Trivia

MSN news continues to throw out the odd bit of trivia of interest, that is to say things which catch my eye when I open a new window in MS Edge, something I typically do many times every day.

The first bit was to do with something called Dedekind numbers, in particular with the computation of the tenth such number, otherwise D(9), all 41 digits of it. Tenth rather than ninth because the series starts at D(0). The item is at reference 1, the very up-to-date Wikipedia entry for such numbers is at reference 2, and one of the two computations that have surfaced is at reference 3. I got as far as working out what an antichain was.

I wonder whether I will ever come across a problem where knowing the value of such a number for some non trivial value of the argument would be of use?

Not impossible, as partially ordered sets - the context in which antichains are defined - are important in category theory, a theory at which I had a go a few weeks ago. An effort which I might say has yet to bear fruit, in the sense of having some understanding of what the point of category theory is, despite its cropping up at the intersection of programming languages, logic and algebra, the first of which I once knew something about and the last two of which are branches of mathematics in which I once took an undergraduate interest.

While the image above was offered by the Daily Mirror as an intelligence test. Those with big IQ's can find the lady in nine seconds or less. I did not time myself, but I think it was of that order.

A challenge for Google's image processing systems would be to generate such an image, perhaps given a few clues. Something like 'find the heron near the pond'. I think my artistic uncle would have been able to pull off such a trick, at least for clues that fell within his area of competence. His work did not include, for example, much in the way of either animals or people. Much keener on plants, boats and modest country buildings.

PS 1: there is something odd about the link at reference 1b, other than its length that is. Microsoft have included some twiddle in it which disturbs the normal flow, no doubt for cunning reasons of their own.

PS 2: it so happened that after breakfast I came across another vision game. Fixate on the black dot in the snap above (it will work better if you click to enlarge) for a minute or so, then switch to the white dot. One eye or two? All very interesting. Image lifted from reference 4.

References

Reference 1a: Mathematicians finally identify 'seemingly impossible' number after 32 years, thanks to supercomputers - Harry Baker, Live Science - 2023.

Reference 1b: https://www.msn.com/en-gb/entertainment/news/mathematicians-finally-identify-seemingly-impossible-number-after-32-years-thanks-to-supercomputers/ar-AA1dIZhI?ocid=msedgntp&cvid=89c8e95dfd4b44888e05f9d3ffb4de9c&ei=17.

Reference 2: https://en.wikipedia.org/wiki/Dedekind_number.

Reference 3a: A computation of the ninth Dedekind number - Christian Jäkel - 2023.

Reference 3b: https://arxiv.org/pdf/2304.00895v2.pdf.

Reference 4: Reference 9: The role of fixational eye movements in visual perception – Susana Martinez-Conde, Stephen L. Macknik,  David H. Hubel – 2004.