RE: Is there objective Truth?
October 14, 2016 at 12:12 am
(October 13, 2016 at 9:45 pm)Soldat Du Christ Wrote: Just because we gave a name to describe what we observe in the natural world, doesn't mean we invented the observation. The golden rule exists wether or not we are here to observe it.
We didn't give a name to something we observed, Mathematics is invented. It's wholly artificial.
What about complex numbers (described using so-called "imaginary numbers")?
√(-1) = i
i
2 = -1
A complex number is a number in the form of x = a +bi
You can expand from there into the quaternion numbers:
i
2 = j
2 = k
2 = ijk = -1
ij = -ji = k
ji = -ij = -k
jk = -kj = i
kj = -jk = -i
ki = -ik = j
ik = -ki = -j
A quaternion number is a number in the form of x = a + bi + cj + dk
From there you can go to the octonions (used in String Theory).
An octonion number is a number in the form of
"x= a + bi + cj +... + ho", although that's not how they're written they're written thusly:
x = x
0e
0 + x
1e
1 + x
2e
2 + x
3e
3 + x
4e
4 + x
5e
5 + x
6e
6 + x
7e
7
From there you could move on to the sedenions (/hexadecanion numbers), and probably not of much use in anything at all:
x = x
0e
0 + x
1e
1 + x
2e
2 + x
3e
3 + x
4e
4 + x
5e
5 + x
6e
6 + x
7e
7 + x
8e
8 + x
9e
9 + x
10e
10 + x
11e
11 + x
12e
12 + x
13e
13 + x
14e
14 + x
15e
15
And you can keep on expanding your dimensional plane as far as you wish to go. Don't forget you have to come up with all the other increasing complicated rules for calculating hypercomplex numbers in ways other than straight addition as well. An interesting property of sedenions is they contain zero divisors - that is it is possible to construct an product where numbers in the equation are non-zero but divide to zero:
(xn1en1 + xn2en2)(xn3en3 + xn4en4) = 0
Where:
x
n1e
n1 + x
n2e
n2 ≠ 0
x
n3e
n3 + x
n4e
n4 ≠ 0
So what we apply in mathematics is constricted to what we need because it ultimately leads to nonsense like the above. Or equations that just cannot be solved anyway like 1/0 = ?