So I’ve decided that I want to build a 64-level Tower of Hanoi game. What should I make it out of? I suppose that some of the design considerations would have to be:
-Resistance to friction. Careful as you are, the disks and posts are still going to rub against each other, and you’re going to be moving the disks a lot.
-Chemical resistance. After all, this is going to have to last a long time, and the composition of the atmosphere may change. We could end up with another Deccan Traps incident tossing all sorts of crud into the air, for example.
-Resistance to shock. At some point, we’re going to get at least one dinosaur-killer asteroid impact, which is probably going to knock the game off the table and onto the floor.
-Resistance to compression. The bottom disk is going to have to last, what, 300 billion years before it’s moved to the target pillar? I don’t want it to flatten out or fuse to the base in the interim.
Any thoughts? Or should I just leave a note asking the Morlocks to please check the pieces for nicks and scratches and replace as necessary?
How about Polytetrafluoroethylene (PTFE) aka Teflon[sup]TM[/sup]? It meets all but the last criterion, as far as I recall, and it’s easy to machine. But it’s kind of heavy. Another plastic might be good, but PTFE is famous for low friction. I don’t know how strong PTFE posts would be - you may want to make them out of non-corrosive metal, or a corrosion-resistant stone. Diamond spikes are traditional, but are brittle and expensive.
Boy, at first you had me worried! I saw 64 levels and immediately thought :eek: is this guy totally clueless? But clearly you understand the order of the algorithm.
Still, you’re stuck with a conundrum: none of the materials we can observe have lasted more than 13.5 billion years, as far as we can tell.
Current theory suggests that the lower limit of the durability of a proton is 10**35 years. That would be a good starting point, except that protons have charge, so you might find that building something out of protonium would be like herding cats. The same limitation applies to electrons.
Neutrons are, of course, neutral. Free neutrons decay rapidly, but “neutronium” (or whatever you choose to call a neutron star’s material) can supposedly exist. Your limitation there is trying to move the stuff; a teaspoon would “weigh” 100 million metric tons. You either need a very small tower or a very large crane. Also, theory suggests that neutron-degenerate matter can only exist in quantities equivalent to 1.35 to 2 solar masses, where its gravitation keeps it stable.
DeBeer’s propoganda notwithstanding, diamonds are not stable and gradually decay to graphite. I don’t recall the half-life, but if it can even be measured it is not going to last the length of time needed. I wonder how tungsten carbide would do. Perhaps it has the same problem. Best might be something like a platinum-iridium alloy. Still, I think you would have to be ultracareful not to rub it on anything or it will wear away. And you had best keep it in a vacuum since even friction with air will lose something. Maybe something ferromagnetic would be better since it could be manipulated without contact. And it would work best in null-G since even the act of placing it on the base will result in some wear.
I was wondering whether a buckyball-type structure might work (i.e., something built out of carbon), but if diamond would decay to graphite I suppose that’d also put the kibosh on other 3-d carbon structures.
The best material that I can think of that is easily available is gold. I’m not a chemist or a metallurgist, but I would think it would last at least as long as a anything else, and it’s very resistant to corrosion.
If you stack bits of gold on top of each other, I think they will eventually weld themselves together - at least it seems like it might be a risk over the timescales we’re talking about here.
Also, it’s fairly inert chemically, but it’s not very durable mechanically.
I think the best way to make it last a really long time might be to make it really, really big - having engineered wear-expectations into it - perhaps planet-sized discs of pure titanium would remain tolerably recognisable and usable, or make it really, really small - build it atom by atom so that there are no surface imperfections to affect friction and fit, then enclose it in a vacuum inside a really hefty hermetically sealed casing (moving and observing the pieces by remote control).
Let’s suppose we have unsormountable problems mining the unobtainium to build this. Would it be possible to just build replacement disks? Is there enough stuff to build all the replacements needed? Can we build them fast enough?
I think after some time passes, you’d just end up with a rotating sphere, perhaps with an equatorial bulge. In other words, it would be like a planet made of titanium.
Make them normal-sized, and leave instructions to the monks who will perform the moves:
(1) Each of the 64 monks is assigned to make a disc.
(2) Each of the 64 monks is assigned to move a disc.
(3) Between moves, monks care for the abbey and meditate (the #1-20 monks should be selected for patience and/or OCD).
(4) When a monk dies, an initiate may take his place, but must bring an offering: a replacement disc crafted to the original specifications.
(5) Yeah, that #1 monk is going to go completely crazy. Maybe you only need 16 monks who rotate disc-moving duties weekly – monk #1 on discs 1-4 for a week, and so on?
The smaller the disc, the more moves it undergoes and the more wear it gets, so you’d have to specify that each disc must be replaced after x number of moves, or something.
Make the discs out of General Products hull material. You can’t abrade that stuff with shadow square wire or Sinclair monofilament, nor need to worry about anything short of antimatter. Make the spikes out of wire enclosed in a stasis field - if it lasted Kzanol for one and a half billion years, it’s not going to let you down any time soon.
Please deposit one million stars to my current account as consultancy fees.
