Month: February 2020

A suspicious proof of God’s existence

~ squarishbracket ~ 2 Comments

Consider the following argument:

  1. If I will have eternal life if I believe in God, then God must exist.
  2. I do not believe in God.
  3. Therefore, God exists.

Intuitively, it seems possible for (1) and (2) to be true and yet (3) to be false.

But now let’s formalize the argument.

B = “I believe in God”
E = “I will get eternal life”
G = “God exists”

  1. (B → E) → G
  2. ~B
  3. Assume ~G
  4. ~(B → E), modus tollens (1,3)
  5. B & ~E, (4)
  6. B, (5)
  7. B & -B, (6,2)
  8. G, proof by contradiction (2 through 7)

This argument is definitely logically valid, so were our initial intuitions mistaken? And if not, then what’s going on here?

Fractal Trees

~ squarishbracket ~ Leave a comment

Consider the following simple algorithm:

We start with a single painted particle moving upwards at a decreasing velocity, with a trajectory that is slowly rotating at a constant velocity. At each step, there is some small probability for the particle to “split” into two particles, one of which begins rotating in the opposite direction. And if a particle’s trajectory is ever about to start turning downwards, it instead reverses its angular velocity and begins turning upwards.

Those are all the rules. So what sort of shapes does this incredibly simple algorithm generate? Take a look!

fracTree_1fracTree_2fracTree_4

fracTree_5

It might be unbelievable that such a simple algorithm could generate such complex and organic shapes, but you can try it for yourself: the images above are produced by only 25 lines of code! And of course, it makes one very curious about whether there is a real connection between this algorithm and the way that plants actually grow.