In other words, do we observe the Fibonacci or golden ratio spiral approximation on the external world because the external world itself is tied to math, or do we do so because we are tied to math in an even deeper way than we realize and could only project what we have inside of our mental world onto anything external?
I wasn’t clear on what this question meant, but the reason the Fibonacci sequence approximates the golden ratio becomes apparent upon seeing it’s closed form solution (which contains the golden ratio).
Hi, yes, I do not mean why the Fibonacci spiral approximates the Golden Spiral. I mean why we happen to see something very close to this pattern in some external objects (for example some shells of creatures) when it is a mathematical formation based on a specific sequence.
I referred to it to note that perhaps we project math onto the external world, including cases where we literally see a fully fledged math spiral.
There are other famous examples. Another is The Vitruvian Man (proportions of man by Vitruvius, as presented by DaVinci). One would be tempted to account for this by saying math is cosmic, yet it may just be it is anthropic and the result is a projection of patterns. That math is very important for us (both consciously and even more so unconsciously) seems certain; yet maybe it is not cosmic at all.
If we are projecting, then is this tendency one we developed (social) or one we inherited (evolution)? If it is evolutionary, then perhaps* if we ran into intelligent aliens (which evolved) they’d “have math” as well.
If it is a property of living things in the external world (which seems to be the case), then it may be the way they are (as opposed to a projection). And that may also be the result of evolution*. So we may be seeing such things as they are (readily) because we have a tendency to see patterns of certain forms, with the downside of occasionally seeing patterns where there are none as a consequence of this fitting.
*While evolution might “work the same way” in other places, what is specific to Earth isn’t super clear, and how much things generalize remains to be seen.
I will try to offer my reflection on the two matters you mentioned.
1)First of all whether this development may have been social. It would—to a degree—but if so then it would be a peculiar and prehistoric event:
If I was to guess, at some point (in deep prehistory) our ancestors could not yet be able to communicate using anything resembling a language, or even words. Prior to using words (or anything similar to words) prehistoric humans would only tenuously tie their inner world (thinking & feeling) to formulated or isolated notions. It is highly likely that logical thinking (by which I mean the basis of later formalization of logic, starting -at the latest- with Aristotle) wasn’t yet so prominent a part in the human mentality. It is not at all impossible, or even (in my view) that improbable that some degree of proto- rationalization had to occur so that prehistoric humans would manage to think and sense less of something less organized, and move towards becoming able to establish stable notions and consequently words and a language.
2) Secondly, this would be also inherited. I do suppose that ultimately math (by which I mean more complicated math than the one we currently are aware of) serves somewhat as a dna-to-consciousness interface. But even if this is so, due to point 1 it wouldn’t really connote mathematical parameters as being more important than other parameters in the human mind or overall organism.
But there is another point, regarding your post. I think that a non-mental object (for example any external object) cannot be identified as it actually is by the observer/the one who senses it. In philosophy there is a famous term, the so-called “thing-in-itself”. That term (used since ancient times) generally means that any object is picked up as having qualities depending on the observer’s own ability and means to identify qualities, and not because the actual object has to have those qualities or anything like them. The actual object is just there, but is not in singularity with the observer; the observer translates it through his/her own means (senses and thought). Your point about the object possibly having math inherently is interesting (I do understand you mean that its form is shaped due to actual, real properties, and those are just picked up by us), yet it should be supplemented with the note that even if the object (for example one of those shells) had properties itself which create that spiral and then we notice it, it would have to follow that either we noticed the spiral without distorting the thing-in-itself as an observer of it, or that we picked up some property which didn’t actually have any mathematical value but was (in some strange way) isomorphic to the spiral when translated for a human observer’s sensory organs. If the latter somehow was true then the external object had no mathematical property, and we picked up some math property because we seem to project math even in more ways than one. If the former was true then we are in singularity with the observed object and nothing is actually distinct in the cosmos (certainly anyone senses their own self as distinct from something external). And in both cases it would not connote that math are cosmic, given the case where math were part of the observed object would present a case where we are so full of illusions that we think (incorrectly in that case) ourselves distinct from a shell, when in “reality” we would not have been.
I do realize this may seem way too “philosophical” (and in a bad way). Philosophy has had problems since ancient times (this itself is already examined by Plato himself: how philosophy may seem very alienating and problematic). Yet the gist of the matter is that (in virtually all serious philosophers’ view) there is no reason to think that we as observers pick up any actual non-anthropic reality. We do pick up a translation of something, and this translation is enough to allow us to advance in various ways, including being able to build space-traveling rockets. This is so because we always stay within the translation, and to us the cosmos is witnessed in translation. But a translation of something is not in tautology with the thing itself. My own suspicion is that different intelligent species will not have compatible translations (because they would likely even lack fundamental notions we have; for example they may not sense space or movement or other parameters, and sense ones we cannot imagine. Intuitively I suspect even so alien a species could develop tech and science of a very high level).
I wasn’t clear on what this question meant, but the reason the Fibonacci sequence approximates the golden ratio becomes apparent upon seeing it’s closed form solution (which contains the golden ratio).
Hi, yes, I do not mean why the Fibonacci spiral approximates the Golden Spiral. I mean why we happen to see something very close to this pattern in some external objects (for example some shells of creatures) when it is a mathematical formation based on a specific sequence.
I referred to it to note that perhaps we project math onto the external world, including cases where we literally see a fully fledged math spiral.
There are other famous examples. Another is The Vitruvian Man (proportions of man by Vitruvius, as presented by DaVinci). One would be tempted to account for this by saying math is cosmic, yet it may just be it is anthropic and the result is a projection of patterns. That math is very important for us (both consciously and even more so unconsciously) seems certain; yet maybe it is not cosmic at all.
As for whether math “is cosmic” or not:
If we are projecting, then is this tendency one we developed (social) or one we inherited (evolution)? If it is evolutionary, then perhaps* if we ran into intelligent aliens (which evolved) they’d “have math” as well.
If it is a property of living things in the external world (which seems to be the case), then it may be the way they are (as opposed to a projection). And that may also be the result of evolution*. So we may be seeing such things as they are (readily) because we have a tendency to see patterns of certain forms, with the downside of occasionally seeing patterns where there are none as a consequence of this fitting.
*While evolution might “work the same way” in other places, what is specific to Earth isn’t super clear, and how much things generalize remains to be seen.
I will try to offer my reflection on the two matters you mentioned.
1)First of all whether this development may have been social. It would—to a degree—but if so then it would be a peculiar and prehistoric event:
If I was to guess, at some point (in deep prehistory) our ancestors could not yet be able to communicate using anything resembling a language, or even words. Prior to using words (or anything similar to words) prehistoric humans would only tenuously tie their inner world (thinking & feeling) to formulated or isolated notions. It is highly likely that logical thinking (by which I mean the basis of later formalization of logic, starting -at the latest- with Aristotle) wasn’t yet so prominent a part in the human mentality. It is not at all impossible, or even (in my view) that improbable that some degree of proto- rationalization had to occur so that prehistoric humans would manage to think and sense less of something less organized, and move towards becoming able to establish stable notions and consequently words and a language.
2) Secondly, this would be also inherited. I do suppose that ultimately math (by which I mean more complicated math than the one we currently are aware of) serves somewhat as a dna-to-consciousness interface. But even if this is so, due to point 1 it wouldn’t really connote mathematical parameters as being more important than other parameters in the human mind or overall organism.
But there is another point, regarding your post. I think that a non-mental object (for example any external object) cannot be identified as it actually is by the observer/the one who senses it. In philosophy there is a famous term, the so-called “thing-in-itself”. That term (used since ancient times) generally means that any object is picked up as having qualities depending on the observer’s own ability and means to identify qualities, and not because the actual object has to have those qualities or anything like them. The actual object is just there, but is not in singularity with the observer; the observer translates it through his/her own means (senses and thought). Your point about the object possibly having math inherently is interesting (I do understand you mean that its form is shaped due to actual, real properties, and those are just picked up by us), yet it should be supplemented with the note that even if the object (for example one of those shells) had properties itself which create that spiral and then we notice it, it would have to follow that either we noticed the spiral without distorting the thing-in-itself as an observer of it, or that we picked up some property which didn’t actually have any mathematical value but was (in some strange way) isomorphic to the spiral when translated for a human observer’s sensory organs. If the latter somehow was true then the external object had no mathematical property, and we picked up some math property because we seem to project math even in more ways than one. If the former was true then we are in singularity with the observed object and nothing is actually distinct in the cosmos (certainly anyone senses their own self as distinct from something external). And in both cases it would not connote that math are cosmic, given the case where math were part of the observed object would present a case where we are so full of illusions that we think (incorrectly in that case) ourselves distinct from a shell, when in “reality” we would not have been.
I do realize this may seem way too “philosophical” (and in a bad way). Philosophy has had problems since ancient times (this itself is already examined by Plato himself: how philosophy may seem very alienating and problematic). Yet the gist of the matter is that (in virtually all serious philosophers’ view) there is no reason to think that we as observers pick up any actual non-anthropic reality. We do pick up a translation of something, and this translation is enough to allow us to advance in various ways, including being able to build space-traveling rockets. This is so because we always stay within the translation, and to us the cosmos is witnessed in translation. But a translation of something is not in tautology with the thing itself. My own suspicion is that different intelligent species will not have compatible translations (because they would likely even lack fundamental notions we have; for example they may not sense space or movement or other parameters, and sense ones we cannot imagine. Intuitively I suspect even so alien a species could develop tech and science of a very high level).