2207: Math Work
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...
| 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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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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