Another Quora Math Answer about Split-Complex Numbers

Well, I’ve been on a role with Quora math answers recently! One person asked the question of whether you can have a negative absolute value. In other words, could you have a negative distance between two points! Rather than dwelling on all the rules this would break (who needs rules!?) I decided to construct such a system.

And I found that it looked like something I’ve seen before: the split complex numbers. The one application I’ve seen for these numbers is in an online dating app, as presented at a RecSys workshop in 2012!

In this number system, you have a new special number called “j” which lives outside our usual number system. This number has the special property that j * j = 1.

The dating application works like this:
You have people of the same gender who are similar (positive numbers)
People of the same gender who are different (negative numbers)
People of the opposite sex who are good matches (positive j numbers)
People of the opposite sex who are bad matches (negative j numbers)

These assumptions correspond to mathematical statements (capital letters for people of the same gender, and lowercase for people of the opposite).
If you’re similar A and A is similar to B, you’re similar to B(1*1=1)
If you’re different from A and A is similar to B, then you’re different from B (1)(-1) = -1
If you match a, and a also matches B, then you’re similar to B (j*j = 1)
If you don’t match a, and a matches B, then you’re different from B (-j * j = -1)
And so on!

So here’s someone talking about negative space and mathematical impossibilities, and we end up with an online dating application! Yeah, I realize this is a heteronormative number system* that also reduces human personality to a single dimension – but still it’s pretty cool!

*That must be why it wasn’t part of the Yale curriculum.

Here’s my full answer on Quora
Here’s the RecSys workshop paper I referenced