How math interprets biology and life, and the cosmos (Introduction)

by David Turell @, Thursday, November 28, 2013, 19:49 (4013 days ago)

http://blogs.scientificamerican.com/guest-blog/2013/11/27/to-what-extent-do-we-see-with... proposals from both Deutsch and Chaitin share the view that mathematics is integral to biological processes. Perhaps they each represent an evolution of thought in science, where the distinction between what was once considered mechanical action and thoughtful action becomes less clear and where thoughtful action is understood as part of the life of the universe"

How math interprets biology and life, and the cosmos

by dhw, Friday, November 29, 2013, 16:03 (4012 days ago) @ David Turell

DAVID: http://blogs.scientificamerican.com/guest-blog/2013/11/27/to-what-extent-do-we-see-with... "The proposals from both Deutsch and Chaitin share the view that mathematics is integral to biological processes. Perhaps they each represent an evolution of thought in science, where the distinction between what was once considered mechanical action and thoughtful action becomes less clear and where thoughtful action is understood as part of the life of the universe"-I found some of this hard to follow, but the conclusion you have quoted above rings all kinds of bells. It also has a wonderful ambivalence. If there is no clear distinction between mechanical action and thoughtful action, we can end our long debate on the nature of the cell (it is both mechanical and thoughtful), and if the principle extends to the life of the universe, we can embrace panpsychism, in which "each spatio-temporal thing has a mental or 'inner' aspect" (Oxford Companion to Philosophy). Of course it still gets us nowhere nearer solving the mystery of how thought originated.

How math interprets biology and life, and the cosmos

by David Turell @, Saturday, November 30, 2013, 00:08 (4012 days ago) @ dhw

DAVID: http://blogs.scientificamerican.com/guest-blog/2013/11/27/to-what-extent-do-we-see-with... 
> QUOTE: "The proposals from both Deutsch and Chaitin share the view that mathematics is integral to biological processes. Perhaps they each represent an evolution of thought in science, where the distinction between what was once considered mechanical action and thoughtful action becomes less clear and where thoughtful action is understood as part of the life of the universe"
> 
> dhw: I found some of this hard to follow, but the conclusion you have quoted above rings all kinds of bells. It also has a wonderful ambivalence. If there is no clear distinction between mechanical action and thoughtful action, we can end our long debate on the nature of the cell (it is both mechanical and thoughtful), and if the principle extends to the life of the universe, we can embrace panpsychism, in which "each spatio-temporal thing has a mental or 'inner' aspect" (Oxford Companion to Philosophy). Of course it still gets us nowhere nearer solving the mystery of how thought originated.-My take-away is that mathematics discovers so much and predicts so much and fits the processes so well.

How math interprets biology and life, and the cosmos

by xeno6696 @, Sonoran Desert, Saturday, December 14, 2013, 23:10 (3997 days ago) @ David Turell

DAVID: http://blogs.scientificamerican.com/guest-blog/2013/11/27/to-what-extent-do-we-see-with... > 
> > QUOTE: "The proposals from both Deutsch and Chaitin share the view that mathematics is integral to biological processes. Perhaps they each represent an evolution of thought in science, where the distinction between what was once considered mechanical action and thoughtful action becomes less clear and where thoughtful action is understood as part of the life of the universe"
> > 
> > dhw: I found some of this hard to follow, but the conclusion you have quoted above rings all kinds of bells. It also has a wonderful ambivalence. If there is no clear distinction between mechanical action and thoughtful action, we can end our long debate on the nature of the cell (it is both mechanical and thoughtful), and if the principle extends to the life of the universe, we can embrace panpsychism, in which "each spatio-temporal thing has a mental or 'inner' aspect" (Oxford Companion to Philosophy). Of course it still gets us nowhere nearer solving the mystery of how thought originated.
> 
> My take-away is that mathematics discovers so much and predicts so much and fits the processes so well.-So I catch you at this again! ;-) I've missed hanging out here, I wish I could do it more!-Mathematics by itself doesn't do any of these things. Math as a "thing-in-itself" is a study of logical structures that may or may not have any physical reality in any universe, using a precise language--the most precise language man has ever invented. -That the natural sciences have been able to use the logical structures of mathematics to explain SOME things about the universe isn't shocking. Here's a different way to look at it: A scientist observes a phenomena, writes down a sentence, and then experiments until his sentence allows him to predict the outcome. There's no magic and no mystery here, unless we consider trial and error to be magical and mysterious!-I've said it a couple times before: We ought not be shocked that the most precise language ever invented explains things precisely! Dawkins falls into this all the time, an amazement that the universe is comprehensible. Well, I would posit that if the universe was incomprehensible, we really wouldn't know the difference, because we simply would have evolved with this "new normal." (Consider the old book "Flatland.") -I agree with dhw here, I think you inadvertently stepped into a trap. If we cannot differentiate between mechanical and thoughtful action, what does this mean for your creator argument? You rightly agree that it muddies the waters, but it muddies them worse for you than it does for those of us on the fence, because you're undermining your own conviction that you can "know intelligence when you see it!" If intelligence is "thoughtful action" and the lack of intelligence is "mechanical action," and you posit that we can't tell the difference... then we cannot know "thoughtful action" when we see it.

--
\"Why is it, Master, that ascetics fight with ascetics?\"

\"It is, brahmin, because of attachment to views, adherence to views, fixation on views, addiction to views, obsession with views, holding firmly to views that ascetics fight with ascetics.\"

How math interprets biology and life, and the cosmos

by David Turell @, Sunday, December 15, 2013, 01:18 (3997 days ago) @ xeno6696

My take-away is that mathematics discovers so much and predicts so much and fits the processes so well.
> 
> Matt: So I catch you at this again! ;-) I've missed hanging out here, I wish I could do it more!-We'd love having you back. We know you are very busy, but dhw has kept me busy writing the new book ,fighting with the publisher, but dhw is an awesome style editor and the book is about to appear.
> 
> I've said it a couple times before: We ought not be shocked that the most precise language ever invented explains things precisely! Dawkins falls into this all the time, an amazement that the universe is comprehensible. -Einstein said it first and wasn't as amazed as Little Richard. - 
> Matt: If we cannot differentiate between mechanical and thoughtful action, what does this mean for your creator argument? You rightly agree that it muddies the waters, but it muddies them worse for you than it does for those of us on the fence, because you're undermining your own conviction that you can "know intelligence when you see it!" If intelligence is "thoughtful action" and the lack of intelligence is "mechanical action," and you posit that we can't tell the difference... then we cannot know "thoughtful action" when we see it.-That is not the intent of my statements. "Mechanical action" is driven by intelligent information in the genome. It makes the cells seem intelligent of their own volition, but they use implanted information from an intelligent source.

How math interprets biology and life, and the cosmos

by xeno6696 @, Sonoran Desert, Sunday, December 15, 2013, 04:08 (3997 days ago) @ David Turell

That is not the intent of my statements. "Mechanical action" is driven by intelligent information in the genome. It makes the cells seem intelligent of their own volition, but they use implanted information from an intelligent source.-How can you say that with conviction when we don't even know what the DNA of the first organisms really look like? I'm all for challenging Dawkins, but with the exception of abiogenesis, we have a pretty clear picture of the life of biology, and the picture painted is from incredibly simple to incredibly complex. And I still have never seen anything that suggests that the genome is informed by any source other than the external environment, evolution and epigenetics included.

--
\"Why is it, Master, that ascetics fight with ascetics?\"

\"It is, brahmin, because of attachment to views, adherence to views, fixation on views, addiction to views, obsession with views, holding firmly to views that ascetics fight with ascetics.\"

How math interprets biology and life, and the cosmos

by Balance_Maintained @, U.S.A., Sunday, December 15, 2013, 05:32 (3997 days ago) @ xeno6696

David: That is not the intent of my statements. "Mechanical action" is driven by intelligent information in the genome. It makes the cells seem intelligent of their own volition, but they use implanted information from an intelligent source.
> 
> Matt: How can you say that with conviction when we don't even know what the DNA of the first organisms really look like? I'm all for challenging Dawkins, but with the exception of abiogenesis, we have a pretty clear picture of the life of biology, and the picture painted is from incredibly simple to incredibly complex. And I still have never seen anything that suggests that the genome is informed by any source other than the external environment, evolution and epigenetics included.-
Ummm....if we have such a clear picture than why are scientist constantly surprised by their discoveries? (Read: Why don't their new discoveries don't fit with their 'pretty clear picture'?)

--
What is the purpose of living? How about, 'to reduce needless suffering. It seems to me to be a worthy purpose.

How math interprets biology and life, and the cosmos

by xeno6696 @, Sonoran Desert, Sunday, December 15, 2013, 14:44 (3996 days ago) @ Balance_Maintained

David: That is not the intent of my statements. "Mechanical action" is driven by intelligent information in the genome. It makes the cells seem intelligent of their own volition, but they use implanted information from an intelligent source.
> > 
> > Matt: How can you say that with conviction when we don't even know what the DNA of the first organisms really look like? I'm all for challenging Dawkins, but with the exception of abiogenesis, we have a pretty clear picture of the life of biology, and the picture painted is from incredibly simple to incredibly complex. And I still have never seen anything that suggests that the genome is informed by any source other than the external environment, evolution and epigenetics included.
> 
> 
> Ummm....if we have such a clear picture than why are scientist constantly surprised by their discoveries? (Read: Why don't their new discoveries don't fit with their 'pretty clear -
You'll have to give me a more specific case. I haven't seen any earth-shattering science from biology lately unless we're talking GMO, or the company proposing to put firefly genes into plant leaves to reduce our reliance on electric light.

--
\"Why is it, Master, that ascetics fight with ascetics?\"

\"It is, brahmin, because of attachment to views, adherence to views, fixation on views, addiction to views, obsession with views, holding firmly to views that ascetics fight with ascetics.\"

How math interprets biology and life, and the cosmos

by Balance_Maintained @, U.S.A., Monday, December 16, 2013, 06:14 (3996 days ago) @ xeno6696

Tony: Ummm....if we have such a clear picture than why are scientist constantly surprised by their discoveries? (Read: Why don't their new discoveries don't fit with their 'pretty clear 
> 
> 
>Matt: You'll have to give me a more specific case. I haven't seen any earth-shattering science from biology lately unless we're talking GMO, or the company proposing to put firefly genes into plant leaves to reduce our reliance on electric light.-Well, for starters, that the shape of the genome and proteins are as important as their content. This is not new, but it was shocking when it was discovered. Or how about the the fact that gene expression can cause major and reversible changes in the physiology of a creature without passing through the gates of reproduction and without locking the traits in to the subsequent generation.(See the Grasshopper and the Locust)-This website is full of articles that defied sciences expectations.

--
What is the purpose of living? How about, 'to reduce needless suffering. It seems to me to be a worthy purpose.

How math interprets biology and life, and the cosmos

by xeno6696 @, Sonoran Desert, Monday, December 23, 2013, 16:28 (3988 days ago) @ Balance_Maintained

Well, for starters, that the shape of the genome and proteins are as important as their content. This is not new, but it was shocking when it was discovered. Or how about the the fact that gene expression can cause major and reversible changes in the physiology of a creature without passing through the gates of reproduction and without locking the traits in to the subsequent generation.(See the Grasshopper and the Locust)
> 
> This website is full of articles that defied sciences expectations.-Well, to me you're just describing the process of science. We don't know--that which we don't know. When someone comes up with a discovery that overturns the table... well that's not just to be expected, but embraced. -Regardless, I'll still hold to the fact that because science forces itself to change its views constantly, its a really good candle to use in the permeating darkness of knowledge.-[EDITED]

--
\"Why is it, Master, that ascetics fight with ascetics?\"

\"It is, brahmin, because of attachment to views, adherence to views, fixation on views, addiction to views, obsession with views, holding firmly to views that ascetics fight with ascetics.\"

How math interprets biology and life, and the cosmos

by David Turell @, Sunday, December 15, 2013, 06:50 (3997 days ago) @ xeno6696


>Matt: How can you say that with conviction when we don't even know what the DNA of the first organisms really look like? I'm all for challenging Dawkins, but with the exception of abiogenesis, we have a pretty clear picture of the life of biology, and the picture painted is from incredibly simple to incredibly complex. And I still have never seen anything that suggests that the genome is informed by any source other than the external environment, evolution and epigenetics included.-And where did the information come from that ran the original life. Based on current research it was highly complex, not simple, from the start. The basic cell is not simple.

How math interprets biology and life, and the cosmos

by xeno6696 @, Sonoran Desert, Sunday, December 15, 2013, 14:37 (3996 days ago) @ David Turell


> >Matt: How can you say that with conviction when we don't even know what the DNA of the first organisms really look like? I'm all for challenging Dawkins, but with the exception of abiogenesis, we have a pretty clear picture of the life of biology, and the picture painted is from incredibly simple to incredibly complex. And I still have never seen anything that suggests that the genome is informed by any source other than the external environment, evolution and epigenetics included.
> 
> And where did the information come from that ran the original life. Based on current research it was highly complex, not simple, from the start. The basic cell is not simple.-Yeah, because you're looking at cells that have undergone a few billions of years of evolution. Have we done the experiments to build a cell from scratch? That's the only way you're going to get any kind of answer. -Rehashing old ground, but you ceded that point to me years ago. (of course a cell that has undergone that much evolution would be complex.)

--
\"Why is it, Master, that ascetics fight with ascetics?\"

\"It is, brahmin, because of attachment to views, adherence to views, fixation on views, addiction to views, obsession with views, holding firmly to views that ascetics fight with ascetics.\"

How math interprets biology and life, and the cosmos

by David Turell @, Sunday, December 15, 2013, 15:59 (3996 days ago) @ xeno6696


> Matt:Rehashing old ground, but you ceded that point to me years ago. (of course a cell that has undergone that much evolution would be complex.)-The latest research on definitions of life have concluded that the first truly living cells were as complex as cells today. (It's in my new book)

How math interprets biology and life, and the cosmos

by xeno6696 @, Sonoran Desert, Monday, December 16, 2013, 01:58 (3996 days ago) @ David Turell


> > Matt:Rehashing old ground, but you ceded that point to me years ago. (of course a cell that has undergone that much evolution would be complex.)
> 
> The latest research on definitions of life have concluded that the first truly living cells were as complex as cells today. (It's in my new book)-Well, for those of us who aren't fully clear...-What is the current "state of the state" on the idea of "definitions of life?" -What are the role of Prions in evolution?

--
\"Why is it, Master, that ascetics fight with ascetics?\"

\"It is, brahmin, because of attachment to views, adherence to views, fixation on views, addiction to views, obsession with views, holding firmly to views that ascetics fight with ascetics.\"

How math interprets biology and life, and the cosmos

by David Turell @, Monday, December 16, 2013, 05:09 (3996 days ago) @ xeno6696


> Matt;Well, for those of us who aren't fully clear...
> 
> What is the current "state of the state" on the idea of "definitions of life?" -Still can't give a fully acceptable definition. Still debating. 
> 
> Matt;What are the role of Prions in evolution? -None that I know of. They are thrown in to confuse the issue. How do viruses fit into evolution, is just a good a question.

How math interprets biology and life, and the cosmos

by xeno6696 @, Sonoran Desert, Tuesday, December 17, 2013, 00:29 (3995 days ago) @ David Turell


> > Matt;Well, for those of us who aren't fully clear...
> > 
> > What is the current "state of the state" on the idea of "definitions of life?" 
> 
> Still can't give a fully acceptable definition. Still debating. 
> > 
> > Matt;What are the role of Prions in evolution? 
> 
> None that I know of. They are thrown in to confuse the issue. How do viruses fit into evolution, is just a good a question.-I'm not throwing it out there to confuse... come now... we have much history! :-) -There are tantalizing puzzle pieces here. I'm reminded of Number Theory: Tons of problems--trivially easy to define. Nearly impossible to solve.

--
\"Why is it, Master, that ascetics fight with ascetics?\"

\"It is, brahmin, because of attachment to views, adherence to views, fixation on views, addiction to views, obsession with views, holding firmly to views that ascetics fight with ascetics.\"

How math interprets biology and life, and the cosmos

by David Turell @, Tuesday, December 17, 2013, 00:53 (3995 days ago) @ xeno6696


> Matt: I'm not throwing it out there to confuse... come now... we have much history! :-) 
> 
> There are tantalizing puzzle pieces here. I'm reminded of Number Theory: Tons of problems--trivially easy to define. Nearly impossible to solve.-I think the legitimate answer is we don't know where prions fit in. I'm glad you are back, and I hope it is for a good length of time. What's happened with your book?

How math interprets biology and life, and the cosmos

by David Turell @, Tuesday, December 17, 2013, 04:51 (3995 days ago) @ David Turell

David: I think the legitimate answer is we don't know where prions fit in. I'm glad you are back, and I hope it is for a good length of time. What's happened with your book?-I dug into the final proof of my book for prions: -"Another alternative to early information-bearing proteins,
other than RNA, is prions. These are the same type of proteins
that cause mad cow disease. Recently, prions have been found to
manage changes in wild yeast, changes that are beneficial and
helpful especially when the the yeast is under stress. And these
changes are inheritable.-Quoted study: Prions were first found to produce heritable new traits
more than a decade ago in laboratory studies of simple
baker's yeast. The key discovery then was that some proteins
could spontaneously switch from a normal shape into
a self-perpetuating prion conformation. The switch to the
prion state alters protein function, which can result in the
appearance of new traits, some helpful, some detrimental.
Sophisticated cellular machinery ensures that replicating
[reproducing] prion templates are chopped into pieces
that can be passed to daughter cells during cell division.
Importantly, the rate at which proteins switch into and
out of the prion state increases in response to environmental
stress, suggesting that they are part of an inherent
survival mechanism that helps yeasts adapt to changes in
their surroundings. All the prions appear capable of creating
diverse new traits, nearly half of which are beneficial.
Convinced of the impact prions have had on yeast evolution,
the researchers speculate that these shape-shifting
The Atheist Delusion: Science IS Finding God 91
proteins may be "remnants of early life," from a time when
inheritance was predominantly protein-based rather than
nucleic-acid based (Prions are a common mechanism for
phenotypic inheritance in wild yeasts. Nature, 2012; 482
(7385): 363 DOI: 10.1038/nature10875).-This discovery with information-bearing prions opens up a
new theoretical area of an early attempt at an origin of life. But
it is a surprising odd-ball discovery considering what has been
thought to be reasonable in the past. Prions are proteins. The big
issue is how did they start? Where did their information come
from? In other words, prions have the same problems all the
other molecules have, which have been considered or attempted."-As I said, interesting but don't advance any theories.

How math interprets biology and life, and the cosmos

by xeno6696 @, Sonoran Desert, Tuesday, December 17, 2013, 21:35 (3994 days ago) @ David Turell

This discovery with information-bearing prions opens up a
> new theoretical area of an early attempt at an origin of life. But
> it is a surprising odd-ball discovery considering what has been
> thought to be reasonable in the past. Prions are proteins. The big
> issue is how did they start? Where did their information come
> from? In other words, prions have the same problems all the
> other molecules have, which have been considered or attempted."
> 
> As I said, interesting but don't advance any theories.-Why not? Unless you can make your God fit in a test tube, what else do I have? -;-)

--
\"Why is it, Master, that ascetics fight with ascetics?\"

\"It is, brahmin, because of attachment to views, adherence to views, fixation on views, addiction to views, obsession with views, holding firmly to views that ascetics fight with ascetics.\"

How math interprets biology and life, and the cosmos

by David Turell @, Wednesday, December 18, 2013, 01:31 (3994 days ago) @ xeno6696

This discovery with information-bearing prions opens up a
> > new theoretical area of an early attempt at an origin of life. But
> > it is a surprising odd-ball discovery considering what has been
> > thought to be reasonable in the past. Prions are proteins. The big
> > issue is how did they start? Where did their information come
> > from? In other words, prions have the same problems all the
> > other molecules have, which have been considered or attempted."
> > 
> > Matt: As I said, interesting but don't advance any theories.
> 
> Why not? Unless you can make your God fit in a test tube, what else do I have? 
> 
> ;-)-Considering we have no solidly accepted definition of life, things like viruses and prions keep dancing around. I have a section on the recent definition of life debate.

How math interprets biology and life, and the cosmos

by xeno6696 @, Sonoran Desert, Tuesday, December 17, 2013, 21:32 (3994 days ago) @ David Turell


> > Matt: I'm not throwing it out there to confuse... come now... we have much history! :-) 
> > 
> > There are tantalizing puzzle pieces here. I'm reminded of Number Theory: Tons of problems--trivially easy to define. Nearly impossible to solve.
> 
> I think the legitimate answer is we don't know where prions fit in. I'm glad you are back, and I hope it is for a good length of time. What's happened with your book?-Finals week this week, and I needed a diversion. -I'm back, it'll still be intermittent, but the next few weeks I'll be free. (Selling the house, so not THAT free, but still...)-As for the book, stalled. I need to get on the Hemingway plan of "Every day, 500 words."

--
\"Why is it, Master, that ascetics fight with ascetics?\"

\"It is, brahmin, because of attachment to views, adherence to views, fixation on views, addiction to views, obsession with views, holding firmly to views that ascetics fight with ascetics.\"

How math interprets biology and life, and the cosmos

by David Turell @, Wednesday, December 18, 2013, 01:28 (3994 days ago) @ xeno6696


> Matt; As for the book, stalled. I need to get on the Hemingway plan of "Every day, 500 words."-Great fun to have you back. As for the book, try dhw as the taskmaster. Took me about eight months, but I'm very free with my time and driving interest. I'll be finally in print in January, because the publisher is so hide bound and compartmentalized as if an Army outfit, doing everything by rules and regs, most of which slow everything down and end up counterproductive to authors.

How math interprets biology and life, and the cosmos

by xeno6696 @, Sonoran Desert, Saturday, December 21, 2013, 19:53 (3990 days ago) @ David Turell


> > Matt; As for the book, stalled. I need to get on the Hemingway plan of "Every day, 500 words."
> 
> Great fun to have you back. As for the book, try dhw as the taskmaster. Took me about eight months, but I'm very free with my time and driving interest. I'll be finally in print in January, because the publisher is so hide bound and compartmentalized as if an Army outfit, doing everything by rules and regs, most of which slow everything down and end up counterproductive to authors.-Maybe next time you could opt for self-publishing via the Amazon route. I'd think that the fees they charge aren't horrific, since I know there are several just-graduate english majors that use that avenue.

--
\"Why is it, Master, that ascetics fight with ascetics?\"

\"It is, brahmin, because of attachment to views, adherence to views, fixation on views, addiction to views, obsession with views, holding firmly to views that ascetics fight with ascetics.\"

How math interprets biology and life, and the cosmos

by David Turell @, Saturday, December 21, 2013, 20:24 (3990 days ago) @ xeno6696


> Matt: Maybe next time you could opt for self-publishing via the Amazon route. I'd think that the fees they charge aren't horrific, since I know there are several just-graduate english majors that use that avenue.-Non-carborundum illegitimus. In this case, I have ground them down. I am in publication and will have books by mid-January. The reason I chose them is two fold ,as dhw knows. They are a declared Christian publishing company, are angry about atheism, and they have a good marketing arm, with which I have already been in contact. I have a TV trailer made, a website under their umbrella, and I'm on their speakers bureau. As for a next time, only if dhw convinces me again.

How math interprets biology and life, and the cosmos

by David Turell @, Monday, January 06, 2014, 21:19 (3974 days ago) @ David Turell

More confusion about prions. They can change folds without DNA guidance:-http://blogs.scientificamerican.com/lab-rat/2014/01/05/evolving-proteins-no-dna-required/?WT_mc_id=SA_DD_20140106

How math interprets biology and life, and the cosmos

by David Turell @, Tuesday, September 05, 2023, 16:27 (445 days ago) @ David Turell

The math hidden in genetics:

https://www.sciencealert.com/scientists-discover-pure-math-is-written-into-evolutionary...

"Luckily for us, a motley team of researchers has just uncovered another striking connection between math and nature; between one of the purest forms of mathematics, number theory, and the mechanisms governing the evolution of life on molecular scales, genetics.

"Abstract as it may be, number theory might also be one of the more familiar forms of math to many of us. It encompasses the multiplication, subtraction, division, and addition (arithmetic functions) of integers, or whole numbers and their negative counterparts.

"The famed Fibonacci sequence is but one example, where each number in the sequence is the sum of the previous two. Its patterns can be found all through nature, in pinecones, pineapples, and sunflower seeds.

"'The beauty of number theory lies not only in the abstract relationships it uncovers between integers, but also in the deep mathematical structures it illuminates in our natural world," explains Oxford University mathematician Ard Louis, senior author of the new study.

***

"Mutations accumulate at a steady rate over time, charting the genetic relationships between organisms as they slowly diverge from a common ancestor.

"Organisms need to be able to tolerate some mutations though, to preserve their characteristic phenotype whilst the genetic lottery continues to deal out substitutes that may or may not be advantageous.

"This so-called mutational robustness generates genetic diversity, yet it varies between species, and can even be observed in the proteins inside cells.

"Studied proteins can tolerate around two-thirds of random errors in their coding sequences, meaning 66 percent of mutations are neutral and have no effect on their final shape.

***

"Louis and colleagues wondered how close nature could get to the upper bounds of mutational robustness, so ran numerical simulations to compute the possibilities.

"They studied the abstract mathematical features of how many genetic variations map to a specific phenotype without changing it, and showed mutational robustness could indeed be maximized in naturally-occurring proteins and RNA structures.

"What's more, the maximum robustness followed a self-repeating fractal pattern called a Blancmange curve, and was proportional to a basic concept of number theory, called the sum-of-digits fraction.

"'We found clear evidence in the mapping from sequences to RNA secondary structures that nature in some cases achieves the exact maximum robustness bound," says Vaibhav Mohanty, of Harvard Medical School.

"'It's as if biology knows about the fractal sums-of-digits function."

"Once again math appears to be an essential component of nature that gives structure to the physical world, even on microscopic levels."

Comment: God, the master designer, is a master mathematician.

How math interprets biology and life, and the cosmos

by David Turell @, Tuesday, September 05, 2023, 16:46 (445 days ago) @ David Turell

Brain neurons follow lognormal patterns:

https://www.livescience.com/health/scientists-reveal-the-hidden-math-that-governs-how-n...

"The density of neurons in the brain is governed by a fundamental mathematical function, new research finds.

"The discovery, which holds true across a variety of mammals, could help researchers make better computer models of the brain in the future.

***

"During their attempts to build models of the brain, van Meegan told Live Science, the team realized scientists knew little about what dictated the density of neurons in the brain. While previous work had compared densities from species to species or from some layers of the cortex — the outer, wrinkly part of the brain — there was little information about how the density of nerve cells might vary within cortical regions.

"The researchers combined previously collected data from mice, marmosets, macaques, humans, galagos (also known as bush babies), owl monkeys and baboons. They found that neurons were distributed in a common pattern across all of these mammals: Within different cortical regions, the density could be described with a lognormal distribution.

"On a graph, a lognormal distribution is skewed to one side, with a long tail tapering off to the right. What this represents, van Meegen said, is that there are a lot of regions with average neuron densities, but a few regions have much higher density. And those higher density regions may be important, because they represent rare but important deviations from the norm.

"'If we only look at the mean number of neurons, maybe one doesn't see the difference," van Meegen said. But the long-tailed distribution means that a few changes to extreme outliers in density might make a big difference in brain connectivity or even function.

"The researchers also investigated why this pattern might hold across very different mammals. They found that given the way neurons arise — by cells dividing in a somewhat variable environment — the lognormal distribution arises naturally, without any need for regulatory processes.

"'It may originate from how the brain comes to be, by cells splitting over and over with a little bit of noise, possibly from internal variability or changes in the environment," or variability in the environment, Morales-Gregorio said. "This probably explains why it's everywhere."

"The researchers are now looking at how this pattern of distribution affects how neurons communicate with one another, and whether disruptions in the pattern might lead to neurological problems."

Comment: Look at the article to see the patterns which are logarithmic. More of God the math wizzard.

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