Talk:2529: Unsolved Math Problems

2021-10-18T19:19:23Z

Domi:

Does anyone have any clue whether the writing on the board in the weirdly abstract panel means anything? Maybe add an explanation about it?[[Special:Contributions/162.158.227.91|162.158.227.91]] 13:23, 17 October 2021 (UTC)

Center panel possibly related to "The drunkards walk" and theories on randomised motion.
https://www.quantamagazine.org/random-walk-puzzle-solution-20160907/
More references https://mathworld.wolfram.com/RandomWalk.html

Someone's gotta point out that "walking randomly on a grid, never visiting the same square twice" would rapidly trap you in a corner (even the example has a 50/50 chance of that happening on the next move) [[Special:Contributions/172.70.130.125|172.70.130.125]] 04:29, 16 October 2021 (UTC)

Not if it's an infinite grid.

I think there's two different ways to interpret the question - as a uniform random element of the set of all non-self-intersection NxK length paths, in which case it's fine, or as a path defined by a random walk in which moves onto your own path are not allowed, which doesn't seem well defined, since you might end up in a situation where you are surrounded by your own path and cannot continue for all NxK steps.

An early example of a cursed problem is the Cantor Function. https://en.wikipedia.org/wiki/Cantor_function

I admire whoever wrote the description of the curve in the "cursed" panel. [[User:Barmar|Barmar]] ([[User talk:Barmar|talk]]) 05:36, 16 October 2021 (UTC)

"Algebreic" is a misspelling of "algebraic". Could Randall really have made this mistake, or is it another malamanteau? What does "breic" come from? [[User:Barmar|Barmar]] ([[User talk:Barmar|talk]]) 06:10, 16 October 2021 (UTC)

I wonder if Randall was actually referring to that quote about "Into the Woods", or he just thought "Sondheim calculus" sounded cool and it was a total coincidence. I found it when I googled "sondheim calculus" to make sure it wasn't a real thing. [[User:Barmar|Barmar]] ([[User talk:Barmar|talk]]) 06:29, 16 October 2021 (UTC)

In panel 2, what would 'k' be? [[Special:Contributions/172.69.35.108|172.69.35.108]] 08:00, 16 October 2021 (UTC)

'k' would represent the number of marbles placed on the ground. [[Special:Contributions/162.158.88.127|162.158.88.127]] 08:09, 16 October 2021 (UTC)
:Though probably correct, I think the implied state is that an integer multiple (k) of N steps is made (s=N*k), with that number of marbles dropped, not s=(N*k)+c steps (for N>c) which would have the same result (uselessly) for all values of s where c ranges 0..N-1. It just introduces inflections into the graph (with s as an axis) that needn't be there (with just a k-based one). Or, in other words, selectively poll all s-values that are exactly divisible by N, and forget all the rest. (That divisor is k, and hence k is the number of marbles. Or perhaps k+1 if you leave one on the starting spot too.) [[Special:Contributions/162.158.159.25|162.158.159.25]] 21:59, 16 October 2021 (UTC)

To me, the cursed curve looks a bit like a crosier https://commons.wikimedia.org/wiki/File:Crosiere_of_arcbishop_Heinrich_of_Finstingen.jpg

--> I had the same impression and added it. --[[Special:Contributions/162.158.94.219|162.158.94.219]] 11:40, 16 October 2021 (UTC)

No explanation of the "Euler Field Manifold Hypergroup (Isomorphic to a)..." part?

The cursed curve looks almost like someone took a graph of the Binet formula in the complex plane, stretched it out a bit, and rotated it onto the i axis.
: This was my first thought too when I saw it. [[Special:Contributions/172.69.34.87|172.69.34.87]] 17:16, 16 October 2021 (UTC)
: It looks like Vulcan script to me. [[User:LtPowers|LtPowers]] ([[User talk:LtPowers|talk]]) 13:51, 16 October 2021 (UTC)
: That's what it looks like to me too; recognized it from that Numberphile video on Fibonacci numbers in the complex plane [[Special:Contributions/108.162.245.245|108.162.245.245]] 07:36, 17 October 2021 (UTC)

Could the cursed curve be a reference to the logistic map?

Can someone produce a high resolution image of the Cursed Curve? It needs to be on a T-shirt [[User:Avimimus|Avimimus]] ([[User talk:Avimimus|talk]]) 21:39, 16 October 2021 (UTC)

Is someone going to mention the title text?

I swear I've seen that third plot, I thought it was in XKCD, but a quick run through tagged entries didn't find anything... unfortunately I consume a lot of math media so I can't place it. It's bugging me so I hope this note will serve as encourgement to someone that DOES remember [[Special:Contributions/162.158.106.221|162.158.106.221]] 21:29, 16 October 2021 (UTC)
:I'm sure I've seen components of the cursed-curve, not sure if they fit together like that, easily, though. The differentiation of dy/dt (which is odd in itself) of the first (lower) bit looks discontinuous, followed by a chaotic oscilation (may just be the culmination of the less frenetic chaos that created the first set of x=f(y) - again, an unusual way round) that then settles into a pattern where ''regardless'' of the 'prime axis', you have multiple real roots on the other, towards some great-attractor value.
: In more standard x/y (or y=f'(x)?) notation, it is clear that there are multiple real roots for various values of x within a range, and possible none at all beyond that (or it's a plotting error insofar as x tends to ±infinity it has a very narrow range of y that is never sampled properly, but should connect to that pulse 'randomness'). If it's a plot of real vs imaginary components of a complex function to a different continuous value, I suspect someone is playing silly-buggers with multiple (perhaps nested?) trigonometric functions, polynomials and variable-shifted powers. But it's nearly thirty years since I did mathematics at the level needed to disentangle this neatly (back when Mandelbrots and Julias were still a staple wall-poster for any student not more into the likes of Iron Maiden skull-motifs or <insert your favourite classic film here>, and even then it might be) so don't ask me where to start. [[Special:Contributions/162.158.89.140|162.158.89.140]] 16:48, 17 October 2021 (UTC)

To me the curve in panel three looks like a cursed (ha) mixture of an oscillatory time responses of dynamic systems with either an Nquist plot or simply trajectories of eigenvalues (of a stable system) at the end. Links: https://en.wikipedia.org/wiki/Nyquist_stability_criterion#Nyquist_plot , https://electronicscoach.com/time-response-of-second-order-system.html https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors [[User:Domi|Domi]] ([[User talk:Domi|talk]])Domi

Are there any examples of "cursed" math problems? I've seen "weirdly abstract" and "weirdly concrete" ones, but not "cursed" ones. [[Special:Contributions/162.158.63.117|162.158.63.117]] 01:03, 17 October 2021 (UTC)

The symbol in the third panel looks like an unalome, which is not a mathematical symbol but a Buddhist or mystical one https://en.wikipedia.org/wiki/Yantra_tattooing#Types_and_designs

There is at least one paper on arxiv defining quasimonoid, 1401.7748. It's from 2014 so it existed long before the comic. --[[Special:Contributions/162.158.88.253|162.158.88.253]] 14:04, 17 October 2021 (UTC)

Links, '''please'''! Not all of us are mathematicians. If you mention something that you think the cursed curve might represent, please provide a link to something describing that something so the rest of us can read it and attempt to learn more. [[User:Shamino|Shamino]] ([[User talk:Shamino|talk]]) 17:44, 17 October 2021 (UTC)

That cursed squiggle sure looks like the sort of thing that used to flow from {{w|Saul Steinberg}}'s pen, as seen in the pages of the New Yorker back in the 60s. The most relevant example I can find right now is from 1965: https://fineartamerica.com/featured/new-yorker-february-20th-1965-saul-steinberg.html [[Special:Contributions/162.158.255.177|162.158.255.177]] 03:38, 18 October 2021 (UTC)

So, is the middle one an actual unsolved problem? --[[Special:Contributions/162.158.91.236|162.158.91.236]] 16:07, 18 October 2021 (UTC)

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Talk:2529: Unsolved Math Problems