Do numbers really mean anything?

[FBM]

we haven't even gotten outside our own heads.

I think we have, to a point. When the law of gravity was applied to the orbits of our planets, it became obvious that the planets did not quite travel along the path gravity said they should. Astronomers did some calculations (on the assumption that the law was correct) and hypothesised the existence of as yet unknown masses that would account for the difference between theory and observation. Based on mathematical calculations (rather than direct observation) Neptune was discovered in 1846 and Pluto in 1915/1930.

I think this sort of thing indicates that we are getting outside of our heads to an extent. What it does not mean is that we apprehend unmediated reality. We are forever limited to systematising the behaviour of phenomena as they are filtering in through our senses (and even those observations (in the widest sense) are theory-laden). "Reality" can only be known to us in regard to what it does, not what it is. So we fit formulae to the phenomena that filter into our minds via our senses as best we can. The formulae become more accurate and cover greater areas of behaviour, but ultimately we cannot say they describe reality. Nor can we even say we are approaching a description of reality. Given a different starting point, and perhaps a different set of senses, we might have come up with a completely different system, a system that is just as good as the one we do have now, or better, but can't be mapped to it.

Quite right, I think. I also reject the notion that reliabilism is a source of knowledge about anything other than logical and mathematical identities and tautologies, as some here seem to (unwittingly?) maintain. That is, it doesn't solve the problem of induction, nor the epistemological problems of perception. However, the way that the universe is described as being inherently numerical independent of the human mind (the one I objected to in earlier posts) promotes a naive realism that is pretty easily picked apart. It is dangerous, I admit, to publicize these problems, what with people running around trying to stick their favorite deity into every gap in knowledge, but the proper response is not to deny the gaps (or limits) in our ontology, but to work on fleshing them out with careful and disciplined reasoning.

[Rum]

Forgive what probably seems a naive and ignorant question from a maths retard (who is none the less very interested in the subject). There is probably much discussion about this subject amongst mathematicians.

Maths (and physics) can predict the behaviour of all sorts of phenomena. Take a ball fired from a canon. Knowing the mass of the ball the velocity and angle it leaves the cannon and a few simple laws one can easily predict where the ball will land.

And yet the ball, the canon and the phenomenon itself does not have top perform any calculations - it just happens.

This is about the simplest example I can think of, but there are thousands more of course. How is it that we seem to have stumbled upon a system with which we can measure and predict all sorts of things to such a level of accuracy with an abstract set of symbols which have no intrinsic meaning. Why and how does maths 'represent' behaviour in the real world?

[PsychoSerenity]

I think we simply make our maths to fit the universe. I assume it would be possible to make all sorts of abstract but still complicated and interconnected mathematical systems that had no relevance to our universe at all - but it wouldn't be much use to us. In the same way as it would be possible to make up an entirely new language that nobody speaks - even languages that are constructed in quite different ways from how humans have evolved to understand them.

And for the reason we can make a maths that fits the universe, I think you can call the anthropic principle. Our universe has simple laws and regular patterns (or at least emergent laws and patterns at our level) because if it didn't, and it was completely random at all levels, life couldn't evolve in it.

[Robert_S]

Rum, your question reminds me of a short story I once read.

I think I'll reread it now. Here's a link to it.

http://yudkowsky.net/rational/the-simple-truth

[Hermit]

Just a sidenote: What is it with the Stanford Encyclopedia of Philosophy's take on epistemology? How can you write about it without a single reference to Hume, Popper, Nagel and Kuhn? How can you not mention instrumentalism and positivism? Is that a peculiarity of the article's author, the approach taken by the university's philosophy department, or the US academic one in general? And reliabilism. WTF? Proposed by a mathematician clearly out of his depth in regard to epistemology who died aged 26, so he didn't even have a chance to polish his incredibly naive and simplistic proposition. I have studied epistemology under Alan Chalmers for two years without encountering 'reliabilism' or Ramsay, and I really doubt that was a grievous omission by Chalmers. [/dummyspit]

[Hermit]

http://rationalia.com/forum/viewtopic.php?f=38&t=30465

[devogue]

This reminds me of music.

I have always been intrigued by the fact that musical notation is described as the "Theory of Music". It's incredible how intricate and accurate musical notation has become over the centuries, in terms of time signatures, pitch, note length etc.

This "theory" reached its apogee (IMVHO) with the music of Olivier Messiaen, a passionate ornithologist who transcribed birdsong and made music from it.

Of course, the birds twitter and sing blissfully unaware of any "laws" or uniform idea about their music, but humans are clever enough to create order from seeming chaos.

[Rum]

This reminds me of music.

I have always been intrigued by the fact that musical notation is described as the "Theory of Music". It's incredible how intricate and accurate musical notation has become over the centuries, in terms of time signatures, pitch, note length etc.

This "theory" reached its apogee (IMVHO) with the music of Olivier Messiaen, a passionate ornithologist who transcribed birdsong and made music from it.

Of course, the birds twitter and sing blissfully unaware of any "laws" or uniform idea about their music, but humans are clever enough to create order from seeming chaos.

The fact that harmonics are half the length of the preceding pitch and that humans find the sounds you get from this (i.e. halving the length of a string to make another noise) pleasing is very odd don't you think? Why should this be beautiful - or potentially so?

[Gawdzilla Sama]

Could it be beautiful because we've learned to think it's beautiful?

[Tero]

Yes. It has predictive value. It is as real as we are. Are we real?

[devogue]

This reminds me of music.

I have always been intrigued by the fact that musical notation is described as the "Theory of Music". It's incredible how intricate and accurate musical notation has become over the centuries, in terms of time signatures, pitch, note length etc.

This "theory" reached its apogee (IMVHO) with the music of Olivier Messiaen, a passionate ornithologist who transcribed birdsong and made music from it.

Of course, the birds twitter and sing blissfully unaware of any "laws" or uniform idea about their music, but humans are clever enough to create order from seeming chaos.

The fact that harmonics are half the length of the preceding pitch and that humans find the sounds you get from this (i.e. halving the length of a string to make another noise) pleasing is very odd don't you think? Why should this be beautiful - or potentially so?

I think the key is that why find beauty in creating order from disorder, from creating patterns, so to speak. JimC and others speak of the "beauty" of mathematics, and I think it's similar to the "beauty" of music.

wrt music, over the centuries various chordal sequences, chromatics and other devices have been used by musicians to create a certain tension followed by a satisfactory resolution. Perhaps the only difference with mathematics is that the tension with maths is inherent, and that the beauty and satisfaction comes from the resolution.

Perhaps beauty = resolution of an emotional question.

(stick that fucker in Pseud's corner )