To be fair, his universe was much simpler than ours. He didn't need a nuclear reactor or particle accelerator to transmute lead into gold in his theory.
Well actually, "reversible driving" is perfectly apt in the sense of acceleration being a reversible process. It means that in theory the net energy needed to drive anywhere is zero because all the energy spent on acceleration is gained back on braking. Yes I know in practice there's always friction loss, but the point is there isn't a theoretical minimum amount of friction that has to be there. In principle a car with reversible driving can get anywhere with asymptotically close to zero energy spent.
Put another way, there is no way around the fact that a "non-reversible car" has to have friction loss because the brakes work on friction. But there is no theoretical limit to how far you can reduce friction in reversible driving.
Cars specifically dissipate energy on deformation of the tires; this loss is irreversible at any speed, even if all the bearings have effectively zero losses (e.g. using magnetic levitation).
A train spends much less on that because the rails and the wheels are very firm. A maglev train likely recuperates nearly 100% of its kinetic energy during deceleration, less the aerodynamic losses; it's like a superconducting reversible circuit.
Actually, a non-reversible car also has no lower energy limit, as long as you drive on a flat surface (same for a reversible one) and can get to the answer arbitrarily slowly.
An ideal reversible computer also works arbitrarily slowly. To make it go faster, you need to put energy in. You can make it go arbitrarily slowly with arbitrarily little energy, just like a non-reversible car.
This is fine as a beginner rule of thumb but it shouldn't be regarded as a universal truth about recursion. Its also possible for a simple evaluation without recursion to happen at infinity rather than at zero. In practice this usually means picking a large value of the input as a cut off point to apply an approximation or return a standard value instead.
For example, take an implementation of exp(x). The exponential function is defined as the sum to infinity of (x^n)/n!. This could be implemented recursively as exp(x,n) = 1+(x/n)exp(x,n+1). The challenge is to figure out the value (or criteria) for what value of n to cut this infinite evaluation short. Well, once n is larger than x all future terms will be multiplied by a factor less than 1. So pick some proportionality constant k such that if x is k times smaller than n (that is, x * k < n) then the remainder is presumed negligible and the function returns 1.
Another really nice example I know involves finding the resistance across a simple but infinitely repeating circuit. At very large n, there are so many resistors in the way that the contribution of the remaining circuit connected in parallel is basically nothing. So pick whatever value of net resistance R_N for an arbitrary cut off point N, then recursively find the net resistance in the circuit up to point N-1 connected in parallel with everything remaining in the circuit after point N.
There are other cases I can think of where the base case is actually the function converging (or becoming linear) for large rather than small inputs. And still other cases I know of where the function has more than one input argument, and thus it might make sense to increase the size in one input to reduce it in another etc.
The imperfect mirror means that epsilon% of the time the light goes through to a much larger "back room" whereas (1-epsilon)% of the time the light just reflects like normal. The point being made is that this is an extension of an ordinary ideal cavity to include unavoidable (but weak) interaction with the much larger system outside of it (aka the whole universe). It just so happens the much larger external system is also being modeled as a simple 1d cavity.
In other words, entropy is equivalent to bits of information needed to specify the complete state of the system leaking outside of the confines of where those bits are being observed by an experiment (eg tunneling through an imperfect mirror).
Entropy is an accounting tool to keep track of how many bits are missing, and how far this ignorance has percolated into what you can safely predict about the system.
Japanese artistic depictions of America have an interesting way of having an "accent" so to speak but in a manner that doesn't mistranslate but rather adds something unique to it. I'm reminded of a series of illustrations from the 1800s explaining the American revolution for a Japanese audience where all the depictions of the important historical characters look like traditional samurai drawings and they take on a sort of mythological character to them. Its like different enough to appreciate that its different while also familiar enough to understand what its saying.
Interesting point. I feel the same about the old SNES classic, Earthbound.
It was a different perspective on America, making small towns and suburbia (a sometimes looked down upon aspect of the country) look appreciated, cozy, nice.
Japan doesn't have suburbs in the same way as the US, small towns often look and feel the same as the outskirts of major cities; although very small towns, as depicted in the Hamaguchi's most recent film Evil Does not Exist, are qualitatively different from both.
Well, if the requirement is to stay in the type, you could extend the type to include the point at infinity. That satisfies both programmer and the mathematician.
Given we are talking about jamming a repeater in a rather extreme orbit, you have to account for the speed of light delay. By the time a bad actor gets news that a message they don't like is being transmitted and starts up the jammer the broadcast may already be over (assuming its a data transmission that comes in bursts of packets)
That's a very good point. I suppose that, if we assume a bitrate, and we assume partial messages are irrecoverable, then this puts a limit on the "uncensorable bandwidth." But it's easy to imagine a protocol that splits large messages into very small pieces to so that each message is below that limit.
Nothing really prevents continuous jamming the whole time it's overhead for an area you care about. All a government needs to do is broadcast noise at a high power on the band(s) of interest to completely drown out dissident signals.
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