You think CPU is basics of electronics? CPU is just a very small part of a very large field. What you did was just a combination logical elements which you later simulated in a program (because I am sure you didn't physically build it). Did you consider how these elements worked or how the simulation program worked?
No, I think CPU is a big part of everyday electronics, and the knowledge in it is tremendous in comparison to other areas. Although it boils down to 1's and 0's, there is still math involved that is not logical at all (as much as you think a gate passes the information clearly, there is drag on some parts, and the clock speed has to be just right to be able to catch them). I could go on, but why should I backpedal?
And yes, I did _build_ it myself...using the same litho methods that the big boys use, it was a hobby of mine when I was real young.
Spectrums are the basics of analog electronics, signal transmission, filters and so on. There wouldn't be any mobile phones, satellites, wi-fi or anything else if people didn't understand spectrums. You are clearly not educated in much of electronics. You know only digital 1's and 0's and that is the reason why you don't know the significance of imaginary numbers. You are just as limited as the computers themselves. And if you have this cynical point of view on every human technological advancement then you don't also understand the basics of science as a whole.
So you are saying that these "spectrums" cannot be shown in real world math? Because y=2.1844*sin(x) seems like a real wave to me, and subtracting it can filter out that "wavelength"....where exactly does the 'i' come in?
Can I get someone who is actually in a field that is useful to the human race and society to come forward and vouch that 'i' is used in their every day life? And actually show me where it applies that absolutely no
other math can possibly be used other than imaginary math?
May not have? Pi is a irrational number (thus infinite) and humans can't come up with something infinite. If a man invented pi then he would just make it 5 or something (or just 1) to make calculations easier. Pi is constant of 3.1415.. which is true in every part of the galaxy. Even aliens know pi and they have the same value for it. They of course will write it differently, but the value stays.
The bold text is my point exactly. "Pi" <-- the word and it's constant in our
lives is our
invention...to an alien or any other creature, "pi" and "3.1415" may not have any meaning whatsoever to them.
And then why does CPU has instruction set for sqrt? Why can't we program it manually with "other maths"? As previously stated, things like quaternion are very useful in 3d graphics.
Because 'sqrt' is commonly used in everyday life, imaginary numbers are not as common. It's self-defined logic here, thought you would see that.
@xshortguy: Thanks for the explanation of the imaginary space....buuuuut...where does that fall in line with making 3D math "easier" or "more efficient"?
The only point I made was that imaginary numbers don't actually exist
+1 to that! I'm not being ignorant here, but I feel that you _cannot_ take the square root of a negative number. I understand that when used properly, you can come up with an answer that is in the real, like:
sqrt(-1) * sqrt(-1) = -1
Although you cannot take the sqrt of -1, the above formula is derived because you reduced the actual functioning (square or a sqrt is itself). To me, that doesn't make the imaginary space "exist", it just means that there is an identity shown and proven:
sqrt(A) * sqrt(A) = A
'i' is just used to show that this identity can be used at _some_ point later down the line in order to come up with an answer.
If I have '2i * 4' apples, how many do I have? ... exactly
Until you reduce any formula to get rid of any and all 'i' references (and its brethren j,k and others), then you do not have a 'real' number, only a partial answer with a function attachment.
Do not misread me though. I know that humans have invented all these forms of math and complex number arithmetic for our own purposes (and other species may have as well), but I am talking about the physical nature of the number and not the concept. Just like you cannot touch infinite (and spawns a whole other part of math I won't get into), you cannot touch imaginary numbers either....but when you bring certain parts together, the imaginary parts get reduced out (until then, I consider that 'not existing').
I have still not seen anyone produce to me the 3D mathematics that would show any plausibility for the need of these things in GM?
Edited by sabriath, 23 March 2011 - 07:57 AM.