Hackfoofery

Alson Kemp

Science Fiction: The Economics of Star Travel

While I’m a fan of Alastair Raynold‘s science fiction and recently finished Poseidon’s Wake, I’m rather unsure of his treatment of interstellar travel. Within reasonable bounds, making allowances for the fact that it’s science fiction (hey, Conjoiner drives) and recognizing that he, not I, is a bona fide rocket scientist, his treatment of how to conduct interstellar travel seems realistic and sobering, though perhaps not sobering enough…

So let’s talk about money now and then…

Economics/Finance Backgrounder

The problem of how much money to spend now in order to reap a future gain is well studied in economics and/or finance. A discount rate is used to forward or backward project financial amounts, recognizing that $1 gained or spent at a future date is not valued at $1 now. For example, assume you had $10 and could invest it at a 5% rate in a completely instrument (say a bank bond) (you can’t right now, hey thanks Fed, but let’s assume that you could…). After 1 year, you’d have $10.50. Likewise, if I needed $10 now, you could lend me the $10 but you’d want me to promise to return you more than a total of $10.50 after one year. You wouldn’t lend it to me for less than $10.50 because you could just lend it to a bank or government via a bond and get back $10.50. I’m riskier than a bank or a government so you’d want more from me than from a government or bank. Simple.

Likewise, if I needed the $10 now and couldn’t pay it back for two years, you’d want two years worth of interest (plus some extra for the additional risk incurred over two years but we’ll leave that aside for now). So I’d need to pay you back more than $11.03 ($10 * 1.05 * 1.05) at the two year mark. And so on for three years, four years, etc.

How about I offer to pay you $15 in two years? How much is that worth to you right now? Same logic. Rather than having $10 in two years, you’d be just as happy (indifferent) to have $13.61 ($15÷1.05÷1.05) now.

The same applies to costs as well as incomes/benefits. In fact, that was implicit in some of the prior calculations: if you lend me $10 now, that’s equivalent to -$10 to your account now; when I pay you $11.03 in two years, that’s equivalent to +$10 ($11.03÷1.05÷1.05) now. So you lent me $10 and you’re getting back in the future the equivalent of $10 now.

Simple math. Using discount rates is a bit more complicated than that (often times the actual discount rate is pretty hard to guess-timate), but the gist is accurate enough.

To make it a bit more clear, imagine that you’re leading a big company and one of your employees approaches you asking for a bunch of money for project. Of course, other employees are asking you for bunches of money for other projects. How do you figure out which projects to fund? Project1 might pay off in 7 months while Project2 might not pay off for 22 months. Using the company’s internal discount rate, you can figure out how much each project is worth now against how much it will cost over its time to produce.

But now you’re talking about months instead of years…? Well you can figure out a monthly discount rate from the yearly discount rate: sticking with a 5% yearly rate, the equivalent monthly rate is (1.05^(1÷12)) 0.41%. Project1 is going to cost $1 per month for 7 months or $1+$1/1.0041+$1/1.0041^2+$1/1.0041^3+… now (spreadsheets have formulas (e.g. NPV or PV) to calculate so it’s left as an exercise for the reader). While Project1 doesn’t actually cost $7 now, we will wind up spending 7*$1. You can start the project now, pay $1 and invest ~$6 in a bond. Then, after one month, you sell $1 of your bond and pay $1 to the project, etc, etc. Eventually, 7 months pass, you’re out ~$7 and you have yourself Project1.

With that out of the way…

Back To Interstellar Travel

Congrats! Now you’re planning Earth’s first interstellar travel! Luckily for you, this is just a gedankenspiel so you get to work with the following:

  • While velocity is limited to 10% of light speed (0.10c), acceleration is infinite so mass is not a problem and the vessel gets to 0.10c instantly (oops. Squashing any human travelers…) and (relatively) stops instantly. Neat.
  • The prevailing, safe interest rate is 5% and you’re working for the government so your money is good. But you could be using money to build roads, rail lines, subways, parks and other stuff to make citizens happy so maybe aim for a bit more than 5%? And you might be taking a lot of money/productivity out of circulation, so aim for a bit more than a bit more than 5%? Meh. The entire world’s worth of politicians are going to be mad at you. Better use a discount rate of 8%.
  • Launching the interstellar travel project will cost $100,000,000,000 each year for ten years and will launch immediately on the 10th year. [We can quibble about yearly cost and duration, but it’s going to be large and take a while… The real whopper is going to be the journey time so the construction cost/time don’t matter too much.]
  • Scientists have recently identified a remarkably Earth-like planet around the closest star.
  • The closest star is Proxima Centauri and is about 4.3 light-years away.
  • The ship can take enough fuel to reach the star and can pick pick up fuel there over about 2 years.
  • Communication is still tough at that distance so no communication once the vessel is past Pluto. Since the vessel gets to 0.1c instantly, it only takes about 56 hours to pass Pluto so the vessel is basically out of communication range the whole time.

Great. Sounds simple. Build ship, fly ship there, refuel ship, fly ship back. But it sounds as if it’s going to cost quite a bit. Shouldn’t you bring something back? Yes! Scientific knowledge! Well, that sounds great but we’re not going to be building as many roads, railways, subways, etc so shouldn’t we get, like, a little more? Right, we’ll bring back a really neat alien bug! So:

  • Build ship, fly ship there, refuel ship, fly ship back. Check.
  • Spend return journey writing up scientific knowledge. Check.
  • Get a really cool (but safe!) alien bug. Check.
  • Try not to attract the attention of berserkers while fiddling around… Check.

Some numbers:

  • See here for some light calculations.
  • The current cost of sending the ship is $724,688,791,085.
  • The ship launches ten years from now, flies for 43 years, does immediate exploration/analysis, takes two years to refuel and then flies 43 years back. Total time expended is 10+43+2+43 years or 98 years.
  • If the ship returns in 98 years with something of value, it needs to return with something worth more than $725 billion now (which will be $1,366,720 billion in 98 years),

Whatever ship you’re going to build better be really smart! Of course, we don’t actually know if anything really interesting is at Proxima Centauri so you should probably return with something really valuable. Say 3x the current cost or about $2.2T (or about $4,000T then). Hell, we might not even be here anymore to enjoy whatever the vessel returns!

Back to Science Fiction

I’ve worked with simple and reasonable assumptions (minus the bits about infinite acceleration and mass not mattering) in this exercise and this trip will still cost a fortune. More realistic assumptions just mean the trip will cost more.

What could the vessel possibly bring back in 98 years that would be worth roughly the current market capitalization of a combined Microsoft-Amazon-Apple-Alphabet/Google? How much is it worth to know about the exact contents of Proxima Centauri and to get a neat alien bug (and, maybe, to get some other scientific knowledge)? Maybe it’d be worth a lot to you but it probably wouldn’t be worth to someone with a food-service job struggling to make ends meet or to a recently-out-of-work coal miner. Or, more importantly, to a politician voting on whether to fund this vessel while trying to get the votes of said food-service worker or out-of-work coal miner.

I’ve read a lot of science fiction and the most realistic/constrained stories never touch upon the economic costs of interstellar travel (except for mystical bits, such as somehow damaging the fabric of space-time). Lots of science fiction skirts the problem by assuming the existence of faster-than-light travel. Maybe possible, maybe not, but it’d make the time-based costs lots cheaper.

Building an interstellar civilization around humans would be incomprehensibly expensive. Worse, most or all of the people alive at the launch of the vessel wouldn’t survive to see its return. The discount rate they’re (implicitly) using is more like 100% (as in, nothing of value will never come back to them)…

So how would interstellar travel be funded?:

  • Generation ships: these make no sense (possibly for lots of reasons) because it’s nearly inconceivable that a society would undertake a project to eject enormous amounts of value from itself on a one-way trip to the unknown. “It’s going to cost $1T and then we’re going to throw it away in space? Well, get about it, then!” (Obligatory reference to Bob Newhart’s bit on smoking…)
  • Benefits: as noted above, it’s unlikely that anyone would invest in a project with no possible return within their lifetime unless those returns are nearly guaranteed or are smart to make (see: timber). Those on the ships might see useful time dilation or might “sleep” for the journey so would realize gains within a “reasonable” time (say a perceived 5-10 years).
  • Material: any returned material or knowledge must not be acquirable within the 98 years (in this exercise) because why not just research it here/now for less money/time?

I really enjoyed Nancy Kress’s realistic exploration in Beggars in Spain of how near-future advancements in genetic engineering (namely, enhanced intelligence and “sleeplessness”) would affect society. Back to Alastair Reynolds: his realistic-ish treatments of interstellar exploration are great, but I’m waiting for a realistic treatment of near-mid-term interstellar exploration.

Written by alson

July 3rd, 2019 at 2:40 am

Posted in Geekery

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