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I've always thought math as we know it is a result of both deep underlying relationships between natural constructs and how we perceive them. For example, a spe
by hliyan 7y ago
I've always thought math as we know it is a result of both deep underlying relationships between natural constructs and how we perceive them. For example, a species who has no sense of vision will not develop geometry the same way we would. A species that has a sense of vision that also includes a direct distance perception (as opposed to our stereoscopic vision) will probably come up with a very different form of geometry.
Though I'd like to think that most species would come up with some version of calculus, even though the notation will be obviously different. Afterall, two of our own species did so independently.
- Kaiyou 7y agoCombining the words "most" and "species" feels a little bit silly. Among all the millions of species on this planet only humans have displayed the intelligence necessary to contemplate any of this.
- ableal 7y ago> on this planet Location was not specified ...
- foldr 7y agoThat's only true if you limit this to conscious thought. Lots of organisms perform impressively complex calculations. The desert ant odometer is one classic example: https://jeb.biologists.org/content/210/2/198 https://jeb.biologists.org/content/210/2/198
- Phenomenit 7y agoI've always figured it's our visions ability to perceive wholes, one of something. A clear conceptual border between two entities.
- hliyan 7y agoYes, but it's possible to perceive distict objects without vision, except the separation is in time, rather than space. Or, depends on the number of sense organs available (e.g. a blind person can sense two different objects simultaneously by holding one in each hand).
- Phenomenit 7y agoAgreed, I wonder if the same amount of abstract concept would be possible though, can you feel a graph? could you do trigonometry with just hearing and sense of touch?
- pm321 7y ago"could you do trigonometry with just hearing and sense of touch?" Can you get data on this from a Monte Carlo method of study on match play between sighted and blind players playing go and chess at distance and blind which requires a mental model of the board state and translations?
- jbotz 7y ago"two of our own species [discovered calculus]"..? Which two species are those? I assume by "own own" you mean Terran species, and one of them is Homo Sapiens, which is the other one? Really curious...
- deleted 7y ago[deleted]
- red75prime 7y agoLeibniz and Newton. Two [members] of our own species.
- sunstone 7y agoAnd Archimedes makes three.
- bregma 7y agoTake your stinking paws off me you damn dirty ape!
- jerf 7y agoProbably Homo Econimus. If Homo Econimus is good at one thing, it's math, to the exclusion of pretty much everything else.
- satori99 7y agoDo Dogs Know Calculus? http://www.math.pitt.edu/~bard/bardware/classes/0220/dkc.pdf http://www.math.pitt.edu/~bard/bardware/classes/0220/dkc.pdf
- phaemon 7y agoAnd yet, most blind mathematicians are geometers, which suggests your theory is incorrect.
- deleted 7y ago[deleted]
- used_noise 7y agoI'm not convinced that blind mathematicians count as their own species, nor that they echolocate, and so it doesn't seem to say much about his theory one way or the other.
- Koshkin 7y ago> nor that they echolocate How can you be sure?
- red75prime 7y agoHumans can learn/be taught echolocation. https://en.wikipedia.org/wiki/Human_echolocation https://en.wikipedia.org/wiki/Human_echolocation
- cossatot 7y agoWe could perhaps modify the theory, thinking of the mechanics of research. Progress is made by an individual in the niches where others have not managed yet. Therefore the advantage in geometry for a blind mathematician may be in a different mental model of spaces. It is not surprising at all that almost all blind mathematicians are geometers. The spatial intuition that sighted people have is based on the image of the world that is projected on their retinas; thus it is a two (and not three) dimensional image that is analysed in the brain of a sighted person. A blind person’s spatial intuition on the other hand, is primarily the result of tile and operational experience. It is also deeper – in the literal as well as the metaphorical sense. […] recent biomathematical studies have shown that the deepest mathematical structures, such as topological structures, are innate, whereas finer structures, such as linear structures are acquired. Thus, at first, the blind person who regains his sight does not distinguish a square from a circle: He only sees their topological equivalence. In contrast, he immediately sees that a torus is not a sphere […] This is a quote from a book by Alexei Sossinsky, quoted here: https://onionesquereality.wordpress.com/2011/07/31/blind-geometers/ https://onionesquereality.wordpress.com/2011/07/31/blind-geo...
- DeathArrow 7y agoMaybe vision is helpful with elementary geometry. I don't know how vision would help with differential geometry, geometry of affine spaces, topology, algebraic geometry. Maybe visualization is more helpful, but you can visualize things without seeing. A sense of depth and distance, or any kind of metric is helpful, and senses like vision and hearing might be helpful in forming that, but I'm not sure they are required. From another point of view, math theories are congruent, and you can explain the same things without using geometry, but using algebra, or differential equations or number theory and so on. You certainly can explain any math concept using just modern set theory - maybe it is not the most convenient thing to do.
- Koshkin 7y agoCategory theory is thoroughly visual, though.
- deleted 7y ago[deleted]
- sorokod 7y agoA species that has a sense of vision that also includes a direct distance perception (as opposed to our stereoscopic vision) will probably come up with a very different form of geometry. Except once axioms have been fixed, the resulting geometry will be the same wether you perceive reality via visible light or echolocation.
- henrik_w 7y agoI really liked this perspective from Bartosz Milewski in this (very good) podcast episode: mathematics is not inherent to the world, it is inherent to the human brain (paraphrased, around minute 32 in the episode) https://corecursive.com/035-bartosz-milewski-category-theory/ https://corecursive.com/035-bartosz-milewski-category-theory...
- StandardFuture 7y agoAnd really one of the biggest pieces of proof of this is that some of the earliest mathematics developed was planar geometry. But, planar geometry (primarily involving triangles and squares) does not actually exist in nature. Which means that planar geometry is an approximation technique developed by the brain in order to begin to understand the actual much more complex geometries that appear in the real world. This also suggests that mathematics is 100% constructed by the human brain, even if it is highly-influenced by relationships found in the physical world. But, this makes sense because we really don't ask the same question about human language. We almost never ask: is human language constructed or discovered?
- DeathArrow 7y ago>This also suggests that mathematics is 100% constructed by the human brain, even if it is highly-influenced by relationships found in the physical world. As I see it, mathematics is both discovered and invented. We can model every existing thing in every possible world using math. Even if both the set of all things that might exist and all possible mathematical constructions are infinite, the later is larger. That's because we can also construct mathematical models of things that doesn't exist. So it looks that from the set of all possible mathematical constructions, we extracted a subset that maps to objects in reality. That looks like a discovery process. But we also constructed mathematical models of things that don't have corespondents in reality, so that much be more of an invention process. Let's pretend for a bit that we forget all what we know and tomorrow we will start inventing things again. Or that a species of aliens start fresh on a planet. The mathematic theories and notions we and the aliens might discover, build or invent might be different than the theories and notions we know today but would probably be equivalent. That suggests that mathematics just exists somewhere in its own world waiting to be discovered.
- lazyant 7y agoNot exactly the same but 2-dimensional beings on a curved surface can discover the 3rd dimension using math, we did this proof in a differential geometry class.
- lavp 7y agoI would love to see a proof of it if you happen to have it!
- lazyant 7y agohttps://fsw01.bcc.cuny.edu/luis.fernandez01/web/texts/dgcs.pdf https://fsw01.bcc.cuny.edu/luis.fernandez01/web/texts/dgcs.p... Ctrl-F for "2D" (2-dimensional creatures), although I can't find the "discovery", maybe I remember it wrong. Btw, this was one of the mindfucks I learned studying physics. Other ones are: - dimensional analysis: checking if formulas can be wrong, and more importantly, finding formulas (eg, period of a pendulum) just by analyzing units that can be involved (no constants obv) - similarly, rate of growths in dimensions: why giants can't exist (bone resistance is proportional to section area and load (weight) is proportional to volume - Conservation laws derive easily from symmetries (energy from invariance in time, momentum from invariance in direction etc)
- lavp 7y agoThis is brilliant, thank you!
- Koshkin 7y agoI think you may be talking about the curvature of the surface (the Riemann tensor). It is intrinsic, i.e. does not depend on the notion of the surface being embedded into a higher-dimensional space.
- SkyBelow 7y agoAssuming a species is intelligent enough to discover math, if they have some significantly different way of experiencing the world I think they would take a different path but would eventually reach the same destination we are heading towards, likely merging with us by the point we are at now. I could see the layman understanding of geometry being quite different than ours, limited by their own visual system. But their mathematicians and our mathematicians would discover the same math, through different paths and perhaps with different strengths and weaknesses and a different path of educating budding mathematicians from the grade school level to the post doc level.