Imitating biology

[shunyadragon]

I'm not saying that science cannot imitate nature, the point is that actually they do! The point is that human designs come behind nature as a rule, and we look to nature to see how to do better.

Blessings,
Lee

NOT the point you previously made.

Still more nonsense that does not reflect your assertions. Both natural evolution and technology are based on Natural Laws, and there is absolutely no evidence for design in nature. No one including Beha has come up with a falsifiable hypothesis to support 'Intelligent Design,'

[lee_merrill]

In order to travel a distance d,

N ≈ (d/l)^2

steps are therefore required.

In any direction, correct? What I am after is the average motion, which is zero:

Source: Wikipedia

The expectation E(S_n) of S_n is zero.

Source

© Copyright Original Source

Blessings,
Lee

[lee_merrill]

Humans have been designing for a few thousand years at best, only a few hundred with the benefits of technology. Nature has had over 4 billion years and a whole planet to tinker with. So why are you surprised?

Because hill-climbing algorithms such as evolution are expected to get stuck at a local optimum. To see highly optimized objects surrounding us in nature is indeed, therefore, surprising. Especially when you see similar designs such as here, which must have arisen independently, if evolution is true:

Source: Cornell

Source

© Copyright Original Source

Blessings,
Lee

[lee_merrill]

The fossil record shows plenty of examples of gradual change that can easily be drift (in most cases, we can't distinguish drift from selection). And we know from DNA sequencing that genetic drift occurs when there's no morphological indicator of it, so you can't rule out genetic drift based on the fossil record.

I'm not saying there's no variation, I'm just saying the average motion in a random walk is zero, which you can prove mathematically (see above).

Blessings,
Lee

[Stoic]

In any direction, correct? What I am after is the average motion, which is zero:

Yeah, but I don't think you ever said why you think the average motion is important to you.

After a given amount of time, the odds are good that the actual motion is significant. You just don't know in advance what direction it's going to be in (hence "random").

[HMS_Beagle]

To see highly optimized objects surrounding us in nature is indeed, therefore, surprising.

It's not surprising at all to those who have studied and understand how evolution actually works. But that group doesn't include you now does it?

[rossum]

I'm not saying there's no variation, I'm just saying the average motion in a random walk is zero, which you can prove mathematically (see above).

The average is zero when averaged over a number of different walks, all starting from the same origin. Follow any individual walk and it will not, in general end at its starting point. It is offset by a different walk that ends on the opposite side of the starting point, and the two average to zero. Neither of the two is actually back at the starting point. Given random walks, you end up with a cloud of end-points evenly scattered round the common origin.

Hence, when the local maximum does move, the new maximum might be within the existing cloud, though offset from the centre, or else closer to one side of the cloud, with some closer and some further away.

The local maximum for humans recently moved slightly with the advent of Covid-19. End points nearer the new maximum have an advantage over end points further away. The centre of the cloud of end points will move to account for the slightly changed environment.

[shunyadragon]

Because hill-climbing algorithms such as evolution are expected to get stuck at a local optimum. To see highly optimized objects surrounding us in nature is indeed, therefore, surprising. Especially when you see similar designs such as here, which must have arisen independently, if evolution is true:

Source: Cornell

Source

© Copyright Original Source

Blessings,
Lee

Absolutely nothing to do with the subject at hand. Randomness in mutations is not a hill climbing algorithm.

[shunyadragon]

In any direction, correct? What I am after is the average motion, which is zero:

Source: Wikipedia

The expectation E(S_n) of S_n is zero.

Source

© Copyright Original Source

Blessings,
Lee

Absolutely nothing to with Randomness in mutations. Randomness in mutations has to do with individual mutation events and not averages. Beyond that the processes of evolution are not random.

Besides this reference has nothing to do with evolution.

[TheLurch]

Because hill-climbing algorithms such as evolution are expected to get stuck at a local optimum.

How many times do i have to say this: that is not true. Whether they do or not depends on a variety of factors. I've explained what they are, and even spelled out why they influence things.

Stop making false statements, please.

[lee_merrill]

Yeah, but I don't think you ever said why you think the average motion is important to you.

So genetic drift would not be a major source of evolutionary change.

After a given amount of time, the odds are good that the actual motion is significant. You just don't know in advance what direction it's going to be in (hence "random").

No, the average motion is always going to be zero, though the maximum variation will increase.

The average is zero when averaged over a number of different walks...

No, the average of any walk is zero, seek the example on Wikipedia of flipping coins.

The local maximum for humans recently moved slightly with the advent of Covid-19.

Yes, the landscape can change...

Blessings,
Lee

[lee_merrill]

How many times do i have to say this: that is not true. Whether they do or not depends on a variety of factors. I've explained what they are, and even spelled out why they influence things.

Yes, I understand your points, and I still disagree with you, as evidenced by the article on evolutionary algorithms having a problem with local optimums.

Blessings,
Lee

[Stoic]

So genetic drift would not be a major source of evolutionary change.

I don't know whether genetic drift is a "major" source of evolutionary change. But it is obviously a source. And how major it is should be determined by observation, rather than by overly simplistic mathematical models.

No, the average motion is always going to be zero, though the maximum variation will increase.

The average of many random walks will be approximately zero, because the odds that you will move in one direction on one walk are balanced out by the odds that you will move in the opposite direction on another walk.

No, the average of any walk is zero, seek the example on Wikipedia of flipping coins.

That's just false. If you flip a coin very many times, the odds are extremely low that the number of heads will exactly equal the number of tails.

[TheLurch]

Yes, I understand your points, and I still disagree with you, as evidenced by the article on evolutionary algorithms having a problem with local optimums.

What makes you think you understand this better than someone with a PhD in it? I would like to have that answered.

In any case, evolutionary algorithms are only an approximation of biological evolution - they do not recapitulate all its features. Things that are problems for algorithms may not be issues for actual, biological evolution. So, you're latching on to something that may not be relevant just because it supports what you want to believe, not because it's actually evidence.

[TheLurch]

The average of many random walks will be approximately zero, because the odds that you will move in one direction on one walk are balanced out by the odds that you will move in the opposite direction on another walk.

Correct, but also irrelevant. Random walks end up being directional in biology because you have things like population isolation, genetic linkage to favored/unfavored traits, founder effects, etc. etc. Lee's dragging out this issue because he doesn't understand logic or biology enough, so he thinks that a mathematical random walk is a good analogy for genetic drift, and he's convinced that if something's true for an analog, it must be true for the actual thing.

Neither of those is true.

Lee will never be convinced that's the case, because the argument he wants to believe depends on them being true.