The arithmetic of space travel (crossposted from Crooked Timber)

There’s been a lot of excitement about the discovery of two Earth-like[^1] planets, a mere 1200 light years away. Pretty soon, I guess, we’ll be thinking about sending colonists. So, I thought it might be worthwhile to a little bit of arithmetic on the exercise.

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, given the need to accelerate to near lightspeed), that’s a cost of around $100 trillion per light-second for 10 000 people. 1200 light-years is around 30 billion light-seconds, so the total cost comes out roughly equal to the value of current world GDP accumulated over the life of the universe.

Even supposing that technological advances made travel possible over such distances possible, why would we bother. By hypothesis, that would require the ability to live in interstellar space for thousands of years. A civilisation with that ability would have no need of planets.

[joke alert on] On behalf of my fellow Australians, I’m going to make a counter-offer. For a mere $10 trillion, we can find you an area of land larger than a typical European country, almost certainly more habitable than the new planets, and much closer. We’ll do all the work of supplying water and air, build 10 000 mansions for the inhabitants and guarantee a lifetime supply of food. I’m hoping for a spotters fee of 0.01 per cent.[joke alert off]

On a related point, what should we be wishing for here? The fact that no-one has sent a detectable signal in our direction suggests that intelligent life forms similar to humans are very rare. If habitable planets are very rare, then this is unsurprising – interstellar distances preclude both travel and any kind of two-way communication. If on the other hand, the emergence of intelligent life is common, then the evidence suggests that its disappearance, through processes like nuclear war, must also be common.

[^1] Where Earth-like means somewhere between Venus-like and Mars-like.

110 thoughts on “The arithmetic of space travel (crossposted from Crooked Timber)

  1. Grimbister replies to – J-D at # 19

    What?
    You reckon some nerd et me lunch?
    Far from the truth.
    Wrong, so unfortunately wrong. It was that Arthur, the tealad at Calligulashorse.

    Can’t keep his big teeth off anything.
    Lost a few girlfriends that way, has Arthur.
    (Raiding their fridges, I mean.)

    Which causes me to speculate what would happen if a bloke like Arthur ended up signed on as crew on some starship.
    By the time it reached Betelgeuse he’d have eaten everything on board.
    The trail of ‘spacejunk’ along the line of flight would definitely be a navigational hazard for the next ship out.
    They never touched that sore of embarrassing stuff in ‘Startrek’ or ‘Blake’s Seven’.

    But then again; consider that Arthur could be connected to the reverse pointing plumbing and be fed an intense diet of fried beans –
    Admittedly it would still take a while to get up to light speed with such a ‘green’ form of propulsion – and there’s no way I’d pretend it would be ‘clean’.
    And if anyone doubts what I say here – consider DARPA’s help with the American bicycle team at the Olympics (was it Atlanta?) some years back.

    There is, of course, the problem that if the prototype starship ran out of beans that Arthur would unplug himself and search for some other form of tucker.

    But I suppose that is why ‘the immaculate one™’ stretched space out so far as to preclude the loose cannons (like Arthur) of a hunter gatherer species such as homo sapiens from getting too far away from their home planet.

    PS – Arthur – you’ll see him over their on the right hand side of those despicable pages of Calligulashorse . com.

  2. On a more serious note – consider Churchill’s summation of the Royal Navy.
    “Rum, bum and baccy.”
    If interstellar navigation ever happens it’ll be accomplished by a standing crew of the psych profile of male airline attendants.

    They’ll assiduously attend the frozen fertilized blastulae of the arriving generation – take risk management to the stage that the entire enterprise will hover in space somewhere mid-path like that apocryphal donkey stuck between two bales of feed.

    Nope. Thankfully the species is subject to exactly the same rules as is the individual.
    Best we make the best of the allotted time we have.

  3. @Newtownian

    I’m quite excited by the prospect of extremely large telescopes. I like to see one in space in a sensible orbit where it could take long exposures of objects of interest. It would be possible to make out the surface features of planets around other stars. But just being able to reliably image exoplanets at all will let us detect markers of life such as oxygen or methane and detecting pollution could indicate technology using intelligent life. (Or would that be technology using stupid life?)

  4. I think this is a great topic to stimulate lateral thinking in an entertaining way and shows John Q’s skill as an educator.
    While I have always had a keen interest in Astronomy I have resigned myself to the inescapeable fact that with our present knowledge of physics, we will never achieve interstellar travel.
    I’m going to suggest that Humanity requires a period of introspection before we set out for the other planets in our solar system, let alone around other stars.
    I think there is much to explore about ourselves, our brains and the way things happen when we really work together for common good.
    If the Human race were technologically able to set off among the stars in our present state of ‘development’, what damage would we do?

  5. This is the outer limit of our enterprise –
    http://www.couriermail.com.au/news/opinion/professor-john-quiggin-finds-fault-with-peter-costellos-commission-of-audit-report-findings/story-e6frerdf-1226639617267

    Anyone reasonable might suppose that Quiggin has a point.

    The MAJOR point might be not to let anything like Costello oversee even minor projects.
    We are discussing here grand leaps of the imagination.
    The grand problem with the island of Oz is that we cannot find the means to put anyone in charge who can display imagination – or the means to develop their imagination toward any sort of acceptable outcome.
    The acceptable outcome I mean is about providing benefit for all stakeholders within society.
    We seem to be stuck in a blind.
    The masters keep droning on forever about pettifogging stuff that might have bankers, numbercrunchers and all sorts of mindless dolts going back trying to analyse their drivel.
    Perhaps they might find a word, phrase or two encouraging to believe that they are right.

    The next press release will tell ‘em that they were astoundingly wrong..
    Or so it appears on the propaganda pages and in the thirty second grab of the bullshine news.
    But where do the sweaty little buggers who either believe, or take advantage of this sort of crapola – where do they live?
    What corrosive littoral zone of habit do they inhabit?

    And how could any ‘happy band of brothers’ (ask Lord Nelson) ever find a way to escape the clutches of their sort in order to undertake any great enterprise of discovery into space and out toward the stars?

  6. PS –
    I’d love to be a fly on the wall at a Costello family barbecue.
    I doubt very much whether Tim, the do-gooder would grumble overmuch when Pete gave him a few hints about how to pick up some extra credits on the fast money market.
    What an incestuous mob of bludgers they all are!

    Rocket science?
    I believe not.

  7. I refer you back to Krugman’s paper on the Economics of Interstellar Trade.

    And we in the States will see your Outback and raise you the water-table-less West.

  8. It must be a fascinating thing to have the imagination of an economist.

  9. Because it was discovered a long, long time ago that group objectives are better met by community action. Have you tried building your own sewerage system recently?

  10. One prime example of a NASA public good, close to the hearts of all Australians but even closer to their integumentary systems, was them eventually figuring out, “Hey, we’ve made some sort of massive hole in the ozone layer. Maybe we should stop doing that.”

  11. Agreed. Yes, NASA (and its dinospace subsidiaries LockMart/Boeing etc) is/are littered with unparalleled volumes of white collar welfare, but they have done an awful lot of public good IMHO. Companies like SpaceX are game changing the light/medium and heavy lifting markets – a good thing – but you still need a government funded space administration like NASA to manage the science and the missions to gather and analyse the science.

  12. hc @44:

    Carter uses Bayesian methods to argue that if you had to guess where we are in the evolution of the human species then, because human populations are greatest now with greatest likelihood, humanity is towards the end of their evolutionary span.

    The Carter Prophecy is the jumping-off point for Stephen Baxter’s Time. At one point in the story Baxter has an anonymous blogger circulating arguments against Carter to be used in debate with people, including:

    Appeal to common sense. Look back in time. A human of, say, AD 1000 would likewise have been sitting on top of an exponential curve reaching back to the Palaeolithic. Would she have been correct to deduce she was in the last generations? Of course not, as we can see with retrospect. (You may find Carter proponents countering this one by saying this is a false analogy; humanity today faces far graver extinction threats than in AD 1000 because of our technological advancement, the way we have filled up the Earth, etc. And it took our modern-day sophistication to come up with the Carter argument in the first place. So we have formulated the Carter prophecy at precisely the moment it is most applicable to us. But then you can argue that they are appealing beyond the statistics.)

  13. @TerjeP
    Terje, you might possibly in the near future have the beginnings of a point, but if you think that private enterprise would have achieved anything whatsoever over the past six decades in space, you’re deluded. Without NASA, the rest of the US military, the Soviet programs and European government efforts, all by that accursed government, we would not yet have a single satellite in orbit. There is no way whatsoever that Elon Musk’s or Richard Branson’s (barely economic, mostly ego (not that I have a problem with that)) endeavours could have existed without several decades of government investment.

  14. wilful :
    There is no way whatsoever that Elon Musk’s or Richard Branson’s (barely economic, mostly ego (not that I have a problem with that)) endeavours could have existed without several decades of government investment.

    The Branson suborbital venture could be debatable with regards to requiring or even relying on any form of previous government investment. The propulsion system technology was actually from a completely non government base; what’s more, it was from a purely amateur/hobbyist development process. The aircraft (WK2) and spacecraft(?) (SS2) were mostly developed by Burt Rutan (revisions of XPrize winning WK1 & SS1 Combo) who is famous for his unique and out-of-the-box designs. I think it’s safe to say neither was based on or borrowed unique design features from existing craft or design concepts that originated from government ink. It could be argued the turbofan engines that power WK2 are a somewhat distant derivative of government sponsored R&D, but whether that’s enough of a dependence to confidently claim that excluding such a link would be a showstopper is marginal.

  15. Suborbital space flight is a bit like circumnavigating the world by walking around one of the poles: it satisfies the standard definition, but doesn’t really achieve much. That’s why real space programs skipped that step and went straight to orbital flight, more than 50 years ago now.

  16. @wilful
    Of course, I should have also pointed out that Branson’s VG is probably the only prominent exception to the point you were making (maybe XCOR’s Lynx too), but there’s no true examples of completely private *orbital capable* operations out there with no reliance on both government support and previous R&D.

  17. John Quiggin :
    Suborbital space flight is a bit like circumnavigating the world by walking around one of the poles: it satisfies the standard definition, but doesn’t really achieve much. That’s why real space programs skipped that step and went straight to orbital flight, more than 50 years ago now.

    That’s probably a touch unfair. All previous government orbital capable space programs didn’t skip that step and those at Scaled/Virgin & XCOR would probably argue that their suborbital capability is a steppingstone for orbital aspirations.

  18. @Troy Prideaux

    The Soviet Union didn’t bother with sub-orbitals. Unless one defines space as being so low the Nazis got there first, Yuri Gargarin was the first person in space and the first to orbit the earth. He actually holds the record for doing the least number of orbits – one.

  19. The year Yuri Gagarin went into space is also easy to remember. In weightlessness there is no up or down and 1961 is the same whether it is the right way up or upside down. (Turn your monitor upside down if you don’t believe me.) But oddly enough this wasn’t the reason the Soviet Union shot a person into space that year.

  20. I’ll just second that Burt Rutan is a brilliant engineer. If there is anyone who could build a functioning space ship without the benefit of a century of research and development into heavier than air flight by others it would be him. Or possibly a wizard.

  21. Ronald Brak :
    @Troy Prideaux
    The Soviet Union didn’t bother with sub-orbitals. Unless one defines space as being so low the Nazis got there first, Yuri Gargarin was the first person in space and the first to orbit the earth. He actually holds the record for doing the least number of orbits – one.

    Yes indeed, they did bother with them. After building an entire V2 production capability after the war, they further went on to develop a suborbital program even more extensive than the Americans – R2, R5, R11, R3, R7 etc. You couldn’t just jump straight into orbital capability from nothing.

  22. Why the desire to see humanity continue forever ? How to justify this wish ? Where does it come from ? Im not sure I was there when god handed that one out . I do care about those currently living members of the animal world, but if those trillions of unborn future ones didnt get to live ? Not so sure that matters much to me, or for any other reason. The universe may just as well be better off without them , .

  23. Paul Norton @14, Was there a population surge leading up to 1000 AD? I think if there was then it was a pimple compared to the massive increase over the last 200 years.

  24. Jim Birch is right. You simply can’t travel at anywhere near the speed of light, because collisions with atoms are too damaging. Just imagine how bad hitting a grain of sand would be. So you are going to be in space for a few thousand years.

    But don’t worry, we’ll have suspended animation by then!

  25. AFAIK there is no empirical evidence for life anywhere in the universe other than here. There may be inferences that we can make that indicate that there should be life elsewhere but sadly up to today we have not been able to detect any intelligent life other than what we find on earth.
    It’s a bit like this book I’m reading on the historical figure of Jesus, its in a small font, it’s well footnoted and it’s a few hundred pages. After reading a third of it the message from the author is plain: there is almost no direct evidence whatsoever for the historical figure of Jesus.
    OK, a bit OT but it fascinating how belief in alien life has become a characteristic of recent western culture to the extent that it is largely unquestioned and unquestionable.

  26. @wilful

    Satellites are fantastic. The rest of the achievements in space seems mostly about nationalistic ego. It’s nice we visited the moon and built a space station, and these feeds our dreams. But they aren’t particularly useful outcomes for humanity in any practical sense. I enjoy knowing about the planets and what they look like and pondering settlements on Mars or terraforming Venus but NASA seems to be a big money pump designed to give engineers big toys. Sure there are spin offs but there are also plenty of other clever things Americans could have done instead. They could have had more missions to the ocean floor. Or better homes. Or rid the world of polio already.

  27. A rat done bit my sister Nell,
    With Whitey on the moon,
    Her face and arms began to swell,
    And Whitey’s on the moon,
    I can’t pay no doctor bill,
    But Whitey’s on the moon,
    Ten years from now I’ll be paying still,
    While Whitey’s on the moon…
    -Gil Scott-Heron

  28. True Terje, but they insist on wasting their money starting wars that they can’t finish.

  29. In data communications we gain efficiency and security by compressing and encrypting data, which turns the stream of bits into something closely resembling noise. So even if aliens were broadcasting using a technology we could “hear”, we might not be able to tell it apart from the background noise.

    But then consider how much radio communications has changed just in the last 20 years – from analogue mobile phones at 1200bps to LTE at 25+ Mbps. Samsung have just invented a system which essentially sends a tight, point to point radio beam to each terminal (phone) at gigabit speeds – this would be pretty much impossible to detect from any distance, and at the suggested speeds would obviate almost all other radio communication, including radio and TV.

    And this all assumes that we won’t one day soon discover something better than electromagnetic radiation for communication. If for example we were to discover a means of low power, high bandwidth point to point communication over long distances, it’s difficult to believe that radio transmission of any kind would continue for more than a couple of decades after commercialisation. I’m looking forward to someone discovering how to communicate using quantum entanglement – which would have the additional advantage of perhaps being instantaneous.

    Given the march of human technology, it seems to me that we would struggle to identify evidence of even moderately advanced alien technology even if it was right in front of us. Why would we send a space ship when a swarm of nanites equipped with instantaneous long distance low power communications would do the job? These things could easily be everywhere, and yet we don’t have the technology to see them.

    The Fermi paradox is perhaps not a paradox, and the Drake equation is misleading. Perhaps the reason we haven’t seen any little green men just yet, is because they are much smaller than we expect?

  30. hc @74, I was quoting an imaginary blogger in a work of fiction, and the words quoted shouldn’t be taken as representing my own views.

    As it happens there does seem to have been something of a population surge around 1000 AD, but it was followed by a decline soon after, and in any case, as you say, it was at a much slower rate of growth, from a much lower base, than the current population surge.

    http://en.wikipedia.org/wiki/File:Population_curve.svg

    Paul Walter @80, can you elaborate?

  31. Why this dream of intergalactic escape velocity, and balanced budgets?

    “If we grant that human existence is the state of damnation, two possibilities follow. Either we can learn to retrace the stages of our fall into matter, and so escape, or we can devise some means of extinction of personality. The pagan art and culture of the world, past and present, is divided in the pursuit of these alternatives. On one hand art is followed as a continuous labyrinth in which by blind, dogged persistence we may struggle upward by means of will power and ethical struggle. On the other hand there is the intellectual course presented by Mr. Eliot, in which we move from one intensity to another, towards a final flash of awareness and extinction. In the one art – that linked with Plato’s cave man – Time, continuity, dialectic, are of the essence. In the other, time is lost in simultaneities and juxtapositions.”

    H. M. McLuhan,
    Eliot and the Manichean Myth as Poetry (unpublished),
    p.3, 1952.

  32. @TerjeP
    I agree . lots of scientific techno goodies have come from space research . But they could sill have come otherwise . Much good could have been done here on earth with that money .

    Space programs are not just nationalistic ego. -Desire to send embryos or digitised human consciousness into space to spread ,save or continue the race I just dont get . Theres been no mention here yet of saving any of the non human consciousness either .I care about the future for humanity because those here now will be living in it tomorrow etc , and because our kids will, and they will probably want to have kids too . So theres a kind of connection that rolls forward like that . But whether we are around in 1 or 50 million years or not doesnt seem vitally important to me .

    I know this is an isolated thought experiment thread of a blog, and some have expressed concern for our earth , but I get the feeling that ,when it comes down to it ,the mere concept of distant future human consciousness is more important than the sum total of all non human consciousness (and possibly a good deal of the human consciousness too ) which is alive here now . Im getting impression that the entire biosphere -all of life – doesnt seem to compare much to the apparent glory of human consciousness or continuation. Humanistic not just nationalistic ego .

    I hope that doesnt sound too unfair to some as I know there are lots of caring souls who read this blog .

  33. michaelfstan @3 is the only person thus far to mention wormholes. This concept is deployed by, among others, Baxter & Clarke in The Light of Other Days, Peter Hamilton in his Commonwealth Saga, and the Killer Bs in the Second Foundation Trilogy. It would be good to get some comments and/or links to current knowledge on the practicalities of wormholes.

    Wormholes have nothing to do with Frank Herbert’s sandworms, Stephen Donaldson’s Worm of the World’s End, or the Channel Nine election worm.

  34. @Mark L
    This has probably already been mentioned (apologies if I missed it) but if we are relying on electromagnetic based (say radio) communications to detect transmissions from intelligent life, we also must allow for the lag time of the message to reach us. In terms of interstellar communications, we could be talking thousands of (earth) years lag. What’s more, the power of the transmission will need to be really substantial when you factor in inverse-square losses etc.

  35. I am nervous about suggesting that John Q got his maths wrong, but I think he may have perhaps possibly got his maths wrong.

    Consistent with what has been said by others above eg Peter @ #10, I can’t see that the average cost per light second of a short trip is necessarily the same as the marginal cost per light second: the considerable costs of escaping gravity and initial acceleration apply once per trip, twice in a return trip, but not every klight second, for example.

  36. @Paul Norton

    Wormholes are things that we have no good reason to think exist, but which aren’t impossible as far as we know. While interesting to speculate about, the least brain taxing option given the lack of evidence for their existence is to assume they don’t exist, as it seems unlikely that the universe is arranged to make it easy for us to have Star Trek type adventures. If wormholes do exist then it could be possible to arrange it so the entrance and exit are next to each other and you will come out of the exit before you go into the entrance. Whether or not this woudl instill a desire within you to kill your grandparents is unknown. If you don’t think the universe would allow these sorts of shenanigans, then the universe may not allow wormholes.

  37. @John Brookes

    “Jim Birch is right. You simply can’t travel at anywhere near the speed of light, because collisions with atoms are too damaging. Just imagine how bad hitting a grain of sand would be. So you are going to be in space for a few thousand years.”

    If you’re travelling near the speed of the light, you may as well imagine yourself as particles getting bounced around in an accelerator – hence the massive amounts of radiation produced when you collide with hydrogen atoms…

    OTOH, short of bringing several million tonnes along with you, the energy from colliding with all those hydrogen atoms is probably the only feasible way of fuelling the journey in the first place 🙂

  38. I am interested in the fact that this post has aroused so much interest both here and at Crooked Timber. Apart from being an interesting post – well done John – isn’t it nice to use our brains to think about things that are not defined by politics? (I agree some of the discussion at CT has become political but most isn’t).

  39. Worms can be a problem. Had a dose of threadworm as a kid and had to swallow this awful stuff from the chemist. After that, no more itchy wormhole.@Paul Norton

  40. Mike Smith :
    I am nervous about suggesting that John Q got his maths wrong, but I think he may have perhaps possibly got his maths wrong.
    Consistent with what has been said by others above eg Peter @ #10, I can’t see that the average cost per light second of a short trip is necessarily the same as the marginal cost per light second: the considerable costs of escaping gravity and initial acceleration apply once per trip, twice in a return trip, but not every klight second, for example.

    Dunno, you need mass to enable energy to be useful (provide propulsion), alas, an inconvenient and unavoidable fact and for every kg of mass used to propel the craft through the cosmos, many multiples of mass and energy are required to actually lift and accelerate that mass, so you’re constrained to the rocket equation with the added inconvenience of having to lift through a gravity field.
    John’s equations, whilst very simplistic, are probably (maybe^2) not that far off the mark.

  41. well the space cadets at the fin have surprised me.

    i expected them to go ballistic yesterday.

    splashed headlines and incompetence everywhere.

    but it was all mealy mouthed.

    i had to hunt around to even find the size of the deficit.

    around 19 thousand million.

    disability cost turns out to be around the same.

    does that mean without helping out the disabled the budget was balanced?

    i don’t know if i’m joking or not.

    yesty also had a heartwarming story of profit taking medical person gifting 85 million dollars to his family.
    isn’t that nice.

  42. Many years ago 10,000 people was a number more or less pulled out of a hat for a minimum colony size, based upon how many people would be required to prevent inbreeding. (Given how long ago this was I can’t help but wonder if it was actually how many people of northern European decent were required to prevent inbreeding.) But given that we can now print out DNA and that we’re not likely to shoot anyone into interstellar space before we finish work on developing reliable artificial sperm, inbreeding is not a problem. But DNA is a kind of an old fashioned molecule and it seems likely that our star colonists will have something a bit less shoddy than that in their cells by the time they are ready to shoot themselves across the universe. And cells are a bit squishy too, so they may as well get rid of them as well. After all, it would probably help save on their insurance premiums. It might be safest to send simulated humans in a computer instead of physical ones. According to Ray Kurzweil computers will be able to simulate a human brain in 26 years time, but assuming you don’t buy into his particular brand of nuttiness a much more realistic estimate is that it will take at least 28 years. So just sending a computer instead of squishy people full of water who are addicted to oxygen and food could save a lot of resources. Program people can be switched off to save on energy on the way. (Yes, switching them off will kill them, but they will be ressurected when the power returns. It’s kind of like how electroshock therapy kills us, but then we reboot.) Since there’s no hurry when sending program people there’s no need to try to approach the speed of light to go as fast as possible. And since program people won’t need an earthlike planet we can send them to a nearby solar system instead of some distant place with oxygen. Once they get to their destination they can print out some robot bodies, which is something we’re working out how to do at the moment, and build a “laser” or other communication device to let us know what they’ve found. And if anyone else wants to go there they can send the relevant details down a laser beam and get printed out at the end. Or it might be cheaper to use snail mail and send information in a physical medium. It all depends on how the technology pans out.

  43. Ronald Brak @46:

    It might be safest to send simulated humans in a computer instead of physical ones.

    But look at what Voltaire and Joan of Arc got up to in the second Foundation Trilogy. 🙂

  44. @John Quiggin

    “Thanks, Salient. Compliments are few and far between in this business, but always appreciated.”

    If it was up to me you would be named President-for-Life, all school children would be forced to read Zombie Economics and all your enemies would be put to the sword.

    There you go, another compliment 🙂

  45. See #157, #162 and #165 over at that Crooked Timber thread. Some questions are philosophical, but basic physics doesn’t care much. The only signals we’d ever see from nearby aliens would happen only if they are contemporaneous and spend massive amounts of energy beaming at us, at least now and then, over long periods.
    Forget about picking up alien broadcast leakage.

    As for belief in aliens, it is (oddly) included in recent US survey mentioned in National Geographic.
    It is summarized and the actual questions and % are here.

    Q10 (Do you believe aliens exist, or not?) is badly-posed if it was supposed to be a conspiracy-theory question. Actually, it’s badly posed, period, when folks at NASA tell me they wouldn’t be able to answer it.

    A good conspiracy theory question would be:
    Do you believe aliens exist here on Earth, but governments have hidden this fact, i.e., like Men In Black?

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