Documentary Stupid

[lil_shepherd]

Yesterday at 8pm the BBC showed what purported to be a programme in the Natural World series on The Wild Places of Essex (I am not going to link to it in iPlayer for reasons that shall become clear.) It was a personal view by someone called Robert MacFarlane (who has just written a book) and it was, to be frank, absolute crap. It ought to have

Comments

[purplecthulhu]

Actually infinity has quite a number of useful non-philosophical uses in mathematics, and there is a very clear distinction between aleph-0, the so-called countable infinity which can eb equated with the number of integers, and higher infinities like aleph-1. Cantor's diagonal proof shows clearly that you can have a number larger than the number of integers.

So no, this is not just a philosophical concept.

[lil_shepherd]

Well, I would argue that both numbers (unless allied with a physical object) and infinity are abstract concepts, and that theoretical, as opposed to applied, mathematics is itself a philosophical concept and not a scientific one.

You can have as large a number as you like, but it is still an abstract concept and not a physical fact. Until you have an infinity of atoms or bananas it remains a concept, and, I would argue, a philosophical rather than a scientific one. Furthermore, until you can design an experiment that proves infinity exists, it cannot be a scientific concept. Rather like the supernatural and god(s), in fact.

[purplecthulhu]

You don't need a physical object for something mathematical to be more than abstract. Issues of different infinities come up in algorithmic complexity theory about when (and if) computational tasks finish. All encryption systems are based on these results. So the fact that I can't crack your bank's passwords and steal all your money is reliant on the nature of infinity.

And does the square root of -1 exist? It's used throughout physics, electronics, signal processing etc. but other than giving it a symbol, i you can't touch it.

[lil_shepherd]

And does the square root of -1 exist?

Who knows? I would say not, except as the aforementioned abstract concept. This all comes down to the philosophical question as to whether something that cannot be detected but is thought about actually exists. Furthermore, things do not have to actually exist to be of use.

For instance, anger exists only as a behaviour pattern resulting from a flow of hormones and as a human mental concept - an emotion. It can, however, be of great use within human societies...

[purplecthulhu]

Which makes all of them, including i and infinity, more than just philosophy.

[lil_shepherd]

I think at this point we are coming down to semantics.

[starcat_jewel]

Even theoretical math is subject to the scientific method. You propose a hypothesis and subject it to testing, and if the tests don't work the hypothesis is abandoned. It's just that the tests in question are logical rather than physical -- but still, if your hypothesis* can be shown to prove that 1=2, it's invalid.

* That one can divide by zero, in this instance.

[lil_shepherd]

Pure theoretical math is subject (partially) to the scientific method, but 'tests' are by pure mathematical logic and are therefore self-referential.

It's the reason that many scientists (and mathematicians) do not regard mathematics as a science, though it is a scientific tool.

However, use of the 'scientific method' (itself an abstract concept until put into practice in individual cases) is not an argument for the actual existance of infinity, however useful that concept is in pure mathematics or the higher reaches of theoretical physics, which have to be completely speculative and nothing more than philosophy until actual experimental tests can be devised, or confirmatory observations made.

After all, there was nothing wrong with the math behind how many angels can dance on the head of a pin, or how many years had passed since the Creation, based on Biblical tests.