[spindritf]

> he merely pointed out (correctly) that there will eventually be a limit to productivity

I don't understand this point. Why would there be a limit to productivity, especially with machines and computers to leverage our efforts thousandfold and more?

And how could anyone know that such limit exists, even if it is actually reached one day? That would require predicting any possible innovation of the future.

[brazzy]

As long as the measure of productivity corresponds to something physical (which even bits on a harddisk are), then an exponential increase in productivity (as we have seen in the past) would eventually require humanity and its products to form a sphere whose radius grows faster than the speed of light.

Do you agree that that is a pretty hard limit?

[TheSOB88]

I think you may have skipped some steps... Could you fill in the middle a bit? I'm confused.

[Retric]

Let's suppose the amount of physical goods produced increases 1% each year. Let's add that as physical objects they take up some space minimum amount of time. Now let's add that humanity is spreading out in all directions at the speed of light. If humans cover 1 light year of space they can expand faster than the new amount of stuff. However Volume = 4/3 pi * radius ^ 3 so what happens when humanity covers 1,000 light years. Well, next year they need to put 1% more stuff into 1002^3 / 1000^3 = 0.6% more space which means they need to increase the density which at some point means you have a black hole.

PS: 1% growth per year seems slow and sustainable but in 20,000 years your talking about 2.7 with 86 zeros after it. Start with 1 atom for one second and compare it with every atom in the earth for a year and your only at 4.2 with 57 zeros. So if the total economic output of humanity was 1 atom we could not sustain 1% economic growth per year for 30,000 years.

Edit: This assumes that the economy is based on physical goods, if we assume intangibles can take up 99.99...9% of the economy then 1% growth is possible for long periods of time even if it's somewhat meaningless.

[brazzy]

In out three-dimensional space, volume grows with radius at r^3. If something physical grows exponentially (2^t), then the radius of its volume needs to increase over time at an accelerating rate, which means the growth of that radius will eventually surpass c.

[barry-cotter]

I don't understand this point. Why would there be a limit to productivity, especially with machines and computers to leverage our efforts thousandfold and more?

There are limits to what you can do with matter. It's unlikely the economy (our productive capacity) will continue to grow much for 100,000 years after all mass we can get at is weird ass artificial quark composite computronium.

[6ren]

Yes, I think a limit on productivity amounts to a limit on knowledge. Does knowledge have a limit? There's no evidence for it; all our present mathematics of complexity suggests not (but it's possible one will be discovered...)

However, energy needs do seem to increase with productivity, and there's limit on how much energy we can get from the sun (a dyson sphere encloses the sun, capturing all its energy). But there's some assumptions here: that we can't discover ways of being productive that require less energy (and wouldn't that enhancement itself be "productive"?); that we can't discover other sources of energy (e.g. room temperature fusion micro-suns - or something better).

Once you factor in the unknown (i.e. knowledge that we don't yet have) it's hard to know what the limits are. I guess the entire universe is a limit on matter... if we can't discover a way to make more matter... or more universes.

[Symmetry]

There are actually mathematical limits to the amount of information that can be stored within a given volume, the Bekenstein bound, which is a lot like a limit to knowledge.

[6ren]

Well... if we can make new universes, the volume isn't limited.

[G_Morgan]

Actually we know for a fact such a limit exists. There are physical limits on how much energy can be extracted from a certain mass.