Using up all the particles in the universe (Numberphile video question)

Factual Questions
1

Here is a link to the video in question:

In it he explains that humans will equate for 100% of the particles in the universe in 8604 years.

This seems crazy to me…surely there are red giant stars that contain a trillion humans worth of particles.

But then again I am not a math genius.

So what does the SD think?

2

The point is that any positive growth rate whatsoever, if continued long enough, will eventually overtake any limit whatsoever. He says that the current population growth rate for the human race is just 1.11% per year. That sounds small, but if continued for 8604 years more, there will be more than 10 to the 51st power (i.e., 1 followed by 51 zeroes) people, and that’s enough to use up every particle in the observable universe. Do the calculation yourself on Google. Have it calculate 7.5 billion times (1.0111 to the 8604th power), and see how large it is.

3

At that very modest growth rate, it would take the population 63 years to double, and another 63 years to double again. In 630 years, it would have doubled ten times, which is a factor of 1024. In 6300 years, it would have gone up by a factor of 1024 ten times, which is a factor of more that 10 to the 30 the power. That is an unfathomably large number:

1,000,000,000,000,000,000,000,000,000,000.

Give it a couple thousand more years and you add even more zeros. This is the power of exponential growth. As Wendell has noted, exponential growth is unsustainable in the real world.

4

In high school, my brother’s (math?) class was set the problem of calculating the point in time a sphere of humanity (initially enclosing 2 people) with exponential volumetric growth would exceed a similar sphere whose radius increased at the speed of light.

Unimaginable, but there is a finite number of time. Exponential growth RULZ. Except as noted above, it can’t be sustained. My head hurts when I imagine the sphere of human flesh growing faster than the speed of light, to catch up with the light sphere.

5

The one thing to know about any exponential growth is that it always breaks down somehow. It might be gentle or it might be catastrophic, but there’s always some sort of breakdown.

Except possibly for the Universe as a whole. That, we have no clue about.