3 ms·

Feynman once talked about this eloquently [1] and agreed with you about not making assumption that things are elegant. That said, it's interesting to me that t

Feynman once talked about this eloquently [1] and agreed with you about not making assumption that things are elegant. That said, it's interesting to me that the universe is actually much simpler than it appears, just based on the idea that the information contained in a region of space is proportional to the surface area, _not_ the volume [2]. The larger the area of space we look at, the more the discrepancy grows between how much information we think there is (using our human 3 dimensional intuition with x,y,z for each particle) vs how much there actually is (based on Bekenstein Bound) [3]. [1] https://www.youtube.com/watch?v=yjOV3xgydXE https://www.youtube.com/watch?v=yjOV3xgydXE [2] https://en.wikipedia.org/wiki/Bekenstein_bound https://en.wikipedia.org/wiki/Bekenstein_bound [3] https://en.wikipedia.org/wiki/Surface-area-to-volume_ratio#/media/File:SAV_n3.png https://en.wikipedia.org/wiki/Surface-area-to-volume_ratio#/...

mushishi 6y ago
Not directly related, but I find the aforementioned proportionality fascinating as I found recently that the cell size is critically bounded by it: "Therefore, as a cell increases in size, its surface area-to-volume ratio decreases. [...] If the cell grows too large, the plasma membrane will not have sufficient surface area to support the rate of diffusion required for the increased volume. In other words, as a cell grows, it becomes less efficient. One way to become more efficient is to divide; another way is to develop organelles that perform specific tasks. These adaptations lead to the development of more sophisticated cells called eukaryotic cells." Source: https://bio.libretexts.org/Bookshelves/Introductory_and_General_Biology/Book%3A_General_Biology_(Boundless)/4%3A_Cell_Structure/4.1%3A_Studying_Cells/4.1D%3A_Cell_Size https://bio.libretexts.org/Bookshelves/Introductory_and_Gene...
- twelfthnight 6y ago
  Is this link your writing? It's very interesting!
  - mushishi 6y ago
    No, unfortunately not! I am reading The Vital Question by Nick Lane, and he tells about the cell size in that book. After I noticed the parent comment (of mine), I just googled some reference to my point.
- saeranv 6y ago
  Is the area/volume constraint in space related to the one in organisms? The latter I can understand intuitively as a function of scaling metabolic rates for different organism sizes. Specifically, there's some power-law relationship between growing volume and area[1], which means you require proportionally more metabolism (energy production) as you get smaller because your surface heat loss is smaller, to maintain the same heat rate as a larger animal. I think there might be a rough analogy/relationship to space if we think of heat loss in terms of increasing entropy/loss-of-information, and the higher probability of low energy/low-information states in a volume over time? But, I don't have enough physics knowledge to know if this is the right way to think about it... [1] This is the rough intuition, but the actual exponent is not consistent with square-cube rate: https://en.wikipedia.org/wiki/Kleiber%27s_law https://en.wikipedia.org/wiki/Kleiber%27s_law.
amelius 6y ago
Yes but I can imagine that if you start packing atoms really tightly (as in a black hole) then you lose entropy. On a normal scale, the number of harddrives you can pack in a sphere grows faster than the surface of that sphere.
- twelfthnight 6y ago
  Yeah, agreed this probably isn't very relevant at human scales. The more hard drives you can fit in a station wagon speeding down a highway, the higher your bandwidth ;) [1] BTW, check out this video (especially starting at 10:15) for a better explanation than I gave for the Bekenstein bound [2] [1] https://en.wikiquote.org/wiki/Andrew_S._Tanenbaum https://en.wikiquote.org/wiki/Andrew_S._Tanenbaum [2] https://www.youtube.com/watch?v=Ab8JIzckx_M https://www.youtube.com/watch?v=Ab8JIzckx_M
tsimionescu 6y ago
Note that this bound is not proven, it is for now a conjecture. There are solutions to Einstein's field equations that would violate it ('Wheeler's bags of gold', different volumes contained in the same surface area, with different entropies, possibly greater than a black hole's), so it remains open whether the holographic principle holds.

mushishi 6y ago

Not directly related, but I find the aforementioned proportionality fascinating as I found recently that the cell size is critically bounded by it: "Therefore, as a cell increases in size, its surface area-to-volume ratio decreases. [...] If the cell grows too large, the plasma membrane will not have sufficient surface area to support the rate of diffusion required for the increased volume. In other words, as a cell grows, it becomes less efficient. One way to become more efficient is to divide; another way is to develop organelles that perform specific tasks. These adaptations lead to the development of more sophisticated cells called eukaryotic cells." Source: https://bio.libretexts.org/Bookshelves/Introductory_and_General_Biology/Book%3A_General_Biology_(Boundless)/4%3A_Cell_Structure/4.1%3A_Studying_Cells/4.1D%3A_Cell_Size https://bio.libretexts.org/Bookshelves/Introductory_and_Gene...

twelfthnight 6y ago
Is this link your writing? It's very interesting!
- mushishi 6y ago
  No, unfortunately not! I am reading The Vital Question by Nick Lane, and he tells about the cell size in that book. After I noticed the parent comment (of mine), I just googled some reference to my point.
saeranv 6y ago
Is the area/volume constraint in space related to the one in organisms? The latter I can understand intuitively as a function of scaling metabolic rates for different organism sizes. Specifically, there's some power-law relationship between growing volume and area[1], which means you require proportionally more metabolism (energy production) as you get smaller because your surface heat loss is smaller, to maintain the same heat rate as a larger animal. I think there might be a rough analogy/relationship to space if we think of heat loss in terms of increasing entropy/loss-of-information, and the higher probability of low energy/low-information states in a volume over time? But, I don't have enough physics knowledge to know if this is the right way to think about it... [1] This is the rough intuition, but the actual exponent is not consistent with square-cube rate: https://en.wikipedia.org/wiki/Kleiber%27s_law https://en.wikipedia.org/wiki/Kleiber%27s_law.

amelius 6y ago

Yes but I can imagine that if you start packing atoms really tightly (as in a black hole) then you lose entropy. On a normal scale, the number of harddrives you can pack in a sphere grows faster than the surface of that sphere.

twelfthnight 6y ago
Yeah, agreed this probably isn't very relevant at human scales. The more hard drives you can fit in a station wagon speeding down a highway, the higher your bandwidth ;) [1] BTW, check out this video (especially starting at 10:15) for a better explanation than I gave for the Bekenstein bound [2] [1] https://en.wikiquote.org/wiki/Andrew_S._Tanenbaum https://en.wikiquote.org/wiki/Andrew_S._Tanenbaum [2] https://www.youtube.com/watch?v=Ab8JIzckx_M https://www.youtube.com/watch?v=Ab8JIzckx_M

tsimionescu 6y ago

Note that this bound is not proven, it is for now a conjecture. There are solutions to Einstein's field equations that would violate it ('Wheeler's bags of gold', different volumes contained in the same surface area, with different entropies, possibly greater than a black hole's), so it remains open whether the holographic principle holds.