8 ms·

The Hindu Temple as a Model of Fractal Cosmology (2015)

266 points by vkreso 9y ago

bitwize 9y ago
This sort of thing doesn't just happen in Hinduism. Behold, the Sagrada Família: https://en.m.wikipedia.org/wiki/Sagrada_Família https://en.m.wikipedia.org/wiki/Sagrada_Família
- curiousDog 9y ago
  I think the cool thing about this from what I gather is that the instructions to the masons were basically a recursive procedure and they got to decide on the recursive depth.
  - canoebuilder 9y ago
    That is cool, a compressed blueprint. Also cool is that it is still under construction, maybe someone reading right now is involved and can tell us more.
    - saeranv 9y ago
      I'm not involved, but I've met the researcher at a couple of computational architecture conferences: Mark Burry - https://www.rmit.edu.au/media-objects/multimedia/video/projects/sagrada-familia-and-rmit-university https://www.rmit.edu.au/media-objects/multimedia/video/proje... The other interesting thing about the Sagrada Familia is that Gaudi based the primary structure on catenary structures. Off the top of my head, I believe he first made weighted string assemblies of the vaults, such that the string structure is held in perfect tension from the gravitational force of its own weight. Then by casting the resulting shape in concrete, and flipping the shape over, the resulting structure is optimized for compression. The tensile structure reflects the force of gravity on the string assembly - it is "optimized" for its own weight, so when flipping it over, and swapping the tension members for compression members, we know this new structure is perfectly shaped to distribute internal and self-weight for compression.
  - theoh 9y ago
    Hmm, really it was more like a geometric progression. David Gelernter has commented on the lack of familiarity art/architectural historians have with terminology like "recursive" or "self-similar" (I prefer the latter because it leaves room for the judgements and conspicuous non-exact applications of recursion in architecture): https://www.edge.org/response-detail/10574 https://www.edge.org/response-detail/10574 Also this, and the article it was saved from, bringing music and the proportions of the human body into the equation: https://www.pinterest.com/pin/358317714073877302/ https://www.pinterest.com/pin/358317714073877302/ Finally this: "Every society has seen architecture as something that transcends its functional role, as a diagram of the cosmos," https://www.theguardian.com/artanddesign/architecture-design-blog/2013/may/15/charles-correa-india-greatest-architect-exhibition https://www.theguardian.com/artanddesign/architecture-design... Edit: I'm an architecture historian so I didn't mean it if I came across as pompous -- but that Gelernter link conveys a weird sense of CS being superior to the art historians, and at the same time makes more of recursive patterns in physical architecture than is justified. I have mixed feeling about this projection of the ideas of one field on to another: something like the Sierpinski gasket is not good architecture, and it takes a real expert in building to understand the difference, not a mathematician/computer scientist who can spot recursion. So my possibly contentious point was that a schematic reading of architecture as recursive (or even cosmic) is valid but also kind of the most superficial non-aesthetic form of thinking about architecture...
- canoebuilder 9y ago
  And if you care about your civilization and the heritage thereof, then support preemptive and proactive, actions and policies to protect it. http://www.unz.com/isteve/nyt-finally-confirms-barcelona-terrorists-planed-to-blow-up-gaudis-masterpiece/ http://www.unz.com/isteve/nyt-finally-confirms-barcelona-ter...
- JoBrad 9y ago
  It would be odd if it only occurred in one place in the world. But I do wonder if the deep embedding of mathematical concepts in various forms of Buddhism encouraged higher order thinking.
wbhart 9y ago
The article seems to assume that the universe is fractal, but Wikipedia can't seem to make up its mind whether fractal cosmologies are fringe ideas or not. It's certainly far outside the consensus.
- cbennett 9y ago
  In terms of cosmology, the physically observable universe does have (some) fractal structure or features--, primarily to the existence of multi-scale primordial (quantum) fluctuations. https://en.wikipedia.org/wiki/Primordial_fluctuations https://en.wikipedia.org/wiki/Primordial_fluctuations https://arxiv.org/abs/astro-ph/0003124 https://arxiv.org/abs/astro-ph/0003124 On the other hand, at very large scales the universe is expressly homogenous (smooth) https://www.space.com/17234-universe-fractal-large-scale-theory.html https://www.space.com/17234-universe-fractal-large-scale-the... W/r to larger and more wide-ranging questions, e.g. if the mutli-verse has some sort of deep fractal meta-structure, and/or the recursion of fundamental quantum computing operations, the jury is still entirely out.
  - posterboy 9y ago
    > On the other hand, at very large scales the universe is expressly homogenous (smooth) I assume that's because of looking at it through low pass filters, inadvertantly.
    - llamaz 9y ago
      As elec. engineers (and c. scientists) one of our only hammers is signals theory and cosmology looks like a nail. But the physicists probably have it right.
      - posterboy 9y ago
        ... have what right exactly? Pictures (i.e. measurements) of faint celestal bodies are but mushy wish-washed smears of a point is what I'm talking about for example. Quite simply, our band-width is limited by position, the ammount that we can observe is likely just a tiny fraction, the known universe only accounts for ca. 10% of theoretical total energy. In that sense the low energies are likely lost on us, then we actually see through a highpass (redshift?).
kuwze 9y ago
This reminded me of mandelbulb[1] and on a somewhat unrelated note the original demo video of Euclideon[2]. [1]: https://www.youtube.com/watch?v=tsuYZg8k-Zc https://www.youtube.com/watch?v=tsuYZg8k-Zc [2]: https://www.youtube.com/watch?v=00gAbgBu8R4 https://www.youtube.com/watch?v=00gAbgBu8R4
nabla9 9y ago
Mathematician Felix Klein (famous for Klein bottle) used Hindu concept of Indra's Net as a inspiration for developing algebra for infinite reflections. It produces nice fractals. https://www.amazon.com/Indras-Pearls-Vision-Felix-Klein/dp/1107564743 https://www.amazon.com/Indras-Pearls-Vision-Felix-Klein/dp/1...
carapace 9y ago
Cf. Christopher Alexander's "Fifteen Properties" http://www.livingneighborhoods.org/ht-0/fifteen.htm http://www.livingneighborhoods.org/ht-0/fifteen.htm
Cozumel 9y ago
This is another good read on it, Hindu temples are built to reflect the human body. http://www.surya-world.org/hindu-temple-and-the-structure-of-human-body-comparison/ http://www.surya-world.org/hindu-temple-and-the-structure-of...
FullMtlAlcoholc 9y ago
When something is referred to as fractal, does it always imply a degree of self-similarity? As I understand it, Mandelbrot developed fractal geometry as a tool to examine the "roughness" of reality as opposed to the smoothness of calculus and fractal dimension is a measure of complexity at every scale, with a self-similar pattern being an easy example to follow. If that is so, that the universe has a high degree of complexity at every scale, is that really controversial? Here is an excellent 20 min introduction to fractals: https://www.youtube.com/watch?v=gB9n2gHsHN4 https://www.youtube.com/watch?v=gB9n2gHsHN4
amriksohata 9y ago
Incredible, Hindu temples are not churches or mosques, they were made with incredible thought about positioning, with size and geometry taken into consideration. All optimised using numerics, we've lost a chapter in human history as to how Vedic structures were created with such elegance. https://www.facebook.com/238044912896496/videos/1639732932727680/ https://www.facebook.com/238044912896496/videos/163973293272...
- chimeracoder 9y ago
  > we've lost a chapter in human history as to how Vedic structures were created with such elegance. Just to be clear, this knowledge wasn't lost accidentally. It's part of what was contained in the books and manuscripts destroyed intentionally by colonizers.
  - amriksohata 9y ago
    Yes I agree with you, Muslim (Mughal) invaders burnt a lot of scriptures.
    - chimeracoder 9y ago
      > Muslim (Mughal) invaders burnt a lot of scriptures. Actually the particular books I'm referring to were burned by the Portuguese, but lots of invaders destroyed Indian books - Portuguese, British, French, Dutch, and yes, Mughal as well.
      - dmix 9y ago
        One interesting historical narrative which helps put this into perspective was how the Spanish conquest of Aztec and Mayan regions resulted in a lot of burning of "heretical" books by the Christians missionaries, "which they (the Maya) regretted to an amazing degree" [1]. But further research showed that most of the books burned were already heavily biased historically by the Aztecs - as the Aztecs had already burnt all of the Mayans books when they conquered them before the Spanish arrived. So it really is a (shameful) repeating pattern of many conquering human civilizations throughout history rather than one of a particular culture which happens to be dominate. This is another piece of history which doesn't fit neatly into the colonizer narrative, which is popular today, from which people try to hold modern cultures responsible for past generational cultural events, somewhat like an 'original sin' which needs to be attuned. One could go further and try to point to religion itself as the main driver - but even then that is merely another abstraction over standard human tribalism. Which is somewhat ironic as the colonizer narrative is typically used today as a tool for pushing other forms of tribalism (political, cultural, etc). [1] https://www.wikiwand.com/en/Book_burning https://www.wikiwand.com/en/Book_burning

266 points by vkreso 9y ago

This sort of thing doesn't just happen in Hinduism. Behold, the Sagrada Família: https://en.m.wikipedia.org/wiki/Sagrada_Família https://en.m.wikipedia.org/wiki/Sagrada_Família

curiousDog 9y ago
I think the cool thing about this from what I gather is that the instructions to the masons were basically a recursive procedure and they got to decide on the recursive depth.
- canoebuilder 9y ago
  That is cool, a compressed blueprint. Also cool is that it is still under construction, maybe someone reading right now is involved and can tell us more.
  - saeranv 9y ago
    I'm not involved, but I've met the researcher at a couple of computational architecture conferences: Mark Burry - https://www.rmit.edu.au/media-objects/multimedia/video/projects/sagrada-familia-and-rmit-university https://www.rmit.edu.au/media-objects/multimedia/video/proje... The other interesting thing about the Sagrada Familia is that Gaudi based the primary structure on catenary structures. Off the top of my head, I believe he first made weighted string assemblies of the vaults, such that the string structure is held in perfect tension from the gravitational force of its own weight. Then by casting the resulting shape in concrete, and flipping the shape over, the resulting structure is optimized for compression. The tensile structure reflects the force of gravity on the string assembly - it is "optimized" for its own weight, so when flipping it over, and swapping the tension members for compression members, we know this new structure is perfectly shaped to distribute internal and self-weight for compression.
- theoh 9y ago
  Hmm, really it was more like a geometric progression. David Gelernter has commented on the lack of familiarity art/architectural historians have with terminology like "recursive" or "self-similar" (I prefer the latter because it leaves room for the judgements and conspicuous non-exact applications of recursion in architecture): https://www.edge.org/response-detail/10574 https://www.edge.org/response-detail/10574 Also this, and the article it was saved from, bringing music and the proportions of the human body into the equation: https://www.pinterest.com/pin/358317714073877302/ https://www.pinterest.com/pin/358317714073877302/ Finally this: "Every society has seen architecture as something that transcends its functional role, as a diagram of the cosmos," https://www.theguardian.com/artanddesign/architecture-design-blog/2013/may/15/charles-correa-india-greatest-architect-exhibition https://www.theguardian.com/artanddesign/architecture-design... Edit: I'm an architecture historian so I didn't mean it if I came across as pompous -- but that Gelernter link conveys a weird sense of CS being superior to the art historians, and at the same time makes more of recursive patterns in physical architecture than is justified. I have mixed feeling about this projection of the ideas of one field on to another: something like the Sierpinski gasket is not good architecture, and it takes a real expert in building to understand the difference, not a mathematician/computer scientist who can spot recursion. So my possibly contentious point was that a schematic reading of architecture as recursive (or even cosmic) is valid but also kind of the most superficial non-aesthetic form of thinking about architecture...
canoebuilder 9y ago
And if you care about your civilization and the heritage thereof, then support preemptive and proactive, actions and policies to protect it. http://www.unz.com/isteve/nyt-finally-confirms-barcelona-terrorists-planed-to-blow-up-gaudis-masterpiece/ http://www.unz.com/isteve/nyt-finally-confirms-barcelona-ter...
JoBrad 9y ago
It would be odd if it only occurred in one place in the world. But I do wonder if the deep embedding of mathematical concepts in various forms of Buddhism encouraged higher order thinking.

wbhart 9y ago

The article seems to assume that the universe is fractal, but Wikipedia can't seem to make up its mind whether fractal cosmologies are fringe ideas or not. It's certainly far outside the consensus.

cbennett 9y ago
In terms of cosmology, the physically observable universe does have (some) fractal structure or features--, primarily to the existence of multi-scale primordial (quantum) fluctuations. https://en.wikipedia.org/wiki/Primordial_fluctuations https://en.wikipedia.org/wiki/Primordial_fluctuations https://arxiv.org/abs/astro-ph/0003124 https://arxiv.org/abs/astro-ph/0003124 On the other hand, at very large scales the universe is expressly homogenous (smooth) https://www.space.com/17234-universe-fractal-large-scale-theory.html https://www.space.com/17234-universe-fractal-large-scale-the... W/r to larger and more wide-ranging questions, e.g. if the mutli-verse has some sort of deep fractal meta-structure, and/or the recursion of fundamental quantum computing operations, the jury is still entirely out.
- posterboy 9y ago
  > On the other hand, at very large scales the universe is expressly homogenous (smooth) I assume that's because of looking at it through low pass filters, inadvertantly.
  - llamaz 9y ago
    As elec. engineers (and c. scientists) one of our only hammers is signals theory and cosmology looks like a nail. But the physicists probably have it right.
    - posterboy 9y ago
      ... have what right exactly? Pictures (i.e. measurements) of faint celestal bodies are but mushy wish-washed smears of a point is what I'm talking about for example. Quite simply, our band-width is limited by position, the ammount that we can observe is likely just a tiny fraction, the known universe only accounts for ca. 10% of theoretical total energy. In that sense the low energies are likely lost on us, then we actually see through a highpass (redshift?).

kuwze 9y ago

This reminded me of mandelbulb[1] and on a somewhat unrelated note the original demo video of Euclideon[2]. [1]: https://www.youtube.com/watch?v=tsuYZg8k-Zc https://www.youtube.com/watch?v=tsuYZg8k-Zc [2]: https://www.youtube.com/watch?v=00gAbgBu8R4 https://www.youtube.com/watch?v=00gAbgBu8R4

nabla9 9y ago

Mathematician Felix Klein (famous for Klein bottle) used Hindu concept of Indra's Net as a inspiration for developing algebra for infinite reflections. It produces nice fractals. https://www.amazon.com/Indras-Pearls-Vision-Felix-Klein/dp/1107564743 https://www.amazon.com/Indras-Pearls-Vision-Felix-Klein/dp/1...

carapace 9y ago

Cf. Christopher Alexander's "Fifteen Properties" http://www.livingneighborhoods.org/ht-0/fifteen.htm http://www.livingneighborhoods.org/ht-0/fifteen.htm

Cozumel 9y ago

This is another good read on it, Hindu temples are built to reflect the human body. http://www.surya-world.org/hindu-temple-and-the-structure-of-human-body-comparison/ http://www.surya-world.org/hindu-temple-and-the-structure-of...

FullMtlAlcoholc 9y ago

When something is referred to as fractal, does it always imply a degree of self-similarity? As I understand it, Mandelbrot developed fractal geometry as a tool to examine the "roughness" of reality as opposed to the smoothness of calculus and fractal dimension is a measure of complexity at every scale, with a self-similar pattern being an easy example to follow. If that is so, that the universe has a high degree of complexity at every scale, is that really controversial? Here is an excellent 20 min introduction to fractals: https://www.youtube.com/watch?v=gB9n2gHsHN4 https://www.youtube.com/watch?v=gB9n2gHsHN4

amriksohata 9y ago

Incredible, Hindu temples are not churches or mosques, they were made with incredible thought about positioning, with size and geometry taken into consideration. All optimised using numerics, we've lost a chapter in human history as to how Vedic structures were created with such elegance. https://www.facebook.com/238044912896496/videos/1639732932727680/ https://www.facebook.com/238044912896496/videos/163973293272...

chimeracoder 9y ago
> we've lost a chapter in human history as to how Vedic structures were created with such elegance. Just to be clear, this knowledge wasn't lost accidentally. It's part of what was contained in the books and manuscripts destroyed intentionally by colonizers.
- amriksohata 9y ago
  Yes I agree with you, Muslim (Mughal) invaders burnt a lot of scriptures.
  - chimeracoder 9y ago
    > Muslim (Mughal) invaders burnt a lot of scriptures. Actually the particular books I'm referring to were burned by the Portuguese, but lots of invaders destroyed Indian books - Portuguese, British, French, Dutch, and yes, Mughal as well.
    - dmix 9y ago
      One interesting historical narrative which helps put this into perspective was how the Spanish conquest of Aztec and Mayan regions resulted in a lot of burning of "heretical" books by the Christians missionaries, "which they (the Maya) regretted to an amazing degree" [1]. But further research showed that most of the books burned were already heavily biased historically by the Aztecs - as the Aztecs had already burnt all of the Mayans books when they conquered them before the Spanish arrived. So it really is a (shameful) repeating pattern of many conquering human civilizations throughout history rather than one of a particular culture which happens to be dominate. This is another piece of history which doesn't fit neatly into the colonizer narrative, which is popular today, from which people try to hold modern cultures responsible for past generational cultural events, somewhat like an 'original sin' which needs to be attuned. One could go further and try to point to religion itself as the main driver - but even then that is merely another abstraction over standard human tribalism. Which is somewhat ironic as the colonizer narrative is typically used today as a tool for pushing other forms of tribalism (political, cultural, etc). [1] https://www.wikiwand.com/en/Book_burning https://www.wikiwand.com/en/Book_burning