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155200.  Fri Mar 09, 2007 6:12 am Reply with quote

I’m sure all other denizens of Elfland will know this very well, but I daresay some of the panel share my ignorance of such matters ...

I’ve just read about the Principle of Induction, in a beautifully-written book “Everything and more, a compact history of infinity” by David Foster Wallace (Weidenfeld, 2003). He says:

“It is the fundamental precept of modern science. Without the Principle of Induction, experiments couldn't confirm a hypothesis, and nothing in the physical universe could be predicted with any confidence at all. There could be no natural laws or scientific truths. The PI states that if something x has happened in certain particular circumstances n times in the past, we are justified in believing that the same circumstances will produce x on the (n + 1)th occasion.”

The example he gives is, when you're lying in bed of a morning, trying to get up, how do you know that the floor of your bedroom will take your weight?

So, as a way into the topic of Everything, how about a question along the lines of: “Not that I want to alarm anyone, but how do you know the chair you're sitting on isn't about to explode?”

155208.  Fri Mar 09, 2007 6:20 am Reply with quote

The simple answer is: "you don't".

This is a pretty fundamental idea behind science. If something seems to happen repeatedly (e.g. dropping apples from trees or your chair not exploding), you can use this prior behaviour to predict what will happen next. When you're proved right, you can look terribly smug.

All scientific theories are then based on this Principle of Induction idea you explained. However, there's no way of truly knowing for sure that something will happen again in the future.

For sure, the more often something behaves as predicted, the less likely it becomes that it'll ever do anything different. But just because something is extremely unlikely, doesn't mean it's impossible.

It's possible that one day someone will drop an apple from a tree and it will fall upwards. Or that your chair will suddenly explode. If this does happen, then pretty much the whole of science will have to be looked at again and adapted (or completely changed from scratch) to accommodate this new information. Until such a time as it does happen, though, I think we'll stick with the theories that have worked pretty well up 'till now.

This is the fundamental truth that, contrary to public opinion, science actually knows nothing and freely admits it. All science does is to try and predict what will happen in certain circumstances based on prior behaviour.

155211.  Fri Mar 09, 2007 6:23 am Reply with quote

Exactly, Bob - that's what, to my non-scientific mind, makes it such an exciting question! It's as if the whole of science is based on a principle which says "We don't know anything, but ..."

155225.  Fri Mar 09, 2007 6:39 am Reply with quote

We toyed with this once before, but didn't use it. For me, the problem is that it depends what you mean by 'know'. You might define it backwards, ie say that to 'know' something is to ascribe to it the same level of certainty as you do to the belief that your chair isn't about to explode. Maybe no-one actually articulates it that way round, but that's effectively how the word is used all the time.

If I say that I know what's going to be on television tonight, no-one over the age of 6 would be pedantic enough to correct me, even though all sorts of things could prove me wrong in the event; we all just go along with the equivalence of the phrases "I know" and "I'm sure enough for all practical purposes".

155255.  Fri Mar 09, 2007 7:17 am Reply with quote

The same source as above says that “some infinities are bigger than others, as in arithmetically bigger.” I’ve no idea what that means (Bob?), but it sounds promisingly counterintuitive.

155258.  Fri Mar 09, 2007 7:22 am Reply with quote

There are, it seems, numbers which are too big for any computer, existing or imaginable, even a computer the size of the Earth calculating for as long as the Earth has existed, to compute. This is known as Bremermann’s Limit.

155261.  Fri Mar 09, 2007 7:26 am Reply with quote

It's simple set theory.

If you have a list of all the numbers in the world it is an infinite set of numbers, if you have a list of all the even numbers it is also of infinite size but is contained by the first set.

MatC style Disclaimer:
It's a long time since I did any pure maths and even when I did it was half-hidden under a haze of hangover.

155274.  Fri Mar 09, 2007 8:04 am Reply with quote

There are also an infinite number of prime numbers, apparently.

155301.  Fri Mar 09, 2007 8:54 am Reply with quote

MatC wrote:
Exactly, Bob - that's what, to my non-scientific mind, makes it such an exciting question! It's as if the whole of science is based on a principle which says "We don't know anything, but ..."

That's precisely what science is based on.

It's always amusing if you get into a science vs religion debate with a real fundamentalist. Once they start talking about what science "claims to know", you can point out that science freely admits it knows absolutely nothing. I usually follow that up with the viewpoint that anyone who claims to really know things tends to scare the bejeezus out of me.

Flash wrote:
If I say that I know what's going to be on television tonight, no-one over the age of 6 would be pedantic enough to correct me

Well, actually, I think you'll find....

155306.  Fri Mar 09, 2007 8:58 am Reply with quote

I usually quote Timon at this point. So, not wishing to add to the idea that the universe is unpredictable, I shall:

“That honey is sweet I refuse to assert; that it appears sweet, I fully grant.”

157124.  Fri Mar 16, 2007 10:30 am Reply with quote

Everything in the universe is (perhaps) made of a “string-net liquid” called herbertsmithite.

S: NewScientist

163837.  Sat Apr 07, 2007 7:50 am Reply with quote

Chris - can we find some way of getting p-branes into a question on the theory of Everything? (or elsewhere)

"P-brane" must have scope, but maybe it's just too difficult for our purposes:

In theoretical physics, a brane or p-brane is a spatially extended, mathematical concept that appears in string theory and its relatives (M-theory and brane cosmology). The variable p refers to the spatial dimension of the brane. That is, a 0-brane is a zero-dimensional pointlike particle, a 1-brane is a string, a 2-brane is a "membrane", etc. Every p-brane sweeps out a (p+1)-dimensional world volume as it propagates through spacetime.


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