While playing with evolutionary algorithms, I had the startling realization that all genetic mutations are bad. It’s common knowledge that biology abhors genetic mutation, and I assumed that was only because mutations cause cancer. But my computer programs are immune to cancer, and they also abhor mutations. This is counterintuitive, given that evolution requires mutations to procede.
For proof of the fact that mutations are bad, consider that evolution is an optimization algorithm, and after it reaches a local optimum further mutations will be strictly detrimental. The concept of evolutionary pressure is the ability of an evolutionary algorithm to remove deleterious mutations from a population. If mutations accumulate faster than they can be removed then the population will suffer a genetic collapse. This is a common failure mode of evolutionary algorithms.
The ideal evolutionary algorithm would have at most one mutation in each individual, and each of their lives would be an experiment to evaluate that single mutation. And then through many generations of chromosomal crossover the best mutations would combine into a single genome.
You might be rediscovering Fisher’s geometric model. A refinement to your current model you could consider is that close to, but not exactly at, the local optima, sufficiently small mutations have a 50% chance of being beneficial.
Hello. Today I’d like to talk about something a bit different. I’d like to talk about theology, my own personal creation myth: something to explain why the world exists, when it seems like the world could just as easily not exists. I posit that the universe is a mathematical construct, and that all mathematical constructs inherently exist.
Now, First I’d like to a take a moment to define what exactly math is and to appreciate some of it’s properties. Broadly speaking, mathematics is the study of rules and rule-based systems. The basic premise is that you start with some very simple rules (called the axioms) and working from these rules you can prove other more complex facts about the system.
And what’s important is that all of the rules are being followed all of the time. At every step along the way, and at every point in the system, the rules are uniformly and consistently applied.
If ever any of the rules are broken, then the whole system becomes meaningless. For example if you can prove that “0 == 1” then, with some trivial rearrangements of the equations, you can show that every number is equal to every other number, and also that no number is equal to anything else, not even itself. The introduction of an invalid equation into a mathematical system results in an infinite number of non-sensical results.
Clearly, you can not have a meaningful existence with broken or inconsistent mathematics. Contemplate with me, an existence with broken equations. You would be unable to count the things that exist, and even the most basic of facts about our reality would become unhinged.
But that is not the world we live in. In our universe math is eternal and omnipresent. An equation like “1 + 1 == 2” is as true today as it was true yesterday and it will be true tomorrow. There is no corner of space or point in time where this equation is wrong.
Now I’d like to mention another property of mathematical systems; that once you have a system of equations, you can rearrange and combine those equations in order to introduce new equations to the system. Assuming that you did the math correctly, then the new equations are going to be valid members of that system of equations, and this is a direct consequence of the rules of mathematics.
In a way, those new equations were always there, even if you were unaware of them. When you prove a new fact about the world, that fact was already true even before you proved it.
When we think about systems of equations, we like to think about small finite sets of equations, but really every system of equations contains infinitely many equations, and what we’re doing when we do arithmatic is we’re searching for one equation in specific, out of all of those infinite equations.
So what we think of as a system of equations is actually just some arbitrary a subset of the set of all valid equations. So if you have any mathematical system, then in fact you’re working with all mathematical systems, in a way.
Now let’s discuss our world, and where it came from. I believe that our physical universe can be perfectly modeled using mathematics, that there exist some equations which accurately describe everything in our universe, down to the smallest iota of matter and all of the forces acting upon it.
And I’m not talking about Newton’s or Einstein’s laws or any such crude approximations of our physical reality, but rather a perfect description of the universe which yields 100% accuracy.
If we assume that such equations do exist then they are part of the set of all valid equations. And if on the other hand, our universe does not follow any logic or abide by any rules then, as we already saw, it would be very difficult for anything to meaningfully exist in our universe.
Now back to the question of creation, the question of “why does anything exist” can be reduced to the question of “why does mathematics exist?” And does mathematics really need to justify its own existence? Math is simply the idea that you can have rules, and that what follows is a consequence of following those rules. And you don’t even need to follow the rules, it’s just that if you don’t follow the rules you get meaningless results.
Mathematics is just an abstract concept. I do not think that mathematics needs to justify its own existence, given that it does not have any tangible or concrete implementation. And yet, starting from this abstract concept of mathematics, we can prove that our very real universe exists as a direct consequence. Our universe is a set of physics equations embedded inside of the set of all valid equations, and with us animals embedded inside of the physics of our universe.
Our world exists because the equations that describe our world exist. From one point of view, it may seem like I’m equating all of existence with an ethereal abstract concept which does not really concretely exist, but from another point of view I’m saying that we must exist as an inevietable result of the very concept of rules and rule-based systems.
In conclusion, this creation myth places very few constraints on the physics of our universe; it allows for worlds that are deterministic or probabilistic; discrete or real valued; computable or containing the number PI; finite or infinite! It even permits conventional religions to exist, assuming of course that the gods are mathematically consistent. And finally all of this implies that other universes exist, goverened by different sets of physics equations, and, undoubtedly, some of those other universes also support intelligent life.
Personalities are inherited. Identical twins separated at birth are statistically more similar than fraternal twins.
The human population has almost zero genetic variation, and there is significant mixing so variations do not systematically cluster. Therefore, it seems unlikely that subtle personality differences are due to genetic variation.
My hypothesis is that animal personalities are encoded in epigenetic changes.
This allows personalities to be inherited, crossover, and evolve. Life experiences can induce epigenetic changes, which allows animals to reliably adapt in a single generation. All of this without requiring any genetic variation. A population of clones could have diverse personalities stored in their epigenome.
This is also just not really true. Natural Selection (as opposed to genetic drift) can maintain genetic variations especially for things like personality, due to the fact that “optimal” behavioural strategies depend on what others are doing. Any monoculture of behavioural strategies is typically vulnerable to invasion by a different strategy. The equilibrium position is therefore mixed. It’s more common for this to occur due to genetic variation than due to each individual using a mixed strategy.
Furthermore, humans have undergone rapid environmental change in recent history, which will have selected for lots of different behavioural traits at different times. So we’re not even at equilibrium.
Personalities are inherited. Identical twins separated at birth are statistically more similar than fraternal twins.
This is unclear: are you saying that identical twins separate at birth are more similar than fraternal twins who are raised together (therefore suggesting nature > nurture)? Or that identical twins separated form each other at birth are more similar to each other than fraternal twins separated form each other than birth? (Only suggesting that nature > uhhh less samey nature).
I would also really like to read the abstracts of all the papers that you’re alluding to here because they sound like some quite fantastic claims.
Compare like-to-like: separated identical twins to sepaparted fraternal twins.
I think the best introduction to the topic would be this lecture, which is mostly about all of the problems with separated twin studies. Identical twins starts at 37 minutes.
While playing with evolutionary algorithms, I had the startling realization that all genetic mutations are bad. It’s common knowledge that biology abhors genetic mutation, and I assumed that was only because mutations cause cancer. But my computer programs are immune to cancer, and they also abhor mutations. This is counterintuitive, given that evolution requires mutations to procede.
For proof of the fact that mutations are bad, consider that evolution is an optimization algorithm, and after it reaches a local optimum further mutations will be strictly detrimental. The concept of evolutionary pressure is the ability of an evolutionary algorithm to remove deleterious mutations from a population. If mutations accumulate faster than they can be removed then the population will suffer a genetic collapse. This is a common failure mode of evolutionary algorithms.
The ideal evolutionary algorithm would have at most one mutation in each individual, and each of their lives would be an experiment to evaluate that single mutation. And then through many generations of chromosomal crossover the best mutations would combine into a single genome.
You might be rediscovering Fisher’s geometric model. A refinement to your current model you could consider is that close to, but not exactly at, the local optima, sufficiently small mutations have a 50% chance of being beneficial.
Thank you
This is a sermon I wrote.
Hello. Today I’d like to talk about something a bit different. I’d like to talk about theology, my own personal creation myth: something to explain why the world exists, when it seems like the world could just as easily not exists. I posit that the universe is a mathematical construct, and that all mathematical constructs inherently exist.
Now, First I’d like to a take a moment to define what exactly math is and to appreciate some of it’s properties. Broadly speaking, mathematics is the study of rules and rule-based systems. The basic premise is that you start with some very simple rules (called the axioms) and working from these rules you can prove other more complex facts about the system.
And what’s important is that all of the rules are being followed all of the time. At every step along the way, and at every point in the system, the rules are uniformly and consistently applied.
If ever any of the rules are broken, then the whole system becomes meaningless. For example if you can prove that “0 == 1” then, with some trivial rearrangements of the equations, you can show that every number is equal to every other number, and also that no number is equal to anything else, not even itself. The introduction of an invalid equation into a mathematical system results in an infinite number of non-sensical results.
Clearly, you can not have a meaningful existence with broken or inconsistent mathematics. Contemplate with me, an existence with broken equations. You would be unable to count the things that exist, and even the most basic of facts about our reality would become unhinged.
But that is not the world we live in. In our universe math is eternal and omnipresent. An equation like “1 + 1 == 2” is as true today as it was true yesterday and it will be true tomorrow. There is no corner of space or point in time where this equation is wrong.
Now I’d like to mention another property of mathematical systems; that once you have a system of equations, you can rearrange and combine those equations in order to introduce new equations to the system. Assuming that you did the math correctly, then the new equations are going to be valid members of that system of equations, and this is a direct consequence of the rules of mathematics.
In a way, those new equations were always there, even if you were unaware of them. When you prove a new fact about the world, that fact was already true even before you proved it.
When we think about systems of equations, we like to think about small finite sets of equations, but really every system of equations contains infinitely many equations, and what we’re doing when we do arithmatic is we’re searching for one equation in specific, out of all of those infinite equations.
So what we think of as a system of equations is actually just some arbitrary a subset of the set of all valid equations. So if you have any mathematical system, then in fact you’re working with all mathematical systems, in a way.
Now let’s discuss our world, and where it came from. I believe that our physical universe can be perfectly modeled using mathematics, that there exist some equations which accurately describe everything in our universe, down to the smallest iota of matter and all of the forces acting upon it.
And I’m not talking about Newton’s or Einstein’s laws or any such crude approximations of our physical reality, but rather a perfect description of the universe which yields 100% accuracy.
If we assume that such equations do exist then they are part of the set of all valid equations. And if on the other hand, our universe does not follow any logic or abide by any rules then, as we already saw, it would be very difficult for anything to meaningfully exist in our universe.
Now back to the question of creation, the question of “why does anything exist” can be reduced to the question of “why does mathematics exist?” And does mathematics really need to justify its own existence? Math is simply the idea that you can have rules, and that what follows is a consequence of following those rules. And you don’t even need to follow the rules, it’s just that if you don’t follow the rules you get meaningless results.
Mathematics is just an abstract concept. I do not think that mathematics needs to justify its own existence, given that it does not have any tangible or concrete implementation. And yet, starting from this abstract concept of mathematics, we can prove that our very real universe exists as a direct consequence. Our universe is a set of physics equations embedded inside of the set of all valid equations, and with us animals embedded inside of the physics of our universe.
Our world exists because the equations that describe our world exist. From one point of view, it may seem like I’m equating all of existence with an ethereal abstract concept which does not really concretely exist, but from another point of view I’m saying that we must exist as an inevietable result of the very concept of rules and rule-based systems.
In conclusion, this creation myth places very few constraints on the physics of our universe; it allows for worlds that are deterministic or probabilistic; discrete or real valued; computable or containing the number PI; finite or infinite! It even permits conventional religions to exist, assuming of course that the gods are mathematically consistent. And finally all of this implies that other universes exist, goverened by different sets of physics equations, and, undoubtedly, some of those other universes also support intelligent life.
These two facts seem incompatible:
Personalities are inherited. Identical twins separated at birth are statistically more similar than fraternal twins.
The human population has almost zero genetic variation, and there is significant mixing so variations do not systematically cluster. Therefore, it seems unlikely that subtle personality differences are due to genetic variation.
My hypothesis is that animal personalities are encoded in epigenetic changes.
This allows personalities to be inherited, crossover, and evolve. Life experiences can induce epigenetic changes, which allows animals to reliably adapt in a single generation. All of this without requiring any genetic variation. A population of clones could have diverse personalities stored in their epigenome.
No need to invoke epigenetics, the answer is that 2 is false. Who is claiming 2 to be the case?
Humans clearly have large genetic variation in physical traits, why would mental traits be an exception?
I think a better argument than #2 would be that evolution tends to remove genetic variantions.
This is also just not really true. Natural Selection (as opposed to genetic drift) can maintain genetic variations especially for things like personality, due to the fact that “optimal” behavioural strategies depend on what others are doing. Any monoculture of behavioural strategies is typically vulnerable to invasion by a different strategy. The equilibrium position is therefore mixed. It’s more common for this to occur due to genetic variation than due to each individual using a mixed strategy.
Furthermore, humans have undergone rapid environmental change in recent history, which will have selected for lots of different behavioural traits at different times. So we’re not even at equilibrium.
This is unclear: are you saying that identical twins separate at birth are more similar than fraternal twins who are raised together (therefore suggesting nature > nurture)? Or that identical twins separated form each other at birth are more similar to each other than fraternal twins separated form each other than birth? (Only suggesting that nature > uhhh less samey nature).
I would also really like to read the abstracts of all the papers that you’re alluding to here because they sound like some quite fantastic claims.
Compare like-to-like: separated identical twins to sepaparted fraternal twins.
I think the best introduction to the topic would be this lecture, which is mostly about all of the problems with separated twin studies. Identical twins starts at 37 minutes.
Weird Synchronicity. I literally started reading “Why Don’t Zebras Get Ulcers” last week.