2+2=5
I'm just figuring out how witty George Orwell is.
2+2 is not necessarily 4. We work within a base-10 counting system.
That is, we count
1 2 3 4 5 6 7 8 9 (and now we start over again) 10
If we work within a base-2 system for instance, we would count...
1 2 3 (and now we start over again) 10 11 12 13...
In a base-3 system 2+2 is not 4, but 10!
We get a different answer for 2+2 in a base-2 system as well. In this case, 2+2 = 11.
In a base-1 system, we cannot add 2 and 2 because the number 2 does not exist.
In a base-4 system, 2+2 still equals 4, since the number 4 still exists in this system:
1 2 3 4 (and now we start over again) 10 11 12 13 14...
Now here comes the funny thing about George Orwell. If he had said 2+2=11, that is actually possible. It does not look right to us, because we are used to a base-10 counting system, but if we used base-2, this would be absolutely correct. However, because 2+2=5, the smallest counting system Orwell's fictional society might use is base-5. This means that 2+2 would still equal 4! There is, in fact, no counting system in which 2+2=5 is a mathematical possibility.
It is possible, through modulo arithmetic, for 2+2 to be CONGRUENT to 5, but this, of course, is not the same as being the SAME as 5. Or maybe it is.
At any rate, just a bit of a mathematical/literary geekery there.
2+2 is not necessarily 4. We work within a base-10 counting system.
That is, we count
1 2 3 4 5 6 7 8 9 (and now we start over again) 10
If we work within a base-2 system for instance, we would count...
1 2 3 (and now we start over again) 10 11 12 13...
In a base-3 system 2+2 is not 4, but 10!
We get a different answer for 2+2 in a base-2 system as well. In this case, 2+2 = 11.
In a base-1 system, we cannot add 2 and 2 because the number 2 does not exist.
In a base-4 system, 2+2 still equals 4, since the number 4 still exists in this system:
1 2 3 4 (and now we start over again) 10 11 12 13 14...
Now here comes the funny thing about George Orwell. If he had said 2+2=11, that is actually possible. It does not look right to us, because we are used to a base-10 counting system, but if we used base-2, this would be absolutely correct. However, because 2+2=5, the smallest counting system Orwell's fictional society might use is base-5. This means that 2+2 would still equal 4! There is, in fact, no counting system in which 2+2=5 is a mathematical possibility.
It is possible, through modulo arithmetic, for 2+2 to be CONGRUENT to 5, but this, of course, is not the same as being the SAME as 5. Or maybe it is.
At any rate, just a bit of a mathematical/literary geekery there.