Title text: "röntgen" and "rem" are 20th-century physics terms that mean "no trespassing."
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This comic refers to elements of (mostly mathematical or engineering) notation commonly used in various fields of math and science. Each piece of notation is presented as "symbolizing" not what it specifically means, but a typical context in which it might be encountered. Many of the individual descriptions look like verbiage that might be found on informational or warnings signs or placards, although typically with a silly edge.
- d⁄dx: An undergrad is working very hard
d/dx is the symbol for a single-variable derivative. This is one of the basic operations in calculus and consequently is ubiquitous in the work of undergraduates in the sciences. A hard-working undergraduate in the relevant fields would churn through exercises using this symbol.
- ∂⁄∂x: A grad student is working very hard
The replacement of the standard "d" letters with the curly letters "∂" denotes the partial derivative, which generalizes the ordinary derivative to multi-variable calculus. Problems with partial derivatives, especially partial differential equations, can be extremely challenging. Although PDEs would typically be first taught at an undergraduate level, difficult partial derivatives would be encountered in graduate-level work.
- ħ: Oh wow, this is apparently a quantum thing
ħ (pronounced "h-bar") is a symbol used for (the reduced) Planck's constant, a universal, fundamental constant in quantum physics. ħ is equal to the energy of a photon divided by its frequency, and angular momentum in quantum mechanical systems is measured in quantized integer or half-integer units of ħ. Classical physics appears as a limit of quantum physics if all "actions" (quantities of dimension energy * time, momentum * length, or angular momentum) are much larger than ħ. Conversely you can also formally set ħ=0 to get classical results from quantum formulae. This means that effects which are proportional to some power of ħ cannot be explained classically, and instead are "a quantum thing".
- Rₑ: Someone needs to do a lot of tedious numerical work; hopefully it's not you
The Reynolds number (which is actually usually denoted by "Re," not "Re" as it appears in the comic) is the most important dimensionless group in fluid mechanics. Named for Osborne Reynolds, Re characterizes the relative sizes of inertial and viscous effects in a moving fluid. Large values of Re are indicative of turbulent flow, which cannot usually be solved for analytically, and so numerical modelling is necessary. Accurate numerical studies of high-Reynolds-number flows are notoriously difficult to create and program.
Alternatively, Rₑ could stand for electronic transition dipole moment in a molecule. This appears in quantum-mechanical calculations of transition probabilities and also includes a lot of unpleasant numerical work. Rₑ is also a term used for the radius of the Earth at mean sea level, though this is not necessarily a complex term in and of itself.
Another alternative is that Rₑ could refer to Relative Error, a measurement of precision or accuracy. Used often in the analysis of scientific data and in numerical analysis.
- (Ta⁴ - Tb⁴): You are at risk of skin burns
The Stefan-Boltzmann law says that a perfectly absorbing ("black body") source emits electromagnetic radiation with a power per unit area of σT4, where σ is a known constant and T is the absolute temperature. The quantity (Ta4 – Tb4) thus appears in any calculation of purely radiative energy transfer between two bodies, one at temperature Ta and the other at Tb. 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.
- NA: You are probably about to make an incredibly dangerous arithmetic error
NA, or Avogadro's number, is the number of molecules in a mole of a substance—roughly the number of protons plus neutrons in 1 gram of matter. This is an enormous number, exactly 6.022 140 76 × 10²³, or 602 214 076 000 000 000 000 000. Adding up molecular weights and converting between grams and moles of several substances is a lot of arithmetic on a scale where intuition won't help you catch mistakes. Working with NA, it is easy to make errors of one or more powers of ten without noticing. If this kind of error is made in the calculation of the stoichiometrically correct amount of a reagent in a chemical reaction, it is possible to accidentally create dangerous amounts of unwanted chemical products.
- µm: Careful, that equipment is expensive
Micrometers are a very small unit of distance. Micrometers are commonly used to measure wavelengths in the infrared, and infrared detectors are very expensive, compared with visible wavelength counterparts. 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. Similarly, tools used to create or calibrate items within micrometer tolerances can also be expensive.
- mK: Careful, that equipment is very expensive
Kelvin is a temperature scale roughly speaking similar to Celsius, but taking absolute zero as its zero point instead of the freezing point of water (rigorously speaking, its definition is now based on the Boltzmann constant). Millikelvins (1/1000 of a Kelvin) are used for high precision temperature work. Frequently this is used in processes of cooling temperatures to near absolute zero - such as superconductors or other quantum effects that occur when atoms are almost still. This is suggesting that the symbol appears on a sensitive experimental system probing quantum mechanical behavior that would likely only exist in an advanced laboratory. Any equipment that works down at mK temperatures, or at least to mK precision and accuracy, is likely to be very expensive.
- nm: Don't shine that in your eye
Nanometers are frequently seen in the listed wavelengths for lasers. Pointing a visible or infrared laser at someone's eye is notoriously dangerous; the tightly-focused coherent light can cause permanent damage very quickly.
- eV: Definitely don't shine that in your eye
Electron volt energies are typical of moderate-energy particle beams, produced by accelerating electrons (or protons) over macroscopic voltages. These particle beams can be even more damaging to soft tissues than optical-wavelength lasers.
- mSv: You are about to get into an Internet argument
The millisievert is a unit of radiation dose absorbed. It is actually a very small dosage, but the joke refers to Internet trolls debating the effects of low-dose radiation sources, such as 5G wireless networks. Randall's comment may also be referring to this chart.
- mg/kg: Go wash your hands
This unit measures the dose of a drug or other chemical in milligrams per kilogram of body mass. If the appropriate dose - or worse, the lethal dose - is measured in mg/kg (parts per million), then the substance may be quite toxic.
- µg/kg: Go get in the chemical shower
A unit 1/1000 times the size of mg/kg. If a dosage is measured in micrograms per kilogram (parts per billion), any accident probably requires whole-body decontamination procedures.
- π or τ: Whatever answer you get will be wrong by a factor of exactly two
π is defined as the ratio of a circle's circumference to its diameter, while τ is defined as the ratio of a circle's circumference to its radius (and is therefore equal to 2π). π has been used as the primary constant for describing the circumference and area of circles for millennia, but proponents of τ claim that τ is actually more natural in most contexts, since it makes working in radians more straightforward. The joke here is that whichever constant you use, it will probably be the wrong one (off by a factor of two, one way or the other) for the formula you are trying to use. The debate over Tau vs Pi was solved by Randall in this compromise: 1292: Pi vs. Tau.
The title text refers to two non-SI units of radiation measurement, röntgen and rem. In the mid-20th century when they were in use, the dangers of radiation weren't as well understood as today, so an area with radiation that was noteworthy back then is probably dangerous ( https://www.bloomberg.com/news/articles/2019-08-28/france-is-still-cleaning-up-marie-curie-s-nuclear-waste ), hence the no trespassing part.
- [A list with 14 different scientific constants/symbols are shown. Next to each symbol is a description. Above the list is a heading and beneath that a subheading.]
- And what they mean
- 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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