> thankfully this isn't how it works.

Care to elaborate what lowers this probability down to "computable within adolescent age" levels?

You want people to explain natural selection and evolution to you?

No, I want the computational feasibility explanation with some nice O(function) on biological processes. To the best of my knowledge, we still have no idea.

Something like "the computational complexity of a beached fish to invent and grow a leg is O(n^2 log n) hours where n is the number of neural spikes in frontal cortex" or similar.

This is not intended as a mean comment, but you should learn some basics about evolutionary biology _before_ jumping into much harder questions like that (in this case the answer is nil - individuals do not evolve, populations do, and neuron spikes are not involved in the process).

Fish aren't the only things that live in water. There are other marine organisms, some of which have leg-like things. What if one of those organisms, already equipped with legs, evolved to survive on the surface?

That would be fine; but we have some lineages coming from fish living on the surface. Those are the interesting ones.

While metabolic advantage is a thing, I'm not sure if organisms are expected to carry minimum amount of genetic code that they actually use; in what little I know about developmental biology, I recall there's a high-level structure to the genetic code - some genes are doing more of flow control than encoding actual proteins. It's conceivable that the fish which walked on Earth was the one that managed to accumulate inactive adaptations for walking and switched them on.

Also, there's horizontal gene transfer to account for. It further complicates the picture.

> one that managed to accumulate inactive adaptations for walking and switched them on.

https://www.discoverwildlife.com/animal-facts/fish/can-fish-...

Genes get duplicated by accident, then accumulate mutations which are usually neutral or worse. Occasionally they help you achieve something slightly more useful than before. Lobed fins that helped you heave yourself back into water when you get beached would have helped. bigger lobed fins would help you get back when stranded further up the beach, or get from pool to pool. It's unlikely that an entire set of limbs, other necessary body upgrades to support them and neural circuits would just hang around waiting for all the right mutations to collect like hole punches on a restaurant loyalty card before some critter slapped their thighs and stood up and walked. Evolution does not plan ahead.

This argument is however an argument from faith and not from computability perspective. Random garbage genes flipped on won't grow a leg with intricate mechanical abilities. Those abilities have to be computed somewhere and need to be useful right from the start to appear in offsprings otherwise they get eliminated as a waste. Yet everyone puts their faith in some random process instead of pinning down the concrete mechanisms how does this happen. So you basically end up forcing some idiotic faith on everyone instead of digging deep and figuring it finally out. I would be more inclined to believe if you told me that pre-adolescent brain spends 25% of its computing capacity on figuring out how to improve its body and encoding it into genes instead of trusting some random mutation (likely error-corrected) to do the heavy lifting.

It's not a faith thing. Yes, metabolic advantage is a thing and useless adaptations can get eliminated over time (it seems to matter more in single-cellular organisms, though). However, often enough, unused adaptations can persist for a long time - for example, pythons still have the whole blueprint for "a leg with intricate mechanical abilities" and nerves and stuff, it's literally just switched off. We know because some researchers figured out how to flip it back on, and behold, snakes grew their legs back. That's what I've been alluding to in the prior comment - genes aren't encoding a flat blueprint, but a complex program with many genes working as flow control or signalling superstructure, able to toggle or modify whole complex body parts.

> I would be more inclined to believe if you told me that pre-adolescent brain spends 25% of its computing capacity on figuring out how to improve its body and encoding it into genes instead of trusting some random mutation (likely error-corrected) to do the heavy lifting.

this is an argument from personal incredulity. just because you are too dumb to understand how something works doesn't mean that your fantasy/sci-fi version is accurate. brains changing genes belongs in a discussion of Neal Asher's polity, not in a biology discussion.

So you are saying that e.g. a large mammal lifespan of 70 years is sufficient to generate as many good random mutations as needed to grow a new leg over 10,000 generations if necessary? Where is the evidence of a fast algorithm requiring so few selections to come up with a complex new organ? How is that not blind faith? Not sure who is the dumb one here...

> a large mammal lifespan of 70 years is sufficient to generate as many good random mutations as needed to grow a new leg

thankfully, nobody is claiming that happens. i can explain more, but there's the issue of my fees. £200,000 seems reasonable, given how dumb you are.

Have you ever tried genetic algorithms?

Those are great models for local adaptations. They won't grow a leg with extricate mechanical properties we have trouble modeling in state-of-art robotics/mechanics.

I didn't say it had to simulate real physics. Have you ever tried *a* genetic algorithm? They grow legs all the time in their toy universes, if that helps them increase their objective function.

All genetic algorithms are created by conscious intelligent beings. So I'm more interested in how a genetic algorithm develops by chance, with what probability. I guess typing monkeys wouldn't create genetic algorithms in the existing universe's timeframe even if the monkeys themselves have some (also random) fitness function that by chance has the ability to replace dumb monkeys with smarter ones.

Genetic algorithms are everywhere. Every time (1) something copies itself with mistakes, and (2) ....... actually there's just (1), no (2). Every time things copy themselves imperfectly, you have a genetic algorithm, and the fitness function is how much they copy themselves in the long run.

The current best hypothesis is that RNA randomly developed and evolved. Some if it happened to be self-copying. If there are self-copying things, there will be lots of self-copying things - that's common sense. And a genetic algorithm fitness function. In an ocean with RNA, sometimes it will happen to bump into other bits of RNA and swap over. Sometimes they randomly get better at copying. Zillions of molecules and hundreds of millions of years is a long time for small chances to happen. We want genetic algorithms to run in seconds on a PC. Ones that run for millions of years in the Earth's whole ocean don't have to be nearly as good.

The Miller-Urey experiment demonstrated that chemicals we know as building blocks of life can come into existence by themselves in early Earth conditions. What we don't know yet is exactly how they got from there to cells, since we don't have a time machine to go and look. Scientists keep finding plausible stepping stones, though.

my favourite far out there version of chemical evolution is the one where the entire Hubble volume was in the goldilocks zone for a few million years! sadly we may never be able to confirm it with samples, as there will always be the worry of contamination from earth.

I offer paid tuition. For £50/h, I will learn stuff for you and then teach you. Prep time is typically ~3h for each hour I teach you. Minimum 1h lessons.

I will pay you £50,000/h if you could give me a convincing answer like "the computational complexity of a beached fish to invent and grow a leg is O(n^2 log n) hours where n is the number of neural spikes in frontal cortex".

a beached fish doesn't grow legs. the problem isn't what you're willing to pay here, the problem is what you are willing to learn.

my fees are not conditional on you liking the lessons. they are to be paid upfront. i accept the higher offer though.

> a beached fish doesn't grow legs

Can you prove it? Show me some sort of an environment where a water-based complex organism is able to survive and thrive in dry environment prompting it to grow a new movement organ useless in the water but needed on surface and give me some less-than-exponential algorithmic complexity bound for it. If you can't do it, you don't offer valuable lessons.

i told you something that you claim to be true isn't what is claimed to happen by the theory of evolution by natural selection, and you want me to provide proof that it does in fact happen? have you taken leave entirely of your senses?

edit: sorry dang, I fell for it again, didn't I?

edit 2: actually treprinum, I have a sensible answer here, although you're not going to like it. if you were smart enough to understand what you are asking, you really wouldn't have picked body plan as your "gotcha". you would have picked something truly wonderful like the genetic code, or the ribosome, or mechanisms of gene regulation, or embryology, or eukaryotic cells.

the evolution of new body plans is very well understood. i won't explain it to you though, until and unless I get paid. I believe we agreed £50,000/h for an hour minimum lesson which is three hours of prep - so £200,000 total for the first paid lesson? this one here is free.

The Lungfish survives prolonged droughts where its freshwater habitat dries up. It has evolved the ability to breath fresh air, secrete a mucous membrane to form a protective cocoon that helps it retain moitsture, and its fins are heavily modified to aid with land based locomotion. Lungfish are the closest relatives to tetrapods who likely evolved under similar conditions.

https://education.nationalgeographic.org/resource/west-afric...

> where n is the number of neural spikes in frontal cortex

If neural spikes had anything to do with it, if any of this worked like that, bacteria wouldn't develop resistance to antibiotics (they can), and I would be able to shapeshift (I can't).

So that question is like asking for a route finding algorithm that's O(n) where n is the number of letters in the destination.

The point was to give me a correct estimate based on some measure of time. Pick whatever works for you and give me a formula one can use.

And my point is the the question suggests a worldview so incorrect that the question is meaningless.

If you seek understanding, you must decide upon a specific better question of your choice; if you leave it up to us to devise the question, we can do that, but it's overwhelming unlikely that our free choice will connect with whatever it is that led you to ask the question in the first place.

For example, I could ask you to consider a model of a fish where each bone length is controlled by some gene, and then evolution converting fins to legs is some function of the magnitude of reproduction selection pressure on those changes over multiple individuals and generations… and nothing at all to do with one individual's brain.

Or were you thinking of a specific fish species which develops legs when it reaches adulthood?

You were giving examples of local adaptations (bacteria building resistance) instead of paradigm shifts (beached fish growing legs). The science behind the former is established (mutations favored by environment); the science behind the latter is not. You are mixing the two together and complaining the second one is non-sense, but is it? Somehow fish had to learn to walk ("evolution from one organism to another") in a limited time including complex mechanics that our computers can't solve exactly; I am waiting for any computational biologist to give us some mechanism behind it that is realistic, i.e. computable. So far nothing and people keep mentioning local adaptations only.

> The science behind the former is established (mutations favored by environment); the science behind the latter is not.

That's not even an example of a paradigm shift. Continuous transformation trivially gets us between superficial differences like mere body shape, there are many examples of us applying selection pressure to other species to make that category of thing happen, including our crops, livestock, and pets — no more than 10k years separated Chihuahuas and Corgis from Newfoundlands and Afghan Hounds. Likewise even more extreme changes between crops and their wild relatives, the wild versions are almost unrecognisable except to experts.

> You are mixing the two together and complaining the second one is non-sense, but is it?

What I'm calling nonsensical is your description. You're calling for the time complexity for a brain to invent changes that aren't caused directly by brains.

> Somehow fish had to learn to walk ("evolution from one organism to another") in a limited time including complex mechanics that our computers can't solve exactly

1) Exact solutions aren't necessary; 2) computers have solved walking; 3) the boundary between walking and floundering is an arbitrary one. And #4 after the next quote…

> I am waiting for any computational biologist to give us some mechanism behind it that is realistic,

4) One of the ways computers solve problems like this is simulated evolution.

If you don't consider the working demonstrations to be realistic, that's a "you" problem, not something the rest of us care to waste time on.

> So far nothing and people keep mentioning local adaptations only.

Do you also insist nobody has ever climbed Mount Everest on the grounds that nobody has legs long enough to do it in one step?

Or that motion pictures are impossible because each frame is stationary?