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All of wizardcheetah's Comments + Replies

Gödel's Legacy: A game without end
wizardcheetah40

I have LW in my RSS reader. I can't see that you wrote the article until I open it in a browser.

This is a technical comment about the site. But yours is also the article that was interesting enough for me to care enough about who wrote it.

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Gödel's Legacy: A game without end
wizardcheetah10

The rss seems not to have the by line. I don't know the proper place for this comment.

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2Hazard
I'm not sure what this means. Is this a question about if I'd prefer comments on LW instead of my other site? LW, since my other site has no comments section.
On why mathematics appear to be non-cosmic
wizardcheetah20

I'm interested to know if you think this is an argument for cosmic math. Even if you are not convinced by it I am still interested to know if it is arguing against your position of anthropic math.

Consider 'momentum'. It is a concept that comes straight out of math. The only reason momentum is named is because it is conserved. You have a system, you do some direct measurements, and combine those measurements into a derived measure of momentum, m1. You keep the system closed, but otherwise do a bunch of whacky stuff to the system and you mea... (read more)

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1KyriakosCH
If those aliens are able to understand notions such as momentum, it would be because they can (in whatever way; sense or other) understand more fundamental notions which may be non-cosmic. Some good examples of such notions, from Eleatic philosophy (Parmenides, Zeno etc) are size, form, position, movement (change) and time. To a human, those ideas tie to something evident. An alien may not have them at all. An alien closely resembling humans may have them (as well as math).
On why mathematics appear to be non-cosmic
wizardcheetah20

So you are comparing math to a pursuit that is clearly an exploration of the human mind like graphic design or other arts. But I am still fuzzy on the 'why'? I can share that wild crows, too, can count up to 4. But because I am not clear on your why I'm not sure how this observation will affect you. It shows that there are at least some part of math that are useful to non-humans. But perhaps you are referring to more sophisticated math systems like ZFC set theory, in which case the crows don't have a say.

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2KyriakosCH
Indeed, crows are a good example of non-human creatures that use something which may be identified as math (crows have been observed to effectively even notice the -its practical manifestation, obviously - law of displacement of liquids :) ) I used human as a synecdoche here, that is chose the most prominent creature we know that uses math, to stand for all that (to some degree) do. Even if we accept that crows or other creatures have a similar link (itself debatable) it still would link math to dna found on our planet. My suspicion is that what we identify as math is a manifestation of relations, sequences or outcomes of dna, more easily observable in human self-reflection and sense (which is why I mentioned the shells we see in the form approximating the golden ratio spiral). In essence my suspicion is that math is tied to specific dna-to-conscious animal logistics, and serves as a kind of interface between the deep mind and consciousness, parts of which are occasionally brought up and examined more rigorously. (humans being the species which is more apt to self-reflection, makes us likely the main one here to be conscious of math concepts). I am not of the view that math is cosmic. Approaching this philosophically, it basically connotes that the external world is not mathematical, but because human examination of phenomena in scientific manner presupposes use of the human mind it inevitably is examined through math. One could hypothesize the existence of some other field, non-human, which is equally applicable to the study of the cosmos, and possibly some intelligent species of alien uses that, with compatibility with math being probably non existent.
On why mathematics appear to be non-cosmic
wizardcheetah20

Why does this matter? It felt like it was missing.

Is your question well formed? I'm not sure what a proof would demonstrate.

Have you considered the original purposes of math? My understanding is that it was for accounting, rather than elaborating on axioms.

Newton was the first to try to model the universe mathematically. Others had taken quantitative observations and even noted that specific things in nature could be modelled with math. But Newton was the one that sought and found universal laws that could be expressed in math, like his law of universal gravitation.


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2KyriakosCH
Thanks for the reply. I think that it does matter, because if math is indeed anthropic then it should follow that humans are in effect bringing to light parts of our own mental world. It isn't a discovery of principles of the cosmos, but of how any principles (to the degree they exist in parts of the cosmos) are translated by our mentality. I do find it a little poetic, in that if true it is a bit like using parts of yourself so as to "move" about, and special kind of "movement" requires special knowledge of something still only human. To use another common metaphor: people who are born blind have no sense of how the world looks. They do come up with theories. To a degree those theories, coupled with sensory routines (counting steps to known routes, hearing and noticing smells) provide a personal model of some environment, translated in their own way. Yet the actual phenomenon, the visible world, is not available. Likewise, it seems that math is not part of anything external, and is an own, human tool, composed of particularly human ingredients and enough to model something of the world that it may allow quite complicated movement through it (including space travel).