There are thoughts

(Warning - Technical)

In the previous posting I described how a problem has a problem-surface and that for natural selection to be effective that surface needs to be smooth.

Clearly many problems do not fall into the smooth problem surface category. What about our natural environment? The received wisdom is that natural selection is the (only) process that explains the development of complex life forms. I could easily accept this if the problem surface is smooth, I would find it doubtful if the problem surface was complex.

In some cases it looks to be smooth. Consider the classic illustration of the giraffe and it’s long neck.

click to enlarge

Nice small changes toward improved fitness.

It needs to be pointed out that there is an implicit assumption here – that there is a direct mapping between a small change in the genetic code and a similar small change in the organism, but I’ll leave that on the side.

The giraffe’s neck example works nicely on paper as I’m sure do many others. Bear in mind however that in real life a giraffe has more going on than the length of it’s neck; mating, young to rear, drinking, predators. That’s a complex fitness function and that means a complex problem-surface. I’m going to sticking my neck out here (haha) and say I have my doubts that in a real world situation natural selection would get you from horse to giraffe.

However, that is not what is under consideration, the proposition is that natural selection (on it’s own) can take us on our long journey from slime to homosapien. For this to hold we need a smooth continuous path of ever increasing fitness all the way from A to B. No chance.

(warning – technical posting)

K, Having described how to use simulated natural selection as a means of solving problems in computing, does it actually work?

Yes and No.

When I was messing about with this stuff, the leader in the field was a guy called Koza at Stanford. I ran a number of simulations from Koza’s books and they all worked brilliantly.

At this point I should have stopped to wonder why the process hadn’t been used to develop something complex. I should also have noticed that all the problems in the book had a certain similarity.

As I began applying the process to other problems I noticed it didn’t fare so well. In fact for some problems it just wasn’t going to get there – Ever.

It dawned on me that I was only seeing half the picture. I was familiar with the solution I wanted to use but not the problem I was trying to solve. Problems have characteristics and attributes, they have a problem-space (or a solution-space depending on your outlook)

Imagine a 3D graph, with some peaks and troughs. At one extreme, some problems are binary, there’s one and only one answer. Alternatively some problems have a smooth gradient of fitness values, leading up to a single maxima, the solution.

All the problems in the book were very much of the second kind. If you can get to the solution via small changes, the process gets there quickly, if not then you may be waiting a very long time.

The easiest way to understand why this must be the case is to imagine a huge staccato landscape with just a few narrow high peaks, the population will invariably get stuck in a small local peak (the population becomes optimised for the local peak) and never reach the high peaks. This is hard to describe, it’s really best seen, but I can’t help you there.

Now the problem of “local maxima” that I have just described is only part of it. It gets worse, imagine a more complex requirement, say “driving a car”, there are multiple goals with different priorities at different times. Changing up a gear is real important if the engine is revving, but become subordinate to braking in certain situations.

With a complex fitness function, you get a kind of multi-dimensional surface pulling in many different directions. Additionally the number of “holes” in the problem surface increase, what I mean by a “hole” is an area in the problem surface which yield a zero fitness value. So the area of the surface permitting viable solutions becomes small, most programs just break.

Basically the problem space had better be simple and smooth as a babies bottom.

next posting – Wild speculation about the natural environment as a problem space.

(Warning – technical posting)

In the last posting I described the population of computer programs, where the programs exhibiting the highest fitness were reproduced and the least fit were discarded.

There are two types of reproduction, asexual and sexual.

The technical detail of reproduction is important; firstly this is where randomness is introduced through mutation. Mutation is where a piece (usually one element or “gene”) of code is changed. This occurs both in asexual and sexual reproduction. Most mutations are harmful but without mutation the population would be static. For asexual reproduction this is the only way change is introduced.

Sexual reproduction also introduces change though “crossover”, you and I have inherited our DNA part from mother and part from father. Similarly, if we are running this type of simulation, our programs undergo a crossover operation to produce children. The programs exhibiting the most fitness will be reproduced more aggressively with more partners. The benefit is that useful chunks of code will be propagated through the population.

There are many details I’ve omitted but this basically completes the technical description of the simulation. Over many generations the programs will become more adapted to the fitness function.

next posting – does it actually work?

(Warning – technical posting)

It’s pretty obvious that plants and animals have evolved over time. The simple stuff appears early on, the more complex stuff later on.

The idea is that natural selection is the process which gets us from A to B.

Note – the reader needs to be clear on what natural selection is – during surveys, it is common to find a majority that agree with the statement “I believe in natural selection”, they are then asked to describe what natural selection is, often up to half say something like; “the children born are more adapted to the environment than their parents” – i.e. they describe some kind of Lamarckian process, not natural selection.

I’m no biologist but I have spent sometime dabbling with genetic algorithms and genetic programming. These fields of study fall within computer science. The idea is that if the process of natural selection can get you from a bit of green slime to a human, then it’s probably good for solving just about anything.

So it’s basically a kind of simulation. The way this works technically is that you have a population of computer programs. The computer programs are evaluated against a “fitness function”, in nature reproducing is the fitness function, but in our simulation the fitness function would be the problem we are trying to solve. The programs that have low fitness are discarded; the programs exhibiting high fitness are allowed to reproduce. Programs exhibiting the highest fitness will be allowed to reproduce many times.

Next posting – the programs have sex!

Following on from my last post, I idly wondered; What kind of experiment or test *would* be sufficient to show that the mind was purely material.

My first reaction was to say; If a functioning example were to be artificially created. – that would show the mind was purely material.

But actually that would be insufficient.

If the material part, the brain, was mainly some kind of calling function – and the real processing happens elsewhere, then cloning the calling part would yield the same result, without proving anything.

Do not multiply entities unnecessarily.

Or to paraphrase; the simplest explanation is probably the best one.

Useful heuristic thought it is, the simplest explanation is not necessarily the correct one.

I was recently talking to someone about discoveries resulting from brain surgery. It seems that in the case of some severe mental illness, all medication failing, doctors have resorted to surgery. Basically cutting out bits of the brain or bits that link the left and right hemispheres.

The result of this (apart from alleviation of the illness) is that behaviour is changed. The left and right hemispheres act independently, eg. the patient while getting dressed tries to put on two different pairs of trousers. Also it becomes clear that the separate parts of the brain are related to different functions. He had a lot of examples about people involved in accidents, part of the brain was damaged, they could no longer perform certain functions.

Fascinating.

What gave me pause for thought however was his conclusion. He believed that this pretty well proved that the human mind was purely material. That thoughts, reason etc. were products of a living machine.

Of course he could be right, but what an unwarranted leap.

Consider the same reasoning applied to a mobile phone.

I hear a voice coming out of the phone. I bang the phone on the table. Now I hear sporadic crackling. I bang the phone harder on the table. Silence. And I conclude from that the voice was purely the product of the phone!

I'm a Christian, so I do believe in a personal God and that he does miracles. But perhaps not quite as many as people make out.

It's curious, quite a few atheists I know see just about everything in the world as a reason for why God doesn’t exist. Likewise quite a few Christians I know, see every little thing as the Hand-of-God.

During my time in churches I’ve spotted the following 2 issues coming up again and again – both (to me at least) appear like reasoning defects. Having said that, you don’t need to be in churches to spot these, they crop up everywhere.

1. Confusing a Correlation with Causation.

Example;

A preacher is talking to large, middle class congregation, where the majority are early 20s. He says something like, “God will bless you financially if you give your tithe” or something like that. Sure enough over the next couple of years the majority experience promotions and financial progression.

Most of them uncritically conclude that it is as the preacher said and God is the cause of their promotions.

In fact the correlation between middle class, early 20s kids and promotions will be very high – And completely independent of their belief system.

2. Only Winners Tell their Story.

Example;

“A tornado was coming toward our district, we prayed for the house as we left, and when we came back our house was the only one standing – God had preserved our house”

I heard this story on the news about 5 years ago. The unchallenged assumption is that none of the other people prayed for their house. Does that seem likely to you? It doesn’t to me.

Thing is, who is going to go on TV and say ; “I prayed that my house wouldn’t be knocked down but God let it be knocked down anyway”

These situations are prevalent.

Consider the school assembly where a number of successful entrepreneurs talk to the children about starting a business. A child may come away from that believing that starting a business is easy. What the child cannot see are the hundreds of failed businessmen who have not come to talk at the assembly.

I think it’s difficult to spot this kind of thing, precisely because there is nothing to argue with, nobody is lying as such - They prayed and the house was preserved - The entrepreneur truly was successful. Rather it is a case of spotting that the picture is incomplete. We have to step back and imagine the larger silent number who are not telling their story.

“Intelligent Design” is a theory that states that the universe is here and is the way it is because of a designer. How much designing the designer did is up for debate. Some proponents claim every detail. For example, eagles have exceptionally good eyesight so they can spot prey from a great height. Some one advocating Intelligent Design (ID) would say that the reason for this is that the eagle has been designed that way. Others claim the bare minimum, a handful of universal physics constants. In any case, there is a designer or an initiator who knows what he’s doing.

An alternate theory is that no one designed the eagle at all (never mind it’s eyes), rather natural selection refined the optic ability of the eagle over time. And more generally there isn’t a designer, it doesn’t need one, it’s all natural processes – we might not know the details yet, but wait, soon we will.

Now it’s commonly considered that ID is bad science, and it may well be. But I do not think the idea itself is obviously crazy.

With further advances in computing power, simulations will become much more advanced. It might be possible to someday create simulations that have intelligent, self aware “beings” in them. And if we did, and those beings asked themselves how is it that we are here – Intelligent Design would be the answer.

Just a thought.

Having written my Carl Sagan tribute, I was somewhat alarmed to find this book on Amazon.

Probability 1 - Why there must be intelligent life in the universe

Written by Amir Aczel, mathematician, statistician and top science author.

Editorial reviews;

Amazon.com: “In a universe infinitely large, what is the probability of intelligent life on another planet? Sounds like a trick question, but for anyone versed in cosmology and statistics, the answer is 1; that is, there must be life on at least one other planet in the universe [bla bla bla] Probability 1 delivers on its promise to prove Aczel's conjecture through a clearly explained application of known statistical theory”

Scientific America “Probability 1, meaning a certainty that the thing will happen, is what mathematician and probability theorist Aczel assigns to the discovery of intelligent life elsewhere in the universe… [bla bla bla] … Hence, even though the probability of life around any one star is extremely small, the compound probability with such vast numbers of stars to consider rises to 1…”

Authors Choice Excerpt from the book “Mathematics is the key to probability theory, and the math always wins-sometimes despite our intuition. And the mathematics and probability theory always pointed in one direction: the probability of life in outer space is one, just as Carl Sagan had believed. This book will take you through my journey of discovery leading to this conclusion.”

Well, that’s done it for me. Seems pretty convincing, this guy is an expert after all….

Well, of course I shit my pants. I take it all back, I’m so sorry Carl.

Of course not – don't swallow anything from someone just because they claim to be an expert.

Moving past the editorial reviews, I started paging through the online reviews submitted by punters

Alexis Brandeker “The problem is of course that the author, and no one else for that matter, has any slightest idea of what the probability for life to develop is, more than that it's positive less than 1. For all we know, it may well be infinitesimal [small]. So his argument is strictly false.”

Well done my son.

AReader “In the end, we are still left with no answer at all to the question at hand because we don't know the probabilities of DNA forming and then life forming after that. The author supposes that it is something like 1 in a trillion. What if it is 1 in a trillion trillion trillion? The title could just as well be Probability Zero.”

Many reviewers made similar points.

If you are the type to believe “experts” and big publications (apparently this book got the OK from the Sunday Times, FT and Independent) – Go back read the editorials and analyse how you “feel” at that point. How convincing it all seems... Then read each and every review and how you feel at the end of that.

It’s good medicine.

In case you didn't know Carl Sagan is now dead, his spirit lives on however in the legacy of dubious reasoning he left behind.

There's a cultural assumption that the universe is filled with life and that there are thousands if not millions of intelligent species out there. That is in a large part down to Sagan - His argument went something like this;

There are billions of galaxies in the universe and each of them containing billions of stars and these stars have planets. We know that intelligent life developed on this planet AND since there are such a mind bogglingly utterly huge number of planets it is a practical certainty that there is intelligent life out there.

I've heard this argument a lot, next time you hear it do the following, just go “hummmmm, do ya think” frown a little and wait for the response. It will always be the same “but the universe is just so utterly huge, I’m talking billions and billions…”

It’s in the same category of reasoning as “given enough time anything could happen, the earth has been around a long time, I’m talking billions and billions of years”

There is a probelm right here. You must not confuse a very very large number with infinity. Yes, the number seems very very large to you, but that is different from infinity.

There is a popular illustration for this “Given a thousand monkeys at a thousand typewriters they would eventually produce the whole works of Shakespear” – it’s true, however the age of the universe is dwarfed by the amount of time it would take them.

In this particular case, yes, there are very many planets but under what conditions can life exist and how common are these conditions. This is the other half of the equation. The requirements for life may be very stringent, the odds for their occurrence may be as small as your plant count is large. With a sample of 1, you have no clue at all.

As an aside - the argument also has implicit assumption; that life is a ‘naturally’ occurring phenomenon. To a lot of people that would be a no-brainer however if you take it away you can throw your statistical arguments into the bin. So, just as a crazy example, take the film “The Matrix”, their whole reality is artificially constructed for them, there would be no aliens if the constructors had not made any aliens.

In 1950, Enrico Fermi, a physicist, asked the obvious question “If the universe is so full of intelligent life, where are all the buggers?” This is known as the Fermi Paradox and is well worth a wiki.