Sunday, May 12, 2013

A question for Quiggin on interstellar travel

He presents some inconvenient arithmetic here. This caught my eye:
"I’m going to assume (generously, I think) that the minimum size for a successful colony is 10 000. The only experience we have is the Apollo program, which transported 12 astronauts to the Moon (a distance of 1 light second) at a cost of $100 billion or so (current values). So, assuming linear scaling (again, very generously), that’s a cost of around $10 trillion per light-second for 10 000 people."
My question is - how in the world is linear scaling of pricing "very generous"?!?!

Apollo was the first time we transported people to another world. We usually think that the cost of doing something highly complex like sending people to another world drops precipitously as it is done over and over again. It's called "learning by doing". The average cost savings from going from a moon program to an interstellar program are going to be tremendous (although of course you need to do some "doing" to get "learning by doing" between now and then!).

It seems highly ironic that the author of Zombie Economics is using increasing marginal costs assumptions to call linear cost projections "very generous" when I thought we moved past that sort of thinking in these cases many, many decades ago.

I'm not saying we should be working on an interstellar trip right now. We should be working on Mars, and just pay a few theoretical physicists to bend the cost curve on interstellar travel for the time being. But nobody - certainly no economist - should be under the misapprehension that learning by doing isn't going to apply in space exploration.


  1. Yeah, I am almost tempted to click the link because I can't believe he means what it sounds like he's saying. I would imagine if you are taking a one light-year trip, that the first 1% of the trip bears more than 1% of the marginal costs.

  2. You did not notice that he seems to have dropped a factor of ten in his approximation:

    100 Billion / 12 astronauts times 10,000 colonists equals approx 100 trillion per light second.

  3. Do we have any evidence as concerns the learning curve of inter-whatever travel? I mean, not all costs drop thanks to learning by doing:

    1. I would imagine it's comparable to aerospace, where there has been learning by doing.

      The nuclear thing is interesting... but it sounds like (from the abstract) that scale had a lot to do with the increasing costs. In other words, they're not making the same product! Nothing says a big nuclear power plant has to be proportionally more costly.

  4. One reason I think the linearity assumption is generous is that I assume the spacecraft has to accelerate to something close to lightspeed, and decelerate on the way down. That’s much more demanding than reaching escape velocity from earth.

    Obviously, if you’re willing to take a million years or so over the journey, you can save a lot on fuel.

  5. And, although I didn't spell this out, the main observation that has led me to my conclusion is the absence of *significant* learning by doing in transport technology over the past 50 years or so, particularly with respect to space travel. It took 50 or so years to go from Kittyhawk to Apollo, and now, 50 years later (and with the abandonment of the Shuttle) we are back to using solid fuel rockets.

    NASA is now suggesting a mission to Mars might be feasible by 2037. That's not exactly exponential progress (or rather, if it is, the exponent is very small).

    1. Right, but NASA is a political - not a profit maximizing - institution.

    2. Can you explain this a bit further? The idea that travel to Mars could be profitable any time before 2037 strikes me as far-fetched. But maybe you're making a different point.

    3. Prof. Quiggin,

      I will bet you up to $100 that by 2037, space tourism companies will be profitably offering trips to Mars. Daniel, are you willing to hold the money in escrow?

    4. Not an appealing bet, given that I may not be around to collect. But I'm surprised at your confidence. Other than by hitching rides on Soviet era craft, space tourism companies have delivered zero trips so far. And the first unmanned linkage with a space station, something government space agencies have been doing routinely for 40 years, was in 2012. To get from zero to Mars in 25 years seems far-fetched.

      Alternatively, you could look at the business model. The last costing I saw was $400 billion. Suppose private sector efficiency halves that. Interest alone on $200 billion is $10 billion a year for maybe 2 or 3 passengers. What's the world supply of multi-billionaires who want to fly to Mars?

    5. "Not an appealing bet, given that I may not be around to collect."

      Do you have children? I'd be glad to pay out the winnings to your heirs.

      I'll offer the first $100 at even money. If you're completely confident in your predictions, you should have no problems giving me 10:1 odds on additional bets.

      Far-fetched or not, I'm willing to make this speculation interesting, if you are.


    6. I'd be more interested in a defence of your claim than in a bet. After all, I have $100 in my wallet right now, and there's more where that came from, but I don't have any idea how anyone could make a profit out of going to Mars. So, maybe I can learn something here.

    7. This isn't nearly as much fun as betting :) Actually, I think 2037 is somewhat unrealistically early (I was trying to make the bet as enticing as possible; FAIL). But these points summarize my viewpoint:

      1. Extremely high popular and commercial interest in travel to Mars

      Of course, wishing alone won't make it happen. There are other trends to watch.

      2. Neuromorphic and/or quantum computing

      (**Highly recommended**)

      Superhuman AI will lead to breakthroughs in physics, such as in

      3. Fusion power

      4. Which would lead to a fusion powered spacecraft, shortening Mars trips to a few months.

      You are correct that 2037 is an overoptimistic estimate of when these trends will come together, which is why I would insist on at least 10:1 odds for any amount wagered beyond $100. But push the date back to 2055, and I would be very happy to halve those odds.

      Incidentally, advances in medical technology will make it highly likely you'll be around in the 2040s! is a good source for this type of news.

    8. Incidentally, while you're here, your statement that:

      "on any plausible definition of the term, the US had free banking from the Jackson Administration to the Civil War and that didn’t stop the business cycle"

      is simply wrong. I say this purely in the interest of truth, w/o any hint of ill will. There were quite plainly two key restrictions on US banks: 1) Prohibitions on bank branching; 2) Requirements that, prior to issuing banknotes, banks had to first buy a slightly larger amount of state (and after the Civil War, fed. govt) debt (ex: to issue $90 of currency, a bank first had to buy $100 worth of state bonds). To criticize economic performance under such a "free" system would be akin to criticizing the performance of a central bank w/o a lender of last resort role (which in fact led to multiple panics in England when the BoE was had a de facto currency monopoly but was not a LOLR until Bagehot).

      Restrictions on branching caused banks to be overexposed to regional economic fluctuations. It also caused banks in the interior to be totally reliant on NY "correspondent banks" for access to the NY money market. Naturally, this created more fragility in the system (esp. during panics).

      The limitation on issuing currency also was a direct cause of the currency panics of the 19th century. Banks should have been allowed to lower their reserve ratios and issue currency w/o restriction in times of exceptionally high demand for banknotes (such as during harvest season, when workers needed to be paid). The govt debt purchase requirement needlessly tied currency issuance to the govt bond market (and also caused banks to accumulate too many state bonds, which often later turned into junk).

      George Selgin explains these limitations on the US "not-so-free" system here (from 10:50) and contrasts it with Canada's system, which really was free banking system and worked very well until it was ended for political, rather than economic reasons, in 1935:

    9. As I mention in the post you link, free banking in Australia failed spectacularly in the 1890s. Everything I know about Canadian economic history I learned in the last 5 minutes, but Wikipedia casts some doubt on the claim that the banking system was "working very well" in Canada in 1935

    10. Yes, I've read that Wikipedia link. It states:

      "Canada did have some advantages over other countries, especially its extremely stable banking system that had no failures during the entire depression, compared to over 9,000 small banks that collapsed in the United States."

      Canada’s downturn during the Great Depression stemmed primarily from the large negative shock to the demand for its primary exports, a huge portion of its economy (Bordo, Calomiris, and Gorton all state this point in the links below):

      (Wikipedia) "Canada was hurt badly because of its reliance and other commodities, whose prices fell by over 50%, and because of the importance of international trade. In the 1920s about 25% of the Canadian Gross National Product was derived from exports. The first reaction of the U.S. was to raise tariffs via the Smoot-Hawley Tariff Act, passed into law June 17, 1930. This hurt the Canadian economy more than most other countries in the world"

      But there doesn't seem to be any evidence that Canada's banking system caused or worsened the downturn. On the contrary, the fact that it performed so well under such stress compares favorably to the US banking system under central banking. Gorton, Bordo, and Calomiris all acknowledge the soundness of the Canadian banking system (though they disagree on the causes and implications of this fact) in the first half of the 1930s (following a long period of stability in the 19th century).

      Bordo, pp. 13-16:

      Gorton and Calomiris, p. 116-17:
      (there is some dispute over whether the Bank of Montreal was a true LOLR; nevertheless neither author here cites competitive private note issuance, a core aspect of free banking, as problematic).

    11. You are correct that the Australian episode presents a challenge to the idea of free banking. But is it really fair to summarily dismiss free banking based on this one case (out of 60 known historical free banking systems) w/o further investigation? Central banking has had its missteps as well, but we should reserve judgement on that system also until after a thorough vetting. Free banking deserves the same treatment.

      A few comments on the Australian depression:

      1. Australia had very many unique conditions. It was a small, isolated economy (“tyranny of distance”) which nevertheless produced a huge share of the world’s gold supply. Free banking theory acknowledges that a system based on gold as outside (or base) money could experience an expansionary boom due to a huge positive supply shock of outside money. However, such cases are rare historically and virtually impossible now, due to the exhaustion of most of the easily extracted alluvial gold deposits.

      2. There is reason to believe that the Australian boom/bust cycle of the 19th century was fueled by real supply shocks (specifically, pastoral and commodity exports). In contrast to the high growth in these sectors until 1890,

      “Mining output grew at just a slower pace (Table 2) and shrank from 4.4% of GDP in 1890 to 1.6% in 1965. The wool industry decelerated to an average growth rate of 1.8% and, while the beef industry benefitted from innovations such as refrigeration, the pastoral industry overall declined from 11.2% to 6.3% of GDP.”

      “There had been high levels of investment in the pastoral sector in the late 1880s, which reflected what proved to be excessive optimism about future demand, contributed to the boom conditions. The negative shock to wool prices in the 1890s brought a sharp decline in investment which was then exacerbated by drought conditions in the period 1896-1902 which caused a sharp fall in the stock of sheep.”

      Given these conditions, how can we say that a central banking system would also not have led to an overinvestment binge until the 1890s? Sure, in retrospect we can see that commodities slowed down for a time until the current boom, but that outcome could only be known ex post, not ex ante.

      Furthermore, it isn’t obvious that the slow recovery in Australia from 1895-1900 was related to the financial crises of 1891-93. The impact of the rabbit, which began taking a serious toll on NSW in the late 1880s, and the Federation droughts surely caused significant damage to the pastoral and agricultural base.

      3. The pre-1890 boom was to a large degree fueled by an influx of foreign (British) capital, the flow of which started to dry up in the wake of the Barings Crisis of 1890.

      “The ratio of British to domestic deposits in Australia consequently rose from perhaps 10 per cent in the mid–1870s to 40 per cent by the eve of the Depression (Pope 1989:15–16).”

      Dowd, p. 55:

      Again, it’s hard to see how a central bank could have predicted the Barings Crisis any better than a free banking system. Perhaps a central bank might have been able to mitigate the effects of capital flight by increasing bank reserves in response. However, this is at best an argument for a night-watchman monetary policy akin to the Aldrich-Vreeland Emergency Currency in the US, which prevented a panic in 1914, rather than full monopolization of currency issuance and base money creation and control of interest rates by a central bank.

      The Australian free banking period is a a fascinating episode from which we learn a lot. But as far as the case against free banking goes, I feel the jury is still very much out.

  6. Oh oh oh! So little time and so many oxen to gore! A couple of points, for a starter:

    Just to be sane (or a bit less silly) perhaps instead of dispatching 10,000 colonists all at once to some interesting, suppose we send say a dozen people with a hundred thousand embryos and some amount of mechanical wombs? I don't know that this drops the weight and energy requirements for the starship by a full factor of a thousand, but the numbers would come down, right?

    We might assume somewhat smaller velocities as well. Perhaps 1/3 of light speed, or 1/2 would do the trick. Granted, people confined to a spaceship for a dozen years or so (assuming Alpha Centauri as a goal) might find the confinement irksome, but possibly most of them would survive with their sanity intact (helpful hint, read some recent newspapers from Cleveland Ohio).

    Modern day chemical rockets are not very practical devices for interstellar spacecraft. Something like a group of solar-orbiting lasers aiming their beams at a vessel with a large sail for say a year could probably get a craft up to a reasonable portion of light speed. Granted, it'd stretch our current technological ability, but what are R&D budgets for?

    As Daniel notes, learning by doing ought to bring costs down -- and it's worth noting just how little "doing" we're doing. Counting all the nations on Earth, we generally launch about 60 spacecraft per year, most of them limited to Earth orbit. If we built automobiles or jetliners at this rate, they'd be pretty expensive too -- so much so that only governments could afford them.

  7. Mike Shupp and John Quiggin you really really do not understand the implications special relativity. If you are sending 10,000 people you are going to need a craft about the size of an aircraft carrier. Very doubtful that you will ever be able to accelerate that mass to any material fraction of the speed of light.

  8. Absalon -- What'd I write? I suggested sending a dozen people (or more realistically, several hundred) with a large number of embryos (eggs and sperm would also work). As for size, I did some calculations a year or so back for a novel, and wound up with a weight of 8000 metric tonnes (lighter than a carrier) for a structure which basically a mirror about 40 miles across (much bigger than a carrier). For structural material I assumed chicken wire on mile long stretchers of linked nanotubes-- assuming most of the ship was excavated to vacuum, that'd give you a starship which floated in any respectable atmosphere... Interesting enough, my numbers look reasonably achievable, according to some texts on solar sails -- not anything you'd build this decade, but perhaps by the turn of the century. And assuming this were driven by enough lasers, maintaining one gee acceleration, this ship would get to about 1/2 c in just about a year, still inside the Oort cloud. (I concede, it takes a LOT of lasers.)

    So those numbers seem large to you? It's a large universe; we need to think on an appropriate scale. You want to think of something really bonkers? Imagine going back in time to meet King Louis XIV of France, and telling him about this great invention called a "car," propelled by a strange chemical called "gasoline" which comes from inside the earth. Then tell him that in one country alone in early 21st century, there are over one hundred million cars, not just for the nobility but for ordinary working peasants. He'd know you were lying.

    1. At one half the speed of light relativistic effects have become important (the effective mass of the object being accelerated has increased). Even if we assume that: (1) there are no relativistic effects; (2) we don't have to worry about the space ship generating its own energy or needing to expel reaction mass; and (3) that a structure 40 miles across could be strong enough to take the forces necessary to accelerate the central module at 1 g we still have a problem with the amount of energy involved.

      Using classical mechanics and a quicky calculation I get to your space ship having 9 x 10^24 joules of kinetic energy when it reaches 1/2 C. This seems to be about 20,000 times annual global energy consumption.

    2. Absalon: The relativistic mass correction at 1/2 C is on the order of 12%, as I'm sure you can compute. As for the energy required to reach this speed, I assumed something like 100 radiation collectors with ten mile diameters circling the sun at a distance of about ten million miles. Granted this seems imposingly large by current standards (in fact it was imposingly large by the standards of people in my novel), but two centuries of technical and economic progress ought to permit some improvements in our capabilities, right? Look at it this way: the size, mass, and difficulty of construction of my spaceship and its sail and the beamed propulsion system would probably be less than the size, mass, and difficulty involved in constructing the road and subway system and underground cabling and drainage systems of a major metropolis. There's probably well over a hundred billion bucks of roads and piping under San Francisco or Paris, for example, but we tend to ignore that because it was built and improved over a period of centuries. With starships, you get comparable "infrastructure" costs in maybe a decade.

      (Damn! I need to get back to work on that book.)

      Making a more serious point, on rereading Quiggin's original post at Crooked Timber, I tend to think he's less interested in the economic nuts and bolts of star travel than with philosophical issues: Given the sizable costs of money and time, and the likely low reward for such expenditures, why should anyone even want to go to the stars? Which reduces to existentialism, as best I can see; the answers aren't to be found in economics or engineering, even if economists and engineers -- and all the rest of us -- choose to grapple with such questions.

  9. @Absalon I understand that perfectly well. That's why my cost estimate is stupendously large.

    1. @Quiggin

      If you understood special relativity you would not have written: "I assume the spacecraft has to accelerate to something close to lightspeed"

  10. The Apollo program was so expensive because of the outdated chemical rockets. But the cost of space travel is to become awesomely affordable with the advent of nuclear fusion propulsion.

    1. Nuclear fusion is the energy of the future, and always will be

    2. I agree with you, mostly because all the money is being wasted on gargantuan fusion experiment (ITER) rather than other cheaper fusion programs.

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