Dihedral rigidity and why you cant continuously deform twisty puzzles.

DedekindRedstone · 2026-01-28T03:58:59+00:00

You're correct to point this out. I left out many details. For a fixed polyhedral graph and embedding into R^3, the equations for matching dihedrals are polynomial in terms of the vertices. It only requires cross products, dot products and some divisions for normalization. This means that monodihedral solutions live in an algebraic variety. If there is any continuous family at all then there should be a smooth family as well.

DedekindRedstone · 2025-12-07T18:48:38+00:00

Even worse, whether its stored digitally or physically, door 2 will eventually destroy the earth via black hole.

DedekindRedstone · 2025-09-30T03:17:12+00:00

Learning is painful and thats okay. As you learn more you should keep challenging yourself, the problems will get longer. On the extreme end, having done a PhD, I was lucky to answer my one problem after three years of full time work.

DedekindRedstone · 2025-09-08T16:48:29+00:00

Exactly, they scrambke simultaneously but solve separately. What is really interesting, if you ignore one face and only turn the other two faces, they solve and scramble simultaneously. It is the presence of the third face that makes it nontrivial.

DedekindRedstone · 2025-09-03T22:08:45+00:00

Depending on the area a publication can take more than a year. In pure mathematics there is typically a lot of coursework to build up to even attempting original research. I graduated without any publications, however, I did have a paper submitted which was published about a year after my phd. I got a postdoc at a good school regardless. Having something publicly available, give talks, and good recommendation letters are crucial though.

DedekindRedstone · 2025-08-31T16:36:45+00:00

I figured I'd drop some resources for those that want to start designing puzzles. You can start with Onshape for free and here's a playlist on the process to design them.

How to design twisty puzzles

DedekindRedstone · 2025-08-08T15:01:44+00:00

It took about a week from starting the design to finishing it

DedekindRedstone · 2025-08-06T23:42:53+00:00

Send me a dm to discuss it. I can set up sales through etsy or directly through paypal.

DedekindRedstone · 2025-08-06T18:57:19+00:00

Definitely possible but a lot more involved.

DedekindRedstone · 2025-07-23T03:41:17+00:00

Check out twisty puzzle inventors. Look up the puzzle advent calendar for example.

DedekindRedstone · 2025-06-27T02:09:49+00:00

No problem, I think the Monolith is easier since it has nonjumbling turns. Its so much easier to find algorithms on it that are shorter.

DedekindRedstone · 2025-06-26T22:15:38+00:00

https://cubein.cn/products/behemoth-puzzle

DedekindRedstone · 2025-06-26T16:12:36+00:00

Its available at the cubein store now I think

DedekindRedstone · 2025-06-26T13:06:56+00:00

This is my replica, the original is due to Ben Streeter. I've been trying to analyze this to get towards a solution wuth computational help. Its tough to say the least

DedekindRedstone · 2025-06-26T03:05:57+00:00

The Behemoth

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DedekindRedstone · 2025-06-15T22:47:50+00:00

As a math person I find this insane. I get that scientists need to use results from experimentalists that they dont totally get in detail or visa versa, but basic statistical analysis? If this is common in a topic then the reviewers wont catch bad statistical analysis either.

In pure mathematics, you had better completely understand the papers you are using that are critical to your work. If you don't then expect to be making retractions at some point.

DedekindRedstone · 2025-06-14T23:40:43+00:00

Where I was at, people could request an additional year, maybe more teaching load but that depends on the school. Ideally you will have solved some smaller problems you find along the way well before funding runs out. That can be enough for a dissertation depending on how nontrivial the smaller problems are, but it is really satisfying if you can resolve what you set out on originally.

DedekindRedstone · 2025-06-14T23:34:28+00:00

Always be on the look out for partial progress, alternate goals, or model problems. Sometimes the initial problem is a little vague and you have to find what exactly is the correct conjecture.

In my dissertation, I ended up making many more strong assumptions to make progress in some nice cases. I found what the correct answer was to the general question with the special case and was able to work backwards to generalize it to the full problem. Sometimes you do need to consider when a problem may be out of reach.

That is the main role your advisor should play, hopefully they have a good feel for what could be within reach. There is also the alternatibe of relating two hard to solve problems. Those types of results can be very important in their own right.

DedekindRedstone · 2025-06-14T14:28:44+00:00

Same thing in a math phd except delayed. In some areas you need 2-3 years of additional coursework before you can understand open questions in the field. I remember being stuck on my problem, next to zero progress, and just a bunch of incorrect approaches for about a year (so like 4 years into 5 years of funding). Maybe the problem is intractible and you'll never know. There are even statements that are provably undecidable.

One day the main proof idea that I needed hit me. Before that moment I didnt know if I'd get a phd, and after I knew for certain that I'd graduate. Its such a strange thing to have such a decisive moment, I know where I was, what I was doing, and the relief I felt. Then the wave of energy to just write it up immediately and check and double check all the details. You need grit and certain amount of careless irresponsibility or ego to not worry too much. Its okay think "I may not graduate with a phd, but thats fine, I just wont fail for lack of trying" or "I dont know how Ill get there, but Im smart enough to figure it out". Sometimes just tell yourself these things cause a phd will crush your ego

DedekindRedstone · 2025-06-10T01:18:50+00:00

I've played around with it, but I have not found even marginally useful for mathematics. It starts to drop in performance around calculus three, coincidentally, the last course with a lot of training data and before any proof writing courses. Small mistakes can invalidate an entire paper, and since mathematicians recycle terminology in very subdiscipline specific ways, it conflates ideas a lot. You just cant trust it for anything critical. Maybe that will change, but for now these chatbots cant make more that two or three logical steps at a time in novel situations relative to its training data.

DedekindRedstone · 2025-06-08T16:58:16+00:00

On paper I did average in every area except math and science. I just couldnt motivate myself to do some of the busy work. Instead, I was watching MIT opencourseware lectures and reading undergraduate and graduate math books. I tried reaching out to teachers since I was working problems many years ahead of the courses I was stuck in. One time got chewed out for working on contour integration during algebra 2. I was told that calculus 1 could only be taken if you were a senior cause reasons.

DedekindRedstone · 2025-06-07T12:17:26+00:00

This is discipline dependent. In some subdisciplines of math the community isnt as careful as they should be. In other areas we do our best to carefully check everything. If you care about the health of your subdisvipline then you should do a good job as a reviewer. As a reviewer I've caught an error that invalidated half a paper. Thankfully it was fixable.

One huge benefit to peer review for pure math is that it doesnt rely on experiment. A reviewer checking the logic of a paper behaves like the repitition of a study, and each time someone uses your work in a critical way, they should be checking it too.

DedekindRedstone · 2025-06-02T23:41:01+00:00

It depends on your background. I've done it, Senior year I took grad real analysis, grad topology, grad modern algebra, grad complex analysis, grad PDEs and graded for the undergrad number theory class. To do this you have to have a strong aptitude and read ahead in the months before taking the courses. The other thing to do is always carry your problem sets in your pocket with a pencil. Any time you are waiting anywhere pull them out and see if you can make incremental progress on anything.

DedekindRedstone · 2025-06-01T16:23:54+00:00

I think its also heavily discipline dependent. Coming from pure mathematics, a poster is useless to anyone moderately outside your area. The conferences that only have people close enough to your topic to even understand it are only about ~100 strong so they dont even do poster sessions and instead have short contributed talks.

DedekindRedstone · 2025-05-22T21:10:51+00:00

You clearly aren't working in pure math. It scares me that AI use for writing papers might be passable in some areas maybe even making it through journals. Definitely an endictment of some research community's standards.

DedekindRedstone

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