Editing 2520: Symbols

{{comic
| number    = 2520
| date      = September 24, 2021
| title     = Symbols
| image     = symbols.png
| titletext = "röntgen" and "rem" are 20th-century physics terms that mean "no trespassing."
}}

==Explanation==
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, see [[#Symbols|below]]. 

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. 

The title text refers to two non-SI units of radiation measurement, {{w|Roentgen (unit)|röntgen}} and {{w|Roentgen equivalent man|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 [https://archive.md/v3dME probably dangerous], hence the no trespassing part.

Later [[Randall]] made a similar comic, [[2586: Greek Letters]], regarding the use of Greek letters in math.

===Symbols===
'''<sup>d</sup>⁄<sub>dx</sub>: An undergrad is working very hard'''  d/dx is the symbol for a single-variable {{w|Derivative|derivative}}. This is one of the basic operations in {{w|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.

'''<sup>∂</sup>⁄<sub>∂x</sub>: 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) {{w|Planck's constant}}, a universal, fundamental constant in quantum physics. h, the normal version of Planck's constant, is equal to the energy of a photon divided by its frequency. ħ is equal to h/2π, 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 that 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 {{w|Reynolds number}} (which is usually denoted by "Re," not "R<sub>e</sub>" 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 retrieved analytically, and so numerical modeling is necessary. Accurate numerical studies of high-Reynolds-number flows are notoriously difficult to create and program.

Alternatively, Rₑ could stand for electronic {{w|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 numerical analysis.

'''(T<sub>a</sub>⁴ - T<sub>b</sub>⁴): You are at risk of skin burns'''  The {{w|Stefan-Boltzmann law}} says that a perfectly absorbing ("black body") source emits electromagnetic radiation with a power per unit area of σT<sup>4</sup>, where σ is a known constant and T is the absolute temperature. The quantity (T<sub>a</sub><sup>4</sup> – T<sub>b</sub><sup>4</sup>) thus appears in any calculation of purely radiative energy transfer between two bodies, one at temperature T<sub>a</sub> and the other at T<sub>b</sub>. When the 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.

'''N<sub>A</sub>: You are probably about to make an incredibly dangerous arithmetic error'''  N<sub>A</sub>, or {{w|Avogadro's number}}, is the number of molecules in a mole of a substance, approximately the number of carbon atoms in exactly 12 grams of carbon-12. This is an enormous number, exactly 6.022 140 76 × 10²³, or 602 214 076 000 000 000 000 000. Working with N<sub>A</sub>, it is easy to accidentally divide by it instead of multiplying or vice versa, leading to erroneous and nonsensical answers such as ~10<sup>-23</sup> molecules (even though you can't have less than 1 whole molecule) or ~10<sup>46</sup> moles (>10<sup>43</sup> to 10<sup>45</sup> kilograms, depending on the chemical) of a substance.

'''µm: Careful, that equipment is expensive'''  {{w|Micrometre|Micrometer}}s 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 <i>very</i> expensive'''  {{w|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 {{w|2019_redefinition_of_the_SI_base_units#Kelvin|based on the Boltzmann constant}}).  {{w|Millikelvin}}s (1/1000 of a Kelvin) are used for high precision temperature work.  Frequently this is used in processes of cooling temperatures to nearly 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'''  {{w|Nanometre}}s 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: <i>Definitely</i> don't shine that in your eye'''  {{w|Electronvolt}} energies are typical of moderate-energy particle beams, produced by accelerating electrons (or protons) over macroscopic voltages. These particle beams can be {{w|Anatoli Bugorski|even more damaging (and are probably a direct reference to Anatoli Bugorski)}} to soft tissues than optical-wavelength lasers.

'''mSv: You're about to get into an Internet argument'''  The {{w|millisievert}} is a unit of radiation dose absorbed. It is 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|Randall's]] comment may also be referring to [[Radiation]].

'''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). {{w|pi|π}} has been used as the primary constant for describing the circumference and area of circles millennia ago, but proponents of {{w|Turn (angle)|τ}} claim that τ is more natural in most contexts since it makes working in radians more straightforward. Actually, the "Pi" symbol used to be occasionally used for the constant now called Tau. 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 Pi vs. Tau was solved by Randall in this compromise: [[1292: Pi vs. Tau]].

==Transcript==
:[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.]
:::::<big>Symbols</big>
::::And what they mean

:::<sup>d</sup>⁄<sub>dx</sub>&nbsp;&nbsp;&nbsp; An undergrad is working very hard
:::<sup>∂</sup>⁄<sub>∂x</sub>&nbsp;&nbsp;&nbsp; A grad student is working very hard
:::ħ&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Oh wow, this is apparently a quantum thing
:::Rₑ&nbsp;&nbsp;&nbsp;&nbsp; Someone needs to do a lot of tedious numerical work; hopefully it's not you
:(T<sub>a</sub>⁴ - T<sub>b</sub>⁴)&nbsp;&nbsp;&nbsp; You are at risk of skin burns
:::N<sub>A</sub>&nbsp;&nbsp;&nbsp; You are probably about to make an incredibly dangerous arithmetic error
:::µm&nbsp;&nbsp;&nbsp; Careful, that equipment is expensive
:::mK&nbsp;&nbsp;&nbsp; Careful, that equipment is <i>very</i> expensive
:::nm&nbsp;&nbsp;&nbsp; Don't shine that in your eye
:::eV&nbsp;&nbsp;&nbsp;&nbsp; '''''Definitely''''' don't shine that in your eye
:::mSv&nbsp; You're about to get into an internet argument
::mg/kg&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Go wash your hands
::µg/kg&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Go get in the chemical shower
::π or τ&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Whatever answer you get will be wrong by a factor of exactly two

{{comic discussion}}

[[Category:Math]]
[[Category:Physics]]
[[Category:Chemistry]]
[[Category:Biology]]
[[Category:5G]]