I Arguments leading to the speed of light as a dimensionless constant

[Saw]

Then how do you define the word "perpendicularly" when you write "the light will come perpendicularly to the analyzed vector"? You rely on it in your definition of orthogonality.

The shadow idea is not for defining perpendicularity, it is only for illustrating the fact that perpendicularity is independence to a higher extent: it is instead of some shadow, no shadow at all.

 

[Saw]

You (or that simile) are presupposing a Euclidean space. Spacetime is Minkowski, not Euclidean, so it does not work as a mental guide in spacetime.

And no, it does not sound like it would be a good textbook simile even in Euclidean space. At least not at higher level. It may have more of an intuition point in lower level maths but even then it is flawed as presented in this thread.

If you read my posts, you will find out that I am not positing the simile for Minkowski space, at least not for the orthogonality that is based on the dot product with negative sign, which is not the same thing, sure. I just said that the shadow simile pops up however also in Minkowski space under forms that would deserve discussion.
As to the goodness of the shadow simile in Euclidean space, I find it perfect for that domain. Does it work or not? Does it serve to tell a perpendicular vector from one that is not or not? That is all that matters. Rest is subjective: I think, I don’t think, I like, I don’t like...
But thanks indeed for the comments and bye! I said that I would not insist on these concepts that mentors are clearly rejecting and so this is over!

 

[PeterDonis]

The two vectors at the extremes are orthogonal, i.e. totally linearly independent

Not if they are null vectors.

 

[PeterDonis]

here the orthogonality concept has been generalized in a way that picks up the dot product leg, but drops the full independence leg.

I don't understand what you are talking about. This looks like a personal theory of yours. Personal theories are off limits here.

I can understand that you are suspicious about this speculation, which is what it is, I can perfectly concede that.

So it is a personal theory of yours. See above.

I have convinced myself that I will not move you an inch from your positions.

Since the "positions" that everyone but you in this thread are taking are the standard "positions" about vector spaces in both math and physics, your apparent expectation that we should "move" from them is mistaken. Particularly when, as you admit, you are expounding your own personal theory. Get your speculations published in a peer reviewed journal and then you can discuss them here.

 

[PeterDonis]

I said that I would not insist on these concepts that mentors are clearly rejecting and so this is over!

Since the "concepts" you refer to are your personal theory, yes, it is indeed over. Thread closed.