May 2020 - mathfun@mailman.xmission.com

Re: [math-fun] Complex modulo function?
by Keith F. Lynch 19 May '20

19 May '20

Tomas Rokicki <rokicki(a)gmail.com> wrote: > Can't its last digit also be 7? No, that's the last digit of -i. :-) I did say, "Or vice versa if you prefer." The *second* thing everyone asks when they learn about i is which number is i and which is -i. Imagine the horror if they go through their whole mathematical career getting those two swapped. In quaternions, perhaps my i, j, and k are your j, k, and i, respectively. I've long been fascinated by such symmetries, in both math and physics. How can we know whether the Peano postulates are really referring to the integers rather than to, say, sevenths? How can we be sure we haven't gotten positive and negative charges swapped? Or that what we think is an E field isn't actually a B field, and vice versa; maybe magnetic monopoles are ubiquitous, and it's electric charges that don't exist. Brian Aldiss's novel _Cryptozoic_ had the premise that we're mistaken about the direction of time, i.e. that what we think of as the future is actually the past, and vice versa. If aliens are picking up our TV signals, how can they be sure they don't have left and right swapped? Maybe they've been watching all those "I Love Lucy" broadcasts backwards, and will have to go back and watch them again the right way around.

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Re: [math-fun] Alive or not
by Dan Asimov 19 May '20

19 May '20

Henry Baker wrote: ----- In junior high school in the early '60's, I grew a large variety of crystals for a science project. I concluded that my crystals met many/most definitions of "alive", hence the whole discussion was bogus. ----- Which whole discussion are you referring to? —Dan

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

18 May '20

> From: Dan Asimov <dasimov(a)earthlink.net> > Date: 5/18/20, 10:43 AM > To: math-fun <math-fun(a)mailman.xmission.com> > > For the past three or four years I've been seriously > considering the question of how far does consciousness > extend and Â— as ridiculous as it may sound, Â— have > concluded that there is nothing in the universe that > doesn't possess at least a very, very tiny degree of > consciousness. I would like consciousness to be something a little complicated and specific-- more complicated than a Universal Turing Machine, say. So for sure something simpler than the simplest physical UTM couldn't have it. And I think it would need some extra blank tape to write its diary on... which reminds me of Douglas Adams' whale whose thoughts we tune into as he comes to consciousness for the first time while on a crash course with a planet. My favorite take on consciousness is Michael Graziano's. Basically, that we are wired to be able to observe, model and control, in a low-res way, what we're paying attention to and relate that to the rest of what's going on. Like proprioceptive senses. One of Graziano's examples I like is *talking* about attention: What are you thinking about? Birds, I guess. Do you see what's just behind that bush? Oh, you mean the bluejay-- yes, I've been watching it too-- what is it doing? That's what *I* can't figure out. The point of talking-about-attention is that we're a species that teach each other how to direct our attention, how to catch our attention getting caught by things and either meta-think about that, or realize we're "getting distracted," etc. And also coordinate who's going to be paying attention to what. So how do we do this around an activity going on silently invisibly inside our heads? By being wired so that attention "is a thing." Anyway, compared to other ideas, it's a plausible subset of equipment and/or skills, not an infinite regress; it fills actual needs; and it makes sense of the way it feels if you ask me whether I'm conscious, and I look around and say "yes, it seems like it." (Which before always struck me as logically empty boasting.) By analogy, if you ask me whether I can grip things, with my eyes closed I could find something to grip, squeeze it, and say, "seems like it." I have nerves to tell my hand to grip, and nerves to tell what's going on there, and memories of gripping things. Likewise, wiring to control and monitor attention, and a familiarity with what it *feels like* to attend--it's not just an empty self-opinion. https://www.aeonmagazine.com/being-human/how-consciousness-works https://grazianolab.princeton.edu/publications/consciousness-engineered I have to admit I think about the Max Tegmark-style radical anthropic multiverse a lot. The universe must have one of the simplest sets of laws that admits of a scientist--somebody wondering about it. But that seems to build the laws of physics around, e.g., *my* awareness, or that plus "simplicity," what does it mean!?! Aargh! --Steve > 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.

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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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