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Re: [math-fun] Alive or not
by Steve Witham 18 May '20

18 May '20

From: James Buddenhagen <jbuddenh(a)gmail.com> Date: 5/17/20, 11:22 AM > Perhaps alive/dead is a false dichotomy. At best it there is a line it is > blurry. > See: https://www.scientificamerican.com/article/are viruses-alive-2004/ Maybe seeking the key to the distinction is a remnant of vitalism, or of the ages-old bad mental habits that led people to find themselves clinging to elan vital, the non-material substance that had to exist. It was like purified wistfulness. The probabilistic, informational, and thermodynamic definitions of life, or the more DSM-V-like lists of required features, sort of but don't really capture just what we mean. The bad mental habit is roughly to think as if any human concept comes from heaven, and so there must be a perfect form of it. Mathematicians can think of (e.g.) numbers as real without embarrassment because we have found workable kinds of perfection to work towards. --Steve

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Re: [math-fun] Alive or not
by Dan Asimov 18 May '20

18 May '20

For the past three or four years I've been seriously considering the question of how far does consciousness extend and — as ridiculous as it may sound, — have concluded that there is nothing in the universe that doesn't possess at least a very, very tiny degree of consciousness. My main reasoning has been based on continuity and my belief that consciousness could not possibly have suddenly sprung into existence at time t = t_0 after not existing whatsoever for time t < t_0. This is strange for me to admit to, for I don't possess even the faintest belief in anything supernatural. Especially since my thoughts on the matter suggest that masses like atoms, clouds, stars, and galaxies each possess some sort of unified consciousness. —Dan

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Re: [math-fun] Alive or not
by Dan Asimov 18 May '20

18 May '20

Steve Witham wrote: ----- Mathematicians can think of (e.g.) numbers as real without embarrassment because we have found workable kinds of perfection to work towards. ----- I see numbers (and other mathematical constructs) as real for much the same reason as I see physics things as real: People all over the world have looked at these things and get the same reading. And I would fully expect that intelligent life anywhere else in the universe — should it exist — would get the very same reading of these things. —Dan

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[math-fun] Alive or not
by Hans Havermann 18 May '20

18 May '20

Some weeks ago I had occasion to correct someone for noting that SARS-CoV-2 lives on surfaces for however-many days. "Of course viruses are not technically alive," I suggested. Since then, every doctor and health professional on TV has used the same "lives on surfaces" that I disparaged! Just English usage I thought to myself. Randall Munroe has now added to my dismay by placing viruses on the "alive" side of his latest xkcd: https://xkcd.com/2307/ I'll counter with the excellent recent Kurtzgesagt on the topic: https://www.youtube.com/watch?v=QImCld9YubE

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Re: [math-fun] Graph question
by Keith F. Lynch 16 May '20

16 May '20

Dan Asimov <dasimov(a)earthlink.net> wrote: > I'd like to see a proof of the claim (that the isomorphism of the > subgraphs taking 1?>1, 2?>2, 4?>5, 5?>6 does not extend to an > isomorphism G ?> G). Without my taking a position on whether my first solution is valid, here's an alternative solution: The countably infinite vertex set consists, not of all integers, but of all rationals except 0, 1, and -1. Each vertex x is connected to every other vertex except -x and 1/x.

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[math-fun] Different graph question
by Keith F. Lynch 16 May '20

16 May '20

Find a connected graph of girth 5 (i.e. no loops of size 3 or 4) in which every integer is a vertex, every vertex has the same valence, and every vertex is part of a loop of size 5. Yes, I have a solution, unless I'm confused. As usual, I'll give it in a week if I get no solutions or requests for more time.

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[math-fun] Complex modulo function?
by Kerry Mitchell 16 May '20

16 May '20

Hi all, Is there a standard, or at least, reasonable, definition of the modulo function for complex numbers? What I've come up with is: a mod b = r means a = qb + r, where q is the Gaussian integer that minimizes |r|, with |qb| <= |a|. Thanks for any guidance, Kerry

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Re: [math-fun] Complex modulo function?
by Keith F. Lynch 16 May '20

16 May '20

Kerry Mitchell <lkmitch(a)gmail.com> wrote: > Is there a standard, or at least, reasonable, definition of the > modulo function for complex numbers? I don't know if it's any kind of standard, but it has occurred to me that, modulo n^2+1, -1 has a real square root. For instance -1 is congruent to 9 mod 10, so i is 3 mod 10, and -i is 7 mod 10. (Or vice versa if you prefer.) Hence i+1 is 4 mod 10, etc. I don't know if this is useful for anything, but it doesn't seem to lead to any inconsistencies. Everyone's first thought when they learn about i is to ask what it *is*. To which I can answer that at least I know its last digit, which is 3. :-) Since no other power of 10 is 1 plus a square, I unfortunately can't find any other digits of i. The same is true in all other bases, thanks to Mihailescu's theorem (better known as Catalan's conjecture).

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[math-fun] Canway
by Bernie Cosell 16 May '20

16 May '20

Article in today's NYT: Travels with John Conway, in 258 Septillion Dimensions The Princeton mathemagician, who died in April, left an engaging legacy of numerical gamesmanship. https://www.nytimes.com/2020/05/16/science/john-conway-math.html /B\ Bernie Cosell bernie(a)fantasyfarm.com -- Too many people; too few sheep --

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Re: [math-fun] Extension of Game of Life
by Henry Baker 15 May '20

15 May '20

I really like the idea of a "quantum" version of Life! Has there been *any* research on Life played on a 2D surface of qubits? Perhaps Roger Penrose has considered these? At 04:53 PM 5/15/2020, Allan Wechsler wrote: >I just now convinced myself that the spooky blinker is a valid oscillator. > >On Tue, Apr 21, 2020 at 7:10 PM Allan Wechsler <acwacw(a)gmail.com> wrote: >> While musing about searching for Life patterns with particular properties, >> I had an idea for a Lifelike cellular automaton rule that surely must have >> been invented before. So I'm hoping somebody can give me references. >> >> The rule has three states. Two are Life's existing "dead" and "alive", and >> any situation involving only these states evolves exactly as in Life. >> >> The third state is like a quantum superposition of "dead" and "alive". >> Call it "spooky". >> >> The principle is this: a pattern P with spooky cells corresponds to a set >> L(P) of ordinary Life patterns. A Life pattern belongs to the set if it >> agrees with P on all non-spooky cells. >> >> A cell is alive in P', the successor of P, if for all patterns Q in L(P), >> it is alive in Q'. >> >> Similarly, it is dead in P' if it is always dead in Q' for all Q in L(P). >> >> A cell is spooky in P' in all other cases, that is, if it is sometimes >> alive and sometimes dead in Q' depending on the choice of Q from L(P). >> >> Spookiness is ignorance. Sometimes it disappears completely -- an isolated >> spooky cell in empty space dies is one step. >> >> This is a well-defined automaton, and its rules can be completely stated; >> an example is "a live cell with two live neighbors and one spooky neighbor >> will stay alive", an "a dead cell with three or more spooky neighbors and >> no live neighbors becomes spooky". >> >> Has anybody implemented this rule for Golly? (I am a Golly tyro and don't >> know the rule-specification language yet.) >> >> Does this rule have any non-trivial interesting patterns? Like -- does it >> have any oscillators involving spooky cells? Any spaceships? I know it has >> at least one still-life: the spooky block is stable.

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