi and tau. Pi is defined as the ratio of a circle's circumference to its diameter, while tau is defined as pi times two. Pi is more commonly used as a circle constant and is helpful when working with areas and volumes, but proponents of tau argue that it is more useful in a pure mathematics context as it makes working with radians easier. The joke here is that whichever constant you attempt to use, it will probably be the wrong one for what you are trying to achieve.

This comic discusses different symbols found in equations, and humorously comments on their implications.

  • d/dx: An undergrad is working very hard

d/dx is the symbol for a single-variable derivative. This is a mathematical operation that, while difficult, is well within the reach of an undergraduate student, particularly in science. Thus, an equation with this operation would be one that would cause an undergraduate student to work very hard.

  • d/dx: An undergrad is working very hard

d/dx is the symbol for a single-variable derivative taken with respect to x. This is a mathematical operation that, while difficult, is well within the reach of an undergraduate student, particularly in science. Thus, an equation with this operation would be one that would cause an undergraduate student to work very hard.

  • ∂/∂x: A grad student is working very hard
Partial derivative. Partial differential equations are typically encountered in higher-level coursework, hence why a grad student would be working hard vs. an undergrad.
Re
Reynolds number, used in modelling the flow of fluids. Fluid flow cannot usually be modelled analytically and so a numerical model is necessary.
(Ta4 - Tb4)
Temperature component of net radiation loss. See Stefan-Boltzmann's law. This is a joke about how the Sun is a very powerful blackbody radiator.
NA
Avagadro's constant. If you are using this and not working in Moles there is a good chance that you will make a mistake of a factor of a power of ten. THis could create dangerous amounts of chemicals
µm
Micrometers are small. Any equipment that is accurate to that degree is likely to be expensive
mK
millikelvin are small changes in temperature, or represent very low temperatures. Equipment that uses mK is very expensive
nm
Describes the wavelength of laser light
eV
describes the energy of a particle beam
mSv
The amount of radiation absorbed. The pun most likely refers to internet trolls debating the effects of radiation like 5G networks, or fans of the Chenobyl series.
mg/kg
The toxicity of a chemical, per kg of body mass. If it is measured in mg/kg it is quite toxic
µg/kg
If the chemical is measured in µg/kg it is extremely toxic
π or τ
τ = 2π, so it would be easy to make a mistake and use π when τ is correct.

The title text refers to two non-SI units of radiation measurement. An area with significant amounts of radiation is probably dangerous, hence the no trespassing part.

Transcript

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d/dx
an undergrad is working very hard
∂/∂x
a grad student is working very hard
ħ
oh wow, this is apparently a quantum thing
Re
someone needs to do a lot of tedious numerical work; hopefully it's not you
(Ta4 - Tb4)
you are at risk of skin burns
NA
you are probably about to make an incredibly dangerous arithmetic error
µm
careful, that equipment is expensive
mK
careful, that equipment is very expensive
nm
don't shine that in your eye
eV
definitely don't shine that in your eye
mSv
you are about to get into an internet argument
mg/kg
go wash your hands
µg/kg
go get in the chemical shower
π or τ
whatever answer you get will be wrong by a factor of exactly two


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Discussion

Great work by whomever did this, but is it possible R_e is something else? I agree that the numerical aspect makes it seem like a fluid mechanics problem, but I've never seen the Reynolds number with a subscripted e... only a regular size e, such that it is Re, not R_e. 108.162.237.93 20:36, 24 September 2021 (UTC)

R sub e (not Re) is Effective Reproduction Number. This is related to infection rates. I'm pretty sure it's R sub e, not Re given that infection rates are very much on his mind right now.
It would be out of place relative to all the other entries, though, which are all physics related. IMO it's more likely this was an error.
Earth's radius is abbreviated "R sub e" 162.158.107.4 21:30, 24 September 2021 (UTC)
Could be the remainder of a series (i.e. the error when using the first terms of the series as an approximation). Determining upper bounds on this error is usually very tedious.
R sub e is tire effective rolling radius (or effective radius)--a radius based on the distance traveled by one rotation of a pneumatic tire. Re is similar to the unloaded radius (for radial tires) and normally larger than the loaded radius (distance from axle to ground).
My first thought was that this referred to the "real part" operator, although that's typically represented by a plain Re (no subscript).

Re seems to be related to number theory, like in those papers where's they tediously prove that there are infinities of different sizes.

Extra vote for number theory theory, I've seen R_e most when referring to Real part of a function, which does often bring in tedious calculations

Re is almost definitely not meant to have any electronic structure meaning here. The subscript alpha in R_alpha is indexing over x,y,z (cartesian coordinates) as a transition dipole moment term.

T to the fourth power looks like blackbody radiation, any ideas what specifically that formula represents? 162.158.203.22 20:40, 24 September 2021 (UTC)

There's an equation for what reflects off a spherical object that is a quartic equation (although I'd expect concave reflectors, not convex ones, to risk skin-burn. Or, more likely something to do with UV (non-)absorbtion or generation, but I imagine someone knows exactly what it is, without someone like me just guessing wildly. ;) 141.101.99.82 21:05, 24 September 2021 (UTC)

This wiki does not seem to have a consistent formatting structure for lists

The NA could also soon become NAN (not a number) thus being only a step away from the dangerous arthmeric error. --162.158.88.43 21:38, 24 September 2021 (UTC)

Bold Title

Content starting with a tab


  • Bold title content continues on same line


  • Regular title

Content on a new line, but not starting with a tab

As well as tables and mixes of these formats. Maybe someone should pick one and apply it to all the explanations. I just noticed it because of the inconsistencies as people are quickly throwing something together for this new comic. 162.158.107.4 21:02, 24 September 2021 (UTC)

I read the penultimate line as "Mg" and was trying to imagine a meaning for "megagrams per kilogram". Sloppy Greek letter there, Randall. Nitpicking (talk) 03:17, 25 September 2021 (UTC)

I find this criticism very unreasonable. Randall's "m" is written very differently, there are plenty of examples of it in this very cartoon to avoid confusion, and micrograms are far more commonly used than megagrams. I had no problem whatsoever recognizing the letter mu, and I don't see how this could be a problem for anyone already familiar with that letter. 162.158.90.85 11:11, 26 September 2021 (UTC)

Why are partial derivatives considered graduate-level? They're typically covered in first level undergraduate science courses, along with gradients and such. FPSCanarussia (talk) 03:34, 25 September 2021 (UTC)

The reference to "micrometer" links to the Wikipedia page for the measuring device, but it should link to the page for the unit of length: https://en.wikipedia.org/wiki/Micrometre Professor Frink (talk) 15:58, 25 September 2021 (UTC)

Adding to “Micrometer/Micrometre” above: this “any” is not really correct:

Of course, micrometers are used as a measurement of distance in other contexts, but any distance-measuring device capable of accurately measuring micrometer distances would also be expensive.

The “Micrometers” as seen in the Wikipedia article can measure distances of some micrometers accurately, but are not really expensive. Probably even cheaper than any equipment which can not measure distances. --162.158.88.239 18:19, 25 September 2021 (UTC)

In certain circles (or, perhaps, between them as they roll), the typical Reynolds number is just three digits... ;) 162.158.159.95 20:04, 25 September 2021 (UTC)

"When radiative transfer is large enough to be the most important form of heat interchange, it is normally also large enough to sear the skin with thermal or ultraviolet burns." Radiative transfer is the dominant heat transfer from a (idle) human body in a 20C room. There is no risk of seared skin in this situation. As an aside if people understood the role of radiative heat transfer we'd have more comfortable and cheaper HVAC systems (and more underfloor heating).172.70.34.91 20:08, 25 September 2021 (UTC)

I cannot recall ever using Avogadro's constant in a stochiometric calculation. You do everything in mole or gram mole. NA implicitly cancels and never even appears.172.70.34.91 20:08, 25 September 2021 (UTC)

mSV (millisievert) is also likely to show up in other internet debates as well, usually related to Chernobyl, Fukushima, Three Mile Island, or [other such nuclear accidents|https://www.ucsusa.org/resources/brief-history-nuclear-accidents-worldwide] Also likely to show up in any discussion on nuclear energy to alleviate global warming, especially given modern reactor designs to reduce such incidents.Seebert (talk) 20:15, 27 September 2021 (UTC)

d⁄dx is not the symbol for a single variable derivative, but the symbol for a total derivative. Partial derivatives and total derivatives happen to be equal when the function depends on only one variable, but in general both partial and total derivatives are used in multivariate calculus 198.41.231.172 05:56, 29 September 2021 (UTC)

I know arguments on the Internet often aren't logical, but the mSV really wouldn't make any sense in the context of arguing about 5G as that is non-ionizing radiation. Ullallulloo (talk) 14:37, 7 October 2021 (UTC)

eV may more specifically be a reference to https://en.wikipedia.org/wiki/Anatoli_Bugorski --172.70.35.70 03:59, 8 October 2021 (UTC)

R_e could also refer to the elastic limit in solid mechanics, where it is the lowest stress at which permanent deformation will occur. At least my university (in Germany) uses that symbol. Interestingly, stress analysis can also involve a lot of numerical work, at least outside of simplified examples. 172.70.250.185 (talk) (please sign your comments with ~~~~)

No comment about your experience, but in response to your edit-comment of "(sorry if I'm editing wrong)", just remember to sign with four tildes ( ~~~~ ) here in the Talk page, to make any discussion easier to read and timestamp things a bit (it was written just now, so I haven't bothered to add that detail, above, future readers can correctly assume just a few minutes have passed from then until now and my own signature addition). 172.69.79.173 19:58, 22 July 2022 (UTC)