Oscar Cunningham

@ianh@mastodon.social Nice! I was coming to the same conclusion myself. I worked out that there are only 12 possible arrangements of black/white around a face that don't have rotation symmetry. So we would need to use each one exactly once. In particular there will be a white face with only one black face touching it, and a black face with only one white face touching it. These sets of six faces can only overlap in a small number of ways. Then you can check that you can't fill in the remaining faces in any way that works.

Can you colour the faces of a dodecahedron black and white so that if you stand on one of the faces you can determine your position and orientation by looking at your face and the adjacent faces? #math #maths #mathematics

@robinhouston@mathstodon.xyz Octahedron wins!

@robinhouston@mathstodon.xyz The poll shows the total number of respondents. So you get five numbers and you want to know five numbers. Just do linear algebra.

@slava This is also related to the braid group on three strands, B₃ = .

@richardelwes @peterrowlett This is getting a bit advanced, but the best way to think about the lowest common multiple is that 'lowest' is meant in the sense of the divisibility ordering. So 0 isn't the lowest common multiple of any two numbers because it is in fact the highest number!

@maxpool@mathstodon.xyz @johncarlosbaez@mathstodon.xyz The numbers are even stronger for your argument than that. The $4000 figure is the average income of the bottom 50% of the income distribution. The average income of the bottom 50% of the wealth distribution will be much higher. It contains a bunch of high income first-worlders whose wealth hasn't yet exceeded their student loans.

@johncarlosbaez@mathstodon.xyz I think people in first-world countries should be giving much more money to those who most need it. But these articles (the ones Oxfam churns out about wealth inequality) are very misleading. Wealth is a slippery concept. One thing is the way that debt affects the measurement. The very poorest people in the world often have a high quality of life (fucking Alex Jones). You personally have more money than the poorest 30% of the world combined. If we took your money we could double their wealth (Alex Jones certainly deserves it). But I think the more fundamental problem is the way that future income is valued. Wealth in the form of stocks is counted based on the market value, which comes from the expected payout those stocks will give in the future. But future income from labour isn't included as 'wealth'. This makes the poor seem comparitively poorer than they really are. A friend of mine switched from being an employee to a self-employed contractor doing the same job. He pays himself minimum wage from his own company and takes the rest as dividends. Did he really become wealthy overnight through a mere administrative change? A fairer way to judge wealth is to convert everything to income. Imagine we took all of the wealth of the world's billionaires and combined it into one fund, with the interest split evenly between everyone on Earth. Each person would get about $150 per year. That would be a big help for the world's poorest (poorest in terms of consumption). But it's a much more moderate change than you might imagine from Oxfam's headlines.

Little Caesars: It's hot and it's ready. Me: Is it good? Little Caesars: It's HOT. And it's READY. @markusde (Source: https://x.com/danblackroyd/status/996494614176542720)

@pianosaurus@c.im That's true. But it's a big improvement just to know what meaning that register assigned to the symbol!

It looks like the ⍼ saga has finally ended!

The unicode character '⍼' was a mystery first noticed in 2022: https://ionathan.ch/2022/04/09/angzarr.html. It's in the Unicode standard as a mathematical symbol. But no one could find any examples of it having been used, and no one knew what it represented. It was like the only record of an extinct species, fossilized in the Unicode standard.

But now someone has found the document it originally came from! It represents the angle 'Azimuth', and the symbol probably comes from the path light takes through a sextant. https://ionathan.ch/2026/02/16/angzarr.html

(@johncarlosbaez@mathstodon.xyz might appreciate this symbol!)

@de_Jong_Tom @dwarn Cool. In particular, people sometimes define lattices in terms of their partial order, and sometimes in terms of their algebraic operations. So it's useful to know that we can prove they're discrete either way.

@dwarn I'm not an expert so this might be a stupid question, but does this also answer this question: https://mathoverflow.net/questions/161190/homotopy-theory-of-suplattices ? A suplattice is a semilattice with extra properties, so they must all be discrete. Like maybe we can't answer the precise question about model categories, but can we at least say that the 'Homotopy Theory of Suplattices' is trivial?

@julesh@mathstodon.xyz (https://oeis.org/A121273)

@kenshirriff@oldbytes.space Actually most of the data is in the black grid! This image shows how it works.

@nixCraft@mastodon.social Machine Learning requires an objective function that you are optimizing. This is known as 'test driven development'.