I also think that we underestimate the amount of unused resources that we haven't tapped into yet (e.g. planets in our solar systems) and the resources that we might not even know about yet (e.g. new forms of matter or "new" laws of physics). Also, it seems likely that paradigm-shifting technological breakthroughs will continue pushing the boundaries of our growth further out. An interesting read in that respect is "Thinking in Systems" by Donella Meadows. In the 60s and 70s, the systems thinking approach outlined in the book also predicted that our planet would soon hit it's "carrying capacity" and further growth would be stunted. A major reason this didn't happen was (IMHO) the rate of technological change, which moved the carrying capacity of the planet well beyond what would've been possible 30 years ago. The same processes that were at work then are still at work today and constantly change the technological background against which we make our assertions, which makes systemic estimates of macro-economic systems a very tricky business.

As they say, the stone age didn't end because of the lack of stones ;)

Starting with 7.4 billion people in 2016 and a population growth rate of 1 % per year we will reach the carrying capacity of Earth in less than 1400 years - the body heat alone will raise the surface temperature above the boiling point of water.

Once we reach the carrying capacity of Earth - no matter when that is - and decide to move into space we have 2685 more years until we run out of places to live in the Milky Way assuming 400 billion stars and one Earth-like colonizable planet per star.

Unfortunately 2685 years is not nearly enough time to reach all the stars in the Milky Way even if you would be traveling at the speed of light, you could cross just about 2 % in that time.

There are very real limits to the possible growth and we are talking about centuries or a few millennia. With a growth rate of 0.1 % per year one can push that to tens of millennia but that is still the blink of an eye in the grand scheme of things. And while I used population growth, things of course don't change if you substitute energy consumption per capita.

It is very unlikely the population of earth will continue to grow at 1%. In the best scenario, we will have worldwide development followed by a fall in fertility that it inevitably brings. In the more morbid ones, climate change, wars etc. will result in a large amount of the population getting destroyed.

Economic growth of 1% per year is exponential growth.

Light of speeds puts limit to the economic growth and it's less than exponential.

Maximum sustainable economic growth in infinite static flat universe is f(t)/dt where f(t) = 4/3×π×t^3.

You assume economic growth is at most proportional to the rate at which we occupy previously unoccupied space.

That may be true, but it is not obvious to me.

My assumption is that all economic growth has some component that is based on matter and energy. Even if it's just firing of a neuron inside consumers head.

If that assumption holds, growth is limited by matter and energy. Assuming that you consume all matter and energy and leave behind maximum entropy (thermal radiation) the growth is limited by the area of an expanding sphere.

Wealth will increase. Economic growth not, because the wealth will be poorly divided. Only few will reap the benefits of AI.

Unless the wealthy somehow manage to consume all the excess production the average can't buy because they're too poor, wealth will have a hard time increasing without general economic growth. There is a pretty hard limit on how much even the most ostentatious trillionaire can consume.

How do you know the size of the universe we live in?

(To be pedantic, even in an infinite universe the size of the human-sphere couldn't grow faster than a ball expanding at the speed of light.)

Because that is the prevalent scientific opinion

We are on a course for a confluence of some major technologies this century which could result in another great leap forward.

Anyways i forgot why i dont bother to reply much on this site, got down voted for my above comment yet no indication as to why (is it my comment about working on advertising? its ok that's what I work in too myself have to pay bills somehow, but would rather do something more interesting).

The observable universe is very much finite. (And if speed of light is a barrier, than the observable universe is about the biggest thing we can ever influence.)

Sure, there will be lots of nice technology coming over the next century. No doubts about that.

Lets assume we develop technology to travel at near light speeds and go mad colonising the universe, what exactly contains us to the observable universe, move 4 light years in another direction and your observable horizon shifts

Except the expansion is happening faster than the speed of light.

http://curious.astro.cornell.edu/about-us/104-the-universe/c...

I'm not sure the idea that we may be able to travel to uninhabitable hellscapes in the future fundamentally changes the basic problem here.

Because we haven't gotten a way to get fuel outside earth yet (that I know of), or a solution to long travel times. As such we are practically still bound to earth, which is finite.

> or a solution to long travel times.

This is a bit of a non-issue. Expecting to be able to travel anywhere within a matter of a few dozen hours is a recent phenomenon.

If we're willing to deal with the (technologically but not politically manageable) consequences, nuclear rockets are a proven technology and can reach most of the solar system within a year's traveling time.

Finite matter tho.

Who says the universe is infinite?