My friend Trent McConaghy attempts to explain the mathematics of the high-five:

It all started with my friend Harondel Sibble who asked:

“At a client [meeting] today, one of the staff members wanted to do a “high-5″ and I missed, she said, stare at her elbow and she’d do the same to me and that with both parties starting at each other’s elbows, one would never miss when doing a high-5. Anyone heard of this before and have any kind of explanation why it works (neurologically and biomechanically)?”

Trent’s response:

“That’s really interesting, I had no idea about the challenge of a high-five, and the easy solution.

I did a 5-min google search and found nothing. The author of this article “searched around fruitlessly for a scientific explanation”.

Here’s my view of it:

  • It’s a search problem. You need to get your hand location, and your friend needs his hand location, at the right place (x, y, z) and the right time (t). That’s a total of (3+1)*2 = 8 search variables, that must be resolved under tight time pressures. To get a really good high five you need all 8 variables to line up. That’s hard!
  • If each of you stare at each others’ elbows, then you’re compressing the dimensionality of the problem: you’re changing each person’s (x, y) to a single “track”, and you just have to line up on that track. So the two variables (x,y) go to a single variable, call it (d) for depth. Now you have (2+1)*2 = 6 variables.
  • By going along the track towards each other, you know that eventually you will hit the user’s hand if the z-coordinates line up. Which means that it will take out the time variable (t) for each of you as well. Which reduces the search problem to (z, d) for each person, or (1+1)*2 = 4 variables total.
  • Finally, during execution of the high five, as your hands approach, you no longer have to track the absolute z-value and d-value of your hand and your friend’s hand. Really, you only have to track the difference between them. So we can compress (z1, d1) for you and (z2, d2) for your friend to a difference: delta_z = (z1-z2) and delta_d = (d1-d2). You now have just two dimensions to resolve (delta_z, delta_d). Solving for two dimensions is literally child’s play to your visual + motor control systems.

In short: the elbow trick compresses the dimensionality of the problem from 8 variables to 2 variables, which is then easily resolved by your visual + motor control systems.”