7 ms·

Fern leaves and cauliflower curds are not fractals (2012)

78 points by minicaionut 3y ago

chinaman425 3y ago
[dead]
michaericalribo 3y ago
> A realistic set of mathematical equations to describe fern leaf or cauliflower curd development is needed I wish the author had derived these equations -- something like the book The Geometry of Pasta https://www.amazon.com/Geometry-Pasta-Caz-Hildebrand/dp/1594744955 https://www.amazon.com/Geometry-Pasta-Caz-Hildebrand/dp/1594...
- deleted 3y ago
  [deleted]
- bannedbybros 3y ago
  [dead]
d--b 3y ago
Of course it's not an actual fractal, because you know, infinity... But take the Romanesco Broccoli, it really looks like a fractal. It can't be just random. There definitely is some kind of mechanism that's fractal-ish somewhere.
- kqr 3y ago
  You can estimate Hausdorff dimensions of non-infinitessimal things, like coastlines.
  - Y_Y 3y ago
    Indeed, and there's a nice list of them here: https://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension https://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_... It's also worth noting that there are other ways of "measuring" fractal dimension that do not always agree so it can be informative to also look at e.g. box counting dimension too.
- wrs 3y ago
  It isn’t random, and it also isn’t a fractal (as is explained in the very short article). In other news, the golden ratio doesn’t really occur in nature as much as people would like to believe. [0] [0] https://www.maa.org/external_archive/devlin/devlin_05_07.html https://www.maa.org/external_archive/devlin/devlin_05_07.htm...
  - kergonath 3y ago
    > as is explained in the very short article It’s a straw man. The fractal is an analogy; nobody seriously thinks you can zoom in or out of a cauliflower infinitely. We know about atoms and stuff. It’s just pointless pedantry.
    - wrs 3y ago
      Analogies are only useful to the extent they have explanatory power. The assertion here is that this one doesn’t: there are several distinct growth mechanisms applied in sequence, not a recursive application of the same mechanism.
      - anigbrowl 3y ago
        Different mechanisms can use the same template. The Romanesco cauliflower is so obviously self-similar that ignoring this in favor of talking about mechanisms that vary according to scale needs is missing the forest for the trees.
        anonymouskimmer 3y ago
        Biology has the concept of convergent evolution. Would you say a Thylacine is a Wolf, and that it's appropriate to treat one as the other? Fractals are a singular example of repeating patterns, but there are additional repeating pattern types that aren't fractals. Just like Thylacines and Wolves were/are examples of apex predators, not versions of each other.
throwbadubadu 3y ago
> Actual fern leaves and cauliflower curds have a very small number of anatomically variable and non-iterating bifurcations, which superficially look self-similar, but do not allow for scaling down of their structure as real fractals do. Sorry, can't help it, but really? You cannot zoom into real-life fractals infinitely like in those math animations, only a few times? What comes next? Even the coast line or mountains fractal analogies are wrong in the mathematical sense, you won't even the same shape once if you try hard?? > The above cases demonstrate a general problem of using mathematical tools to investigate or illustrate biological phenomena in an irrelevant manner. No, I think we have a different problem here..
- bannedbybros 3y ago
  [dead]
- LesZedCB 3y ago
  imagine publishing a whole paper to win an "Um, actually" argument
- ajuc 3y ago
  Fractals don't even need to be self-similar. They just need to have fractal dimension (if you double the size of every feature - the exponent near the scaling factor must be non-integer). Self-similarity is the easiest way to make a fractal, but not the only one. In fact the idea of fractal was invented for real-life non-self-similar objects. The simple self-similar ones are just examples that are easiest to understand.
  - ouid 3y ago
    As far as i can tell, fractal doesn't have a definition. The closest it ever came was the one you roughly gave.
    - idiotsecant 3y ago
      https://en.wikipedia.org/wiki/Fractal_dimension https://en.wikipedia.org/wiki/Fractal_dimension Not only are fractals very well defined in mathematical terms, but there are further mathematics based on those definitions.
freedude 3y ago
"Like fern leaves or any other plant branching system at the organ level, the cauliflower curd develops from the inside out through a process totally different from fractal drawing." Soooo, what the author is stating is they are actually even more amazing and wonderfully made than we originally thought. Even though they look like the mathematical model of a built fractal they grow entirely different and with an internal program that cannot be reproduced by our existing knowledge-base.
- jonathankoren 3y ago
  I read that same line, but came to the opposite conclusion than you. I didn’t find it amazing at all, instead I found it banal. Essentially the author is saying that fern leaf doesn’t grow as single line, and then subdivides. Well, no shit. Literally no one ever thought that. It betrays a lack of imagination where the author is conflating a single algorithm for the construction of a fractal to an actual fractal shape. It’s the same as complaining that something similar to a Sierpinski’s Triangle can’t be a fractal because it wasn’t made by placing atoms at the midpoints between it and a randomly selected exterior vertex. Are fern leaves technically fractals? No. (And no, I am not talking about the sophomoric objection then lacking infinite regression.) Are they similar to fractals? Yes. Is it useful as an illustration of both a feactal, and how complex body plans can be encoded in DNA without actually specifying every point like a literal blueprint? Yes. None of this is different than the discussing the similarities fractals and coastlines. No one thinks Britain is a literal fractal. Honestly, this idea of fractals is very similar to the idea that the irrational number phi shows up it nature. When you actually look deeply at the purported examples, you’ll find out, it’s not actually there.
- ajuc 3y ago
  You can create the same fractal in many ways. For example you get Sierpiński triangle if you repeatedly draw smaller triangles, or you can just do xor.
  - CrazyStat 3y ago
    My favorite way to draw the Sierpinski triangle is Monte Carlo: 1. Pick a point which is in the triangle (e.g. one of the corners of the triangle). Draw that point. 2. Choose one corner of the triangle at random. 3. Move to the point half way between your current point and the chosen corner. Draw that point. 4. Repeat steps 2-3 as long as desired. Obviously this only ever reaches a countable subset of the triangle based on where you start, but that subset is everywhere dense in the triangle so it doesn't matter. You can also start at an arbitrary point that's not actually in the triangle. If you discard the first k (say 10) iterations you'll still get something visually indistinguishable from a Sierpinski triangle. You can also do this with other self-similar fractals, you just have to find the right set of transformations to use. It's quite fun watching the random points coalesce into the shape of the fractal.
jamal-kumar 3y ago
> A realistic set of mathematical equations to describe fern leaf or cauliflower curd development is needed Well if we're talking about Lindenmayer's work on L-Systems being limited to abstract representations of plants, without getting into all the other structures we're seeing that AREN'T self-similar within the plant itself, yet still branching and perhaps representable by a totally different L-system representation from say the branching of stems and leaves (Say networks of vasculature within plants such as xylem and pholem, which we see as 'veins' within the leaves for example) - Then yeah, plants really are WAY more complex than that and they deserve a more accurate representation. I think L-systems are beautiful and I really recommend anyone who's interested check out Lindenmayer's work on it all [1] but I think if this article has any point it's that we need more complex models to really do plants justice. I think that the fractal appearance of stuff like romanesco broccoli sure is cool but I think it's better understood as sort of a holographic projection of fractalline growth into 3d space rather than an actual 3d fractal Like these models are super excellent for making renders of plants in 3D modelling engines but they're not REALLY plants, even if we can make them look incredibly realistic using just that basic level of modelling, some nice shaders, and some trig functions to make it look like it's blowing in the wind [1] https://en.wikipedia.org/wiki/The_Algorithmic_Beauty_of_Plants https://en.wikipedia.org/wiki/The_Algorithmic_Beauty_of_Plan... [1]
- eternalban 3y ago
  I remember reading about L-Systems in Santa Fe Institutes publications in '90s. Just found this book below when searching for that - this looks comprehensive at a glance: The Algorithmic Beauty of Plants, Prusinkiewicz & Lindenmayer, 2004 http://algorithmicbotany.org/papers/abop/abop.pdf http://algorithmicbotany.org/papers/abop/abop.pdf
  - fatneckbeard 3y ago
    amazing
intrasight 3y ago
There have been some HN posts on this recently. Some quick findings: https://www.nytimes.com/2021/07/08/science/cauliflower-fractals.html https://www.nytimes.com/2021/07/08/science/cauliflower-fract... https://www.science.org/doi/10.1126/science.abg5999 https://www.science.org/doi/10.1126/science.abg5999 https://ournarratives.net/cauliflowers-fractal-pattern-a-key-to-understanding-nature/ https://ournarratives.net/cauliflowers-fractal-pattern-a-key... Even if not a "true" fractal, for the layperson, it's close enough and does a good job of showing what is a fractal.
anonymouskimmer 3y ago
People who are complaining about the article: There's this trope about physics and math envy, which I think ultimately boiled down an envy of the funding that physicists received in the cold war (it lead to a lot of equations in Ecology, for instance). But ignoring the reasons for math envy for a moment, there's also a push among some of the more computationally inclined to try to explain other sciences using their tools. This has been going on for a least a few decades, with "holographic universe" ideas, Wolfram's "New Kind of Science", and the like, and of course actual computational modeling such as weather models. And conflating a prediction engine with intelligence (like that guy at Google did). It's good to show that these reductions, at our current level of computational technology, are not that accurate. "Computational hacking" is really no different from "P-hacking", in that it is easily abused by the lay audience and scientists who conflate possibly fictitious correlative modeling with reality. The model is not the thing. The P-score is not the thing. Mechanisms are the thing. Mechanisms are the core of science. All else is preliminary, at best.
- red_trumpet 3y ago
  I don't think I get your point. Especially regarding weather models. I'm pretty sure that to program good weather predictions, you need to know a lot about the mechanisms. And a prediction model can be used to test theories by comparing predictions against reality. That makes the theories falsifiable. And what is it about comparing computational weather models to p-hacking? Good weather predictions provide value to lots of people, while p-hacking is looking for results where there are none, only benefitting the hacker.
  - anonymouskimmer 3y ago
    TLDR: Math and models can aid with understanding, but fundamentally they're about divination, not explanation. And explanation is the core of science. Over application of models is as bad as p-hacking, in that false explanations for phenomena are promulgated. At least with p-hacking, one other paper can say that a correlation was not shown. Whereas with model-hacking, there is often a tendency to "tweak" the model to fit, ala the earth-centric model of the solar system with its epicycles. > And what is it about comparing computational weather models to p-hacking? P-hacking is just an extension of assuming p-values past a certain point are very good evidence of real-world correlation. The Princeton Engineering Anomalies Research has evidence showing human-operator specific effects on computerized random processes at the 7 sigma statistical level: https://pearlab.icrl.org/pdfs/1997-correlations-random-binary-sequences-12-year-review.pdf https://pearlab.icrl.org/pdfs/1997-correlations-random-binar... Do you believe that this evidence of possible psychic phenomena is real without validated mechanistic means? > Good weather predictions provide value to lots of people, while p-hacking is looking for results where there are none, only benefitting the hacker. Except when the p-hacking is, serendipitously, correct. P-hacked results are not necessarily wrong, they're just fraught. > I'm pretty sure that to program good weather predictions, you need to know a lot about the mechanisms. I'm not saying that all use of models and mathematics in science is bad. I'm saying that premature generalizations based on looks is bad. Do you at least get my point regarding reducing the universe to a hologram or to cellular automata? Weather modeling is much better than these because of its predictive power, but most importantly because the weather modelers keep trying to refine their models based on actual mechanisms. Knowledge of the mechanisms help guide the parameters used in the models. But the models are not the thing. The equations are not the mechanisms. And the approximations certainly aren't the thing. And I'm sure that holograms and cellular automata are useful at times in predicting or thinking about reality, just as fractals are useful in some understanding of plants (despite not being accurate models). Just as the Earth-centric model of the solar system with its epicycles was pretty decent at predicting future positions of the planets. Mathematical models are not the end of the scientific investigation. Mathematical models are the intersection of science (understanding of the universe) and divination (trying to predict the future). Statistics are most useful for trying to identify linkages which probably share mechanisms, or for testing a hypothesized mechanism's effect on particular parameters. In physics, equations for quantum stochastic processes does not mean we've finished with our quantum understanding of the universe. Math is not science, it's a separate thing that helps with science. Generalized models are generalized models, not fully accurate representations. And trying to prematurely universalize models is just as bad as p-hacking. Even worse is trying to universalize a single model idea (such as holograms, cellular automata, or fractals) to an entire field. Even if you are right, your model provides a divination understanding of the phenomena, not a scientific understanding of the phenomena. Crap, I have some good points here, but it's probably TLDR at this point.
adzm 3y ago
Long story short, fractal has a specific mathematical meaning, and a common more vague meaning, and these meanings are not the same.
deleted 3y ago
[deleted]
dako2117 3y ago
it really amazes me that someone took the time to write this article.
coremoff 3y ago
3blue1brown has some good fractal videos; one in particular being relevant to this discussion: "Fractals are typically not self-similar" - https://www.youtube.com/watch?v=gB9n2gHsHN4 https://www.youtube.com/watch?v=gB9n2gHsHN4
anigbrowl 3y ago
Somewhat off-topic, but since this thread has attracted people with a prior interest in L-systems: is anyone aware of an algorithm/ research/ anything really into reverse-engineering the - that is, given a degenerate tree or a set of trees, extracting a decent model that produces similar trees? By degenerate tree, I mean messy real-world examples of trees in the computer programming/graph sense. Imagine applying algorithm to large directory trees or taxonomies; I'm interested in whether there's a mathematical way to approximately model the structural features.
cies 3y ago
I have seen some nature museum as a kid, and the older the life forms were in there, the more they looked "fractalish" to me. Ferns, fossils, the older the repeating'er.
mkaic 3y ago
A less prescriptivist title would be "I disagree with how people use the word fractal", as words are defined by how they're used and in what contexts, not by dictionaries or institutions. Considering that many, many people call fern leaves and cauliflower curds fractals, I see no issue with them continuing to do so. English as she is spoke.
rsiqueira 3y ago
...and "3.14159265358979" is also not PI! Because PI is infinite.
- deleted 3y ago
  [deleted]
frou_dh 3y ago
Rosetta Code has a page on how to draw the 'fractal' fern leaf in dozens of different programming languages, probably including your favourite: https://rosettacode.org/wiki/Barnsley_fern https://rosettacode.org/wiki/Barnsley_fern
dekhn 3y ago
Here's a much more interesting (popsci) article: https://www.nytimes.com/2021/07/08/science/cauliflower-fractals.html https://www.nytimes.com/2021/07/08/science/cauliflower-fract... and the paper related to it: https://www.science.org/doi/full/10.1126/science.abg5999 https://www.science.org/doi/full/10.1126/science.abg5999 Note the comment at the bottom of the article (who is the author of the posted article) After reading a fair amount of this I'd conclude that the posted article doesn't really move science farther, it just acts as a pedantry gate.
ssalka 3y ago
There are no true mathematical fractals in nature, only approximations of them. But to say that ferns are not even approximating fractals at all is clearly incorrect to me. Sure, the leaves don't randomly spawn in space, filling the leaf region at various points - they're leaves, they grow like leaves. It's still an iterated function system, the same type of fractal as a Sierpinski triangle. The only difference is it's a limited number of iterations.

78 points by minicaionut 3y ago

[dead]

> A realistic set of mathematical equations to describe fern leaf or cauliflower curd development is needed I wish the author had derived these equations -- something like the book The Geometry of Pasta https://www.amazon.com/Geometry-Pasta-Caz-Hildebrand/dp/1594744955 https://www.amazon.com/Geometry-Pasta-Caz-Hildebrand/dp/1594...

deleted 3y ago
[deleted]
bannedbybros 3y ago
[dead]

d--b 3y ago

Of course it's not an actual fractal, because you know, infinity... But take the Romanesco Broccoli, it really looks like a fractal. It can't be just random. There definitely is some kind of mechanism that's fractal-ish somewhere.

kqr 3y ago
You can estimate Hausdorff dimensions of non-infinitessimal things, like coastlines.
- Y_Y 3y ago
  Indeed, and there's a nice list of them here: https://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension https://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_... It's also worth noting that there are other ways of "measuring" fractal dimension that do not always agree so it can be informative to also look at e.g. box counting dimension too.
wrs 3y ago
It isn’t random, and it also isn’t a fractal (as is explained in the very short article). In other news, the golden ratio doesn’t really occur in nature as much as people would like to believe. [0] [0] https://www.maa.org/external_archive/devlin/devlin_05_07.html https://www.maa.org/external_archive/devlin/devlin_05_07.htm...
- kergonath 3y ago
  > as is explained in the very short article It’s a straw man. The fractal is an analogy; nobody seriously thinks you can zoom in or out of a cauliflower infinitely. We know about atoms and stuff. It’s just pointless pedantry.
  - wrs 3y ago
    Analogies are only useful to the extent they have explanatory power. The assertion here is that this one doesn’t: there are several distinct growth mechanisms applied in sequence, not a recursive application of the same mechanism.
    - anigbrowl 3y ago
      Different mechanisms can use the same template. The Romanesco cauliflower is so obviously self-similar that ignoring this in favor of talking about mechanisms that vary according to scale needs is missing the forest for the trees.
      - anonymouskimmer 3y ago
        Biology has the concept of convergent evolution. Would you say a Thylacine is a Wolf, and that it's appropriate to treat one as the other? Fractals are a singular example of repeating patterns, but there are additional repeating pattern types that aren't fractals. Just like Thylacines and Wolves were/are examples of apex predators, not versions of each other.

throwbadubadu 3y ago

> Actual fern leaves and cauliflower curds have a very small number of anatomically variable and non-iterating bifurcations, which superficially look self-similar, but do not allow for scaling down of their structure as real fractals do. Sorry, can't help it, but really? You cannot zoom into real-life fractals infinitely like in those math animations, only a few times? What comes next? Even the coast line or mountains fractal analogies are wrong in the mathematical sense, you won't even the same shape once if you try hard?? > The above cases demonstrate a general problem of using mathematical tools to investigate or illustrate biological phenomena in an irrelevant manner. No, I think we have a different problem here..

bannedbybros 3y ago
[dead]
LesZedCB 3y ago
imagine publishing a whole paper to win an "Um, actually" argument
ajuc 3y ago
Fractals don't even need to be self-similar. They just need to have fractal dimension (if you double the size of every feature - the exponent near the scaling factor must be non-integer). Self-similarity is the easiest way to make a fractal, but not the only one. In fact the idea of fractal was invented for real-life non-self-similar objects. The simple self-similar ones are just examples that are easiest to understand.
- ouid 3y ago
  As far as i can tell, fractal doesn't have a definition. The closest it ever came was the one you roughly gave.
  - idiotsecant 3y ago
    https://en.wikipedia.org/wiki/Fractal_dimension https://en.wikipedia.org/wiki/Fractal_dimension Not only are fractals very well defined in mathematical terms, but there are further mathematics based on those definitions.

freedude 3y ago

"Like fern leaves or any other plant branching system at the organ level, the cauliflower curd develops from the inside out through a process totally different from fractal drawing." Soooo, what the author is stating is they are actually even more amazing and wonderfully made than we originally thought. Even though they look like the mathematical model of a built fractal they grow entirely different and with an internal program that cannot be reproduced by our existing knowledge-base.

jonathankoren 3y ago
I read that same line, but came to the opposite conclusion than you. I didn’t find it amazing at all, instead I found it banal. Essentially the author is saying that fern leaf doesn’t grow as single line, and then subdivides. Well, no shit. Literally no one ever thought that. It betrays a lack of imagination where the author is conflating a single algorithm for the construction of a fractal to an actual fractal shape. It’s the same as complaining that something similar to a Sierpinski’s Triangle can’t be a fractal because it wasn’t made by placing atoms at the midpoints between it and a randomly selected exterior vertex. Are fern leaves technically fractals? No. (And no, I am not talking about the sophomoric objection then lacking infinite regression.) Are they similar to fractals? Yes. Is it useful as an illustration of both a feactal, and how complex body plans can be encoded in DNA without actually specifying every point like a literal blueprint? Yes. None of this is different than the discussing the similarities fractals and coastlines. No one thinks Britain is a literal fractal. Honestly, this idea of fractals is very similar to the idea that the irrational number phi shows up it nature. When you actually look deeply at the purported examples, you’ll find out, it’s not actually there.
ajuc 3y ago
You can create the same fractal in many ways. For example you get Sierpiński triangle if you repeatedly draw smaller triangles, or you can just do xor.
- CrazyStat 3y ago
  My favorite way to draw the Sierpinski triangle is Monte Carlo: 1. Pick a point which is in the triangle (e.g. one of the corners of the triangle). Draw that point. 2. Choose one corner of the triangle at random. 3. Move to the point half way between your current point and the chosen corner. Draw that point. 4. Repeat steps 2-3 as long as desired. Obviously this only ever reaches a countable subset of the triangle based on where you start, but that subset is everywhere dense in the triangle so it doesn't matter. You can also start at an arbitrary point that's not actually in the triangle. If you discard the first k (say 10) iterations you'll still get something visually indistinguishable from a Sierpinski triangle. You can also do this with other self-similar fractals, you just have to find the right set of transformations to use. It's quite fun watching the random points coalesce into the shape of the fractal.

jamal-kumar 3y ago

> A realistic set of mathematical equations to describe fern leaf or cauliflower curd development is needed Well if we're talking about Lindenmayer's work on L-Systems being limited to abstract representations of plants, without getting into all the other structures we're seeing that AREN'T self-similar within the plant itself, yet still branching and perhaps representable by a totally different L-system representation from say the branching of stems and leaves (Say networks of vasculature within plants such as xylem and pholem, which we see as 'veins' within the leaves for example) - Then yeah, plants really are WAY more complex than that and they deserve a more accurate representation. I think L-systems are beautiful and I really recommend anyone who's interested check out Lindenmayer's work on it all [1] but I think if this article has any point it's that we need more complex models to really do plants justice. I think that the fractal appearance of stuff like romanesco broccoli sure is cool but I think it's better understood as sort of a holographic projection of fractalline growth into 3d space rather than an actual 3d fractal Like these models are super excellent for making renders of plants in 3D modelling engines but they're not REALLY plants, even if we can make them look incredibly realistic using just that basic level of modelling, some nice shaders, and some trig functions to make it look like it's blowing in the wind [1] https://en.wikipedia.org/wiki/The_Algorithmic_Beauty_of_Plants https://en.wikipedia.org/wiki/The_Algorithmic_Beauty_of_Plan... [1]

eternalban 3y ago
I remember reading about L-Systems in Santa Fe Institutes publications in '90s. Just found this book below when searching for that - this looks comprehensive at a glance: The Algorithmic Beauty of Plants, Prusinkiewicz & Lindenmayer, 2004 http://algorithmicbotany.org/papers/abop/abop.pdf http://algorithmicbotany.org/papers/abop/abop.pdf
- fatneckbeard 3y ago
  amazing

intrasight 3y ago

There have been some HN posts on this recently. Some quick findings: https://www.nytimes.com/2021/07/08/science/cauliflower-fractals.html https://www.nytimes.com/2021/07/08/science/cauliflower-fract... https://www.science.org/doi/10.1126/science.abg5999 https://www.science.org/doi/10.1126/science.abg5999 https://ournarratives.net/cauliflowers-fractal-pattern-a-key-to-understanding-nature/ https://ournarratives.net/cauliflowers-fractal-pattern-a-key... Even if not a "true" fractal, for the layperson, it's close enough and does a good job of showing what is a fractal.

anonymouskimmer 3y ago

People who are complaining about the article: There's this trope about physics and math envy, which I think ultimately boiled down an envy of the funding that physicists received in the cold war (it lead to a lot of equations in Ecology, for instance). But ignoring the reasons for math envy for a moment, there's also a push among some of the more computationally inclined to try to explain other sciences using their tools. This has been going on for a least a few decades, with "holographic universe" ideas, Wolfram's "New Kind of Science", and the like, and of course actual computational modeling such as weather models. And conflating a prediction engine with intelligence (like that guy at Google did). It's good to show that these reductions, at our current level of computational technology, are not that accurate. "Computational hacking" is really no different from "P-hacking", in that it is easily abused by the lay audience and scientists who conflate possibly fictitious correlative modeling with reality. The model is not the thing. The P-score is not the thing. Mechanisms are the thing. Mechanisms are the core of science. All else is preliminary, at best.

red_trumpet 3y ago
I don't think I get your point. Especially regarding weather models. I'm pretty sure that to program good weather predictions, you need to know a lot about the mechanisms. And a prediction model can be used to test theories by comparing predictions against reality. That makes the theories falsifiable. And what is it about comparing computational weather models to p-hacking? Good weather predictions provide value to lots of people, while p-hacking is looking for results where there are none, only benefitting the hacker.
- anonymouskimmer 3y ago
  TLDR: Math and models can aid with understanding, but fundamentally they're about divination, not explanation. And explanation is the core of science. Over application of models is as bad as p-hacking, in that false explanations for phenomena are promulgated. At least with p-hacking, one other paper can say that a correlation was not shown. Whereas with model-hacking, there is often a tendency to "tweak" the model to fit, ala the earth-centric model of the solar system with its epicycles. > And what is it about comparing computational weather models to p-hacking? P-hacking is just an extension of assuming p-values past a certain point are very good evidence of real-world correlation. The Princeton Engineering Anomalies Research has evidence showing human-operator specific effects on computerized random processes at the 7 sigma statistical level: https://pearlab.icrl.org/pdfs/1997-correlations-random-binary-sequences-12-year-review.pdf https://pearlab.icrl.org/pdfs/1997-correlations-random-binar... Do you believe that this evidence of possible psychic phenomena is real without validated mechanistic means? > Good weather predictions provide value to lots of people, while p-hacking is looking for results where there are none, only benefitting the hacker. Except when the p-hacking is, serendipitously, correct. P-hacked results are not necessarily wrong, they're just fraught. > I'm pretty sure that to program good weather predictions, you need to know a lot about the mechanisms. I'm not saying that all use of models and mathematics in science is bad. I'm saying that premature generalizations based on looks is bad. Do you at least get my point regarding reducing the universe to a hologram or to cellular automata? Weather modeling is much better than these because of its predictive power, but most importantly because the weather modelers keep trying to refine their models based on actual mechanisms. Knowledge of the mechanisms help guide the parameters used in the models. But the models are not the thing. The equations are not the mechanisms. And the approximations certainly aren't the thing. And I'm sure that holograms and cellular automata are useful at times in predicting or thinking about reality, just as fractals are useful in some understanding of plants (despite not being accurate models). Just as the Earth-centric model of the solar system with its epicycles was pretty decent at predicting future positions of the planets. Mathematical models are not the end of the scientific investigation. Mathematical models are the intersection of science (understanding of the universe) and divination (trying to predict the future). Statistics are most useful for trying to identify linkages which probably share mechanisms, or for testing a hypothesized mechanism's effect on particular parameters. In physics, equations for quantum stochastic processes does not mean we've finished with our quantum understanding of the universe. Math is not science, it's a separate thing that helps with science. Generalized models are generalized models, not fully accurate representations. And trying to prematurely universalize models is just as bad as p-hacking. Even worse is trying to universalize a single model idea (such as holograms, cellular automata, or fractals) to an entire field. Even if you are right, your model provides a divination understanding of the phenomena, not a scientific understanding of the phenomena. Crap, I have some good points here, but it's probably TLDR at this point.

adzm 3y ago

Long story short, fractal has a specific mathematical meaning, and a common more vague meaning, and these meanings are not the same.

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dako2117 3y ago

it really amazes me that someone took the time to write this article.

coremoff 3y ago

3blue1brown has some good fractal videos; one in particular being relevant to this discussion: "Fractals are typically not self-similar" - https://www.youtube.com/watch?v=gB9n2gHsHN4 https://www.youtube.com/watch?v=gB9n2gHsHN4

anigbrowl 3y ago

Somewhat off-topic, but since this thread has attracted people with a prior interest in L-systems: is anyone aware of an algorithm/ research/ anything really into reverse-engineering the - that is, given a degenerate tree or a set of trees, extracting a decent model that produces similar trees? By degenerate tree, I mean messy real-world examples of trees in the computer programming/graph sense. Imagine applying algorithm to large directory trees or taxonomies; I'm interested in whether there's a mathematical way to approximately model the structural features.

cies 3y ago

I have seen some nature museum as a kid, and the older the life forms were in there, the more they looked "fractalish" to me. Ferns, fossils, the older the repeating'er.

mkaic 3y ago

A less prescriptivist title would be "I disagree with how people use the word fractal", as words are defined by how they're used and in what contexts, not by dictionaries or institutions. Considering that many, many people call fern leaves and cauliflower curds fractals, I see no issue with them continuing to do so. English as she is spoke.

rsiqueira 3y ago

...and "3.14159265358979" is also not PI! Because PI is infinite.

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frou_dh 3y ago

Rosetta Code has a page on how to draw the 'fractal' fern leaf in dozens of different programming languages, probably including your favourite: https://rosettacode.org/wiki/Barnsley_fern https://rosettacode.org/wiki/Barnsley_fern

dekhn 3y ago

Here's a much more interesting (popsci) article: https://www.nytimes.com/2021/07/08/science/cauliflower-fractals.html https://www.nytimes.com/2021/07/08/science/cauliflower-fract... and the paper related to it: https://www.science.org/doi/full/10.1126/science.abg5999 https://www.science.org/doi/full/10.1126/science.abg5999 Note the comment at the bottom of the article (who is the author of the posted article) After reading a fair amount of this I'd conclude that the posted article doesn't really move science farther, it just acts as a pedantry gate.

ssalka 3y ago

There are no true mathematical fractals in nature, only approximations of them. But to say that ferns are not even approximating fractals at all is clearly incorrect to me. Sure, the leaves don't randomly spawn in space, filling the leaf region at various points - they're leaves, they grow like leaves. It's still an iterated function system, the same type of fractal as a Sierpinski triangle. The only difference is it's a limited number of iterations.