each block has a "halflife time" of 10 minutes.
This part is factually incorrect. What half life means is that given a sample of radioactive material, half of it will have disintegrated in that time. This is not the case for BTC blocks at all, probably l'Hospital would be more adequate to calculate likeliness of blocks not being solved in 10 minutes (they have 1/diff chances to be solved each hash, so after diff hashes their chances to be solved are X).
I wrote half life in quotes. It is not exactly like half life, but it is analogous.
Imagine a million parallel universes all identical to ours (except for the seeds of random number generators in miners' computers).
After ten minutes from now, in exactly 1/e of these universes a block is not found, and in (1-1/e) of them, a block is found.
Technically 10 minutes isn't a half life, but rather
x = -ln(1/2) * 10 minutes = 6.931 minutes.
Each 6.931 minutes, in half of the universes (at least one) block is found, and in half of them no block is found.
(Thanks for pushing me to review this)