Is Life Mathematical?
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- Опубліковано 2 січ 2022
- Biology certainly uses mathematical methods, but in a seemingly different way to the "hard" sciences of physics and chemistry.
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#biology #math #modelling
SOURCES + FURTHER READING:
Golding, N., Price, D. J., Ryan, G., McVernon, J., McCaw, J. M., & Shearer, F. M. (2021). Estimating the transmissibility of SARS-CoV-2 during periods of high, low and zero case incidence. medRxiv. www.medrxiv.org/content/10.11...
Hutchinson, J. R., & Garcia, M. (2002). Tyrannosaurus was not a fast runner. Nature, 415(6875), 1018-1021. www.nature.com/articles/4151018a
Chauvet, E., Paullet, J. E., Previte, J. P., & Walls, Z. (2002). A Lotka-Volterra Three-Species Food Chain. Mathematics Magazine, 75(4), 243-255. doi.org/10.2307/3219158 Mitchell, S. D. (2000).
Dimensions of scientific law. Philosophy of Science, 67(2), 242-265. www.journals.uchicago.edu/doi...
Frigg, R., & Hartmann, S. (2006). Models in science. plato.stanford.edu/entries/mo...
Pigliucci, M. (2002, January). Are ecology and evolutionary biology" soft" sciences?. In Annales Zoologici Fennici (pp. 87-98). Finnish Zoological and Botanical Publishing Board philpapers.org/rec/PIGAEA
Jumper, J., Evans, R., Pritzel, A., Green, T., Figurnov, M., Ronneberger, O., ... & Hassabis, D. (2021). Highly accurate protein structure prediction with AlphaFold. Nature, 596(7873), 583-589. www.nature.com/articles/s4158...
www.burnet.edu.au/projects/46... (Burnet Institute Modelling)
www.mordorintelligence.com/in... (Growth rate of computational biology)
mathematica.stackexchange.com... (Code for Lotka-Volterra Simulation in Mathematica provided by m_goldberg and Szabolcs)
xkcd.com/435/ (Comic about ‘purity’ of sciences)
Life’s Edge: The Search For What It Means To Be Alive - Carl Zimmer carlzimmer.com/books/lifes-edge/
Infinite Powers - Steven Strogatz www.stevenstrogatz.com/books/...
The Growth of Biological Thought: Diversity, Evolution and Inheritance - Ernst Mayr
Love the video. This is definitely my new favorite channel. One point I would make, is that physics and chemistry have the luxury of constructing simplified systems in which to derive basic laws. Newton's laws break down for things as simple as three body problems and linked pendulums due to the emergence of chaos (and all our math can do is describe the edge of predictability). Biology cannot construct anything as simplified because life by definition exists above the threshold of complexity below which physics and chemistry usually operate. Given the lack of meaningful progress in physics in recent generations one has to wonder if we are already close to the limits of reductionist, mathematically summarized scientific discovery.
Great comment, and thanks for kind words 🥰. I’m going to expand on pretty much exactly what you said here in the next video - unpacking some of Lee Smolin’s ideas on ‘physics in a box’ and why biology can’t be reduced to physics. So stay tuned!
Newton’s Laws of Motion do not break down for the thee-body problem, they just give is differential equations which we are unable to solve analytically. That’s a big difference. They do break down when you get to the quantum scale or relativistic effects (mainly of GR) become large enough
Top 10 videos physicists don't want you to see (gone biological)
I guess physicists do want us to move towards biology. At least this is what I see in my academic envoriement.
A nice example I heard about recently was a use of topology in phylogenetics. You can define an 'ultrametric space' where every three points is related as an isosceles triangle. Sounds purely abstract, but that isosceles relation can be applied to the last common ancestor of two existing species. I know nothing about phylogenetics, I just thought that was cool!
Yeah topology is huge in phylogenetics - ill have to check that out! A particularly difficult problem is trying to work out how to draw the root node from a bunch of species. I.e. what was the earliest common ancestor and how did they relate to the current species. One way to work it out is to use algorithms to compare each topological configuration of the trees, but then your choice of algorithm becomes the problem. It’s super tricky and would be really great if we could just grab a time machine haha. Thanks for watching!
Jake
Except the models for phylogenetics struggle to deal with the reality of speciation through hybridisation and the widespread occurrence of horizontal gene transfer. It is chaos all the way down...
"All models are wrong, but some are useful."
--- George Box
I am really digging the videos of this channel, so I subscribed. Keep up the good work! :)
To be fair before I done my MBBS (bachelor of medicine and surgery) and qualifying as a medical doctor as a postgraduate, I studied biomedical science as my first undergraduate degree. The mathematics was pretty intensive at Oxford, especially pharmacodynamics and pharmacokinetics. Luckily I always had a passion of mathematics and still find myself studying it in my spare time (sad I know). Great video my friend, keep up the good work!
I have since changed my mind on my (hinted at) conclusion at the end of this video. I no longer think it's possible, even in principle, to find biological laws. See my updated video: ua-cam.com/video/oDG_7Ame0m0/v-deo.html Or Stuart Kauffman's brilliant lecture: ua-cam.com/video/EWo7-azGHic/v-deo.html
I had taken down this video for a few months because it didn't represent my updated thoughts. But now that I've made a new video, I think it's ok to un-private it and show a history of my thinking. Surely it shouldn't be an embarrassment to change your mind! (See CGP Grey on opinions: 1:10 of this video ua-cam.com/video/tlsU_YT9n_g/v-deo.html)
I really did have some physics envy back here. But you physicists got the easy problems and that made me jealous of your laws. Turns out biology is just a mess and we're gonna have to come to grips with not having universal laws. Tricky stuff.
Hope you'll all understand and looking forward to the discussion on this old video, or the new one.
Jake
Oh, I had just ranted about the last question only to scroll down and find this. You should PIN this comment so that it shows as the first comment...! Thanks for allowing history, man. It's beautiful to see a fellow theoretician of science online, and your content is amazing.
I understand you as a physicist student. But, curiously, biology subjects exams are easier than physics exams... At least pre - university. And yes, i prefer the physics approach. Sometimes biology is too much data to remember. But nowadays i am studying biophysics, and applying michaelis menten, hodgkin Huxley and some other stuff is much closer to What i Like than remember all the Krebs Cycle....
The thing is, Biologists and Biology Specialists (like Medics) will hire mathematicians. If the thing is too complex Biochemists and biophysicists will get involved. What differentiates biology and chemistry isn't the scale, but the analysis object. Life simply isn't reducible or describable through chemical properties and reactions, and chemistry is not reducible to math, and so on.
In the same fashion behaviour in apparent self-conscious minds without an actual mind seems absurd. Humanity self-consciousness is what justifies the separation from biology and psychology. Self-consciousnes isn't reducible or describable through both biological and chemical properties and reactions.
All this caos in psychology is demerit of social psychologists and other tabula rasa types which not only ignore their premises are paradoxical and the informal use of symbols are neither evident, stable or contingent on aristotelian identity, but also mix teleology (and politics) with the study of mind, or reduce mind to symbol or trend replicators.
Very insightful, can’t wait to see more content
Outstanding work Jake,
This is very impressive.
Good work, Jake!
Well done, this is dope and really well made 😍
Awesome video, mate! Keep at it
Thank you!
I have only read the comments of your first video and i am already impressed about the way you use this feedback to help formulate what you are trying to say. This way it becomes a collective effort. For me this would be the only reason to start making UA-cam video's myself. Looking forward to watching your video's. ❤
Thanks a lot that I've found your channel. Thanks for reigniting my deepest interest at the heart of both Biology and mathematics. Btw, I'm a Biochemist by training, not just a interested person.
Yes Jake! 🙌
Katherine Johnson-- a named I'd never even heard! Thanks
Thanks for the video! I was hoping to see something like this. I have a biology background but have recently developed interest in AI & Robotics. But not the traditional tracks, more into biomimicry and consciousness etc. Like Michael Levin's research. Regarding the theory side of the math in biology, I suppose complexity theory is widely used to describe biological phenomenon?
Similar story to yours... I'm a molecular biologist who's attempting (and failing?) to dive more into the physics and mathematical aspects of biology. I've been falling into the Levin rabbit hole, and Hoffman, and Kastrup, etc.
First off, in my opinion, the Laws of Physics are abstract ideas we have made up to try and understand and predict how the Laws of Nature work. To me, Mathematics is part of this. My point being that the Laws of Nature, in my belief, just are. While I do think it is reasonable to conclude that some types of Mathematics and some Laws of Physics are probably so close to how the Laws of Nature works that any intelligence developing Laws of Physics and Mathematics would develop the same abstract ideas.
But, the Laws of Nature are not thinking and do not have ideas. That may be a small distinction, but I think it i worth keeping in mind.
Now, everything in existence, EVERYTHING that exists, is bound by the Laws of Nature. This includes biology.
So, of course ALL OF biology is bound within the Laws of Nature which we can predictively model with Mathematics within the Laws of Physics assuming we have learned enough about the Laws of Nature in order to do so.
The issue with biology is that all biological systems are incredibly complex intelligent systems which are aware and conscious, functioning 100% completely within the Laws of Nature, but in ways we have not yet learned how to fully understand.
In other words, we have not yet learned, but will eventually learn, the Mathematical models required to understand and accurately predict in detail how these biological systems work from a quantum level upwards to entire whole organisms with swarm intelligence.
thank you for the brilliant video , i was wondering if you know a book on using of mathematical models in biology ?
Nice video! But you should compare the laws of Newton with actually laws in biology, not a model, I mean like the laws of Mendel or the laws in allometry (kleiber's law, for example). Really love your videos, it's something that was necessary in UA-cam!
That is a very good point actually, I can't actually remember why I focussed on models instead of biology's 'laws' (Mendel etc.). I might even remake this video in the future to be honest, there a few things I'd like to change.
I would say though that I think the distinction between a 'law' and a 'model' is in part purely linguistic/a matter of convention. Kleiber's law not so much, that's more of an interesting association. But for Mendel vs COVID modelling: they both only work in particular situations, give good predictions for those situations and describe highly idealised forms of the real world. Though, this is a huge area of debate in the literature. Here are a couple of links if you're curious:
www.jstor.org/stable/188723
plato.stanford.edu/entries/laws-of-nature/
Thanks for your feedback, it is invaluable in these early stages of the channel. Really appreciate it.
@@SubAnima thanxs! That are very good points to put on a future video!
very underrated
Go youtube algorithm make this channel big!
I know nothing of biology but do know math at the undergrad level. My assumption was biology was math heavy. Tho I know a PhD level biologist from top schools who told me she hates and is not good at math.
👏👏👏
EDIT: and now, I've bumped into your newer video, showing something changed as you continued studying. Awesome stuff, mate. Thanks for leaving historical references here too...
About the last question: Or, maybe, an epistemological shift might finally allow us to sometimes move away from these highly Popperian expectations... In some of the channel's other videos, many other epistemes are visited which is refreshing... I wonder why we still try to enforce science in a singular way... And when did we let Descartes colonize our scientific expectations with maths being the only solution to knowledge (only if god is not a deceiver, he says)? For instance, if we think of Maturana and Varella's epistemological contributions, there's plenty of stuff that can be done with biology that does not get all needy for statistics and mathematical modeling.
It's a fundamental error to think that physics is a better science (and you clearly did not fall for this trap, which is refreshing!). NOt only that, even my physicist friends agree that physics is way less "hard" than it's portrayed everywhere...
Found another gem!
Thanks so much! More coming super soon.. like today/tomorrow ;)
I love maths and biology
To us, everything is "mathemathical" becouse math is just natures way of making sence of its surroundings. All animals and insects count.
We are making an educated guess at modeling the universe with maths.
To me it seems inevitable that for a long time we'll never find precise and reliable mathematical theories of life with strong predictive power, for the same reason that we can't predict the weather reliably, simply because biological systems are vastly more complex than simple physical systems. Any model that is rich enough to be complete and reliable would involve simulating a vast system with billions of moving and interacting parts, and that necessarily requires a ton of computational power that we simply do not yet possess.
Greek philosophers were asking some of these exact same questions 2300 years ago. Funny how things work sometimes.
Why is the theory of evolution not in the broadly applicable section for biology? it doesn't make assumptions and it's broadly applicable
The video was very good. I was a little bit disappointed because you talked quite a lot about sharks and fishes which is essentially just a differential equation and nothing new to me.
Hey! Yeah I know, for people like you with a background in DEs it would be quite a tedious section. But it was moreso aimed at people with less experience with math and then introducing how it could be applied to biology in a relatively easy way (with sharks and fish). Hard to cater to everyone so better to err on the side of too simple than too complex. Glad you still enjoyed though.
Jake
COVID math was 💩