Pinned toot

This predates my Mastodon accounts but it ought to be on here so here it is: my interactive blog about the domino computer.

andrewt.net/maths/domputer/

This is excellent. It'd make an amazing bang-bang-bang MathsJam talk but the half-hour version is also engaging and fun.

youtu.be/_hjRvZYkAgA

Spoilery discussion of my solution 

Then I wrote the N=8 version in binary and it clicked and I felt simultaneously like a genius and an idiot.

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Spoilery discussion of my solution 

Then I drew out some coloured tesseracts for low-N cases and that worked well. I found you could step up to the next solution by pulling out a copy of the solution into some new dimension, giving it N new colours, and then pulling out as many permuted versions as you need to fill in the missing flips β€” but it didn't give me an algorithm to devise the permutations.

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Spoilery discussion of my solution 

I got hung up for ages on parity β€” because every possible arrangement you can reach by flipping one coin has the same parity, the 8x8 chessboard can be modelled as colouring a 63-dimensional cube, rather than a 64D one. Somehow I thought the loss of that one dimension would be more useful than the nice factorisability of 64. No idea why. And you can get to it that way but it's inelegant.

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Finally cracked this puzzle over lunch today. Very satisfying, I think it's the first one of these Big Hard Logic Puzzles I've solved start to finish on my own.

This also means I'm no longer messing up Matt's viewer retention stats from having paused it a week ago pretty near the beginning. I'd be interested to see the drop-off in the graph at the point when they say "pause the video now and have a go at it".

youtube.com/watch?v=as7Gkm7Y7h

I've had at least two marketing emails today from companies suggesting I use their products to cheer myself up today but carefully not mentioning any particular calendar-based reason for doing so.

so, how do you solve operator precedence? do you encode it in the grammar? do you use Pratt parsing? hell no

There's a great song lyric in the fact that anything to the power of love gives unity.

@andrewt As if this weren't all confusing enough, I believe the set of points depicted here is what's technically known as collielinear.

@andrewt It's the prefix col- which sometimes occurs in latin-derived words instead of co- or com- with base words that begin with an 'l'. You see it in "collateral" and "colloquial" and even in "college" and "collegial." That said, I think the one-l version, "colinear" is widely accepted as correct these days.

OK so today all the available evidence is telling me that the maths word for "on the same line" is "collinear" with two Ls and it's pronounced like it's spelled, like it's about Colin's ear, and just what the hell? I've been writing and saying "colinear" and just what is this?

Someone posted a gif of this effect on birdsite and I wanted to understand it so I've built it as a space-warping raymarcher.

Its some lovely maths that I think I *mostly* understand now:

shadertoy.com/view/3t2Xzy

A problem shared is equal to the sum of the problems on the other two sides.

@11011110 @andrewt fun fact. there's an exact formula for how many x,y satisfy xΒ²+yΒ²=n. it's 4 times (the number of factors of n of the form 4k+1 - the number of factors of n of the form 4k+3). another fun fact: this ties into the average being Ο€ through the Taylor expansion of arctan(1)=Ο€/4

My latest bloggy thing:

solipsys.co.uk/new/TheSideways

As always, comments, thoughts, criticisms, and feedback, all welcome.

Have to say that this "one blog post per week" is a brutal schedule.

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