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Assuming that it's even possible to give a flawless definition of left and right, you can always say that when reading the definition (in English of course), the reading direction is right and left of course is opposite.

well http://www.thefreedictionary.com/right defines it as "Of, belonging to, located on, or being the side of the body to the south when the subject is facing east." So Left would be 'Of, belonging to, located on, or being the side of the body to the north when the subject is facing east.'

North = The direction along a meridian 90° counterclockwise from east; the direction to the left of sunrise.

South = The direction along a meridian 90° clockwise from east; the direction to the right of sunrise.

East = The cardinal point on the mariner's compass 90° clockwise from due north and directly opposite west.

right: the side pointing east when facing north
left: the side pointing west when facing north.

Assuming that it's even possible to give a flawless definition of left and right,

Why "assuming", left is defined by one transformation matrix and right is defined by another, that's a crystal clear definition.

The transformation matrix depends on your choice of basis of a space, picking a different basis changes the matrix, and of course, to define that matrix you have taken the standard basis, one element of which (intuitively) points right. But of course the reflection of the space is mathematically indistinguishable - the mathematics still works even if you reflect the plane so that "right points left" (in fact any symmetry will give you the same thing, e.g. rotation)

Think for instance if you orient the space so that the vector (0, 1) points down. Then your notion of right may become left and vice versa. The actual way in which you orient a space in your head just serves your intuition, but the space is entirely abstract (for instance, (0,1) could point left or down or half way between etc, its not really well-defined)

In abstract, a vector space (a, b) is just a 2-tuple of numbers, and nothing more.

So in a way its impossible to define left and right mathematically, unless you fix a basis, and then define it - even then the symmetry group still induces uncountably many equivalent spaces (in a real vector space). This is of course fine for mathematics, where you don't really care about left and right.

I think its a very human creation, that is kind of irreducible in some sense, because it is very intuitive. I can't really think of a clean definition, that doesn't rely on some more complicated construction.

with f being a vector in a direction defined as Forward, and u being a vector in a direction defined as Up such that f(dot)u=0, then right will be the direction of the vector r=fxu.

Left is of course the direction of -r.

Works in any number of dimensions.

The transformation matrix depends on your choice of basis of a space, picking a different basis changes the matrix

Frankly, brickhead20 convinced me it's rather not definable... even the vector product depends on the choice of the basis.

Look, guys. Everything ALWAYS needs a fundamental postulate at the basis of it. In mathematics, one of them is called the "infinite set hypothesis." You cannot EVER define something in terms of nothing at all. Of COURSE you cannot define "left/right" with no underlying references. Defining left/right is called (in mathemetics and physics) "chirality".
But it must be defined as a postulate. Or be derivable from some other postulate. But there is always a postulate somewhere! Got it?

relativism is retarded who cares what left is
seriously

MessiahAndrw wrote:Can somebody find the best definition for the directions 'left' or 'right'?

It's relative. You define your context depending on something. Left and Right, + , - , /, * every single thing is like that.
Read theory of Relativity, http://en.wikipedia.org/wiki/Theory_of_relativity