Biology Doesn’t Obey Mathematics. Biology Creates Mathematics.
Physics always obeys equations. Biology does not. It does sometimes… but not always! There is scarcely any formula in biology that is 100% true. In biology, there is NO precise definition of life, species, individual, gene, allele, inheritance, intelligence, sentience, function, or fitness. Compare this to physics, where gravity, waves and particles have incredibly precise mathematical definitions.
This isn’t simply because biology is complex, it’s because biology has agency and the ability to make choices. These choices are not an illusion; they are the only reason life can flourish. This fact, backed by formal mathematical proofs, has vast implications for the very definition of science itself.
In this talk at the American Scientific Affiliation in Boston, Perry Marshall unpacks the vast implications of this.
Based on the paper “The Reasonable Ineffectiveness of Mathematics in the Biological Sciences“
Perry Marshall: Good afternoon.
Great to be at ASA. My name is Perry Marshall. I’m from Chicago. 22 years ago, I went to China to visit my brother. He was a missionary. He had a seminary degree. He was teaching English, and, he had been there for four years, and he said, “Perry, I don’t believe this stuff anymore. I’m not a Christian. I’m quitting my job and going home, and, I’m done with this Christianity stuff.”
And we’re both pastors’ kids, and We were having some existential arguments for a long time, and he was dragging me with him, but I didn’t expect that. And we got into an argument, and I said, “Bryan, look at the hand at the end of your arm. This is a nice piece of engineering, and I’m an engineer, I should know.
You don’t think this is a random collection of accidents, do you?” And he goes, “Hold on.” And he came right back , “All you need to get a hand is random DNA mutations and natural selection, and you’ll eventually get a hand.” And I just stopped right [00:01:00] there and I thought, “That does not sound right to me.
I’ve never heard of that working anywhere else. But I know a bunch of biologists would nod their heads and agree with him and not me, and I’ve never studied this. I’m not getting anywhere in this argument. I’m gonna shut up, and I’m gonna go home, and I’m gonna figure this out.” That is actually why I’m here.
It was because we had this argument in this bus 22 years ago.
Speaker 4: Wow.
Perry Marshall: And I had no idea how deep and fascinating this question was going to become. And the only biology I had ever taken was high school biology, I didn’t like it. I was an electrical engineer. I had designed the speakers in the Jeep Cherokee and the Honda Civic.
I had written an Ethernet book. I had been a manufacturing engineer at Kellogg’s. I had done a lot of things, and I thought, ” Any theory of [00:02:00] evolution is a theory of engineering. And I’m an engineer, so if this is valid-” this should eventually make sense to me. So I started buying books and obsessing about this, and I just, I went as deep as I possibly could.
And after a while, I started to get my bearings, and I started to understand the terminology. And the deeper I went I had two opposing tensions. One of them was, as far as I can tell, an evolutionary narrative appears to be true. I see lots and lots of anecdotal evidence that would suggest common descent and adaptation, all of that.
I have no problem with that. But the story I’m being told of how this works doesn’t make sense. I’m an engineer. [00:03:00] I build things for a living. If you’ve ever been in a profession where if a bunch of products are coming back in pallets as warranty returns, and you go into a design review meeting, and you get your head bashed in, you have an appreciation for how carefully engineers design things.
And I saw a design in biology. and, and like these… Everybody made it sound like these two ideas were incompatible. and in fact, I was appalled, especially in the popular books that you would go buy at Barnes & Noble. I was appalled at the intellectual slop that passed for science in evolutionary biology.
The explanations were vacuous and smoke and mirrors. And I suddenly had a epiphany when I discovered Barbara McClintock, Lynn Margulis, James Shapiro, Conrad Waddington, Evelyn [00:04:00] Witkin. it took about two years to get there, but all of a sudden I discovered an enormous vein of literature that was very well documented that shows that organisms cut, splice, rearrange, re-engineer their DNA, respond to hostile situations at enormous speed, do merger acquisitions in real time, hours, not millions of years.
And I was like, “Why isn’t anybody talking about this?” And so I ended up writing a book called Evolution which came out in 2015. that has led to all kinds of interesting things. it led to a $10 million prize for the origin of the genetic code, to, co-founding the Cancer and Evolution Working Group of the American Association of Cancer Research, which has 5,000 members.
Perry: it led to me co-founding a cancer early detection startup a year and a half ago. I wrote a paper with Sy Garte and [00:05:00] Stu Kaufman a year ago, and it was a springboard off of… This is Eugene Wigner, and he wrote a paper in 1960 called The Unreasonable Effectiveness of Mathematics in the Natural Sciences.
And in this paper, it’s almost a meditation on how beautiful and incredible it is that in physics, everything obeys mathematics, and that there are discoveries that were made in mathematics 150 years ago, somebody with nothing but a piece of paper, and suddenly that exact same thing appears in particle physics, and it works perfectly.
And he’s meditating on the beauty of the correspondence between physics and math. And one day, Sy Gart and I were talking-
Sy Garte: At a meeting of ASA …
Perry: and Sy said, ” We need to write a paper [00:06:00] called The Reasonable Ineffectiveness- … of Mathematics in the Biological Sciences.” Because in unlike physics, and I’m electrical engineer, so I totally get physics.
In biology, there is almost no equation that is always true. Yeah. Almost none. And we published this in Entropy, and I wanna explain the rationale behind this paper because I think this reveals a bottleneck that’s been going on in science for about 100 years. So in, in life, in the world, I see three very different levels of causation that exist.
The first level is physical, chemical laws, and those are the things that Eugene Wigner was talking about in his paper. Gravitation and electromagnetics and waves, and all the things in physics that very often, exact equation, exact answer And that is one level of causation. And as far as I know, if you go to a dead planet with no life on it, that is the only kind of causation that you will find, as far as I am aware.
But then there’s another level so this, these are universal laws and change over time within these laws is order to disorder, entropy
Then there, the second layer is logic, symbolic logic, like we have in computers or DNA. Symbols, communication, computation, languages, machines, algorithms, genetics. That occupies a middle level. And as far as we know, this i- these laws are not derivable from physics and chemistry. Nobody knows how to derive the [00:08:00] genetic code or English or any other language from the laws of physics and chemistry because the symbols are freely chosen, and they are local rules that are local to a system or a culture or to a cell.
And computation under those rules is deductive and deterministic. There is one output for a given input, and that’s how the middle layer works. And also, codes are subject to noise, which is information entropy, which has the same math as thermodynamic entropy, but is not the same thing Then there’s the, the highest level of causation is cognition, which is choice, which is at least somewhat synonymous with consciousness.
Agency, action of self-interest, meaning the ability to create codes. It’s the ability to choose local laws. Cognition [00:09:00] is inductive reasoning, not deductive reasoning, which I will get to, in a second. In other words, it is choice within uncertainty. And change over time is disorder to order, which is negentropy, which is a term that Erwin Schrödinger coined in 1943 in his book, What Is Life?
I raised $10 million from private equity investors and organized a $10 million prize for the origin of the genetic code. we announced it at the Royal Society in 2019. That’s me with Denis Noble, who is a fellow of the Royal Society and an Oxford professor. Sy Garte said, “There are almost always exceptions to any proposed biological law.” And there is no precise… I want you to hear me very carefully. In biology, there is no precise definition of life, [00:10:00] species, individual, gene, allele, inheritance, intelligence, sentience, function, or fitness.
None of those things have a precise definition And so the conventional view, the story that you’re always told, is that the laws of physics and chemistry somehow coalesced, and there was a lucky RNA strand, and then we had code, and then the code started self-replicating with self-replicating cells, and natural selection kicked in, and eventually we got cognition and consciousness So they’re saying that you can get from the laws of physics and chemistry to the laws of codes, and then those will eventually get you consciousness.
There is no example of either of those two steps ever happening in any of the literature. Now, I believe that it is possible, and it’s why we have a $10 million prize. The prize is not a joke and it’s not a, a taunt. But I [00:11:00] think we have to discover new principles of how the universe works in order to solve that.
All of the causation that we know and understand is from cognition to codes to chemistry. In life, the gene does not just build the cell, the cell rewrites the genes. And there is an M.C.
Escher like hand drawing a hand- … way that life works. And it’s not just upward causation from chemistry up, it’s downward causation from cognition down. in the genetic code… yes … the code controls the chemistry, not the other way around
so there are two kinds of reasons Deductive reasoning says all men are mortal, therefore Socrates is mortal. It goes from the general to the specific. Inductive reasoning is when you go the opposite direction. It’s when you go, [00:12:00] “Socrates is mortal, therefore all men are mortal.”
It is a generalization. Computation always runs from the general to the specific. So deduction is going from the left side to the right side. Induction is going from the right side to the left. You can’t prove that all men are mortal just by knowing that Socrates is mortal. Now, when I started digging into this, I started looking for a rigorous definition of induction, and I couldn’t find one, and I had to invent one And the way that I have chosen to define inductive reasoning comes from mathematics in 1936.
Alan Turing defined the halting problem. So Turing invented the idea of a computer. A Turing machine is really just a computer, and what Turing discovered was there is no [00:13:00] program or formula to tell you in advance whether the computer is going to answer the question. It– is the calculation going to successfully converge?
There is– It is impossible for there to be a general formula to prove whether or not it will get to an answer. You just have to try it, and so that’s called the halting problem. A computer can only do deductive reasoning by definition. A, a Turing machine, by definition, only reasons from left to right. The halting problem is any time you’re asking, “Is it going to solve the problem?”
Is it going to solve the problem? Is induction. And so I am defining induction rigorously from Turing’s halting problem Computers only do deductive reasoning, but humans and cells and tissues do inductive reasoning. Which is the [00:14:00] halting problem? Which is, is there an answer So humans and cells and tissues do something that computers by definition can’t do And I think the mechanism of how they do it, which we do not understand, is really the key and the secret to life.
We don’t know what it is. And so cells, tissues, and organisms reason from a desired output to figure out what input will get them the output. All of us do this every day. I want lunch. How am I gonna get it? You might get it a different way every single day So Barbara McClintock discovered that cells actively re-structure their genomes.
Epigenetics, shows that, acquired characteristics do pass to offspring. cancer cells massively rearrange their DNA. new species in weeks or months, not millions of years, that’s [00:15:00] what Evolution is all about. So how do, when do we know that an agent is doing induction and not just calculating? The answer is when it readily solves problems for which analytic solutions are impossible.
It is well known that slime molds can solve the traveling salesman problem and design a most efficient Tokyo subway even though there is not a generalized algorithm for doing that.
I don’t know if any of you have gone down the Michael Levin rabbit hole. if you want to see fascinating examples of this, go to a Lex Fridman interview from, last fall, Michael Levin, Lex Fridman, and listen to a three-hour interview. it will, it’ll blow your mind. So What if negentropy, origin of life, evolution, strong AI, consciousness, and cancer are not six problems?
What if they are one problem? What is the origin of nature of [00:16:00] cognition? And what this implies is that science cannot advance beyond where it is until it lets go of the false certainty of mathematics. and I wanna close with a story. This is my absolute favorite professor, Dr. Robert Knoll. He was one of the most loved professors at the University of Nebraska.
He taught an English class, and every single class was mind-blowing. And one day, he’s in… he’s lecturing and he says, ” Teenagers, very often love to major in math, chemistry, physics, engineering because those are exact answer fields, and you get, multiple decimals of precision.” He said, “The older you get and the more mature you become, the more comfortable you become with ambiguity, and gray areas, and not exact answers, and politics, and imperfection.”
And he goes, “It’s [00:17:00] a sign of maturity if you’re progressing from the exact answers into the gray.” And then he says, “If you wanna spend the rest of your life searching for exact answers, you can go to Indian Hills Community Church.” That was the church I grew up in. That was the church my father was a pastor in.
And I felt as though my favorite professor had taken a two-by-four and whacked me on the side of the head. And I spent the whole afternoon walking around in a daze. And I remember it was about 3:00 that afternoon, I go, ” Wait a minute.” I don’t go to that church anymore. I stopped a few months ago, and I go to a different church with my sister W- why did I stop going there?
Because the exact answers were so excruciatingly exact, I couldn’t stand it anymore. It was dogmatic. It was rigid. And I’m like, ” I’ll be darn, my, my favorite professor just told me I’m growing up now.”
” And I’m only 20.” And he was [00:18:00] right. I think this is where science is at now. Biology has been trying to get rid of the shackles of physics envy- … which is misplaced. I love physics, but biology is a higher level of sophistication than physics. Biology doesn’t obey mathematics, biology creates mathematics, and that means there’s never going to be a perfect mathematical formula that’s gonna tell us how cancer works or how economics works or how marketing works or how psychology or sociology, there was a talk earlier about bipolar.
There are not exact answers. There are heuristics and models, and there’s the judgment and wisdom of choosing which data to, to focus on and which data to throw away because you can’t use all of the data. [00:19:00] So let’s have some questions, and I appreciate you enduring our blackout.
Karma-
Speaker 4: and I think I touched on this last year when you gave a talk. I’m not really comfortable with the concept of natural intelligence like that. But, it… I do see, from your talk a kind of progression very similar to what I see with Simon Conway Morris and his studies of, convergent evolution towards optimal body plan and the determinism.
And I think of, a directed evolution, approach towards optimal body plan. Does that kind of play a lot-
Perry Marshall: Yes. And in fact, if you go back and study history, at the same time that the Wright brothers were working on their airplane at Kitty Hawk, there was, like, six other people- Yeah … in other parts of the world that had no communication with each other, and they were working on the exact same thing.
And, technology had gotten to a certain place, and all these people are searching, and they’re all finding something that looks a lot like an airplane. It’s, you know- Yeah … similar, but This is how all technology works. This is how all biology works. It’s why there’s convergent evolution.
There’s only so many [00:20:00] solutions. And inductively, biology will find them. And it’s through ingenuity. It’s not through random accident. Yeah.
Speaker 4: Yeah. it’s a very deterministic and, a- Yeah … a directed approach. I like that idea. Rather than saying it’s a natural selection, it’s a random thing, there is, a, a directed- Yes
push towards, whatever ecological niche you’re in, for example, towards optimal body plan. Is that-
Speaker 2: Yes. And in the last five years or so, I’ve seen a remarkable openness to teleology and consciousness and cognition in biology that used to be verboten. The, the whole field is completely changing.
Yeah.
Speaker 6: so in other, so in other words, Perhaps I hope I’m not oversimplifying, but in other words, the assumption of evolutionary biology that things come randomly is basically incorrect. And if they view it as we see all these things in evolutionary biology, but there is some in- some purpose behind that, it would [00:21:00] solve a lot of the problems with statistics and probabilities and they would…
They’re actually, hindering their advancement because it might be easier to assume there’s purpose and then look how it advances- Yes … purpose in mind, instead of figuring out, oh, how long do you have to wait for this to happen randomly, and that. and it’s, they’re not focusing on the right path.
Yeah.
Perry Marshall: Yes, cancer is evolution running out of control. Yes. You will never solve cancer if you assume that a cancer cell is purposeless, ever.
Speaker 6: Yeah.
Perry Marshall: It is just as purposeful as a terrorist.
Speaker 6: Yeah.
Speaker 2: It has an agenda. It knows what it wants to do. And if you don’t convince it to do something else, it’s gonna kill everybody.
Speaker 6: This is, this idea I’ve had for many months or a year or so is just thinking about these things, thinking about how, we have a certain things we could observe, how things happen within DNA, or much of what you have mentioned, and the, interconnections and [00:22:00] everything. But to attribute that all to randomness, and then to laugh at people who say that can’t happen because it’s probabilistically impossible.
that basic, would you learn more about how it actually developed if you assume there was a purpose behind it?
Perry Marshall: Abdicating to randomness is anti-science.
Speaker 6: Yeah.
Perry Marshall: Yes, randomness exists.
Speaker 6: Yeah.
Speaker 2: But saying it’s random is the end of the road. You’re out of hypotheses when you declare it’s random. it’s anti-science.
And then
Speaker 6: that might be uncomfortable for a lot of people who don’t want to believe in God.
Perry Marshall: It may.
Speaker: Thank you, Perry. Appreciate it.
