2207: Math Work

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Math Work
I could type this into a solver, which MIGHT help, but would also mean I have to get a lot of parentheses right...
Title text: I could type this into a solver, which MIGHT help, but would also mean I have to get a lot of parentheses right...


Ambox notice.png This explanation may be incomplete or incorrect: Created by TWO UNKNOWNS. About half of the explanation seems insufficiently related to the comic. Do NOT delete this tag too soon.
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White Hat is observing a physicist, Cueball, who is staring at some (in the comic unreadable) equations and diagrams on a chalkboard. White Hat is neither a physicist nor a mathematician, and seems to glorify those professions. He wishes he understood Cueball's work and "the beauty on display here." People who profess a love for mathematics often cite the beauty they see in pure math, how things work out so perfectly, as the reason they love math.

The joke is that Cueball as a physicist is doing something instead quite simple and relatable: Avoiding hard work. Solving many kinds of constraints for two unknowns isn't necessarily difficult, but can be depending on the details. Cueball clearly thinks a solution is possible but would rather find an easier route. The same could be said about the field of mathematics in general: A proof is beautiful to a mathematician when it provides aesthetic pleasure, usually associated with being easy to understand. A proof is elegant when it is both easy to understand and correct, and mathematical solutions are profound when useful. Record numbers of mathematics interest groups and their forums in which such work is done exist today, from academic journals predating the use of electricity to a plethora of internet math and science fora such as Wikipedia Reference Desks and Reddit's /r/theydidthemath forum, which fueled a resurgence of the phrase "they did the math" as a search term in 2014, because it was included in the sidebar of the /r/xkcd subreddit, where it remains five years hence, between "Linguistics" and "Ask Historians," suggesting that the term was popularized by Xkcd fans after its initial appearance c. 1988. The proliferation of mathematics fora is certainly also due to the quickly increasing overall level of education and rapidly growing numbers of internet users.

A mathematical problem involving two unknowns could be a system of linear equations which can often be solved on paper, a blackboard, in a spreadsheet with solver functions, or by a computer algebra system such as WolframAlpha.com. Linear equations are a typical kind of more general constraint satisfaction problems, which in turn are mathematical optimization problems, where the minimization of a difference from a goal state (such as that all of the constraining equations are true, for example) indicates the extent to which constraints are met. Sometimes such problem solving activity arises naturally from economic transactions according to, for example, the laws of supply and demand, arising in the general context of civilization and ecology (both of which have properties associated with beauty and mathematical elegance.) Problems solved by economics are examples of distributed constraint optimization processes. When economic laws are not sufficiently satisfying constraints, that is a market failure, which indicates that more artificial and manual mathematical work is required, instead of the naturally arising or otherwise automatic methods contemplated by Cueball. Other distributed constraint optimization systems can be crowdsourcing games, such as FoldIt and Galaxy Zoo.

Of the graphic elements on the blackboard, the most distinctive appears to be a pair of wedges from a pie chart, where the radius of the slices is being used to represent another variable than the angles which all pie charts use to represent a primary variable. Since the cartoon is in black and white, the use of color to represent category labels or more variables may be ruled out. Such black-and-white wedges represent two variables, the meaning of which may be unknown to us, let alone their values. The only distributed constraint optimization game which uses such wedges may be the climate stabilization wedge game from Princeton University. In that wedge game, angles represent a potential number of gigatons of atmospheric carbon mitigation (out of about 38 for the circle) and radius indicates uptake, or the extent to which the mitigation solution is effective.

That game is an example of a bivariate optimization problem which might not have to be manually solved by anyone, for example under specific assumptions about the market in Project Foghorn plants and power-to-gas upgrades for natural gas power plants. If such market-based approaches to distributed constraint satisfaction are successful, then the work in finding the solution would be performed not entirely by physicists, chemical engineers, mathematicians, or intentional crowdworkers playing a game to achieve the optimal solution(s), but instead in even larger part by far more widely distributed crowdworkers who are simply making their own, ideally self-interested choices regarding their demand for desalinated and potable water, carbon-neutral liquid transportation fuel and carbon-negative sequestration in fiber-reinforced composite lumber, both made from carbonate dissolved in seawater, and for recycling the carbon in power plant flue exhaust for the storage of renewable energy such as off-peak wind power. The relative beauty, elegance, and simplicity of the possible solutions to such problems are subjective, and might involve strong differences of opinion between outside observers, mathematicians and engineers involved with the details, and fossil fuel barons, respected and enriched by society for their part in meeting energy demand. (See "All Chemistry Equations" in 2034: Equations.) Although the original market-focused primary use of ticker tape may be a lost art, the economy is still driven by individual free will leveraging self-interested behavior to achieve social gains for civilization.

The title text continues Cueball's thought process, with the possibility of using an automatic equation solver to find the unknowns. Equation solvers are not often considered beautiful ways to address purely mathematical problems, even if they are often the most efficient and in that sense elegant solutions to applied problems in engineering. Using a formal solver with symbolic, numeric, or both methods requires making sure that the constraints (e.g. equations) are entered correctly, with parentheses balanced in their correct locations for the solution to succeed. While the beauty of mathematics and pure physics may not be associated with automatic solvers in spreadsheets, general optimization methods are considered elegant in applied physics and engineering, with Jaynes (1957) cited more than 12,000 times on Google Scholar, including by a paper cited by the first black hole image astronomers for example.


[White Hat is watching Cueball from a couple of meters away. Cueball is contemplating the formulas and diagrams that fills the blackboard he stands in front of. Cueball holds a chalk in his hand. None of the content on the blackboard is readable, but there is a diagram in the shape of a circle and a another pie shaped diagram. Both are thinking with large thought bubbles above their heads, with small bubbles connecting them and the larger bubble]
White Hat (thinking): Amazing watching a physicist at work, exploring universes in a symphony of numbers.
White Hat (thinking): If only I had studied math, I could appreciate the beauty on display here.
Cueball (thinking): Oh no. This has two unknowns. That's gonna be really hard.
Cueball (thinking): Ughhhhhhh.
Cueball (thinking): Think. There's gotta be a way to avoid doing all that work...

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This makes me think of my profession (software engineer) - Normie: "Oh wow, that looks complicated!" Me: wires two pre-existing libraries together and calls it a day Baldrickk (talk) 09:39, 26 September 2019 (UTC)

Image of Blackboard

I was looking at the blackboard and was wondering if there were any Easter eggs on it. Here is the result of my badly cropped photoshopping skills. [1] idk if it would help to sharpen the image. --DarkAndromeda31 (talk) 01:25, 26 September 2019 (UTC)

The only thing that really jumps out at me are the wedges, as portions of pie charts where radius also controls area, evoking the climate stabilization wedge game from Princeton where the total area of the disk needing to be mitigated is something like 38 gigatons of atmospheric carbon, and the various mitigation solutions have angles representing potential and radius indicating uptake, the proportion of which represents gigatons mitigated as the wedge area. We can offer that game as an example of a bivariate optimization problem which might not have to be manually solved by anyone, if we assume that the local market for surplus potable water, carbon-neutral liquid transportation fuel, and carbon-negative composite lumber for centuries-to-millenia scale sequestration along with wood timber displacement for reforestation represents locally satisfiable economic demand for N shipping containers of Project Foghorn plants and M shipping containers of power-to-gas upgrades for natural gas power plants. That's an example of how a locally market-driven system can solve a bivariate optimization without anyone doing the actual math work in a spreadsheet or otherwise. The economic solution is not necessarily optimal, because even as powerful as the free market can be, it isn't necessarily going to find the bivariate optimums for every point on the planet (although it will likely converge asymptotically in some sense) and defectors such as fossil fuel producers are interested in delaying the optimum solution.
Is that nontangential enough? 20:49, 26 September 2019 (UTC)
Yes that was far out :-) I'm sure there is nothing interesting hidden in the image. --Kynde (talk) 08:36, 27 September 2019 (UTC)
Compare the graph at [2] with that at [3]. When will the latter overtake the former? 19:19, 27 September 2019 (UTC)
Soon one may hope, but that has nothing to do with the drawings on the blackboard...? --Kynde (talk) 21:07, 27 September 2019 (UTC)
"Soon" lacks mathematical precision. How do you feel about distributed constraint optimization? 22:56, 27 September 2019 (UTC)
P.S. I would also point out that this comic appeared during the Global Climate Strike so I stand by my interpretation of the wedges. 19:11, 3 October 2019 (UTC)

Does Wolfram Alpha constitute such a problem solver? Cause both Randall and this site has used it on several occasions. But I have not ever really used such things, and do not know if Wolfram can be used as Cueball thinks about in the comic. But if it could, it could be worth mentioning as a method sometimes used by Randall. --Kynde (talk) 08:43, 27 September 2019 (UTC)

[4] is the first bivariate system of equations example. 17:51, 27 September 2019 (UTC)
Is that then a yes to my question? ;-) --Kynde (talk) 21:07, 27 September 2019 (UTC)
Do you think it's more worthwhile to include a general discussion of avoiding the work of solving for two unknowns than the climate wedges? Why do you suggest that the wedges aren't the only distinctive elements on the blackboard? 22:58, 27 September 2019 (UTC)

I only just now noticed that Randall always puts the crossbars on the I in the word "I" and not otherwise. Looking back, he has nearly always done this, even since the first few comics. That's quite a principled yet subtle stance on letterforms. (There are some exceptions, however, such as comic #87, and a period that goes at least from comic #128 to comic #180. I wonder if it would be too typography-nerdy to put them all in a category.) 14:47, 27 September 2019 (UTC)

Those "crossbars" would be serifs, whereas he normally uses a sans serif font. A sans serif would be quicker/easier to write by hand, but he probably realized early on (perhaps subconsciously) that an I by itself without serifs looks too much like a random line or a numeral 1 so he treats the solo I like a special letter, with serifs. -boB (talk) 15:16, 27 September 2019 (UTC)
Yes so not something for a category! But funny detail. I have no idea where to put this? Maybe in some part of the format of xkcd? --Kynde (talk) 21:07, 27 September 2019 (UTC)

Thank you, person who sees beauty in grammar (Jkrstrt). I thought something looked off when I said "often site the beauty they see" but I didn't catch it until you sighted the error and made it cite instead. -boB (talk) 15:10, 27 September 2019 (UTC)

We need something about the 2014 popularity spike of the phrase "They did the math" with a link to e.g. r/theydidthemath. And ask the Hashtag Research Studies group to figure out the cause of that spike. 15:29, 29 September 2019 (UTC)

This has got to be somehow related to xkcd. But how? 20:42, 29 September 2019 (UTC)

In other olds, Google Books says it started in 1988 but won't show me the 1988 book in question. I'm going to work on the drone fishing now. 05:31, 30 September 2019 (UTC)