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.
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.
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 meaure the momentum again, m2. You will find that m1-m2 = 0. If we go anywhere in the universe we will find the same observation holds true.
If we made contact with ET’s that have progressed to primitive farmers however far humans made it before doing math. If we teach them to do the observations they will find the same phenomenon. If we left them to develop on their own then is there some part of that process that they would be incapable or unmotivated to do?
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).
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.
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.
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 meaure the momentum again, m2. You will find that m1-m2 = 0. If we go anywhere in the universe we will find the same observation holds true.
If we made contact with ET’s that have progressed to primitive farmers however far humans made it before doing math. If we teach them to do the observations they will find the same phenomenon. If we left them to develop on their own then is there some part of that process that they would be incapable or unmotivated to do?
This may be my last contribution.
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).