Wildfalcon

For some time I have been thinking about writing a series of articles on the problems with the scientific approach. I believe in the scientific approach, and I think it’s correct, but there are problems with it and only with a proper understanding of them, can we hope to not be bitten by those problems.

This is the first of those articles, and is about the problems with reasoning within a formal system. It’s a bit of an abstract topic, so I will attempt to explain it, and what is wrong with it.

Consider the case of one of the most famous scientific moments of all time; Newton, sitting under a tree. An apple is supposed to have fallen from the tree, and after hitting poor Newton on the head, inspired him with the theory of gravity.

Before long, Newton came up with a theory, that the force exerted on an object by another object is related to the mass of both, and the
distance between them. He proposed an equation to express what the force is. As soon as you introduce an equation, you have to deal with maths. At this point we have two vitally important questions. How can we be sure that the equation successfully predicts the behaviour of gravity, and how can we be sure that the maths itself is going to give the correct answer?

I want to make it clear the difference between the two. The first question is “Do we have the right idea as to how gravity works – are we using the right equation?”. The second question is “Does maths work?”, does a multiplying two numbers actually give the number that it should.

You may well be wondering at this point, am I asking if multiplying two numbers together gives the answer to multiplying two numbers, or if adding up 1+1=2. That is exactly what I am asking. Of course, there are proofs for this. If you ask any mathematician to prove 1+1=2 they can, (or at least can look it up, it’s rather messy apparently).

But proving 1+1=2 does not prove all of mathematics works, nor would showing that multiplying two numbers works. Before we can be sure of using maths to get the right answer, we need to know that every single part of maths is valid, that it works, and here is the crux – you cannot do this using mathematics. Maths alone is not enough to prove that maths works.

However, maths can be shown to work, using logic. Using the rules of logic, all the basic, atomic bits of maths can be proven, and have been. Problem solved.
Well no, not quite. How do we know that logic works? Logic is made up of statements like “if something is true, then something else is false” and so on, but is that really the case? It might seen obvious to us that it is, but that is because the English language has been built up assuming its true, and our brains and grown up thinking that way. It turns out, we cannot prove it. Can we use logic to demonstrate its true? No, for exactly the same reasons we cannot use maths to prove that maths is true. We need some greater system than logic to prove that logic is a valid way of thinking.

Can you spot the problem yet? Let’s assume we have a way of thinking called Super Logic and this new way of thinking clearly shows that Logic is OK to use. Then we have to ask how we can be sure about Super Logic, and so on, and on, and on. As one great man once said “its elephants all the way down”.

Now it turns out, we do not have Super Logic. We stop at logic. All of our reasoning is based on the assumption that it’s OK to think using logic, but we have no real way of backing that up.

We believe in logic, and we believe in it without any proof. We accept logic as an act of faith.

Now it’s not a complete leap of faith, we have built a hell of a lot of “stuff” based on this belief in logic. Ship, bridges, planes, cars, and all of them work in a way that can be explained using logic. So we have a hell of a lot of evidence that it’s OK to do this, but we still cannot be sure, we can never be sure.

Note: I came accross this article in the amazing book Gödel, Escher, Bach, and if you want to know more about this subject, or just enjoyed reading it, then this book is a must.

Technorati Tags: logic, maths, faith, science problems

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Well it’s a while since I have written anything here. I have been having some down time, relaxing after my PhD submission. I now have a date for my Viva, the 1st Dec. I have also been promoted to webmaster for IVDA, so I’m now in charge of www.universitydancesport.com. It has to change, quite drastically! There are a number of problems with the current site, mostly that it’s falling apart at the seams! Text is overflowing from one column into the next, the forum is a totally different piece of software, and it’s breaking. Probably none of the users have noticed it yet, but the admin side is generating SQL errors left right and centre.

I’m moving in a different direction and am playing with Plone. Plone is a full content management system, written on top of CMF (the Continent Management Framework), which is in turn written on top of Zope, which is an application framework for content management systems. Zope is written in Python, a language I have no prior experience of, but its meant to be nice, and well thought out, with the exception of some strange white space issues. Anyway, the whole project is very well designed, and once you get your head round the strange multi level configuration options, kinda cool. Though it has no good forum products. I have installed Ploneboard, which works, but is missing several features. Firstly it doesn’t let you allow access to some boards to only some groups, but because of the nice security model in Zope, I can set that using Zope (though it’s a bit of a hassle). It doesn’t seem to let you edit posts, not does it tell you how many new posts have been made since you last visited. Looking at the source code for Ploneboard, it’s well structured and clear, so I think I can add the features we need and submit them back to the ploneboard development team for inclusion in future releases.

On a different note, I watched the BBC’s new Rome drama today, and then read the Guardian’s review of it. The reviewer seems to find every fault with it, without much justification, or historical accuracy. Sure, we don’t know that roman women would have showered in bull’s blood for a sacrifice, but given the prevalent religion at the time, it seems more than likely. As for his claim that the political back story is not covered in enough depth, well there is only so much screen time. If you want a good dramatisation of the fall of the republic and the rise of the empire, then Iggulden’s series has to be your first stop. Of course that is 3 books long, and counting…..

Finally I’m writing this in WB Editor 2, which is crap, and I won’t be using it again!

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My mother has always been a very keen proponent of the idea that the English population is indigenous, and has not been replaced several times though history via invasions. In fact this is now the established belief for at least the Roman and Norman invasions of the British Isles (54BC and 1066AD). The current belief is that a small number of invaders took up positions of power, but the majority of the population did not change, at least not genetically speaking.

The Saxon invasions of the dark ages however are more wildly disputed. A new study entitledY Chromosome Evidence for Anglo-Saxon Mass Migration claims to have found evidence that there was a large population change during the Saxon invasions.

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