Force on the projectile of a railgun:
F = B·I·l
B: Magnetic field
l: Length of armature
Current = Voltage / Resistance
Resistivity of seawater:
ρ = 2.00×10^−1 (Ω·m) (because = (Ω/m-length)*(cross-sectional area))
Let cavity be 1cm square, consider section 1cm long:
Volume: 1 millilitre
∴ mass (m): ~1 gram = 1e-3 kg
Cross-section: 1e-4 m^2
Armature length (l): 1e-2 m
Resistance: ((2.00×10^−1 Ω·m)*0.01m)/(0.01m^2) = 0.2 Ω (got that wrong first time! Along with all that followed, which is now updated…)
∴ current (I) = Voltage (V) / 0.2 Ω
Rare earth magnets can be 1 tesla without much difficulty. Assume that here.
F = 1 T · (V/0.2 Ω) · (1e-2 m)
Target velocity: 11.2 km/s = Escape velocity = 11200 m/s
v = at = 11200 m/s
∴ a = (11200 m/s) / t
s = 1/2 · a · t^2
∴ s = 1/2 · ( (11200 m/s) / t ) · t^2
= 1/2 · (11200 m/s) · t
or: t = s / (1/2 · (11200 m/s))
F = ma = (1e-3 kg) · a
∴ a = F / (1e-3 kg)
∴ t = (11200 m/s) / (F / (1e-3 kg))
= (11200 m/s) · (1e-3 kg) / F
∴ s = 1/2 · (11200 m/s) · (11200 m/s) · (1e-3 kg) / F
∴ s = 1/2 · (11200 m/s) · (11200 m/s) · (1e-3 kg) / ( 1 T · (V/0.2 Ω) · (1e-2 m) )
Say V = 250 volts:
∴ s = 1/2 · (11200 m/s) · (11200 m/s) · (1e-3 kg) / ( 1 T · (250V/0.2 Ω) · (1e-2 m) ) = 5020m (not ~501760 meters)
Say V = 25,000 volts:
∴ s = 1/2 · (11200 m/s) · (11200 m/s) · (1e-3 kg) / ( 1 T · (25000V/0.2 Ω) · (1e-2 m) ) = 50.2m (not ~5017.6 meters)
Liquid mercury instead of seawater:
Resistivity: 961 nΩ·m = 0.961e-6 Ω·m
Resistance: 9.6e-7 Ω (got this one wrong the first time, too!)
Density: 13.56 times water
F = 1 T · (V/9.6e-7 Ω) · (1e-2 m)
s = 1/2 · (11200 m/s) · (11200 m/s) · (13.56e-3 kg) / ( 1 T · (V/9.6e-7 Ω) · (1e-2 m) )
@250 volts: s = 0.3266 meters (not 3.266m as before correction)
@25kV: s = 3.266 millimetres (not 32.66 millimetres as before)
Power (DC): P = IV where I = V/R,
R = 9.6e-7 Ω
@250 volts: I = 250 / R = 250 V / 9.6e-7 Ω = 2.604e8 amperes (x10 more than before correction)
∴ P = 65.1 gigawatts (x10 than before)
@25kV: I = 25000 / R = 25000 V / 9.6e-7 Ω = 2.604e10 amperes (x10 more than before)
∴ P = 651 terawatts (x10 than before)
Duration between rails:
From t = s / (1/2 · (11200 m/s))
t = 0.3266 meters / (1/2 · (11200 m/s)) = 5.8321×10^-5 seconds (x10 less than before correction)
t = 3.266 millimetres / (1/2 · (11200 m/s)) = 5.8321×10^-7 seconds (x10 less than before)
Electrical energy usage:
E = P · t
E = 65.1 gigawatts · 5.8321×10^-5 seconds = 3.797×10^6 joules (unchanged by correction)
E = 651 terawatts · 5.8321×10^-7 seconds = 3.797×10^8 joules (unchanged by correction)
(For reference, 1 litre of aviation turbine fuel is around 3.5e7 joules)
The Singularity is one form of the idea that machines are constantly being improved and will one day make us all unemployable. Phrased that way, it should be no surprise that discussions of the Singularity are often compared with those of the Luddites from 1816.
“It’s different now!” many people say. Are they right to think that those differences are important?
There have been so many articles and blog posts (and books) about the Singularity that I need to be careful to make clear which type of “Singularity” I’m writing about.
I don’t believe in real infinities. Any of them. Something will get in the way before you reach them. I therefore do not believe in any single runaway process that becomes a deity-like A.I. in a finite time.
That doesn’t stop me worrying about “paperclip optimisers” that are just smart enough to cause catastrophic damage (this already definitely happens even with very dumb A.I.); nor does it stop me worrying about the effect of machines with an IQ of only 200 that can outsmart all but the single smartest human, and rendering mental labour as redundant as physical labour already is, or even an IQ of 85, which would make 15.9% of the world permanently unemployable (some do claim that machines can never be artistic, but, well, machines are already doing “creative” jobs in music, literature and painting, and even if they were not there is a limit as to how many such jobs there can be).
So, for “the Singularity”, what I mean is this:
“A date after which the average human cannot keep up with the rate of progress.”
By this definition, I think it’s already happened. How many people have kept track of these things?:
Most of this was unbelievable science fiction when I was born. Between my birth and 2006, only a few of these things became reality. More than half are things that happened or were invented in the 2010s. When Google’s AlphaGo went up against Lee Sedol he thought he’d easily beat it, 5-0 or 4-1, instead he lost 1-4.
If you’re too young to have a Facebook account, there’s a good chance you’ll never need to learn any foreign language. Or make any physical object. Or learn to drive… there’s a fairly good chance you won’t be allowed to drive. And once you become an adult, if you come up with an invention or a plot for a novel or a motif for a song, there will be at least four billion other humans racing against you to publish it.
Sure, we don’t have a von Neumann probe nor even a clanking replicator at this stage (we don’t even know how to make one yet, unless you count “copy an existing life form”), but given we’ve got 3D printers working at 10 nanometers already, it’s not all that unreasonable to assume we will in the near future. The fact that life exists proves such machines are possible, after all.
None of this is to say humans cannot or will not adapt to change. We’ve been adapting to changes for a long time, we have a lot of experience of adapting to changes, we will adapt more. But there is a question:
“How fast can you adapt?”
Time, as they say, is money. Does it take you a week to learn a new job? A machine that already knows how to do it has a £500 advantage over you. A month? The machine has a £2,200 advantage. You need to get another degree? It has an £80,000 advantage even if the degree was free. That’s just for the average UK salary with none of the extra things employers have to care about.
We don’t face problems just from the machines outsmarting us, we face problems if all the people working on automation can between them outpace any significant fraction of the workforce. And there’s a strong business incentive to pay for such automation, because humans are one of the most expensive things businesses have to pay for.
I don’t have enough of a feeling for economics to guess what might happen if too many people are unemployed and therefore unable to afford the goods produced by machine labour, all I can say is that when I was in secondary school, all of us young enough to be without income, pirating software and music was common. (I was the only one with a Mac, so I had to make do with magazine cover CDs for my software, but I think the observation is still worth something).