Turns out, production capacity can increase exponentially too,
Yes, for a while. The simplest factor driving this is exponentially more laborers. Then there’s better technology of all sorts. Still, after a certain point we start hitting hard limits.
when any given child has a high enough chance of survival, the strategy shifts from spamming lots of low-investment kids (for farm labor) to having one or two children and lavishing resources on them, which is why birthrates in the developed world are dropping below replacement.
(a) Is this guaranteed to happen, a human universal or is it a contingent feature of our culture? (b) Even if it is guaranteed to happen, will the race be won by increasing population hitting hard limits, or populations lifting themselves out of poverty?
I think “hard limits” is the wrong way to frame the problem. The only limits that appear truly unbeatable to me right now are the amounts of mass-energy and negentropy in our supergalactic neighborhood, and even those limits may be a function of the map, rather than the territory.
Other “limits” are really just inflection points in our budget curve; if we use too much of resource X, we may have to substitute a somewhat more costly resource Y, but there’s no reason to think that this will bring about doom.
For example, in our lifetime, the population of Earth may expand to the point where there is simply insufficient naturally occurring freshwater on Earth to support all humans at a decent standard of living. So, we’ll have to substitute desalinized oceanwater, which will be expensive—but not nearly as expensive as dying of drought.
Likewise, there are only so many naturally occurring oxygen atoms in our solar system, so if we keep breathing oxygen, then at a certain population level we’ll have to either expand beyond the Solar System or start producing oxygen through artificial fusion, which may cost more energy than it generates, and thus be expensive. But, you know, it beats choking or fighting wars over a scarce resource.
There are all kinds of serious economic problems that might cripple us over the next few centuries, but Malthusian doom isn’t one of them.
It’s true that many things have substitutes. All these limits are soft in the sense that we can do something else, and the magic of the market will select the most efficient alternative. At some point this may be no kids, rather than desalinization plants, however, cutting off the exponential growth.
(Phosphorus will be a problem before oxygen. Technically, we can make more phosphorus, and I suppose the cost could go down with new techniques other than “run an atom smasher and sort what comes out”.)
But there really are hard limits. The volume we can colonize in a given time goes up as (ct)^3. This is really, really. really fast. Nonetheless, the required volume for an exponentially expanding population goes as e^(lambda t), and will get bigger than this. (I handwave away relativistic time-dilation—it doesn’t truly change anything.)
the magic of the market will select the most efficient alternative. At some point this may be no kids
Or, more precisely, less kids. I don’t insist that we’re guaranteed to switch to a lower birth rate as a species, but if we do, that’s hardly an outcome to be feared.
Phosphorus will be a problem before oxygen.
Fascinating. That sounds right; do you know where in the Solar System we could try to ‘mine’ it?
The volume we can colonize in a given time goes up as (ct)^3.
Not until we start getting close to relativistic speeds. I could care less about the time-dilation, but for the next few centuries, our maximum cruising speed will increase with each new generation. If we can travel at 0.01 c, our kids will travel at 0.03 c, and so on for a while. Since our cruising velocity V is increasing with t, the effective volume we colonize per generation increases at more than (ct)^3. We should also expect to sustainably extract more resources per unit volume as time goes on, due to increasing technology. Finally, the required resources per person are not constant; they decrease as population increases because of economies of scale, economies of scope, and progress along engineering learning curves. All these factors mean that it is far too early to confidently predict that our rate of resource requirements will increase faster than our ability to obtain resources, even given the somewhat unlikely assumption that exponential population growth will continue indefinitely. By the time we really start bumping up against the kind of physical laws that could cause Malthusian doom, we will most likely either (a) have discovered new physical laws, or (b) have changed so much as to be essentially non-human, such that any progress human philosophers make today toward coping with the Malthusian problem will seem strange and inapposite.
Actually, if we figure out how to stabilize traversible wormholes, the colonizable volume goes up faster than (ct)^3. I’m not sure exactly how much faster, but the idea is, you send one mouth of the wormhole rocketing off at relativistic speed, and due to time dialation, the home-end of the gate opens up allowing travel to the destination in less than half the time it would take a lightspeed signal to travel to the destination and back.
Assuming zero space inflation, the “exit” mouth of the wormhole can’t travel faster than c with respect to the entry. So for expansion purposes (where you don’t need (can’t, actually, due to lack of space) to go back), you’re limited to c (radial) expansion. Which is the same as without wormholes.
In other words, the volume covered by wormholes expands as (c×t)³ relative to when you start sending wormholes. The number of people is exponential relative to when you start reproducing. Even if you start sending wormholes a long time before you start reproducing exponentially, you’re still going to fill the wormhole-covered volume.
(The fault in your statement is that you can go in “less” than half the time only for travel within the volume already covered by wormholes. For arbitrarily far distances you still need to wait for the wormhole exit to reach there, with is still below c.)
Space inflation doesn’t help that much. Given long enough time, the “distance” between the wormhole entry and exit point can grow at more than c (because the space between the two expands; the exit points still travel below c). In other words, far parts of the Universe can fall outside your event horizon, but the wormhole can keep them still accessible (for various values of can...). This can allow you unbounded-growth in the volume of space for expansion (exponentially, if the inflation is exponential), but note that the quantity of matter accessible is still the same volume that was in your (c×t)³ (without inflation) volume of space.
Strange7 is referring to this essay, especially section 6.
Wormholes sent to the Andromeda at near light speeds arrive in approx year 2,250,000 co-moving time, but in year 15 empire-time (setting year zero at start of expansion).
I still don’t get how you can get more than c×t³ as a colonized volume.
With wormholes you could travel within that volume very quickly, which will certainly help you approach c-speed expansion faster, since engine innovations at home can be propagated to the border immediately. And, of course, your volume will be more “useful” because of the lower communication costs (time-wise, & presuming worm-holes are not very expensive otherwise). But I don’t see how you can expand the volume quicker than c, since the border expansion will still be limited by it.
(Disclaimer: I didn’t read everything there, mostly the section you pointed out.)
Yes, for a while. The simplest factor driving this is exponentially more laborers. Then there’s better technology of all sorts. Still, after a certain point we start hitting hard limits.
(a) Is this guaranteed to happen, a human universal or is it a contingent feature of our culture?
(b) Even if it is guaranteed to happen, will the race be won by increasing population hitting hard limits, or populations lifting themselves out of poverty?
I believe it’s a quite general phenomenon—Japan did it, Russia did it, USA did it, all of Europe did it, etc. It looks like a pretty solid rich=slower-growth phenomenon: http://en.wikipedia.org/wiki/File:Fertility_rate_world_map.PNG
And if there were a rich country which continued to grow, threatening neighbors, there’s always nukes & war.
I think “hard limits” is the wrong way to frame the problem. The only limits that appear truly unbeatable to me right now are the amounts of mass-energy and negentropy in our supergalactic neighborhood, and even those limits may be a function of the map, rather than the territory.
Other “limits” are really just inflection points in our budget curve; if we use too much of resource X, we may have to substitute a somewhat more costly resource Y, but there’s no reason to think that this will bring about doom.
For example, in our lifetime, the population of Earth may expand to the point where there is simply insufficient naturally occurring freshwater on Earth to support all humans at a decent standard of living. So, we’ll have to substitute desalinized oceanwater, which will be expensive—but not nearly as expensive as dying of drought.
Likewise, there are only so many naturally occurring oxygen atoms in our solar system, so if we keep breathing oxygen, then at a certain population level we’ll have to either expand beyond the Solar System or start producing oxygen through artificial fusion, which may cost more energy than it generates, and thus be expensive. But, you know, it beats choking or fighting wars over a scarce resource.
There are all kinds of serious economic problems that might cripple us over the next few centuries, but Malthusian doom isn’t one of them.
It’s true that many things have substitutes. All these limits are soft in the sense that we can do something else, and the magic of the market will select the most efficient alternative. At some point this may be no kids, rather than desalinization plants, however, cutting off the exponential growth.
(Phosphorus will be a problem before oxygen. Technically, we can make more phosphorus, and I suppose the cost could go down with new techniques other than “run an atom smasher and sort what comes out”.)
But there really are hard limits. The volume we can colonize in a given time goes up as (ct)^3. This is really, really. really fast. Nonetheless, the required volume for an exponentially expanding population goes as e^(lambda t), and will get bigger than this. (I handwave away relativistic time-dilation—it doesn’t truly change anything.)
Or, more precisely, less kids. I don’t insist that we’re guaranteed to switch to a lower birth rate as a species, but if we do, that’s hardly an outcome to be feared.
Fascinating. That sounds right; do you know where in the Solar System we could try to ‘mine’ it?
Not until we start getting close to relativistic speeds. I could care less about the time-dilation, but for the next few centuries, our maximum cruising speed will increase with each new generation. If we can travel at 0.01 c, our kids will travel at 0.03 c, and so on for a while. Since our cruising velocity V is increasing with t, the effective volume we colonize per generation increases at more than (ct)^3. We should also expect to sustainably extract more resources per unit volume as time goes on, due to increasing technology. Finally, the required resources per person are not constant; they decrease as population increases because of economies of scale, economies of scope, and progress along engineering learning curves. All these factors mean that it is far too early to confidently predict that our rate of resource requirements will increase faster than our ability to obtain resources, even given the somewhat unlikely assumption that exponential population growth will continue indefinitely. By the time we really start bumping up against the kind of physical laws that could cause Malthusian doom, we will most likely either (a) have discovered new physical laws, or (b) have changed so much as to be essentially non-human, such that any progress human philosophers make today toward coping with the Malthusian problem will seem strange and inapposite.
Actually, if we figure out how to stabilize traversible wormholes, the colonizable volume goes up faster than (ct)^3. I’m not sure exactly how much faster, but the idea is, you send one mouth of the wormhole rocketing off at relativistic speed, and due to time dialation, the home-end of the gate opens up allowing travel to the destination in less than half the time it would take a lightspeed signal to travel to the destination and back.
Assuming zero space inflation, the “exit” mouth of the wormhole can’t travel faster than c with respect to the entry. So for expansion purposes (where you don’t need (can’t, actually, due to lack of space) to go back), you’re limited to c (radial) expansion. Which is the same as without wormholes.
In other words, the volume covered by wormholes expands as (c×t)³ relative to when you start sending wormholes. The number of people is exponential relative to when you start reproducing. Even if you start sending wormholes a long time before you start reproducing exponentially, you’re still going to fill the wormhole-covered volume.
(The fault in your statement is that you can go in “less” than half the time only for travel within the volume already covered by wormholes. For arbitrarily far distances you still need to wait for the wormhole exit to reach there, with is still below c.)
Space inflation doesn’t help that much. Given long enough time, the “distance” between the wormhole entry and exit point can grow at more than c (because the space between the two expands; the exit points still travel below c). In other words, far parts of the Universe can fall outside your event horizon, but the wormhole can keep them still accessible (for various values of can...). This can allow you unbounded-growth in the volume of space for expansion (exponentially, if the inflation is exponential), but note that the quantity of matter accessible is still the same volume that was in your (c×t)³ (without inflation) volume of space.
Strange7 is referring to this essay, especially section 6.
I still don’t get how you can get more than c×t³ as a colonized volume.
With wormholes you could travel within that volume very quickly, which will certainly help you approach c-speed expansion faster, since engine innovations at home can be propagated to the border immediately. And, of course, your volume will be more “useful” because of the lower communication costs (time-wise, & presuming worm-holes are not very expensive otherwise). But I don’t see how you can expand the volume quicker than c, since the border expansion will still be limited by it.
(Disclaimer: I didn’t read everything there, mostly the section you pointed out.)