The rough table above describes a system in which “+” denotes a maximum operator. Applied to (x, x) it returns x, applied to (x, x+1) or (x+1, x) it returns x+1. An operator can be redefined, though a question concerning an unknown system “How does a system where “2+2=3″ work?” is open ended, and doesn’t contain enough information for a unique solution. It does have enough information for an arbitrary solution like:
“+” takes two inputs and returns their sum (in conventional terms) minus one. This has a number of properties:
That is, order independence. What it ‘lacks’ relative to the normal definition is distributional invariance, i.e. 1+1+1+1 is different from 2+2 because a more distributed quantity loses more in agglomeration. Though it does have a different ‘equivalence’ - that is, for a given relationship that can be described in “the original system” a new one can be found.
1+2+2+1 = 2+2
or even (not with integers*)
(*nevermind it is with integers, at least in this case)
x+x+x+x = 2+2
can be solved because in original terms that’s 4x-4 = 2+2, which is 4x-4=4, 4x=8, x=2.
2+2+2+2 (new system) = 2+2 (new system)
Even the question itself becomes meaningless wouldn’t it?
The question (w.r.t. 2+2=3) is however meaningless in the sense it doesn’t describe a system ready at hand which exists, though it could be constructed.
+12
112
222
The rough table above describes a system in which “+” denotes a maximum operator. Applied to (x, x) it returns x, applied to (x, x+1) or (x+1, x) it returns x+1. An operator can be redefined, though a question concerning an unknown system “How does a system where “2+2=3″ work?” is open ended, and doesn’t contain enough information for a unique solution. It does have enough information for an arbitrary solution like:
“+” takes two inputs and returns their sum (in conventional terms) minus one. This has a number of properties:
a+b = b+a
a+b+c = a+(c+b) = b+(a+c) = b+(c+a) = c+(a+b) = c+(b+a)
That is, order independence. What it ‘lacks’ relative to the normal definition is distributional invariance, i.e. 1+1+1+1 is different from 2+2 because a more distributed quantity loses more in agglomeration. Though it does have a different ‘equivalence’ - that is, for a given relationship that can be described in “the original system” a new one can be found.
1+2+2+1 = 2+2
or even (not with integers*)
(*nevermind it is with integers, at least in this case)
x+x+x+x = 2+2
can be solved because in original terms that’s 4x-4 = 2+2, which is 4x-4=4, 4x=8, x=2.
2+2+2+2 (new system) = 2+2 (new system)
The question (w.r.t. 2+2=3) is however meaningless in the sense it doesn’t describe a system ready at hand which exists, though it could be constructed.