8:08

Ok I'll stop now

Hei man! I thought your comment to be very interesting but I didn't understand it very well. Could you please explain to me in detail how to get the pattern, or how to write a program that makes it, or something like that?

​@@adamsmainchannel3789 It is not really all that difficult, once figured out, but perhaps difficult to explain. Regardless I shall make and attempt. This subject first came to my attention, when I discovered the "Delta Swap" function, which is quite useful, especially when working with Bit Boards. U64 deltaSwap( U64 b, U64 mask, int delta ) { U64 x = (b ^ (b << delta)) & mask; return x ^ (x >> delta) ^ b; } /* NB: this function can be written in two ways, impacting the needed mask, depending on the direction of the bitshift. The result is essentially the same, just mirrored Chessprogramming DOT org is a great resource for learning more about this and much more.*/ I noticed a pattern in the Masks, and became very focused on completing it, so to speak, though I didn't really understand it. At some point I thought I had, but still, I didn't really see the connection. For some reason I decided to print the masks I had generate out in binary, and lo and behold, out popped the Sierpinski Triangle in one's and zero's. Quite amazing, but still, I didn't have the complete picture, and really it is only just recently that I have arrived at a point have a reasonable understanding. For bit widths of 2^n, there are 3^n patterns and accompanying delta values. though for use with the delta Swap, only (n^3-1)/2(+1) are actually useful, the +1 in parenthesis sort of a NULL pattern, which can be applied without any effect. The remain patterns performed the same task, just in reverse, which in this case is the same, or rather it doesn't make a different if you swap the first and the last bit, or the last and the first. The patterns can be created reasonably easily. let's take the example of bit width 8, or or n = 3. This tells us that there are 27 patterns in total. firstly, we need to generate the base patterns, and there are several ways of doing so. In this case the patterns are: mask / delta 0x0f, 4 0x33, 2 0x55, 1 and my favorite way of generating these is as follow: mask = -1; //-1 = all ones for( delta = 1<<(n-1); d; d >>= 1 ) { mask <<= delta; printf( "Mask: 0x%X, Delta %d ", mask, delta ); } lastly, you take these patterns and AND with each other, in all possible combinations, include the inverse of the masks, and the delta value becomes the sum of the base pattern delta values, negated in case on an inverse mask. Example for swapping the second to last with the seconds to first bit 0x0f & 0x33 & 0xaa (0x>>55) ---- mask, delta 0x02, 5 deltaSwap( 0b00000111, 0b00000010, 5 ) would then return 0b01000101 Other masks and delta values may be used, and the list generated is not exhaustive in that way, but I do believe that this list of patterns is complete relating to arriving at all the rotational symmetries of any Bit Board int any applicable dimension for the given bit width. for N = 3, that would be only 1 and 3 dimensions, while for 64 for bits, it would be 1, 2, 3 and 6. I suppose this is the best I can do just now, but I think it is all correct, and though it may sound complicated, it really isn't and I will do my best to answer any questions. Best regards.

At the moment, I don't let blocks go to 0. The minimum is 0.1. There is currently no good use for a 0 length block. The player can't stand on it, and as you noticed, dividing by 0 could make an infinite block which would break a lot of puzzles.

@@syllabusgames2681 Can't you make 0 with 1-1? What does 1-2 do? And if 0.1 is the minimum, what about 1/100

@@donaldhobson8873 The game just limits the block size, so if it sees a value between 0.1 and -0.1, it instead shows 0.1 or -0.1. 1-2 would show -1, but it would skip over the 0.1 to -0.1 range when animating. So yes, this system would say 1/100=0.1, but I don't plan to make it common for players to even have the pieces to make a 100 block since 100 meters is a long way to walk. The player should mostly be doing whole number math with these blocks as actual equation solving is done with a different, more traditional math system.

@@syllabusgames2681 Sounds like you did a reasonable job covering the obvious edge cases. 🙂

Aw. I thought I finally made it quite enough. I guess it would be best to just have no music while I'm talking.

Sorry about that. This material is new to me too, which made it a little hard to plan things out. If you want to see how this stuff is applied to real problems, I have some pretty interesting videos linked in the description. Sadly, getting to that material in my video would have taken at least 10 more minutes of explaining 2d bi-infinite series, entropy, and likely a few other pieces of groundwork to built up to the examples rather than skipping to them, and I just didn’t have time. In the future, I will focus on topics I fully understand, so the videos should be significantly better structured and more complete.

It’s an interesting approach to teaching math, also using 3B1B's perspective of moving the entire number line. It’s certainly better than many games that teach the same material. Sadly though, I don’t think its approach would integrate well with other forms of gameplay if the system were used in a larger game since all solutions boil down to pressing one of a few buttons in the right order. Thank you for reminding me the game exists though. Its approach is a good perspective for teaching complex numbers if that’s something I end up covering. It certainly wasn't something I was thinking about when I made this video.

@@syllabusgames2681 the creators of Wuzzit Trouble, one of whom is a Stanford math professor who wrote a lot of pop-sci books about math, another one is John Romero, have some compelling ideas about how to make great learning games: web.stanford.edu/~kdevlin/Presentations/Symbol%20barrier.pdf

@@sergesolkatt Thanks! I hadn’t seen that before. I had a hard time finding anything on educational game theory that wasn’t ancient, so I’ll have to check out the book mentioned in the slides when I get a chance.

There is a reason, but not a good one. Most of the script was focused on A^N, so when we were looking for things to cut to get it done on time, we noticed bi-infinite series were only mentioned 2 or 3 times and didn't really connect to anything. I would like to have kept it, but as I was editing this together hours before it was due, I don't think we could have afforded to. But you are right; it belongs in this video. It just didn't fit. As for deleting the first symbol when shifting, while awkward, it is a real thing you have to deal with using singly-infinite series.

@@syllabusgames2681 Makes sense, it's a shame that these things have to get cut, but I understand it's necessary in the process of editing. Nevertheless, great video! :D

the main difference between the shift map on A^N and A^Z is that on A^Z the shift map is invertible, while on A^N the shift map is not invertible in general (due to deleting the first symbol). So if you are studying a dynamical system out in the wild which is not in general invertible, you might expect to be able to encode it using a symbolic system over N rather than Z. Another approach is to try to "extend" the function to a wider domain where it becomes invertible, then use the bi-infinite sequences to encode the dynamics of the extended map.

Thanks, but I'm not sure what you're asking. This was made in Unity using a bunch of script I wrote myself if that answers your question.

Thank you for the suggestions! Yours is the most useful feedback I have received, and I will try to avoid similar problems in the future. 1) There were defiantly more elegant ways to show some parts of the video. Like my explanation of decimal binary: I should have known not to have 5 numbers updating at once. 2) Yes. Rob (who wrote the script) mentioned I was pronouncing it wrong, but after listening to some clips of it being said, I couldn’t hear a difference and just left it. And of course, this was mere hours before it was due. 3) That is a good point. I should have made the windows larger on screen instead of introducing them on a 20+ symbol example shift. At 360p, the window’s sides are probably 2 pixels across.

@@syllabusgames2681 Honest answers. I'm looking forward to more of your work in the future.

That sounds interesting. It’s good to hear someone else thinking of entering the ‘real educational games’ space, and I wish you luck. I really need to remake this video since I’ve stopped updating the list and decided to focus more on making 1 game rather than a lot of little ones. My mission’s the same, but the details are out of date.

Yes, that would have been nice, but the video builds up to about the point where we could start talking about examples and then I ran out of time. We have a brief cellular automata demo, but those are much more interesting in 2d, which we also didn’t have time to get into. Symbolic dynamics is similar to general group theory in that it is a framework you can shift a problem into to get a different perspective or to make things easier to work with. There are also some applications where symbolic dynamics is generally the starting framework, for example: Wave function collapse kzbin.info/www/bejne/aITYp4JqfM5qq7s , kzbin.info/www/bejne/aGGueYF3bs-Hqac Cellular automata kzbin.info/www/bejne/jl7MhISHnLSXZ6M Tiling spaces kzbin.info/www/bejne/amnWdKtjrKemaZY Markov chains I hope that helps.

@@syllabusgames2681 I watched the video hoping for some insight on graph paths or strings to solve some weird problems I currently solve other ways