Luke_A_Somers comments on Intuitions Aren't Shared That Way - Less Wrong

31 Post author: lukeprog 29 November 2012 06:19AM

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Comment author: Luke_A_Somers 06 December 2012 09:53:55PM 0 points [-]

I don't have to implement it at all to see its truth. Maths is not just applied maths.

At the very least, you can make something formally equivalent if you're capable of talking about it.

If your branch of mathematics is so unapplied that you can't even represent it in our universe, I suspect it's no longer math.

Comment author: Peterdjones 07 December 2012 11:21:19AM -2 points [-]

If your branch of mathematics is so unapplied that you can't even represent it in our universe, I suspect it's no longer math.

Any maths can be represented the way it ususally is, by writing down some essentially aribtrary symbols. That does not indicate anything about "correspondence" to reality. The problem is the "arbitrary" in arbitrary symbol.

Lets say space is three dimensional. You can write down a formula for 17 dimensional space, but that doens't mean you have a chunk of 17 dimesional space for the maths to correspond to. You just have chalk on a blackboard.

Comment author: Luke_A_Somers 07 December 2012 03:47:23PM 1 point [-]

Sure. And yet, you can implement vectors in 17 dimensional spaces by writing down 17-dimensional vectors in row notation. Math predicts the outcome of operations on these entities.

Comment author: Peterdjones comment score below threshold [+] (25 children)

Comment author: Luke_A_Somers 07 December 2012 07:25:45PM 3 points [-]

(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6) is a perfectly valid 17-vector.

The predictions of the mathematics of 17-dimensional space would, yes, depend on the outcome of other operations such as addition and multiplication - operations we can implement more directly in matter.

I have personally relied on the geometry of 11-dimensional spaces for a particular curve-fitting model to produce reliable results. If, say, the Pythagorean theorem suddenly stopped applying above 3 dimensions, it simply would not have worked.

Comment author: Peterdjones 08 December 2012 03:50:01AM 1 point [-]

(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6) is a perfectly valid 17-vector.

I'm seing pixels on a 2d screen. I'm not seeing an existing 17d dimensional thing.

The mathematics of 17d space predict the mathematics of 17d space. They couldn't fail to. Which means no real prediction is happening at all. 1.0 is not a probability.

Comment author: Luke_A_Somers 10 December 2012 09:29:50AM 3 points [-]

There are things we can model as 17-dimensional spaces, and when we do, the behavior comes out the way we were hoping. This is because of formal equivalence: the behavior of the numbers in a 17-dimensional vector space precisely corresponds to the geometric behavior of a counterfactual 17-dimensional euclidean space. You talk about one, you're also saying something about the other.

Is this point confusing to you?

Comment author: Peterdjones 10 December 2012 11:51:11AM -2 points [-]

There are things we can model as 17-dimensional spaces,

But they are not 17 dimensional spaces. They have different physics. Treating them as 17 dimesional isn't modelling them because it isn't representing thema as they are.

Comment author: Kindly 10 December 2012 02:23:40PM 1 point [-]

To be concrete, suppose we have a robotic arm with 17 degrees of freedom of movement. It's current state can and should be represented as a 17-dimensional vector, to which you should do 17-dimensional math to figure out things like "Where is the robotic arm's index finger pointing?" or "Can the robotic arm touch its own elbow?"

Comment author: Peterdjones 10 December 2012 02:27:39PM * 0 points [-]

can and should

Not obvious. It would just be a redundant way of representing a 3d object in 3 space.

The point of contention is the claim that for any maths, there is something in reality for it to represent. Now, we can model a system of 10 particles as 1 particle in 30 dimensional space, but that doens;t prove that 30d maths has something in reality to represent, since in reality there are 10 particles. Is was our decision, not reality's to treat is as 1 particle in a higher-d space.

continue this thread »

Comment author: Luke_A_Somers 10 December 2012 02:41:01PM 0 points [-]

Who said vector spaces have anything to do with physics? That's not math anymore, that's physics.

Comment author: Peterdjones 10 December 2012 02:48:39PM -1 points [-]

Using math to model reality is physics. Phsycis doens't use all of math, so some math doesn' model anything real.

continue this thread »

Luke_A_Somers comments on Intuitions Aren't Shared That Way - Less Wrong

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