Question 5: Good luck or good management? Part Two.

In part one I argued that you cannot dismiss a model because it feels unlikely, and you cannot choose one model over another purely on the grounds that it appears less complicated. Something does not become a valid explanation simply because you like it and want it to be true. The observable behaviour of the universe is not subject to human whims and tastes.

(note: the observable behaviour of the universe is subject to human fallibility, see Observer Effect. Quite often the mere act of observing something has an effect on its behaviour. More on that when I get back to omniscience ... just in case Robin is about to pre-empt me again.)

To decide the value of a model you have to objectively test it. The model has to make useful predictions that can be tested against observation. This is an absolutely critical step in the scientific method: your ideas must be expressed in such a way that other people can test them and demonstrate that they do not work. One of the primary reasons for publishing a scientific model is to allow your peers to explain why it is rubbish and, hopefully, propose an alternative and better model in its place.


"The earth is the centre of the universe."


The Geocentric Model (the idea that the earth is a sphere at the centre of the universe and everything else revolves around it) was essentially the first scientific model for how the universe works. It matches quite well with casual observation: the earth does not feel like it is moving and the sun and the moon and the stars appear to revolve around it. Unfortunately, it does not match with closer examination: if you accurately map the position of the stars and planets in the sky, they do not move in the way that a geocentric model predicts they should.

The ancient Greeks and later astronomers dedicated a great deal of effort to modifying and elaborating on the geocentric idea to create a model that did accurately predict the movements of the heavens. Unfortunately, they were hampered by a single assumption: the earth is the centre of the universe. It was only when Copernicus dared to suggest that this assumption was false and that the earth was actually revolving around the sun that a simple model suddenly started to match observation. This led to a fairly dramatic conflict between the scientific method and doctrine: according to the scientific method this was a useful and accurate model of the universe, but according to common belief (and Christian dogma) this was heresy.

Science has since established that not only is the Earth not the immovable centre of the Universe, neither is our Sun, or even our galaxy. In fact, a conventional idea of an immovable centre of the universe may not even make sense.

"Space and Time are absolute"

Isaac Newton came up with a set of models for how objects interact (laws of motion and gravity) that formed the basis of classical mechanics. It is impossible to overstate just how clever Newton was and how important these theories are: very very very. Unfortunately, as in the geocentric model, Newton's model makes some assumptions that mean it is only useful in particular contexts (wiki link not necessarily for the faint hearted). As I claimed earlier, this does not make the model 'false', it just puts limits on when it can be used. It is still very very very useful.

Towards the end of the 19th Century, scientists began to make measurements that did not quite match with the predictions of Newton's model. In the early 20th Century, Einstein proposed alternative models (Special and subsequently General Relativity) that better matched the new observations. In this instance, Newton's model was not supported by quite such a firm religious doctrine as the geocentric model, but there was still some resistance. Newton's model is more intuitive and it had been around for a long time. People liked it. But (how hard can I bang this particular drum?) the value of a model is not measured by subjective popularity, it is measured by objective testing. At large scales and great speeds, the predictions made by Einstein's model are objectively more accurate than those made by Newton's model. The scientific method insists that you choose the better model for the job.

(note: there were, and still are, dogmatic objections to Relativity, but they are not anywhere near comparable in scale to the objections to Copernicus' suggestion that the earth revolves around the sun)

Final bang of the drum: the scientific method does not care what people like or what existing doctrine or tradition says. A model is only as good as the evidence that supports it. Badum tish.

Question 5: Good luck or good management? Part One.

What are the chances that something as amazing as you or me could randomly appear in the universe?


What are the chances that a planet capable of supporting life should happen to exist in the universe? What are the chances that the unlikely combination of events that science asserts caused life to errupt should happen spontanteously on such a planet? What are the chances that random mutation and natural selection should lead from that initial simple life to something as sophisticated as the human race? Is it not true that the scientific model of how mankind came to be is just incredibly complicated and convoluted? Is it not much more likely that there is a simple and clean explanation involving a conscious creator?


Is simple always better?


Albert Einstein had a strong conviction that a good model should be a simple and elegant model: if an explanation for something is too complicated then you have probably got it wrong. But there is no scientific justification for this, it is a personal preference or prejudice. Models in physics that Einstein disliked because they were not elegant have turned out to be highly useful and long-lived models. Our preference for simple explanations may be a property of our brains, not a requirement on the universe in general.


We also need to be aware of things that appear very complex but are actually very simple. Anybody who has had a computer with a screen saver is likely to have come across Conway's Game of Life. A relatively complicated and seemingly unpredictable pattern of moving shapes based upon four very simple rules. And this is not a contrived mathematical curiosity; this is a common feature of scientific models ranging from the movement of minute particles to the growing patterns of plants to the logic in the brains of simple creatures and beyond. Simple rules lead to complicated results.


Just how unlikely is unlikely?

In one of the diversions I mentioned the double-edged sword of intuition. One area where intuition can be extremely unhelpful is probability and coincidence.

Experiment has shown that people are generally very bad at judging the relative likelihood of things. For example, if I were to toss a normal coin, which of the two following sequences is more unlikely?

  1) heads tails tails heads tails heads tails
  2) heads heads heads heads heads heads heads

Or if I were to pick letters entirely at random, which of the following two sequences is more unlikely?

  a) yrqwburix
  b) hellodave

Most people without a basic training in probability will say that sequence (2) and sequence (b) are more unlikely. Hitting a string of seven heads in a row feels unlikely. Randomly generating a recognisable phrase feels unlikely. In fact, in both examples the sequences have exactly the same probability of occuring. If you don't believe this, that is intuition messing with you. It's powerful stuff.

So ... just because a thing seems intuitively unlikely, that does not make it unlikely. You have to take a step back and examine the thing objectively using science.

"What are the chances that a planet capable of supporting life should happen to exist in the universe?"

Likelihood depends broadly on two things: how uncommon the thing is, and how big the sample is. As an everyday example: if one person buys a lottery ticket they are unlikely to win. If several million people buy lottery tickets, one of them is quite likely to win. Most lotteries eventually have a winner.

Lemma: The universe is big.

Very very very big. Our sun is part of the milky way (the vague band of light that you can see in the sky if you live somewhere with a low level of man-made light). The current best estimate for the number of other stars in the milky way is around two trillion (2,000,000,000,000). And the milky way is one of (again at a best estimate) around half a trillion (500,000,000,000) galaxies. A ballpark estimate for the total number of stars in the universe is a septillion (1,000,000,000,000,000,000,000,000). The sun is one of a septillion stars.

A septillion is a great word but not really a number that a human brain can grasp intuitively so let us examine it another way. There are roughly six billion people on the planet. There are an average of 100 thousand hairs (or hair follicles if they're bald) on each of their heads. Now imagine cutting every single one of those hairs into a thousand pieces. There are still around one and a half million stars for every tiny chopped piece of every single hair on every human head on earth. Speaking for myself, I struggle to intuitively grasp six billion people, let alone the hairs on their heads. A septillion is a staggeringly big number.

The random appearance of human beings seems intuitively unlikely. But the universe is even more unintuitively gigantic. So again ... you have to put intuition to one side and attempt to grapple with this subject objectively with science.

A further interlude: a bit on truth

Having promised myself not to get involved in any instant coffee student philosophy discussions, I'm going to have to tread quite carefully around this. But Robin poked me on the subject and it does merit some thought. This still officially counts as an interlude ... I am loathe to attempt to formally define or question the concept of 'truth'. And I have previously stated that for current purposes, I'm assuming science is not a list of absolute facts (or truths).

The earth is flat.

What do we mean when we say something is true or false? I mentioned the flat earth model earlier so let us start with that. The statement "The earth is flat" is definitely false. (False is much easier to spot than true.) Here is a collection of photos of the earth taken from space. Conspiracy theorists may wish to dispute their veracity ... but not with me. Thanks all the same.

A flat earth model is very useful if you are building a house, but architects using the flat earth model know that the earth isn't actually flat. I hope.

What about the statement "The earth is round"? If you were pedantic to the point of being antisocial, you might argue that strictly speaking the earth is an oblate spheroid and not perfectly round at all. Is the statement still true? It's fairly accurate. It's probably the best single syllable description of the shape of the earth. It's not as if 'round' is a strictly-defined geometric term in any case. Biscuits are round. People's heads are round. Round-ish.

So in common usage 'true' and 'false' are not absolute black and white concepts.

The earth is 7000 years old.

Some biblical literalists use the creation stories in the Old Testament to assert that the earth is only six or seven thousand years old. Some will even couch this assertion in scientific terms and claim it can be supported by a legitimate use of the scientific method. A quick google will bring up a number of such papers.

This assertion is false. Uncontroversially and incontrovertibly false. This model of the earth's history is contradicted by a truly massive weight of evidence. It is as easily falsifiable as the suggestion that the earth is flat.

Note that this does not instantly disqualify it from being a scientific model. As I said earlier:

"Scientific models and theories are not 'true' or 'false'. They are 'useful' or 'not useful' in particular contexts."

and

"Science is a set of well-defined models that can be tested against observation."

If you can find a context where the assumption that the earth is 7000 years old has an application, and you can express it in terms that allow it to be tested against observation in that context, then it will become a useful scientific model.

I will buy an iPod for the first person who can give me an example of a context where this assertion is useful and a method for testing it. Any size and colour you like. The answers "to prove the literal truth of Genesis" and "by reading the word of God" will receive a mystery booby prize.

So ... being demonstrably false does not stop something from being science; failing to satisfy the simple criteria of a scientific model and not applying the scientific method stops something from being science.

I have no idea if this satisfies Robin's qualms about "true" versus "useful". I'm sure he'll tell me.

A light-ish interlude.

OK. The last entry was possibly a step and a half. And the final assertion that "nothing that exists is 'outside' science" is something of a brainful. So this post is a gentle meander around the idea until I'm happier with it.

Bud has made an interesting comment:

"... modeling anything with science is, in itself, a leap of faith"

This is worth dwelling on. It's an important part of understanding the difference between the scientific method and a scientific model, and between a model and reality itself.

A model is a leap of faith. You are being asked to accept that what the model tells you is the same as what you would experience in Real Life. Take the seemingly simple example of numbers and arithmetic. As a young child, you are taught to accept that the sum "5 + 3" is comparable to adding five apples to three bananas. You are asked to believe that every single time you bring together five apples and three bananas they will always combine to make eight pieces of fruit.

This is a leap of faith or an act of belief. See the previous posts on belief in science and a belief in belief.

Two things turns this act of belief into a scientific model. Firstly, the model is expressed in a way that is comprehensible and useful. The vast majority of human beings can be taught basic numeracy and can apply it in extremely useful ways to Real Life. Secondly, the model is expressed in such a way that it is testable. We can compare the results that the model of numbers and basic arithmetic give us, with the results that we observe in Real Life. We can go out and buy five bananas and three apples and we can put them together and count them and (fortunately for us) every single time we will count eight pieces of fruit.

Pure Mathematics

While we're meandering and talking about arithmetic, let us take a brief stroll through the scented meadows of Pure Mathematics. Some people don't even label pure maths as a science. Even the term 'pure' has a strange, un-sciency feel to it. Here's what wikipedia has to say about it:

"Broadly speaking, pure mathematics is mathematics motivated entirely for reasons other than application."

Which is more a definition of what it isn't than what it is. Essentially, pure maths takes the 'useful' part of our definition of a scientific model and puts it to one side. It still takes a model and expresses it in comprehensible terms (comprehensible to other pure mathematicians, that is), but it does not care whether the results are applicable to the Real World.

Let's take the schoolboy favourite concept of an infinite number. There is a finite amount of 'stuff' in the universe. So the concept of an infinite amount of something is, to all intents and purposes, entirely useless. At the same time, it is an extremely cool idea (well ... to pure mathematicians and schoolboys at least). Pure maths is built upon piles and piles of extremely cool but generally useless things.

There are of course exceptions. The simple ends of pure mathematics are useful: numbers and geometry for example. Many other abstract and 'pure' mathematical models have turned out to have application in the Real World, although typically they become useful decades or centuries or even millennia after they are first investigated 'for fun'.

Intuition

Intuition is great. The human brain has the capacity to observe the world and make lightning fast decisions about what is happening and what is likely to happen. We can throw and catch a ball without performing any complicated calculus to work out its trajectory. We can distinguish between faces and voices from objectively tiny differences. We can store and recall and relate information about things with unlikely speed.

But intuition has a very definite limit. The human brain works on a human scale. If you go very far outside that scale, either very much bigger or very much smaller, then intuition falls down. Things become quite literally 'strange'.

Take symmetry as an example. Symmetry is an intuitive concept. Imagine you take a square of plain white paper and place it in front of you. You can turn it through a quarter, a half, or three quarters of a turn (90°, 180°, 270°) and it will appear the same. You can reflect it in a mirror and it will still appear the same. It has some symmetry.

Now, I used the word "imagine" there for a reason. You don't actually have to take a square of paper. You know these things from experience and intuition. You've seen a square before. You know how squares work. You can imagine the same process with a rectangle or a triangle or any number of familiar shapes and you would understand how their symmetry worked.

There is a simple model of symmetry in a branch of pure maths called Group Theory (no wiki link as it would confuse more than anything else). It provides a formal model for what we understand intuitively about symmetry. But, because it is pure maths and not bounded by a need to relate to the Real World, it goes some steps further and provides a formal model for aspects of 'symmetry' that are utterly outside our intuitive understanding. It can, for example, model the idea of an object that needs to be turned around twice (720°) before it looks the same. Clearly, that makes no sense at all for our intuitive understanding of the physical world.

Except (either beautifully or irritatingly, depending on your perspective), there is an application for this bizarre and unintuitive model in Quantum Mechanics. It is counter intuitive because it is not on a human scale, but it is still useful. And I'm definitely not linking to the wikipedia article here since the page acknowledges itself that "All or part of this article may be confusing or unclear."

So:

• a scientific model is a leap of faith: the scientific method requires you to TEST the model
• pure maths is only science-ish since it investigates models for their own sake
• a model does not need to be intuitive to be useful or scientific

Lemma 3: science does not know everything

This is less of a lemma and more of a clarification. An exercise in filtering the mud out of the water.

There is a common argument when one attempts to apply science to certain subjects. It runs something like this: "Science does not know everything. Science does not address X. Therefore X is somehow 'outside' science."

One step at a time then ...

Science does not know everything.

This is true enough. But not necessarily in the way that it is typically intended.

It is true in the sense that the universe contains a lot of stuff and it is highly unlikely that the human race will ever have the resources or technology to observe and catalogue and model every single bit of it.

It is true in the sense that existing scientific models explicitly exclude the possibility of knowing 'everything'. On the macro scale, general relativity tells us that there are parts of the universe that are unobservable. We can never 'see' them. They can never have any effect on us. (That's a slightly heavyweight wiki article ... if anybody wants to volunteer to paraphrase it in layman's terms they are more than welcome). At the other extreme of scale, Heisenberg suggests that we can only know a limited amount about the position and momentum of a particle.

And we've already mentioned incompleteness theory.

(Of course, it is more than possible that the current models of relativity and quantum mechanics are wrong and that we can know more than they suggest. As I've already said, science is always wrong. That's why it works.)

But this statement is true in a more abstract and arguably much more important sense. It is true almost by definition. Science does not strictly know anything at all. It does not even claim to. It claims to provide us with useful models that help us advance in the Real World. A claim I defy anybody to refute (unless they're living naked under a bush and communing with The Internet via herbal telepathy).

A better statement would be "Science can model anything."

If there is something that we can observe and attempt to understand then the scientific method can address it. If something can be defined, then we can attempt to model it. If it can be observed, then we can compare our models with the observation. Essentially, if something exists, then it can be approached with the scientific method.

Have we accidentally addressed the third part of the argument here? Apologies for jumping the gun. Back to the second part.

Science does not address X.
This can be interpreted in two ways. The first and simplest is "there is no current scientific model relating to X". This may well be true. This does not mean, however, that a scientific model of X cannot be formed.

The second interpretation is broader and more nebulous and, I think, is what is most typically intended: "X contains some peculiar quality that differentiates it from the usual subjects of science".

This is the meaning used by people who make claims of supernatural abilities such as telepathy. It assumes that 'science' is a finite set of things: theories and test tubes and computers and boffins in laboratories. But, if you'll excuse me hammering the nail in with yet another nail, science is not a finite and complete explanation of everything. Science is a method.

If X contains some quality, however peculiar, then that quality can be expressed and modelled and compared with observation. That quality can be added to the list of things that the scientific method has addressed.

So ... nothing is a priori 'outside' of science. You can, if you wish, apply the scientific method to absolutely anything at all. The response to the original assertion is:

"Science can be applied to anything. If X exists, then science can be applied to it. Therefore nothing that exists is 'outside' science."

Or, expressed in an even more controversial direction:

"If the scientific model is somehow inapplicable to X, then X does not usefully exist."

Question 4: Who created what?

An old man dies and his son buries him and plants a few apple seeds in the ground above. Some years later he passes by the burial plot and notices a small apple tree has grown. He tells his mother who picks some apples from the tree and bakes an apple pie.

Who made the pie?

Not exactly a sphinx-standard riddle: the mother made the pie.

But ... the apple tree made the apples. And the son planted the seeds that made the apple tree. And the father, rest in peace, fertilised the tree. And (for the sake of argument) Mary Ann Brailsford raised the first apple tree from which this particular Bramley variety derives. And an unidentified prehistoric farmer somewhere in central Asia originally domesticated the wild ancestor of the modern apple.

We could go back even further, but I think I've laboured the point enough: it is possible to argue half a dozen different 'creators' for something as simple as an apple pie. We need to narrow down what we mean. Which of these are comparable with God as the creator?

The apple tree: hopefully nobody will object if I discount this one. The biblical God is a conscious entity. This comparison might stretch to work if we were talking about 'Mother Nature', but we are not. God definitely isn't a tree.

The father: the apples are in part made out of the body of the father. He was the fertilizer that fed the tree. But that's not what we mean either. The Old Testament does not say that the universe is 'made out of' God. It is also fairly clear that God cannot die.

Mary Ann Brailsford and the mystery Kazakhstani farmer: we're arguably closer here. Both these people made deliberate efforts to create something. Although neither of them could have had any useful knowledge at the time that their efforts would one day lead to the making of this specific apple pie. And neither of them would live to witness the specific apple pie.

The son: again, the son made a deliberate effort to raise apple trees. And in this case, it is possible that he made that effort knowing that one day his mother could use those apples to make a pie.

The mother: made the pie.

Discounting the father and the tree, which of the remaining three is most comparable with how the Old Testament defines God as creator?

God created everything, but that does not narrow it down: all the apples came from the tree planted by the son, all Bramley apples come from Mrs Brailsford's tree and prior to that from the domestication of wild apples in central Asia.

Back to the source. The whole of the first chapter of Genesis is essentially of the form: "God said 'let there be X' and there was X and God saw that X was good".

(I'm reducing it to that simply to avoid any discussion of the translations or mistranslations of the various 'X', or the possible pedantic knots you can tie yourself in over the order and time in which they were created ... there is plenty of good reading on The Internet about the origins and interpretations of Genesis. It even allows for Genesis to simply be a model or metaphor for the actual creation process.)

This clearly discounts the historic origins of the apple as a comparison. Genesis states that God created each specific X and witnessed that it was 'good'. God did not simply set into motion a sequence of events without knowing what might eventually result.

So there are only two roles in the creation of the apple pie that are comparable with the role the Old Testament assigns to God in the creation of 'everything'. Either the son, who remotely put into progress a sequence of events that he anticipated would one day lead to some good pies. Or the mother, who knowingly made the specific pie in the story.

Question 3: what isn't the question?

There are always more questions than answers. This is a lazy aphorism but it is broadly true. The world is a complicated place and answering every single little question is neither possible nor useful. You need to decide which questions are important, and, perhaps more importantly, decide which questions are unimportant so you can avoid wasting time on them.

Here are some things that I'm not going to waste my time on:

Can God create an object too massive for God to move?

God can move anything. But God can create anything. Oh no! A paradox! It's easy to invent questions like this that appear to poke a logical hole in the idea of omnipotence. Try it for yourself. Literally minutes of fun. The fact that it is so very easy to formulate this sort of paradox ought to be a pretty good indication that it isn't a very useful paradox. It is, at best, an illustration of how you can invent a set of rules and (correctly or not) demonstrate them to be inconsistent. A simplistic version of Gödel's Incompleteness Theorem if you like. (If you don't know about Gödel's theorem, it is well worth reading about. Good stuff to keep you awake at night.)

Bad things happen to good people.

God is omniscient and omnipotent but allows man to do bad things. This is a much (much) more interesting question than the first. But I'm side-stepping it altogether. Observant readers may have noticed that in the two previous posts I did not mention 'goodness' as one of God's attributes.

Two reasons for this:

1. there does not appear to be an unequivocal statement in the Old Testament that God is good. This may seem slightly odd, and the New Testament appears to be more committal on the subject, but I've had a good browse and a good Google and I've turned up nothing.
2. it does not provide any proof for the existence or non existence of God

The first reason may be a mistake on my part. (To repeat what I said earlier, I'm more than happy to be corrected on any biblical interpretation). The second reason is far more important.

If we assume that 'good' and 'bad' are subjective qualities, then the question "why do bad things happen?" can be reduced to a debate on whether or not the "bad things" are actually bad. This is moral philosophy. It should be taught as a compulsory subject to all children, but it isn't useful in the current context.

If instead we assume that there is an objective 'good' beyond the opinion of man, and that God is omniscient, then God knows with absolute certainty what is good and bad. But we do not. So we cannot derive any proof about the existence of God from the fact that we observe things that we consider to be 'bad'.

"Ah but!" I hear you myself say, "the Old Testament contains examples of God proclaiming that particular things are good or bad, and yet appearing to act in a contrary fashion."

Possibly true. But this would only be a conclusive contradiction if you were to accept that the words of God reported in the Old Testament form a comprehensive and infallible definition of what constitutes good and bad. There are, no doubt, some people who do accept this. Those people are unlikely to enter into an attempted rational debate on the very existence of God. This is probably the one and only circumstance where I will give any weight to the "God moves in mysterious ways" argument.