hmm... AK and margin lead me to Vereshchagin and Vitanyi, Kolmogorov’s Structure Functions and Model Selection (ca. 2002) — might this be something you have opinions on, or should I ask Hutter instead?
https://arxiv.org/pdf/cs/0204037
(the description in the abstract of the structure function sounds suspiciously like a galois connection)
You may not agree that facts are better than opinions, but here is one: Aaronson-Carroll’s paper on sophistication, downstream of your link,
is now 10 years’ in the making..
If you manage to access Hutter, let me know if I already know your public key ;)
Marcus and Jürgen introduced me to the notion that the limes marks a node (corresponding to the second eigenvector?) on the Chladni plate of germany; on the southern side, the dot product (with this "barbarianism" eigenvector) has a negative value.
Lagniappe: Grund(Bläbst), Feuer am Limes (1987)
Not doubting that the confoederati were always destined to become Men of Culture!
Just observing that cultural boundaries might be interesting, even if the interiors might not be[0]
Should we close the Rao-Gelman thread then, or are you still working on it?
[0] no time or battery to source out a citation, there was an american (californian?) accusation that the helvetics are only capable of inventing cuckoo clocks
Edit: https://skeptics.stackexchange.com/questions/2587/did-the-sw...
Edit edit: you have to admit M. Kowalski was abit trigger-happy in casting aspersions on Mr Quid? Otoh a flatlander might be blunt but also in their own way circumspect?
Being innocent of the ways of MO, I'm not going to judge sig. Quid either way.
For flatlanders, after reading https://blogs.ethz.ch/kowalski/2015/04/11/worms-brains-and-g... I now worry that procrustean restriction to planarity could be detrimental to their neural networks.
(the 1D graphs, aka the total orders, have no expanders, but on the flip side, that's probably why prime ideals and ultrafilters are so effective?)
EDIT: On Silver's River, a few footnotes on Ez.47:
47:10 In a groysn taykh khapt men groyse fish.
47:22 anticipating Ruth/רוּת?
Yes
They might have discovered that taykh-optimizing the sisyphean is itself sisyphean..
taykh? (Q. what do you call a strawberry from Bretagne? A. Une freizh)
Right now I'm going down the rabbit hole of expander graphs (aha, these also have a spectral gap?), but soon I shall have some bandwidth for coarse-graining coffee automata.
(I doubt you have my public key, but I fear that were you to take the inference closure of our convos and some gumshoe work, you could easily have 33 bits worth of identity)
Lagniappe: https://blogs.ethz.ch/kowalski/zazie-au-pot-de-these/ (I hope Zazie's ultimate commentary has not given her uncle a complex)
Taykh = river, as in Yez 47,12/nathaniel silber (shtetl = … )
Tonton = pork (osaka slang)
So, an algebraic exercise for me, a geometric one for you, and a quantum for both?
Geometric, or even philosophical?
Do I understand correctly that if we were to attempt to explain Kolmogorov Sophistication to Aristotle, we would say "the sophistication of `x` is the smallest essence over all proper[0] descriptions of x by, first[1] its essence, and then[2] its specific accidents"?
Intuitively, this would make sense, because as glass bead game players we are drawn to (beads whose cane was also formed from)* beads. As Körner would say, the height of distinction for a mathematician is to have, not an eponymous theorem, but an eponymous lemma.
[0] I don't understand what constitutes a proper description here yet, but am currently assuming it has to do with lying on a subsumption frontier, otherwise the trivial model would always be minimal.
[1] I think this has to be noncommutative, for otherwise we'd waste description bits on labelling the accidents? Compare canonical Huffman. (.a Lojban)
[2] see also Linnaeus
[0] not sure what you (or I, even) mean here, would the earlier bead of ultrafilters (& ultrametrics) be relevant in dispelling your discomfort?
[1] yes
[2] Linnaeus?
[2] Nomenclature binomiale
(compare the "biped, featherless — with broad nails")