Thanks sense. That makes sense, I think. Could you say that this is a rule that defines maths:

It constructs its own rules/axioms and then proves other things within itself from this and only from these rules/axioms.

Yes, I tend to do that, especially with the evolution thing. Maybe it's just the topic. People don't get as passionate about taxes or electoral reform.

That definition is growing on me, as it includes logic and set theory, which is generally included in maths but doesn't fit well with how you would generally describe maths. I was thinking about points and lines before. You can define a line from two points, but I was not aware of a way to get around defining a point.

Would computer programming satisfy that rule? Is it maths?

freediver wrote on Apr 16^th, 2007 at 4:45pm:


In every sense of the word, yes.

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MY GOD MAN! You have just perfectly summed up my ENTIRE ARGUMENT in a few well placed words. *shakes hand, then bows*

Forget all the dancing around particular topics, sense has it, sense is the man, this is it, this is what it all comes down to. This is what I've been trying to say the whole time and yet my stupid brain could not find the words that sense has used right here, thank you sense! This is perfect!

It does not matter if it is right or wrong, it is science as science is defined.

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Cheers indeed Pity that half the time I can't take my own advice there

So what do you do that makes you so wise to the ways of wonderful maths?

Ok I have calmed myself somewhat...freediver, I no longer care that you disagree, you can have your false understanding of evolution, this thread is not about that argument anyway.

My thinking on the topic (maths, not evolution) stems from observation of how the scientific method plays out in the construction of scientific models, specifically mathematical models. There are many instances in science where the models used are purely mathematical ones, and quite often once rudimentary conditions are discovered through empirical experiment maths takes over entirely in the creation of the model.

Yet again I will resort to Einstein as an example: Einstein used geometric mathematical models to describe what is generally understood as 'the fabric of space-time', on a very simple level, he took 3-d geometry and added a 4th dimension of time and described the whole lot in the standard geometric way: through triangulation and vector algebra etc. The general and special relativity models are purely mathematical, yet they are scientific none the less. Another example is Hooke's laws for linear elastic deformation of solids, empirical experiment shows that for elastic deformation homogeneous solids have a linear relationship between the force applied and the deformation that is observed, through this a linear mathematical model was built to describe the relationship and expand upon it through the use of purely mathematical theorems. Of course there is also Bohrs use of probability to describe the behaviour of matter at the quantum level. Mathematical models are used in almost every aspect of science, and quite often scientific models are expanded upon through purely mathematical methods. Calculus has near ubiquitous presence in all fields of science, as with statistics and probability. Forces are described scientifically as having quantity (magnitude) and quality (direction) and so vectors are used as a model for force, and matrix algebra used to calculate force interactions. Speed and acceleration are defined as change in distance per unit time and change in speed per unit time respectively, acceleration is the rate of change of speed and so acceleration, as described by science, is the derivative of speed, they relate scientifically through a mathematical model in calculus. And so I could go on for thousand of words using hundreds of examples.

What I want to ask now is where does the science end and the maths begin? Yes sense, pure maths is content free, but if you apply it to some scientifically defined content, does it cease to be maths? Conversely, if a scientific theory is derived through purely mathematical methods, does that mean it is no longer science but maths? My point is that there is overlap, sufficient overlap to say that often science is mathematical in nature and often maths is scientific in nature. I would even venture to say that if the original defining characteristics of mathematical method did not stem from observations of nature, that maths would not be so perfectly suited to use in scientific models as it is, indeed quite often modern maths is not so well suited to scientific models (topology used in string theory for example). It is my belief that the methods of science and the methods of maths are very often indistinguishable from each other, not that they are identical always, but they overlap enough to say that science is a mathematical process and maths is a scientific one, to a degree in each case at least.

This is where my argument stems from. It is true yes that the words 'science' and 'maths' are defined differently, and it is true that as fields of study they are separate and distinguishable. However it is also true that they cross over constantly, and one can sometimes define the other. The reason maths is used so extensively as the method of scientific modelling, and that so many say that 'maths is the language of science' is because they both rely on the same methods of logic. In maths it is possible to invent your defining qualities as sense pointed out and in science they are arrived upon through empirical study, however it is not the defining characteristics of each that I am concerned with here, what I am concerned with is the fact that the methods of both are often the same and completely interchangeable with one another.

Of course I am a believer that science is a process, not an outcome.

freediver wrote on Apr 18^th, 2007 at 8:29am:

But that is exactly how Einstein derived his theories of relativity, they could not be empirically tested for decades, indeed nobody even knew how they might be. The fact that they eventually were tested is irrelevant to the argument,at the time it was impossible to say how they might be. Relativity was constructed entirely using mathematical methods only.

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I did actually mention this. String theory is a good example, however there is much debate in the scientific community as to whether string theory is scientific since it cannot be tested, it was derived from purely mathematical methods and yet it attempts to describe the universe. Many have said that while string theory may not be testable, neither was relativity (and often still isn't) and yet relativity was derived in the exact same way that string theory was - using maths and maths alone.

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So you are trying to tell me that if maths is used in science, it ceases to be maths?

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I have taken the time to distinguish them, yet there is still crossover. The world is not clear-cut black and white, not ever, everything overlaps and interrelates with everything else.

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Now you see this is just a different way of wording exactly what I have said, no a hammer and a screwdriver are not the same thing, but yes they are both mechanical tools. This is what I am saying.

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Science does not rely on logic?

I believe that science and maths both rely on the same logic for a large part, and this is why maths is so perfectly suited to scientific models, and is so often used to extend scientific models through entirely mathematical methods.

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The ones you and sense outlined: "It constructs its own rules/axioms and then proves other things within itself from this and only from these rules/axioms.". Science really does this too - no scientific model is anything more than a human construct that roughly approximates what a human witnesses in nature, and as such is only true within the rules/axioms that define the model. The only real difference s that science aims to produce models that have a meaningful outcome and limits itself to the description of nature. Again since science is the process not the outcome, it is still really very similar to maths, often identical.

Again, I am not trying to say that maths == science, I am trying to point out where they use the exact same processes of logic.