Friday, 25 January 2008

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.

Thursday, 24 January 2008

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

Wednesday, 23 January 2008

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.

Thursday, 17 January 2008

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.

Wednesday, 16 January 2008

Definition 4: God part 3.

Apologies. I'm getting a bit cavalier with my choices of titles and numbers. This section is a continuation of this. Feel free to apply a more elegant numbering scheme in your head.

Omniscience and Omnipotence

A few words on these two concepts before we get to the meat.

First things first. Strictly speaking, just because you are capable of something it does not necessarily follow that you must demonstrate that capability. I know the words to the Spice Girls' "Wannabe". I am not necessarily going to sing it.

However, I would argue that when you claim a capability, it is only a useful claim if you can provide evidence of that capability. As an example to illustrate this, it is fairly common for the leaders of personality-driven cults to make claims of supernatural powers: healing, knowledge of the future, even the ability to fly. It is not unusual, when challenged on these claims, for the individuals to then claim that they choose not to use their powers. A very handy cop out.

If I were challenged on my knowledge of the lyrics to "Wannabe", I could sing the song. If I were to simply say "I choose not to sing it" then the challenger would be well within their rights to doubt my claim or even label me a liar. (it may simply be that I am generous and thick-skinned; I may prefer to be thought a liar than to inflict my interpretation of the Spice Girls on the world.)

Bottom line: one cannot easily disprove the claim "I have this power but I choose not to use it", but, I would argue, it is completely irrelevant. Capabilities that are never demonstrated have, almost by definition, no effect on the rest of the universe. Have I overstated this yet?

Back to the point. Does the Old Testament claim that God is omniscient and omnipotent? Some references ... not involving Isaiah this time.

A quick search for the term 'Almighty' on Bartleby brings up lots of references to 'the Almighty' and 'Almighty God'. If you accept 'almighty' and 'omnipotent' to be synonymous then that should be enough to verify that the Bible labels God as omnipotent.

In terms of God's actual claims to power, Job chapters 40, 41 and 42 provide a nice example. This is essentially a list of tasks that are beyond the abilities of a mere man such as Job, but which God claims to be capable of performing. And then we get the meat in Job 42:2

"I know that thou canst do every thing,
and that no thought can be withholden from thee."

Job acknowledges that God can do every thing. That's a pretty direct statement of omnipotence. He also acknowledges that God can see all thoughts, which is a substantial part of omniscience as well.

What about the rest of omniscience? I struggled to browse my way to this, even with the help of Bartleby, so I 'cheated' and googled and lo and behold there is an entire psalm (139) dedicated to the fact that God is omniscient (and also omnipresent).

So ... according to the Old Testament, God is capable of seeing everything and doing anything.

Tuesday, 15 January 2008

Definition 3: God part 2.

Back to God again. And back to the source (or as close as I can get to the source without learning a selection of bronze age middle eastern languages). There are clearly several other versions of the Old Testament in current use, but I don't have the resources to cross check every single one. I'm more than happy to take suggestions of variations and clashes in comments. For current purposes I am simply going to list the usual attributes of God and reference them to the appropriate bits of the King James version of the Old Testament.

Using Bartleby's excellent searchable reference books (one of the finer corners of the Internet) makes the task of finding the biblical definition of God easier. But still not very easy. As you might imagine, or know, the word "God" appears quite a lot in the old testament. The majority of these occurences are statements praising God, or advising God's followers how they ought to behave towards God, or reporting what God said or did, which helps to narrow it down.

In fact, there are relatively few direct statements about what God actually is. I haven't decided yet if that makes this job harder or easier.

The Eternal God

Arguably, one of the most fundamental qualities of God is that God has always existed and is not something that was created or came into being. (oh ... another nice feature of Bartleby is that it provides hyperlinked cross-references ... so if you find one statement in a reference, you can easily find related statements. Nice.)

Isaiah 44:6 "I am the first, and I am the last" and Isaiah 48:12 "I am he; I am the first, I also am the last". (according to Bartleby, this is also repeated in Revelations, but I'm only looking at the Old Testament).

That is fairly unequivocal as a statement: God existed before anything else.

The Creator

This one is easier. God is referred to as a creator in many many places.

Isaiah 40:28 "the everlasting God, the LORD, the Creator of the ends of the earth"
Isaiah 45:7 "I form the light, and create darkness: I make peace, and create evil: I the LORD do all these things."

(I did look further than Isaiah, honestly. It is quite a good book though.)

And of course there is the whole of Chapter 1 of Genesis.

There are some slightly more equivocal statements which refer to God creating more specific and limited things like 'Israel' or 'righteousness', but overall the Old Testament has an uncontroversial position that God created everything.

An aside: there is a whole wealth of material on the internal consistency of the various creation stories in Genesis. I might delve into those at some point, but the intention at the moment is simply to list God's attributes and provide their biblical justification.

God the Trinity.

Happily, I've said that I am only using the Old Testament definition of God. The Trinity is one very good reason for doing that. It has spurned more brain aching theological debate than probably all other biblical questions combined and caused more splits in the church than anything else. It also narrows the scope to mainstream Christianity, as Judaism, Islam, and many smaller branches of Christianity do not accept that Jesus and God are one and the same. In short, I'm not touching it with a barge pole.