Now let's also assume that starting this very second, all those people (our global population of seven billion) each begins to click the button to generate a new bitcoin address every second.
"WHY ARE YOU GENERATING SO MANY FUCKING ADDRESSES! You're going to cause a bitcoin address collision!" yells the supreme bitcoin chancellor of Earth. "STOP IT!" ಠ_ಠ
Let's pretend everyone's in on the joke, and they all ignore him.
( ͡° ͜ʖ ͡°)
With every human on Earth, all generating a new address every second it would still take about 6.5 billion years in order for there to be a 50/50 chance of a bitcoin address collision. For there to be approximately a 99% chance of a collision, the assholes would need to keep up this buffonery for about 11.7 billion years total.
Looking ahead to what scientists think will be the timeline of our planet:
- 500–600 million: Estimated time until a gamma ray burst, or massive, hyperenergetic supernova, occurs within 6,500 light-years of Earth; close enough for its rays to affect Earth's ozone layer and potentially trigger a mass extinction.
- 800 million: Carbon dioxide levels fall to the point at which C4 photosynthesis is no longer possible. Free oxygen and ozone disappear from the atmosphere. Multicellular life dies out.
- 1 billion: The Sun's luminosity has increased by 10 percent, causing Earth's surface temperatures to reach an average of ~320 K (47 °C, 116 °F). The atmosphere will become a "moist greenhouse", resulting in a runaway evaporation of the oceans.
- 1.3 billion: Eukaryotic life dies out due to carbon dioxide starvation. Only prokaryotes remain.
- 2.3 billion: The Earth's outer core freezes, if the inner core continues to grow at its current rate of 1 mm per year. Without its liquid outer core, the Earth's magnetic field shuts down, and charged particles emanating from the Sun gradually deplete the atmosphere.
- 2.8 billion: Earth's surface temperature, even at the poles, reaches an average of ~420 K (147 °C, 296 °F). At this point life, now reduced to unicellular colonies in isolated, scattered microenvironments such as high-altitude lakes or subsurface caves, will completely die out.
- 3.5 billion: Surface conditions on Earth are comparable to those on Venus today.
- 5 billion: With the hydrogen supply exhausted at its core, the Sun leaves the main sequence and begins to evolve into a red giant.
- 7.59 billion: The Earth and Moon are very likely destroyed by falling into the Sun, just before the Sun reaches the tip of its red giant phase and its maximum radius of 256 times the present day value. Before the final collision, the Moon possibly spirals below Earth's Roche limit, breaking into a ring of debris, most of which falls to the Earth's surface
(Source: Wikipedia, https://en.wikipedia.org/wiki/Timeline_of_the_far_future)
Summary: I'm pretty sure there will never be a bitcoin address collision. My math might not be perfect, but it shouldn't be off by more than an order of magnitude. You are welcome to fact check me and I'll correct it if necessary.