Some argue that Elon Musk's plan to build a self-sustaining colony on Mars is effectively impossible for the foreseeable future without discontinuous tech progress. (See e.g. Jess Riedel's claim here, which Robin Hanson agrees with.)

Is there a simple explanation for why this might be so? I'd be especially interested in Fermi estimates of key bottleneck resources.

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There’s a thing where entrepreneurs are optimistic. Sometimes ridiculously so. This is because entrepreneurship requires a lot of optimism to think that what you’re doing can work. But that optimism can lead you astray and cause you to work on things that are too hard.

Jess and Robin will never be entrepreneurs. They aren’t optimistic enough. But Elon may be over-optimistic. The sheer scope of the project makes it hard to guess accurately what the difficulties are going to be without getting pretty far into trying it and seeing where you get stuck.

And I’m just thinking about getting a Mars colony at all. I do think “self-sustaining” is a ridiculously high bar, much higher than simply having some people living on Mars. But how important is “self-sustaining” as a short-term goal? — if the colony works at all, there will be a path where the amount of Earth resources required to sustain it shrinks over time due to market forces.

And I’m just thinking about getting a Mars colony at all. I do think “self-sustaining” is a ridiculously high bar, much higher than simply having some people living on Mars.

This is one of my key takeaways so far from this (and from reading through Carl's three recent posts on the topic) -- that "colony" and "self-sustaining colony" are two very different goals.

if the colony works at all, there will be a path where the amount of Earth resources required to sustain it shrinks over time due to market forces

Why do you think that? On earth, colonies survived because they were able to secure a comparative advantage in the production of goods or services, which allowed them to be a net economic benefit to the originating country. What comparative advantage does Mars possess?

Any Martian colony, under the current technological regime, will require heavy economic subsidies for decades, possibly centuries. Who would pay

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Not sure what Lincoln hand in mind regarding market forces, but one reason the cost to sustain the colony over time should shrink is just tech improvement. Operating the colony (at a given standard of living) should get cheaper over time.
Unless there's a discontinuity (i.e. something like a space elevator resulting in more than one order of magnitude reduction in cost per ton to orbit) I suspect it would still be impossible to sustain a Martian colony for a nontrivial number of people. The physics and chemistry of conventional rockets just won't allow it.

It can't be self-sustain without manufacturing, say, electronics, which requires here on Earth thousands of factories, producing copper, plastic, chips etc - and employ millions of people. Basically, the whole Earth economy should be copied on Mars + a new part of economy which will allow survival in harsh environments. Thus Martian economy needs to be bigger than Earth one for sustainability. This requires delivery of billions of people and tens of billions tons of goods.

Huh. An interesting thing this points to is that when/if eventually there are self sustaining colonies on Mars, there’s a chance the supply chains will be much more legible (because they’ll have been built from scratch, without having to have been built on top of tons of spaghetti towers)

Actually, this seems even more likely when you factor in that Elon's whole deal seems to be looking at an industry, getting fed up with it and rolling his own version of it so that he can fully control everything. Seems likely this'd continue on Mars.
Reduced gravity is deleterious to people's health when you want the people to afterwards survive in higher gravity.  If it's hard for fetus to develop on Mars during pregnancy, there's genetic engineering to solve the problem. If all humans on Mars are genetically engineered that in turn adds additional dynamics.
You drastically underestimate the difficulty of genetics.
If you would told the people who started the human genome project 30 years ago that we have complete* genome sequencing today for a few hundred dollar it's likely that they would have told you that you underestimate the difficulty in sequencing.  Three additional decades of AI development and automatizing lab workflows will make genetics a lot easier then it's now. I think a lot will be possible in the later part of this century and even Elon doesn't believe that a Mars colony will be self-sustainable in the next three decades.  :*: Well, 92% but all the protein coding stuff

AFAIK, the main obstacles are

  • the toxic soil, due to high levels of perchlorates (shipping soil would be prohibitively heavy and, given that arable land might come at a high premium in the coming century, might be a bad idea)
  • high radiation on the surface due to lack of magnetic field,
  • high energy requirements to combat the cold and lack of energy sources (due to distance from the sun and the presence of dust) which would probably require nuclear reactors and their fuel (which are extremely heavy to ship)
  • dust, which is a health and mechanical hazard
  • low gravity
  • shipping enough people is prohibitively heavy too
  • an enormous supply chain to produce and ship all that material from Earth to Mars

Solutions to these problems like space elevators to get rid of the rocket equation, new medical fields built from scratch, artificial wombs, energy production, closed biosphere management count, in my book, as discontinuous tech progress if you want them short term (a century). This also looks like a 'big bang' project management approach in which we have very little time to gather feedback on unforeseen problems which an incremental and long term approach would provide. Big bang projects carry a very high risk of failure and wasted resources (and we are talking a lot of resources here.)

An incremental, long term approach would require sustained, heavy efforts over the course of several centuries which, again in my book, does not count as the foreseeable future.

I think there's at least 2 very different related questions:

  1. Is it possible to have a not-too-large-to-build colony on Mars be capable of surviving if contact to Earth is cut off?

  2. Can you make a colony on Mars that's capable of (1) and is economically viable?

I think the answer to (1) is yes, probably with a lot fewer people than you might think, but the answer to (2) is likely no, regardless of number of people.

Robin Hanson, in other discussions has made a big deal of the importance of specialization and division of labor. While he's right that it's pretty important to our modern economy, another lesson of economics is that things usually have substitutes. We can use less division of labour, but it just costs more and you get less good results.

Another commenter brought up electronics. I agree that electronics would be hard to do without a lot of people. If we are talking about (1), raw survival, then I disagree that electronics is needed. For (1), the question is whether people can survive at all - we can assume that we have a colony full of very capable, hard-working people who work long hours to maintain a bare-survival standard of living. The minimum size of the colony is likely going to largely depend on one or a few products that they absolutely need and require some amount of division of labour to produce - possible examples might be spacesuits and equipment for power generation or mining. By contrast, something like farming or habitats for farming in might take up most of the economic effort, but not lower-bound the colony size so much since less division of labour is needed.

For (2) on the other hand, to have an economically viable colony you need people to be willing to come over from Earth. Earth has free air, cheap water, you can grow stuff outdoors. No amount of division of labour on Mars can make up for this advantage, since Earth already has a lot of division of labour in addition to being habitable. So you need a lot of imports from Earth per person to get a comparable standard of living on Mars, and I don't see enough plausible exports to sustain that large amount of imports.

Of course, if people are willing to sustain a large enough drop in material standard of living in order to live on Mars, it could be economically viable, but you'd need a decent number of people willing to have a really massive drop in standard of living. Are there enough such people? I doubt it, but would be happy to be proved wrong.

Elon Musk at the moment has a solution to the transport problem that he's working on. The economics of starship suggest that he will be able to transport ~100,000 kg to Mars for >20 million. 

Given that NASA currently spends $3 to $4 billion a year for the ISS, having a small Mars colony seems to be within a reasonable budget.

Of course that colony won't be self-sustaining at the beginning. On earth we have the problem that we have laws that prevent a lot that's technical possible from being done.

A Mars colony can do genetical engineering a lot more freely then we can here on earth because there isn't an existing ecosystem on Mars that could be messed up.

Protein folding is a problem that's plausible to be solved soon by Deep Mind and once it's solved it will be a lot easier to design new proteins for various challenges. 

A Mars economy that runs on gene-manipulated organisms with designer proteins might look like discontinuous tech progress. At the same time it does provide the Mars colony with intellectual property that it can sell back to earth. 

Impossible? That's a really tough standard to meet. When you weaken it to "effectively impossible" and further "without X", you need to quantify those better before you can estimate. If you mean "one in a billion chance", that's about as likely as something that happens to 7-8 living humans today. If you only mean "one in a thousand", I'd argue that the "impossible" label stops being applicable.

Then you get into the definitions of self-sustaining. Honestly, it probably_IS_ possible to create a long-term minimal-import colony, with a self-sustaining population and self-expanding territory and facilities, but not fully self-sustaining on all resources - some amount of Earth and interplanetary shipments (using earth-created equipment) would be required. And ongoing research and knowledge from the rest of humanity.

Oh, and the non-tech difficulties - there probably isn't enough human desire to live with the constraints that such a colony would require for very long. It probably won't happen because not enough people want to devote their lives to it.

In one word: economics.

A self-sustaining colony on Mars will require many hundreds of billions (or perhaps even trillions of dollars) of dollars to set up. Imagine all the things you need to survive on Mars. Imagine all the infrastructure to build those those things. Imagine all the infrastructure needed to build that infrastructure, etc. etc. To be truly self-sustaining (i.e able to survive indefinitely without further input from Earth), a substantial portion of that infrastructure will either need to be shipped to Mars or built on-site.

Heck, you may as well ask, "Why don't we have self-sustaining colonies on Antarctica?" Surely Antarctica is an easier terraforming/colonization project than Mars.