Intrinsic mathematics
closed account (E8A4Nwbp)
You may be aware that the sum of the numbers which are not divisible by 2 is a square number.
It may also be in your knowledge that, the sum of the hex numbers is a cube number, and hexagons can arguably be said to resemble cubes, as a shape.
Furthermore, as a final example, forming equilateral triangles on the sides of a scalene triangle, and then joining the midpoints of these equilateral triangles, will subsequently form another equilateral triangle. The main element of this observation can be that from a supposedly random idea, can be an idea with strict principles.
I would just like to ask if such occurrences are anything to be amazed by. Initially, one may be delighted by the idea that, inextricably, such is present in mathematics, but when pondering further into them, you may realise that what initially comes across as intrinsic beauty, is merely the result of intentional manipulation. They're a joy to think about, but I'm not entirely certain if such occurrences are comparable to, for instance, reducing a random element of nature to particles and reconstructing the particles into a structure which, to the eye, is delightful.
It may also be in your knowledge that, the sum of the hex numbers is a cube number, and hexagons can arguably be said to resemble cubes, as a shape.
Furthermore, as a final example, forming equilateral triangles on the sides of a scalene triangle, and then joining the midpoints of these equilateral triangles, will subsequently form another equilateral triangle. The main element of this observation can be that from a supposedly random idea, can be an idea with strict principles.
I would just like to ask if such occurrences are anything to be amazed by. Initially, one may be delighted by the idea that, inextricably, such is present in mathematics, but when pondering further into them, you may realise that what initially comes across as intrinsic beauty, is merely the result of intentional manipulation. They're a joy to think about, but I'm not entirely certain if such occurrences are comparable to, for instance, reducing a random element of nature to particles and reconstructing the particles into a structure which, to the eye, is delightful.
Well, it’s definitely possible but eventually can’t really be perceived without resorting to credible intervention. Otherwise it falls into the well known Trap of Archimedes.
| You may be aware that the sum of the numbers which are not divisible by 2 is a square number. |
EDIT: Ah, I see what you mean, now. Finite sums of consecutive odd integers are square numbers.
| It may also be in your knowledge that, the sum of the hex numbers is a cube number |
| forming equilateral triangles on the sides of a scalene triangle, and then joining the midpoints of these equilateral triangles |
| when pondering further into them, you may realise that what initially comes across as intrinsic beauty, is merely the result of intentional manipulation. |
However, I don't think it's accurate to say that beauty in this sense is the result of intentional manipulation. Sometimes you can define a system with specific rules, and those rules can have consequences you did not foresee, some of which will be aesthetically pleasing.
For example, one time I was playing around with a tree drawing program I'd written, and out of the blue I thought "what if I construct the tree like this?"
1. If the current branch has length 1, its two children should have length 1/sqrt(2).
2. A branch's children are always orthogonal to their parent, and parallel and opposite to each other.
I had no idea what the tree was going to look like, but I was pleasantly surprised when it turned out to look like this:
https://upload.wikimedia.org/wikipedia/commons/a/af/H_tree.svg
An H tree has the property that as more levels are added, the branches approach their ancestors arbitrarily close. This is what's known as a space-filling curve.
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| All that's happening is that humans enjoy unexpected simplicity, happy coincidences, and neatness. |
Beauty not being intrinsic doesn't imply that there are no intrinsic properties. Also, please prove that the ability to recognize beauty is intrinsic to humans.
If you reply with something irrelevant or if you just reiterate your previous point I'll go back to ignore you, so do feel free to do that.
If you reply with something irrelevant or if you just reiterate your previous point I'll go back to ignore you, so do feel free to do that.
What am I free to do - once again your commands aren't clear?
The Golden ratio, stellar constellations, music, art, even the Platonic solids are all examples of intrinsic beauty being recognised by humans.
The coronavirus would not appreciate or recognize the beauty because it/they have no intrinsic ability to do so. Viruses like Argentinians, don't think. They are not conscious.
| please prove that the ability to recognize beauty is intrinsic to humans. |
The coronavirus would not appreciate or recognize the beauty because it/they have no intrinsic ability to do so. Viruses like Argentinians, don't think. They are not conscious.
Beauty is not an intrinsic property of objects, it's a subjective emotion experienced by people. If it was intrinsic there would be no disagreement on how beautiful some thing is. For each of those things you mentioned you'll find someone who thinks it's the best thing in the world and someone else who thinks it's lame.
Honestly, I don't know how anyone can doubt that aesthetics is entirely subjective. Not only is it a topic that's been studied for millennia, but surely disagreeing on the aesthetic merits of a piece of artwork must be a nearly universal human experience.
Honestly, I don't know how anyone can doubt that aesthetics is entirely subjective. Not only is it a topic that's been studied for millennia, but surely disagreeing on the aesthetic merits of a piece of artwork must be a nearly universal human experience.
Universal disagreement. Hardly. Why have art galleries if that is the case?
The Golden Ratio is an accepted universal aesthetic truth. It is innately, intrinsically, human. Viruses couldn't care less - Argentinians even less than that - they are Philistines.
The Golden Ratio is an accepted universal aesthetic truth. It is innately, intrinsically, human. Viruses couldn't care less - Argentinians even less than that - they are Philistines.
I didn't say "universal disagreement". What I said was that just about everyone has at some point disagreed with someone about the beauty of some piece of art, or anything really. It's pretty obvious. Not all musical genres are equally popular, yet they all have their hardcore fans and their detractors.
Again, I don't understand how anyone can object to such an obvious reality of human experience. Are you actually human, or are you some sort of mollusc that learned how to type? Have you ever talked to a human being? Were you raised by an HVAC system?
Art galleries exist to sell art, of course, and the art in art galleries is primarily purchased as a status symbol and to launder money, not for its aesthetic merits.
Even artworks in museums are not there because they're objectively more beautiful. They're there because they're historically and culturally relevant.
Oh, is that so? Please provide the mathematical proof of the objective beauty of phi, then.
Again, I don't understand how anyone can object to such an obvious reality of human experience. Are you actually human, or are you some sort of mollusc that learned how to type? Have you ever talked to a human being? Were you raised by an HVAC system?
Art galleries exist to sell art, of course, and the art in art galleries is primarily purchased as a status symbol and to launder money, not for its aesthetic merits.
Even artworks in museums are not there because they're objectively more beautiful. They're there because they're historically and culturally relevant.
| The Golden Ratio is an accepted universal aesthetic truth. |
| I didn't say "universal disagreement". |
| What I said was that just about everyone has at some point disagreed with someone about the beauty of some piece of art, or anything really. |
| It's pretty obvious. |
| Not all musical genres are equally popular, yet they all have their hardcore fans and their detractors. |
| Again, I don't understand how anyone can object to such an obvious reality of human experience. |
| Are you actually human, or are you some sort of mollusc that learned how to type? |
| Have you ever talked to a human being? |
| Were you raised by an HVAC system? |
| Art galleries exist to sell art, |
| of course, |
| and the art in art galleries is primarily purchased as a status symbol and to launder money, not for its aesthetic merits. |
| Even artworks in museums are not there because they're objectively more beautiful. |
| They're there because they're historically and culturally relevant. |
| The Golden Ratio is an accepted universal aesthetic truth. Oh, is that so? Please provide the mathematical proof of the objective beauty of phi, then. |
closed account (E8A4Nwbp)
| Astra wrote: |
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| It may also be in your knowledge that, the sum of the hex numbers is a cube number |
| heliosInResponse wrote: |
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| This sentence is meaningless. |
(edited image, should make the concept much cleared)
https://www.autodraw.com/share/H4YBEHIZ34LV
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@Astra
Your sentence is not meaningless and the image assists in answering your original question. i.e. The result is amazing. Each of the three examples are both intrinsically beautiful and extrinsically beautiful.
Your sentence is not meaningless and the image assists in answering your original question. i.e. The result is amazing. Each of the three examples are both intrinsically beautiful and extrinsically beautiful.
closed account (E8A4Nwbp)
| There's nothing about the number 2 that's objectively more or less beautiful than the number 39.07. You could define a function that quantifies the beauty of numbers, but then that would still be extrinsic to the numbers themselves. All that's happening is that humans enjoy unexpected simplicity, happy coincidences, and neatness. That's essentially what the concept of "mathematical elegance" boils down to. |
| However, I don't think it's accurate to say that beauty in this sense is the result of intentional manipulation. Sometimes you can define a system with specific rules, and those rules can have consequences you did not foresee, some of which will be aesthetically pleasing. |
| https://upload.wikimedia.org/wikipedia/commons/a/af/H_tree.svg |
I don't suppose you know a particular resource you feel is consummate in explaining the intrinsic elements of the golden ratio?
Furthermore, I don't suppose you know other intrinsic mathematics which is of, to our senses, pleasant? Another in my knowledge is if you take a random point in an equilateral triangle, then, from this point, construct 3 parallel lines which go from the point to each of the triangle's sides, the total length of these line will be equal to the height of the triangle.
Sorry if this is an inordinate amount of enquiries, however, I just would like to ask the following, as we established that the intrinsic mathematics in not quite intrinstic beauty, what is the level of metal ability demonstrated when one demonstrates a high level of intrigument and awe when seeing an example of the given intrinsic mathmatics. Is he demonstrating a low mental ability, as in truth it is merely a particular intentional arrangement of already established laws? (Assume he is not enthralled by the aesthetically pleasing element, rather he is astounded by the fact maths just possessed such intrinsic ideas)
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| https://www.autodraw.com/share/H4YBEHIZ34LV |
But the real question is, can you prove that those two things are equal?
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While there isn’t much elegance coming from china these days there is intrinsic beauty and elegance in an ancient chinese mathematicians proof of the Pythagoras theorem.
If you're going to tell me I said things I didn't say then you don't need me for this conversation. Just imagine I said something and argue with yourself.
Have fun.
Have fun.
closed account (E8A4Nwbp)
| helios wrote: |
|---|
| But the real question is, can you prove that those two things are equal? |
| you don't need me for this conversation |
| Astra wrote: |
|---|
| I don't suppose you know a particular resource you feel is consummate in explaining the intrinsic elements of the golden ratio? Furthermore, I don't suppose you know other intrinsic mathematics which is of, to our senses, pleasant? Another in my knowledge is if you take a random point in an equilateral triangle, then, from this point, construct 3 parallel lines which go from the point to each of the triangle's sides, the total length of these line will be equal to the height of the triangle. Sorry if this is an inordinate amount of enquiries, however, I just would like to ask the following, as we established that the intrinsic mathematics in not quite intrinstic beauty, what is the level of metal ability demonstrated when one demonstrates a high level of intrigument and awe when seeing an example of the given intrinsic mathmatics. Is he demonstrating a low mental ability, as in truth it is merely a particular intentional arrangement of already established laws? (Assume he is not enthralled by the aesthetically pleasing element, rather he is astounded by the fact maths just possessed such intrinsic ideas) |
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