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| quote: | Originally posted by DigiNut
I explained the relevance to the question asked. If you choose to ignore it or discount it, I can't stop you. Referring to it as "calling my bluff", however, makes me have to laugh at you calling me "self-righteous" in the same paragraph. It's hard to swallow a backhanded apology like the one you're presenting to me.
Yes, any 3 LI vectors can describe "a" linear space, but not THE linear space, i.e. the physical world. For that, you need 3 independent and infinitessimally small vectors, which I perhaps mistakenly called "unit" vectors, but could think of no other appropriate word to describe their magnitudes. What would you call them?
Having said that, even if my post in the "2+2" thread was blatantly incorrect and irrelevant (which it wasn't), it would have still hardly warranted you bringing it into ANOTHER THREAD which had NO RELATION to the former one. Because I use the word "ludicrous" in one thread, it's a reason for you to quote something totally unrelated from another thread which you think is wrong? And not just one thread, but two separate threads. Please, there's no legitimate excuse for doing that.
Don't try to imply that I'm just on here trying to sound smart, because I can dig up a lot of posts where you do the exact same thing. I'm not here to impress anyone, in fact I'm rather PO'ed at myself lately for posting so much in the chillout room, because usually I limit myself to the Toronto forum and just talk about the events and the scene and the other random crap that goes on in there.
You sound like a smart guy and I'm sure we'd be better off as friends than enemies (for what that's worth on the internet). I have no intention of starting a war with you, but I do feel the need to defend myself because this isn't the first time you've harped on me for no particular reason (i.e. the drunk driving lawsuit thread). So let's drop all of this, and continue on with our lives.
Now... back to your regularly scheduled programming. |
Wow. My apologies, Digi. After reading this post, I can't deny that you're a mature, thoughtful guy. I also didn't intend to turn this into a war, although I guess it looks as though I was trying to make it one. I had no reason to post those responses in two different threads. That thread had sunk to page 2 where it seemed like you weren't going to read it, and I was already talking to you in this thread.
As for the drunk driving thread... hehe, I didn't even realize that was you. I'm not one for launching campaigns against people, especially in online forums. (By the way, I just re-read that thread, and I'm only trying to debunk your position, not make a personal attack).
I often hear people break out meaningless big words to either make themselves sound smart or make others sound stupid. Usually, it upsets me when I see this. I've misjudged you on both of those, so I apologize. I, too, would rather see us friends than enemies.
Please accept this as a sincere apology, and please try out the problems cuz they really are fun  .
P.S. I'd like to explain where I was going with the "real integral" and "directional vector" posts, sans any personal implications.
The integral number system is necessarily real. But more importantly, the whole question of "when is 2+2=5" depends only on the meaning of the symbols themselves. It's safe to assume that "+" and "=" have their usual meanings. The base is of no importance, since, as you pointed out, "2" and "5" are digits. That said, one could easily come up with different values for those numerals to make the equation true. This can be said regardless of the type of number system (i.e., real, complex, integral, rational, etc...).
For the linear algebra discussion, the vectors don't need to be unit or infinitesimal to describe any linear space, including the "real" one (as you know, ALL n-dimensional linear spaces are isomorphic). If we use a unit vector basis, and we have a point at {x, y, z), then scaling our basis vectors up by N will only change our point's representation to (x/N, y/N, z/N). This is what I meant by "regardless of their magnitude." As long as our basis vectors are non-zero (and they are, by definition), any point can be described as a linear combination of them (they "span" the space). This is a nice result of the spaces being isomorphic.
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