Do numbers need to be compared with one another to understand them better?
Posted: Sun Feb 21, 2016 11:11 pm
If you're familiar with number theory, you may know what I mean. I'll give you a simple example so you can see what I'm driving at.
Say we have these two groups of numbers: (2,16,13,3) and (6,9,15,4). All the numbers are different from one another, right?
If you add up all the numbers in each group, you get 34, right? If you dot multiply the numbers by (1,2,3,4), here's what happens:
1•2 + 2•16 + 3•13 + 4•3 = 1•6 + 2•9 + 3•15 + 4•4 = 85,
right?
Now let's dot multiply by (4,3,2,1):
4•2 + 3•16 + 2•13 + 1•3 = 4•6 + 3•9 + 2•15 + 1•4 = 85,
right?
I could go further. Here's something no one would expect.
The numbers seem independent, yet they share certain properties (similar to quantum states in entanglement).
Why? Why do these numbers act entangled? (number theory is filled with many examples)
PhilX
Say we have these two groups of numbers: (2,16,13,3) and (6,9,15,4). All the numbers are different from one another, right?
If you add up all the numbers in each group, you get 34, right? If you dot multiply the numbers by (1,2,3,4), here's what happens:
1•2 + 2•16 + 3•13 + 4•3 = 1•6 + 2•9 + 3•15 + 4•4 = 85,
right?
Now let's dot multiply by (4,3,2,1):
4•2 + 3•16 + 2•13 + 1•3 = 4•6 + 3•9 + 2•15 + 1•4 = 85,
right?
I could go further. Here's something no one would expect.
The numbers seem independent, yet they share certain properties (similar to quantum states in entanglement).
Why? Why do these numbers act entangled? (number theory is filled with many examples)
PhilX