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Meaningness's profile
David Chapman
David Chapman
David Chapman
@Meaningness

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David Chapman

@Meaningness

Better ways of thinking, feeling, and acting—around problems of meaning and meaninglessness; self and society; ethics, purpose, and value.

meaningness.com/about-my-sites
Joined September 2010

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    1. David Chapman‏ @Meaningness Apr 8
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      Replying to @postreptilian @St_Rev

      Yeah I dunno, there’s so much excitement about it that once every few months I feel like I ought to figure out what it’s about, but every time I spend half an hour looking at it, it seems highly unpromising and I set it aside again.

      1 reply 0 retweets 1 like
    2. David Chapman‏ @Meaningness Apr 8
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      Replying to @Meaningness @postreptilian @St_Rev

      E.g. it’s hard for me to imagine how homotopy, which is about continuous deformations of continuous functions, could give leverage in ToC, where nothing is continuous. Presumably I’m missing something because I haven’t even bothered to look this up, but

      2 replies 0 retweets 0 likes
    3. Kabelo Moiloa‏ @11kilobytes Apr 8
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      Replying to @Meaningness @postreptilian @St_Rev

      To make an analogy: Euclid's Axioms :: Real Cartesian Plane as Homotopy Type Theory :: Spaces of various sorts. We work up to homotopy equivalence, so all the data you care about can be presented combinatorially...

      1 reply 0 retweets 0 likes
    4. Kabelo Moiloa‏ @11kilobytes Apr 8
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      Replying to @11kilobytes @Meaningness and

      e.g. the HoTT "circle" is freely generated by a point and a primitive-axiomatic path between that point and itself. This _means_, e.g. that to map it somewhere else is to give a loop there.

      2 replies 0 retweets 0 likes
    5. David Chapman‏ @Meaningness Apr 8
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      Replying to @11kilobytes @postreptilian @St_Rev

      I’m sorry, without reading up on a bunch of definitions, I don’t know what that means. How does homotopy apply to computation, in which all the “spaces” are at-most-countable sets of discrete objects? What is the topology?

      1 reply 0 retweets 1 like
    6. Kabelo Moiloa‏ @11kilobytes Apr 8
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      Replying to @Meaningness @postreptilian @St_Rev

      Here's an analogy that might help: HoTT is to topology as Euclid's axioms are to the real coordinate plane. In Euclid's axioms we talk about points, by saying what you can do with them (construct lines, circles, intersections, etc.) instead of talking about the reals at all.

      1 reply 0 retweets 0 likes
    7. Kabelo Moiloa‏ @11kilobytes Apr 8
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      Replying to @11kilobytes @Meaningness and

      Similarly in HoTT we have a primitive Paths-Between(x, y) type for any x, y in a type A. It is primarily defined by the axiom that if you want to define something for arbitrary paths with unconstrained endpoints, you can assume that you are dealing with a constant path.

      1 reply 0 retweets 0 likes
    8. Kabelo Moiloa‏ @11kilobytes Apr 8
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      Replying to @11kilobytes @Meaningness and

      This axiomatises the "squishiness" of topology.

      1 reply 0 retweets 0 likes
    9. Kabelo Moiloa‏ @11kilobytes Apr 8
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      Replying to @11kilobytes @Meaningness and

      Now there is a certain subdiscipline of topology called algebraic topology, which is all about "counting," topological features of a space such as its number of holes. HoTT is really interested in the features of topological spacs that are visible to algebraic topology.

      1 reply 0 retweets 1 like
    10. David Chapman‏ @Meaningness Apr 8
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      Replying to @11kilobytes @postreptilian @St_Rev

      Yes I get this in a vague way. I don’t think I’m going to get more without actually learning it, and I’m not motivated to do that because (so far) I haven’t seen that it is useful.

      1 reply 0 retweets 2 likes
      David Chapman‏ @Meaningness Apr 8
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      Replying to @Meaningness @11kilobytes and

      Also, everything I’ve seen seems like it could be done much more simply in the framework of undergraduate abstract algebra.

      1:13 PM - 8 Apr 2020
      • 1 Like
      • Kabelo Moiloa
      1 reply 0 retweets 1 like
        1. David Chapman‏ @Meaningness Apr 8
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          Replying to @Meaningness @11kilobytes and

          I appreciate your trying, though!

          0 replies 0 retweets 1 like
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