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Conceptual synaesthesia as cognitive literacy

madinamerica.com

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Re: Conceptual synaesthesia as cognitive literacy

#11

Post by 082349872349872 »

gsf_emergency_2 wrote: post #3
082349872349872 wrote: post #2

Hey, sorry to not be on HN much these days, but beyond all the distractions in the world of atoms, I was chatting with DeepThink about ways to convert 大鬧天宮 to 连续天宫 (using Scott domain theory to enforce "as below, so above" semantics), and boy did it ever riff on the synaesthetic combination, producing an outline of a cantonese opera in the language of topos theory... Anyway, reminded me I should check in on what you'…

> sorry to not be on HN much these days I envy you, actually :) Actual sheets, or just a metaphor;) I wonder what explains the western obsession with Han-Uman when Rot3K has always been more salient, & still fiction

> Rot3K

Who needs 貂蝉 when we have 英子ちゃん?

(it's not just a western obsession; Deepthink's suggestion for the album cover of a Fonsi vs. Yongming remix "Dale despacito… 愛の火計！" included a photobombing 孙悟空 — only his magical staff is a glowstick)

EDIT: oops, think I hit some guardrails. Inspired by the parallel apartment balcony scenes, I started to get output for "Ya Boy Yongming" remixed with "Ivan Vasilievich Changes His Profession", but then it all disappeared to be replaced by "Sorry, that's beyond my current scope. Let’s talk about something else." What's wrong with asking for party boys crossed with Party boys? «Танцуют все!»

Re: Conceptual synaesthesia as cognitive literacy

#12

Post by 082349872349872 »

gsf_emergency_2 wrote: post #10
082349872349872 wrote: post #9

Earlier quoted context omitted.

Approximate is a verb in this context and not an adjective. The idea under discussion goes roughly like this: the classical ("earthly") Turing Machine has an infinite tape, but each square can only be marked with a selection from a finite number of symbols; let us suppose angels —being more perfect than humans— can discriminate among a (countably) infinite number of symbols, so their ("celestial") turing machines cou…

Continuity does not buy angels (as represented by wukong?) finer distinctions? He has to use the same equivalence (stability) classes? Or rather that he cannot express the distinction to mortals

AIUI, up until Scott, λ-calculus had mathematicians saying "yes, it works in practice, but can it ever work in theory?": say we have a universe of discourse D, and we want, per λ-calculus, to have functions D->D (D->D->D, etc.) be part of this universe of discourse. If D is a windowless monad, with a single object, we're ok: there's only 1 arrow (1^1) from 1 object to 1 object, namely the identity, so we just go ahead and identify it with the object. However, as soon as we have two objects in D, we have a problem: there are 4 arrows (2^2) from 2 objects to 2 objects, so even if we attempt to identify objects and functions we don't have enough for all the functions, and the problem only gets worse (N^N) as we have N>2 objects.

Scott's contribution was to cut down the cardinality of the function space: by restricting it to continuous functions (ie only those functions that have finite approximations, which is to say they don't do anything strange "at infinity") one not only gets what most people would admit is a reasonable model of computation, but -calculus then works in theory, as D->D can now fit inside of D.

What I was trying to explore (and maybe the trouble with asking an LLM about this sort of thing is that they're unlikely to push back hard enough?) is the notion that even given an "angelic turing machine", one still couldn't compute in a way than an earthly turing machine couldn't simulate.

Does that make sense?

Re: Conceptual synaesthesia as cognitive literacy

#13

Post by gsf_emergency_2 »

082349872349872 wrote: post #12
gsf_emergency_2 wrote: post #10

Earlier quoted context omitted.

Continuity does not buy angels (as represented by wukong?) finer distinctions? He has to use the same equivalence (stability) classes? Or rather that he cannot express the distinction to mortals

AIUI, up until Scott, λ-calculus had mathematicians saying "yes, it works in practice, but can it ever work in theory?": say we have a universe of discourse D, and we want, per λ-calculus, to have functions D->D (D->D->D, etc.) be part of this universe of discourse. If D is a windowless monad, with a single object, we're ok: there's only 1 arrow (1^1) from 1 object to 1 object, namely the identity, so we just go ahea…

Grad students Keye Martin & Lemmonier

https://arxiv.org/pdf/2406.07216

Seem to have had measurement problem right next to Scott continuity, -- & left it at that :)

If you want me to look at the details you've got to motivate me by telling what doesn't make sense to you (but ought to?)

Re: Conceptual synaesthesia as cognitive literacy

#14

Post by 082349872349872 »

gsf_emergency_2 wrote: post #13
082349872349872 wrote: post #12

Earlier quoted context omitted.

AIUI, up until Scott, λ-calculus had mathematicians saying "yes, it works in practice, but can it ever work in theory?": say we have a universe of discourse D, and we want, per λ-calculus, to have functions D->D (D->D->D, etc.) be part of this universe of discourse. If D is a windowless monad, with a single object, we're ok: there's only 1 arrow (1^1) from 1 object to 1 object, namely the identity, so we just go ahea…

Grad students Keye Martin & Lemmonier https://arxiv.org/pdf/2406.07216 Seem to have had measurement problem right next to Scott continuity, -- & left it at that :) If you want me to look at the details you've got to motivate me by telling what doesn't make sense to you (but ought to?)

in the priority heap... if you give me some pp's I'll bump it up

Re: Conceptual synaesthesia as cognitive literacy

#15

Post by gsf_emergency_2 »

082349872349872 wrote: post #14
gsf_emergency_2 wrote: post #13

Earlier quoted context omitted.

Grad students Keye Martin & Lemmonier https://arxiv.org/pdf/2406.07216 Seem to have had measurement problem right next to Scott continuity, -- & left it at that :) If you want me to look at the details you've got to motivate me by telling what doesn't make sense to you (but ought to?)

in the priority heap... if you give me some pp's I'll bump it up

Lemonnier only cites

pp22

A first approach to programming with quantum effects is the quantum λ-calculus [SV09]. Nevertheless, that language does not handle quantum programming as an algebraic effect, since it requires measurement into classical data to control the flow of execution.

pp23 1st para has more of the same

In the quantum λ-calculus, a qubit has to be measured before influencing the control of a program. These models are not of interest to this thesis, because the use of measurement breaks superposition, therefore it does not preserve the aforementioned quantum effect.

[SV09] Peter Selinger and Benoit Valiron. Quantum lambda calculus. Semantic techniques in quantum computation, pages 135–172, 2009.

Keye Martin: be right back (I didn't see much there either.)

in my own heap: one might be able to use Scott continuity to replace lemma 7?

https://arxiv.org/abs/2306.10072

pp6-10 "Corrupted geometric sum"

Pay attention to how the "control gates" (as in SV09) are invoked

pp7: The crucial step in Shor’s algorithm, after the quantum Fourier transform, is to take a quantum measurement, with the property that the probability of observing a state that is close to an integral multiple of 2^n/ω is high.

pp12 has this speculation

>At its most fundamental level, it is not permitted to ask the computing machine to scan a continuously deformed symbol from ξ to ζ, while a mathematical homotopy can easily be envisioned.

Re: Conceptual synaesthesia as cognitive literacy

#16

Post by gsf_emergency_2 »

082349872349872 wrote: post #14
gsf_emergency_2 wrote: post #13

Earlier quoted context omitted.

Grad students Keye Martin & Lemmonier https://arxiv.org/pdf/2406.07216 Seem to have had measurement problem right next to Scott continuity, -- & left it at that :) If you want me to look at the details you've got to motivate me by telling what doesn't make sense to you (but ought to?)

in the priority heap... if you give me some pp's I'll bump it up

Keye & Coecke

https://www.researchgate.net/publication/2843975_A_Partial_O...

pp80-82 Section 10.5.1 noise

Martin has an autobiographical chapter in the full book

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