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I'm surprised that this is characterized as such a novel idea in the article because I'm almost certain I've had this discussion ages ago on HN here. I think it

I'm surprised that this is characterized as such a novel idea in the article because I'm almost certain I've had this discussion ages ago on HN here. I think it was someone asking "why the hell are there spirals everywhere" and multiple people pretty quickly pointed out that self-repeating, symmetric, and fractal patterns are simply a very easy, 'low-information' ways to build larger structures.

zitterbewegung 5y ago
A preprint of the information that was derived to make the above article has been available for a year. https://www.biorxiv.org/content/10.1101/2021.07.28.454038v2 https://www.biorxiv.org/content/10.1101/2021.07.28.454038v2
jazzyjackson 5y ago
a mind-rewiring video by numberphile concerning the golden ratio [0] made sense of all the spiral overlay art: yes, plants use it because it is an optimal solution for minimizing overlap when sprouting leaves during growth, maximizing spatial coverage but also, as a number that is least able to be approximated by rational, erm, ratios - it is a pattern that most closely approximates random patterns. So more than any other spiral, a fibonacci spiral has the highest likelihood of overlapping random points in 2D space... (and fibonacci series converges on the golden ratio because they are equivelent expressions of the continued fraction 1+(1/(1+(1/(1+(1/(1+(1/... [0] https://youtu.be/sj8Sg8qnjOg https://youtu.be/sj8Sg8qnjOg
- thaumasiotes 5y ago
  > and fibonacci series converges on the golden ratio because they are equivelent expressions of the continued fraction 1+(1/(1+(1/(1+(1/(1+(1/... Just for fun, note that those numerators and denominators reflect the coefficients (1 and 1) in the Fibonacci recurrence equation F_n = 1*F_{n-1} + 1*F_{n-2}.[1] Any sequence obeying this equation will converge to the same ratio between adjacent terms. But the Fibonacci series is "perfect" in that it bottoms out at 1 and 1, never interrupting the pattern even after an infinite number of terms have gone by. In contrast, if you defined a similar series starting at 3 and 4, that series would converge to the continued fraction 1/(1+1/(1+1/1+(1/ ... 1+(3/4) ))), which is exactly equal as long as you can't get across the infinite number of 1s in the expansion of "...". [1] As an example of how this works, if you have the recurrence relation f(k) = 3f(k-1) + 2f(k-2), then the limit of f(n)/f(n-1) as n goes to infinity is the continued fraction 3 + 2/(3 + 2/(3 + 2/(3 + ...
Aerroon 5y ago
>'low-information' ways to build larger structures. And I assume that these low-information ways are more likely to emerge by random chance, because you have to get fewer bits right?
- philipfweiss 5y ago
  The rationale I remember learning was: Think about your blood vessels. They run, and branch, and then branch again, in an intricate pattern. Your DNA has to encode for this, but our DNA holds a finite amount of information. So does it seem more likely that your DNA holds bit of information for every branch of every blood vessel? Or instead, does it just encode the information of “blood vessel branches half way into a new blood vessel, recursively”. The fractal can be encoded with fewer bits, as the instructions to make the original vessel can be repeated at the split point. It’s kind of like… you don’t store information of all humans in your lineage. Rather, you store information for one human, as well as information for how to make copies.
amelius 5y ago
The problem with spirals, though, is that they are not symmetric. They are either left-turning or right-turning, not both.
- TuringTest 5y ago
  They are not symmetric, but they are self-repeating. You can grow a spiral from a very simple set of rules on its lower level substrate.
- TheOtherHobbes 5y ago
  They're not geometrically symmetric, but they are symmetric in the more general sense of applying an invariant transformation.
Lyapunov_Lover 5y ago
Yeah, it's not a novel idea. Gregory Chaitin has been talking about this for a long time. And a whole bunch of other people. I can't find all that many of them listed in the citations of this work, though. And the Twitter thread on it makes it seem as if their idea of looking at evolution through the lens of AIT was original. Which is not the case at all.
Schroedingersat 5y ago
yeah. 'go forward and up, turn right' don't need to know where you are

zitterbewegung 5y ago

A preprint of the information that was derived to make the above article has been available for a year. https://www.biorxiv.org/content/10.1101/2021.07.28.454038v2 https://www.biorxiv.org/content/10.1101/2021.07.28.454038v2

jazzyjackson 5y ago

a mind-rewiring video by numberphile concerning the golden ratio [0] made sense of all the spiral overlay art: yes, plants use it because it is an optimal solution for minimizing overlap when sprouting leaves during growth, maximizing spatial coverage but also, as a number that is least able to be approximated by rational, erm, ratios - it is a pattern that most closely approximates random patterns. So more than any other spiral, a fibonacci spiral has the highest likelihood of overlapping random points in 2D space... (and fibonacci series converges on the golden ratio because they are equivelent expressions of the continued fraction 1+(1/(1+(1/(1+(1/(1+(1/... [0] https://youtu.be/sj8Sg8qnjOg https://youtu.be/sj8Sg8qnjOg

thaumasiotes 5y ago
> and fibonacci series converges on the golden ratio because they are equivelent expressions of the continued fraction 1+(1/(1+(1/(1+(1/(1+(1/... Just for fun, note that those numerators and denominators reflect the coefficients (1 and 1) in the Fibonacci recurrence equation F_n = 1*F_{n-1} + 1*F_{n-2}.[1] Any sequence obeying this equation will converge to the same ratio between adjacent terms. But the Fibonacci series is "perfect" in that it bottoms out at 1 and 1, never interrupting the pattern even after an infinite number of terms have gone by. In contrast, if you defined a similar series starting at 3 and 4, that series would converge to the continued fraction 1/(1+1/(1+1/1+(1/ ... 1+(3/4) ))), which is exactly equal as long as you can't get across the infinite number of 1s in the expansion of "...". [1] As an example of how this works, if you have the recurrence relation f(k) = 3f(k-1) + 2f(k-2), then the limit of f(n)/f(n-1) as n goes to infinity is the continued fraction 3 + 2/(3 + 2/(3 + 2/(3 + ...

Aerroon 5y ago

>'low-information' ways to build larger structures. And I assume that these low-information ways are more likely to emerge by random chance, because you have to get fewer bits right?

philipfweiss 5y ago
The rationale I remember learning was: Think about your blood vessels. They run, and branch, and then branch again, in an intricate pattern. Your DNA has to encode for this, but our DNA holds a finite amount of information. So does it seem more likely that your DNA holds bit of information for every branch of every blood vessel? Or instead, does it just encode the information of “blood vessel branches half way into a new blood vessel, recursively”. The fractal can be encoded with fewer bits, as the instructions to make the original vessel can be repeated at the split point. It’s kind of like… you don’t store information of all humans in your lineage. Rather, you store information for one human, as well as information for how to make copies.

amelius 5y ago

The problem with spirals, though, is that they are not symmetric. They are either left-turning or right-turning, not both.

TuringTest 5y ago
They are not symmetric, but they are self-repeating. You can grow a spiral from a very simple set of rules on its lower level substrate.
TheOtherHobbes 5y ago
They're not geometrically symmetric, but they are symmetric in the more general sense of applying an invariant transformation.

Lyapunov_Lover 5y ago

Yeah, it's not a novel idea. Gregory Chaitin has been talking about this for a long time. And a whole bunch of other people. I can't find all that many of them listed in the citations of this work, though. And the Twitter thread on it makes it seem as if their idea of looking at evolution through the lens of AIT was original. Which is not the case at all.

Schroedingersat 5y ago

yeah. 'go forward and up, turn right' don't need to know where you are