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

Corollary: do we believe in science?

While we're on the subject of belief, and in keeping with the general theme of meandering up and down side roads rather than heading straight to the point, a bit about belief and science.


I blithely stated here that science is not a belief system. Given that I also made the statement that belief is not enough, I probably ought to justify myself. I'm burdened with a few ounces of integrity.


It is often argued that accepting scientific claims requires belief and that this makes it comparable with other more conventional systems of belief like theism. But 'belief' is a many splendoured thing; it means a dozen things in a dozen contexts. We need to be very clear about what we mean by 'belief' in science before we make such a comparison.


Science exists.


OK. That should be fairly uncontroversial. It is equivalent to the "Elvis exists" example from earlier. When we say "I believe in science" we are not saying "I believe in the existence of science." So the statement "I believe in science" is not comparable with the statement "I believe in God" by this meaning of "believe".


Science is useful.


I would argue that when we say "I believe in science" we are instead using the other meaning of "I believe in the capabilities or qualities of science". We are stating that we believe that the scientific method is a useful tool.


Do we need to justify that belief? Is it subjective or controversial?


The scientific method is the set of tools and techniques by which we have created every piece of technology and every branch of medicine in the modern world. It has demonstrated its efficacy over centuries of almost alarmingly rapid progress. It quite clearly and unequivocally works. I genuinely cannot imagine any way in which this massive body of evidence can be regarded as either subjective or controversial.


But ... I'm going to allow it to be considered controversial. Just for the time being and for the purposes of this discussion. That's how generous I am. I am going to allow that the statements "I believe in Science" and "I believe in God" are comparable within this particular meaning of "believe".

Corollary to the corollary.

Thanks to Robin for pointing out a further clarification that needs to be made.

There is an important difference between the scientific method and a scientific model. The method is a method, a way of doing something. A very successful way of doing something. A model or theory is just a part of that method: an idea that pops out of a person's brain and is proposed as a useful model of some part of the observable world. Newton's idea of gravity was a model. How Newton expressed that model and tested it against observation is the scientific method.

So, there is another use of 'believe' that we should address.

I believe in a particular scientific model.

Again, this is not equivalent to "I believe in the existence of a particular scientific model". Reference libraries are chock full of journals crammed with scientific models. They definitely exist.

What is actually meant is "I believe in the utility of a particular scientific model". I think it is a good model. I think it agrees with what I observe in the outside world. I think it can tell me something useful that I have not yet observed in the outside world. As I said down there somewhere, models themselves are not true or false, so this phrase should not be interpreted as "I believe a particular scientific model is true".

Very importantly, the phrase "I believe in science" is not equivalent to "I believe in all scientific models". For one thing, scientists quite often disagree. Disagreement is an important part of advancing understanding. You cannot (honestly) claim to believe in every single scientific model since they do not necessarily agree with one another.

Question 2: is belief enough?

All you need is love. Love is all you need.

Before heading back up the road towards existence, a quick detour up a quite different path. Does it actually matter whether something exists or not? Is it sufficient that people believe in something? Is that the more important question?

Let's take a couple of examples. I like examples.

The Tooth Fairy. Children's milk teeth fall out. This is quite important for child development but not necessarily pleasant for the child involved. Some parents tell their kids a white lie involving a fairy who collects teeth from underneath children's pillows and replaces them with a coin. This apparently sweetens the blow of losing a tooth. As a bonus, the child can spend the coin on sweets and learn the principles of 'feedback' too.

Medical placebos. The placebo effect is when a person believes that they are receiving medical intervention, and that belief speeds up their recovery or otherwise improves their condition. They may simply be swallowing sugar capsules, or having their feet rubbed. The curative effect is in their minds and their imaginations but the effect is very real.

In both examples, the 'thing' does not exist. There is no tooth fairy and there is no medicine. Or is there? Arguably, the important 'thing' in the second example is the effect itself, not the imaginary medicine. Placebos work. This is a Good Thing™. It makes people better. The placebo effect exists.

God clearly doesn't fall easily into the same category as the tooth fairy. The tooth fairy quite categorically and uncontroversially does not exist. It's a deliberate lie to children. (no comment on whether that's a good or bad thing). So ... does God fall into the same category as a medical placebo? Is it more important that people believe in God and that this has a beneficial effect?

I'm going to argue a strong 'no' for several reasons. Firstly, the statement "God is a placebo" is quite condescending towards people who believe in God and condescension rarely leads anywhere constructive in a conversation. Even a monologue. Secondly, it's a cop out; it is saying "I'm not going to bother proving it one way or the other as it doesn't matter." In which case, why am I talking about it at all? Thirdly, and perhaps most importantly, we know that medical placebos work, but we also know that they only work if the person receiving them doesn't know they are a placebo. The medical practitioner may or may not know that it is a placebo, but the patient must believe it is "real" medicine. See the double blind test for a fuller explanation.

If we substitute 'God' for 'placebo' in this statement, we are effectively saying "The priests and holy men may or may not know that God is real. But God works because the believers think he works." I don't mind this as an argument generally, but I've already said that I'm addressing the Abrahamic religions' definition of God. And they are fairly categorical that God is a real entity, and not something that exists only in the heads of believers.

Lemma 2: I believe in belief.

'Believe' is one of those horrible brain-action words with half a dozen meanings that overlap and clash with one another and with the meanings of other brain words like 'think' or 'know'. I believe I'll have another beer. I believe in Father Christmas. I believe Floyd Mayweather is the greatest living boxer. I believe you. They are notoriously difficult to translate because the way they overlap and cover the broad spectrum of 'thinking' differs from one language to another.

It's also one of those awkward concepts that lives in the mind rather than in the 'outside world' and so can be difficult or impossible to test. If I said "I live in England" or "I have three legs" then these assertions would be fairly easy to verify. If I said "I believe in the tooth fairy" then ... well ... I might do. And if I were cunning and lacking in moral fibre, I could make it quite difficult for somebody outside my brain to prove that I don't believe in the tooth fairy. We can't read people's brains very easily. That's why nobody trusts psychiatrists.

Let's narrow the broad word 'belief' down a bit and apply it to my contrived test statements from earlier:

1) I believe in Elvis
2) I believe in King Arthur
3) I believe in Harry Potter

There are still two different meanings here. Statements (2) and (3) are most sensibly interpreted as "I believe in the existence of X". But Elvis's existence isn't controversial, so that probably isn't what we mean in statement (1). The most likely interpretation of (1) is "I believe in the capabilities or qualities of X". Elvis is perhaps an odd choice here. It is probably clearer with something like "I believe in the president".

God is an awkard case. Perhaps not surprisingly. (remember God? I said I'd sneak back up on God). The statement "I believe in God" can be interpreted as either or both of the above meanings.

"I believe in the existence of God" and "I believe in the capabilities or qualities of God". (where the second statement presumably implies the first). So whenever we address this statement, we need to make completely clear what we mean.

Oh ... and the title of the post "I believe in belief". You could argue that you cannot prove that anybody else believes anything, since belief happens inside people's heads where you can't see it. This is in the same realm as arguing that you cannot prove that anything outside your own head exists. Diverting if you're a 17th century French mathematician or a student sipping cheap instant coffee. Not nearly diverting enough for me to bother about it here. Belief exists. People believe stuff and they believe in stuff. I'm taking that as given.