A question on the mathematics of music

[teuchter]

ETA: Don't forget that that there is also a *minimum* distance between particles.

I don't think this is relevant is it?

There is a minimum distance between integers but still an infinite number of them.

 

[kabbes]

Yes, but the number of particles is bounded, unlike the number of integers.

The point is that there is still an infinite number of numbers between a bounded set of integers (in fact, a larger infinity than the infinity of integers itself!) If there was no minimum distance between particles then there really would be an infinitude of permuations of particles even in a bounded universe.

 

[teuchter]

Yes, but the number of particles is bounded, unlike the number of integers.

I don't see why that matters. Even if you only have two particles, as long as the amount of space you have is infinite, there is an infinite number of distances you can set them apart from each other.

The point is that there is still an infinite number of numbers between a bounded set of integers

I don't think I understand what you're saying here.

 

[kabbes]

I don't see why that matters. Even if you only have two particles, as long as the amount of space you have is infinite, there is an infinite number of distances you can set them apart from each other.

But what if the amount of space you have is not infinite? That's when it matters.

I don't think I understand what you're saying here.

There are an (aleph-one) infinite number of numbers between zero and one. In a similar way, if there was no planck minimum then there would be an infinite number of permutations of particles within a finite space. It is only the presence of a minimum distance between particles that means that the number of permutations is finite in a finite space.

 

[rutabowa]

inspired by this thread i am goin to make a song by banging together a brick and a lizard

 

[rutabowa]

the melody line will be made by crossing blue with fire, divided by happiness

 

[kabbes]

 

[teuchter]

But what if the amount of space you have is not infinite? That's when it matters.

Agreed.

Is it possible to prove that time is or isn't infinite, by the way?

 

[kabbes]

I don't think so. I'm not sure that the question is even meaningful, as it happens. Time is too related to space via light.

 

[ATOMIC SUPLEX]

Digits. You said you had 9 but forgot about 3.

No I said there were nine digits. There are 10 (1234567890). I said nine because I forgot about the number 3 (one digit).

 

[ATOMIC SUPLEX]

I'm saying that this is a possibility, yes. For a start, there are not an infinite number of particles in the universe.

But there is an infinite number of ways they could come together.

 

[ATOMIC SUPLEX]

Yes, but the number of particles is bounded, unlike the number of integers.

I love the way this 'music' thread has turned out.

 

[teuchter]

I forgot about the number 3

How careless of you.

 

[Shippou-Sensei]

Irrelevant. It would be like comparing the same recording on vinyl and a CD and calling them different.

It's easier to compare musical maths than to pictoral ones, as pictoral exists in three dimentions and I guess music only exists in one.

a recording on vinyl and cd are different

a song will be different each time it is played by a person... f it is played by a different person it will also differ

and a painting tends to be two dimentional although i'm sure the texturing of the paint gives some effect


however you could then apply that same concept to music

a recording of a piece is just one interpretation of the song something as physical as moving the mics will drastically change the recording

 

[samk]

Eventually for the possibilities to be distinguishable you'd need a larger short term memory...

 

[kabbes]

But there is an infinite number of ways they could come together.

No, that's the point of the discussion I've been having with teuchter. It is far from clear that there are necessarily an infinite number of ways that they could come together.

 

[ATOMIC SUPLEX]

Just except it and move on.

Electric boogie