That seems great, but then to validate against the schema you must have a full JavaScript interpreter (or almost full, depending on how much you're willing to restrict what can be used in the isValid function). Not to mention that, this being JavaScript, a lot of schemas would end up being a mess, which would defeat half of the purpose of a schema -- being a human-readable documentation of the data format.
Schema validation is a very clear example of a situation where it's not good to have a Turing-complete language. There is a proposal for a JSON schema language (where schemas are themselves JSON documents). Apparently there's not much interest, though.
I've heard this before, and I have trouble understanding how this would change anything.
That is: if your brain is so broken that you can't help but do [unacceptable thing], then you're not fit to live in society, just like an insane person. The concept of "insanity defense" already exists but doesn't invalidate the basic principle of responsibility.
OK, let's try to understand the point of the essay, since reading the title is not enough. At the beginning of the conclusion, he wrote:
As a computer user today, you may find yourself using a proprietary program. If your friend asks to make a copy, it would be wrong to refuse. Cooperation is more important than copyright.
If you stop reading there, you might get the impression he's advocating breaking proprietary licenses. But if you keep reading, you see that, immediately after that (in the same paragraph!), he wrote:
But underground, closet cooperation does not make for a good society. A person should aspire to live an upright life openly with pride, and this means saying no to proprietary software.
Is it too hard to see that he's not saying that you should help your neighbor by violating proprietary licenses, but instead that you should not use proprietary software in the first place?
Stallman clearly says that if your neighbor asks your for a software that you use, it would be wrong not to give it to him, under the 'help your neighbor' pretext.
Yes, he does, but you missed the point. That's his reason for never using proprietary software: if you do, you're put in the position where you must either do the wrong thing and deny helping your neighbor, or do the wrong thing and break the license of the proprietary software.
It's great that a 16 year old discovered this, and it could have been a cute (but not as flashy) story. But the reporter didn't even bother to talk to someone familiar with the field.
I just have a feeling something else is really going on.
A lot of people seem to feel that way. If was even common among physicists in the beginnings of Quantum Mechanics (Einstein -- among many others -- was never satisfied with the theory, and tried without success to find something better).
I'm not sure myself, but it seems that when you begin to understand the math, you realize that it's actually very simple at the bottom -- the same very basic rules predict and explain so many wildly different things we can measure -- interference (the wave-particle duality stuff), the uncertainty principle, entanglement, quantum tunneling, etc. -- that it seems unlikely that there's some simpler explanation that will fit everything as well as Quantum Mechanics.
No, see the intermediate states in the step-by-step walkthrough of quantum teleportation in Wikipedia. Immediately after the first peer (called "Alice" in Wikipedia) does the measurement, the destination qubit (called "Bob's qubit" in Wikipedia) is in one of 4 the states described after the paragraph that begins with "Notice all we have done so far (...)". The state of Bob's qubit is represented to the right of the tensor product sign (the circle with the cross inside, for those not familiar with this notation). The states are completely different -- in fact some of them are orthogonal (the first is orthogonal to the last and the second is orthogonal to the third; that's easy to see because alpha*beta-alpha*beta=0).
What this means is that, if Bob doesn't use Alice's result to perform the right measurement in his qubit, he might as well have a random qubit. That's not surprising, since entanglement can't be used to transmit information. It's only with the information from Alice's measurement that Bob can select the right measurement to perform in his qubit to put it in the desired state (i.e., the state "teleported" from Alice's initial qubit).
[ouch -- overly long comment ahead... I wonder if anyone will read it:( ]
I have also never seen a good popular explanation of entanglement: either they go full weirdo saying things like "instantaneous something" or don't really explain entanglement, like your example about numbers in a hat. The problem is, to understand exactly what physicists understand by "quantum entanglement", you first must understand measurement, and in particular, that you can choose many different ways to measure each particle from the entangled pair. If you're willing to spend some time, I recommend the excellent series of lectures starting in this video. The material is pretty self-contained, except some matrix algebra and complex numbers. The lectures are given by Leonard Susskind, a famous physicist.
Now, if you just want to understand why entanglement is different then your "numbers in a hat" example, I'll try to explain as simply as I can with a simple example (which has the basic idea of Bell's inequalities and their violation, you can search wikipedia if you like).
OK, consider a "game" with these elements:
(1) two people, Alice and Bob, the players in the game
(2) both Alice and Bob each have a coin. Their coins are fair (i.e., 50/50) and, when flipped, give the result "0" or "1". Call the results of Alice and Bob flipping their coins ca (for "Coin-Alice") and cb (for "Coin-Bob"). Clearly, ca and cb are completely unrelated, because the coins are fair. Alice can see the result of her coin, but NOT Bob's, and vice-versa.
(3) the hat from your example, which generates either two "0"s or two "1"s. You'll always give one of the numbers to Alice and the other one to Bob, and each of them can NOT see what the other one got. Call the two generated numbers ha and hb (for Hat-Alice and Hat-Bob). So, you'll always have either ha=hb=0 or ha=hb=1.
(4) both Alice and Bob each have a piece of paper where they have to write either "0" or "1". Call the two written numbers pa and pb (for Paper-Alice and Paper-Bob). Each of them can't see the other one's paper.
The game is played by Alice and Bob collaborating to win -- either they both win or they both lose. To play, they can discuss their strategy, after learning the rules which I'm about to explain. But once the game starts, they can't talk anymore (i.e., no information can pass between them).
The rules of the game are as follows: when the game starts, Alice and Bob are given the numbers from the hat (ha and hb), then flip their coins (ca and cb) and write in their papers (pa and pb). They win if the resulting numbers satisfy the following equation:
pa XOR pb = ca * cb
and lose otherwise. Here, XOR is the usual XOR operation on bits, and "*" is the usual multiplication. Remember that all numbers in the equation (pa, pb, ca, cb) are either "0" or "1"). Also note that the numbers from the hat are not used to determine if they win or lose, but they can use the hat numbers to write their answers, according to whatever strategy they decided.
Now, note that if they both always write "0" in their papers, ignoring the hat completely, they win 75% of the time, because 0 XOR 0 = 0, and ca*cb will only be different than 0 if both coins are 1, which happens only 25% of the time. It's not too hard to prove (mathematically) that if their coins are indeed completely fair, any strategy they use will give them at most 75% of chance to win, it's impossible to do better without cheating.
So far, nothing involves anything quantum, and there's no entanglement. What I described is called a "Bell inequality" (win probability <= 75%), you can look up Wikipedia for a mu
It's actually worse than that. You could send the photons ahead of time (i.e., you could stock photons and use them to perform teleportation whenever you need it), but teleportation is still not "instantaneous".
The problem is that, to perform the teleportation, you must first measure the source, and then send the result of the measurement to the destination (that's just 2 bits of classical information). Given this information, the person in the destination chooses one of four measurements to perform in the corresponding destination photon, and then the teleportation is complete. Wikipedia has a more detailed explanation, including the measurements performed.
That said, I think that what you mean is (and this is true): to perform quantum teleportation, you still need a classical channel. But the reason for the satellites in this case is not that: the satellite is being used to send entangled photons (i.e., it's a quantum channel). The classical information could have been sent in any other way (over the Internet, for example), but to send entangled photons, there must be no measurements of the photon along the way.
This result shows nothing wrong with relativity or quantum theory.
Neutrinos have so little mass (less than 0.28 eV, compared to, for example, about 510000 eV for the electron and about 940000000 eV for the proton) that they're expected be found traveling *very* close to the speed of light. This experiment is simply not precise enough to detect the difference between the speed of the neutrinos and the speed of light.
It's great to study, understand and use Feynman's path integral, especially since it leads to new insights about the nature of Quantum Mechanics (plus, seeing the familiar face of the principle of least action in the quantum world is just awesome). But it seems counter-productive to limit yourself to it. For example, some problems that are relatively simple to solve using the "usual" methods (i.e., thinking about waves and using the Schrodinger equation) can become intractable math nightmares with Feynman's path integral. I'm sure there are problems for which the reverse is true, too.
Most people who work with QM seem to take a very pragmatic approach when dealing with problems outside the foundations of QM: use whatever works for you for the problem at hand. Peter Shor (the guy who invented the quantum algorithm to factor numbers in polynomial time) once wrote:
Interpretations of quantum mechanics, unlike Gods, are not jealous, and thus it is safe to believe in more than one at the same time. So if the many-worlds interpretation makes it easier to think about the research you’re doing in April, and the Copenhagen interpretation makes it easier to think about the research you’re doing in June, the Copenhagen interpretation is not going to smite you for praying to the many-worlds interpretation.
This discussion is mixing two different things: the decimal expansion of irrational numbers and infinite random sequences.
I won't argue about random sequences, but Hatta is right about irrational numbers in general (an pi in particular). It's perfectly possible (as far as we know today) that the decimal expansion of pi does not contain, for example, any "1"s after the n-th digit (for some n).
Considering that pi represented as a decimal number is infinitely long, it would eventually contain the encoding for every song in existence.
Actually, that does not necessarily follow.
It's not known whether pi contains every finite-length sequence in its decimal expansion (although most people believe it to be true). In fact, our knowledge is even worse than that (from Wikipedia):
It is for instance unknown whether sqrt(2), pi, ln(2) or e is normal (but all of them are strongly conjectured to be normal, because of some empirical evidence). It is not even known whether all digits occur infinitely often in the decimal expansions of those constants.
Sure, precognition ("beyond our current, assumed capabilities", as you said) may not be completely ruled out in our current understanding of the universe, I'm not disputing that.
My whole point, again, is that determinism doesn't have all that much to do with that.
I showed limits (under the currently known laws of physics) on precognition even under a completely deterministic universe (note that it's even possible, and even likely, that precognition is completely ruled out under determinism, we just don't know yet).
Conversely, it might be the case that limited precognition ("beyond our current, assumed capabilities") is allowed even if there is indeterminism in the universe. That is: it might be the case that for some types of phenomena, indeterminism (of the kind we know might exist according to quantum mechanics) could never affect the future of a system -- and so precognition is not ruled out even if the universe is not deterministic.
And yes, "as we know them", insofar as it's ever valid to claim as an absolute what "we know".
Well, I'm assuming what "we know", so my arguments might be invalidated if what we know changes. But if we don't base the discussion in what we know, then anything might be possible (it might be possible that precognition has nothing to do with determinism, who could tell?)
The point is that determinism is not a free pass for precognition: even assuming that the laws of physics are deterministic, unrestricted precognition violates at least one pretty basic law of physics (i.e., there exists at least one -- "arbitrary" -- phenomenon that violates a law).
Another way to understand this is to realize that Laplace's demon can't be implemented in the real world, with the laws of physics as we know them.
Indeed, things like precognition overtly violate so very many physical laws...
Not really, if you posit those physical laws are deterministic.
I don't think that's quite enough. You have to remember that the person with precognition must him/herself work under the laws of physics.
Under this reasoning -- disregarding any computational requirements -- for a person to have precognition over arbitrary phenomena (and not just phenomena under his/her complete control), he/she must have access to information about anything that could influence this phenomena. Further, this information must be acquired in a finite amount of time, that is, before the phenomena happens. This means that the person must be able to either:
- (A) pack, in a finite amount of space, information about the state of any part of the universe (at some time in the past, or present) that could influence the phenomena -- which can be, for arbitrary phenomena, an arbitrarily large amount of information; OR
- (B) access, in a finite amount of time, information about the state of an arbitrary portion of the universe (which could be arbitrarily distant).
Our current understanding of physics says that (A) violates the Bekenstein bound and (B) violates special relativity.
You do realize Non-locality of Mind has already been proven, right?
No, it hasn't, despite what one or a few physicists might be saying.
First of all, some interpretations of Quantum Mechanics don't even accept non-locality (e.g., many-worlds).
Second, and more importantly, most interpretations don't attribute any special role to the mind. The "mind" doesn't even appear in the description of the most accepted interpretations, from Copenhagen to many-worlds to Bohm's to consistent histories.
Perhaps you are thinking of this in a purely theoretical sense. In that case then yes, if you can harvest 100% of the energy stored when changing a value, then no additional energy is required.
That's the whole point of IBM's experiment and Landauer's principle: even in a purely theoretical sense, if you erase information when you're changing the state of a bit, you necessarily spend a minimum amount of energy. You can't, even theoretically, harvest 100% of the energy back. I was showing that there are other useful ways to change the state of a bit (e.g. in reversible computing) that do not incur in this purely theoretical energy cost, where you could theoretically harvest 100% of the energy back.
Sure. But the whole point is that the *computation* itself doesn't need to spend energy[1]. The only time you have to spend energy, in principle, is when preparing the computation and when measuring -- the computation itself could run for years and no energy would be necessary (if the system is sufficiently isolated from the environment). In contrast, with "normal" irreversible computation, every time you irreversible flip a bit (e.g., when you apply an AND gate) you must spend energy.
[1] in the "quantum world", that's very easy to see: if you set things up so that the computation evolves with a time-independent Hamiltonian, the energy is necessarily conserved.
Slashdot Mirror
That seems great, but then to validate against the schema you must have a full JavaScript interpreter (or almost full, depending on how much you're willing to restrict what can be used in the isValid function). Not to mention that, this being JavaScript, a lot of schemas would end up being a mess, which would defeat half of the purpose of a schema -- being a human-readable documentation of the data format.
Schema validation is a very clear example of a situation where it's not good to have a Turing-complete language. There is a proposal for a JSON schema language (where schemas are themselves JSON documents). Apparently there's not much interest, though.
I've heard this before, and I have trouble understanding how this would change anything.
That is: if your brain is so broken that you can't help but do [unacceptable thing], then you're not fit to live in society, just like an insane person. The concept of "insanity defense" already exists but doesn't invalidate the basic principle of responsibility.
Yeah. His wife did it for him.
It's almost like creating a theory that revolutionizes physics requires more math than what a non-math-genius physicist is comfortable with.
If a flunked math student can discover a theory of relativity [...]
I hope you're not referring to Einstein, because he never flunked math. See http://physics.about.com/b/2007/09/19/physics-myth-month-einstein-failed-mathematics.htm and http://www.time.com/time/specials/packages/article/0,28804,1936731_1936743_1936758,00.html.
In fact, Einstein absolutely needed math to make the theory of Relativity.
Also, calm down :)
Oh, I'm so dumb... I thought you were talking about my comment (it seemed the kind of mistake I'd make).
Thank you; I wish I could edit my comment. As you might have noticed, english is not my first language :)
OK, let's try to understand the point of the essay, since reading the title is not enough. At the beginning of the conclusion, he wrote:
If you stop reading there, you might get the impression he's advocating breaking proprietary licenses. But if you keep reading, you see that, immediately after that (in the same paragraph!), he wrote:
Is it too hard to see that he's not saying that you should help your neighbor by violating proprietary licenses, but instead that you should not use proprietary software in the first place?
Stallman clearly says that if your neighbor asks your for a software that you use, it would be wrong not to give it to him, under the 'help your neighbor' pretext.
Yes, he does, but you missed the point. That's his reason for never using proprietary software: if you do, you're put in the position where you must either do the wrong thing and deny helping your neighbor, or do the wrong thing and break the license of the proprietary software.
Since we're linking to comments from Reddit: people also found out that this solution was known since at least 1860, and was published in a modern journal in as recently as 1977.
It's great that a 16 year old discovered this, and it could have been a cute (but not as flashy) story. But the reporter didn't even bother to talk to someone familiar with the field.
I just have a feeling something else is really going on.
A lot of people seem to feel that way. If was even common among physicists in the beginnings of Quantum Mechanics (Einstein -- among many others -- was never satisfied with the theory, and tried without success to find something better).
I'm not sure myself, but it seems that when you begin to understand the math, you realize that it's actually very simple at the bottom -- the same very basic rules predict and explain so many wildly different things we can measure -- interference (the wave-particle duality stuff), the uncertainty principle, entanglement, quantum tunneling, etc. -- that it seems unlikely that there's some simpler explanation that will fit everything as well as Quantum Mechanics.
But one can never be sure :)
No, see the intermediate states in the step-by-step walkthrough of quantum teleportation in Wikipedia. Immediately after the first peer (called "Alice" in Wikipedia) does the measurement, the destination qubit (called "Bob's qubit" in Wikipedia) is in one of 4 the states described after the paragraph that begins with "Notice all we have done so far (...)". The state of Bob's qubit is represented to the right of the tensor product sign (the circle with the cross inside, for those not familiar with this notation). The states are completely different -- in fact some of them are orthogonal (the first is orthogonal to the last and the second is orthogonal to the third; that's easy to see because alpha*beta-alpha*beta=0).
What this means is that, if Bob doesn't use Alice's result to perform the right measurement in his qubit, he might as well have a random qubit. That's not surprising, since entanglement can't be used to transmit information. It's only with the information from Alice's measurement that Bob can select the right measurement to perform in his qubit to put it in the desired state (i.e., the state "teleported" from Alice's initial qubit).
[ouch -- overly long comment ahead... I wonder if anyone will read it :( ]
I have also never seen a good popular explanation of entanglement: either they go full weirdo saying things like "instantaneous something" or don't really explain entanglement, like your example about numbers in a hat. The problem is, to understand exactly what physicists understand by "quantum entanglement", you first must understand measurement, and in particular, that you can choose many different ways to measure each particle from the entangled pair. If you're willing to spend some time, I recommend the excellent series of lectures starting in this video. The material is pretty self-contained, except some matrix algebra and complex numbers. The lectures are given by Leonard Susskind, a famous physicist.
Now, if you just want to understand why entanglement is different then your "numbers in a hat" example, I'll try to explain as simply as I can with a simple example (which has the basic idea of Bell's inequalities and their violation, you can search wikipedia if you like).
OK, consider a "game" with these elements:
The game is played by Alice and Bob collaborating to win -- either they both win or they both lose. To play, they can discuss their strategy, after learning the rules which I'm about to explain. But once the game starts, they can't talk anymore (i.e., no information can pass between them).
The rules of the game are as follows: when the game starts, Alice and Bob are given the numbers from the hat (ha and hb), then flip their coins (ca and cb) and write in their papers (pa and pb). They win if the resulting numbers satisfy the following equation:
pa XOR pb = ca * cb
and lose otherwise. Here, XOR is the usual XOR operation on bits, and "*" is the usual multiplication. Remember that all numbers in the equation (pa, pb, ca, cb) are either "0" or "1"). Also note that the numbers from the hat are not used to determine if they win or lose, but they can use the hat numbers to write their answers, according to whatever strategy they decided.
Now, note that if they both always write "0" in their papers, ignoring the hat completely, they win 75% of the time, because 0 XOR 0 = 0, and ca*cb will only be different than 0 if both coins are 1, which happens only 25% of the time. It's not too hard to prove (mathematically) that if their coins are indeed completely fair, any strategy they use will give them at most 75% of chance to win, it's impossible to do better without cheating.
So far, nothing involves anything quantum, and there's no entanglement. What I described is called a "Bell inequality" (win probability <= 75%), you can look up Wikipedia for a mu
It's actually worse than that. You could send the photons ahead of time (i.e., you could stock photons and use them to perform teleportation whenever you need it), but teleportation is still not "instantaneous".
The problem is that, to perform the teleportation, you must first measure the source, and then send the result of the measurement to the destination (that's just 2 bits of classical information). Given this information, the person in the destination chooses one of four measurements to perform in the corresponding destination photon, and then the teleportation is complete. Wikipedia has a more detailed explanation, including the measurements performed.
That's not really true. The real motive is explained in this other comment.
That said, I think that what you mean is (and this is true): to perform quantum teleportation, you still need a classical channel. But the reason for the satellites in this case is not that: the satellite is being used to send entangled photons (i.e., it's a quantum channel). The classical information could have been sent in any other way (over the Internet, for example), but to send entangled photons, there must be no measurements of the photon along the way.
SSH doesn't use SSL, it has its own transport layer protocol (which is described in RFC 4253).
(To confuse things a bit, OpenSSH does use OpenSSL, but only the cryptography functions. The SSL part of OpenSSL is completely untouched by OpenSSH).
This result shows nothing wrong with relativity or quantum theory.
Neutrinos have so little mass (less than 0.28 eV, compared to, for example, about 510000 eV for the electron and about 940000000 eV for the proton) that they're expected be found traveling *very* close to the speed of light. This experiment is simply not precise enough to detect the difference between the speed of the neutrinos and the speed of light.
It's great to study, understand and use Feynman's path integral, especially since it leads to new insights about the nature of Quantum Mechanics (plus, seeing the familiar face of the principle of least action in the quantum world is just awesome). But it seems counter-productive to limit yourself to it. For example, some problems that are relatively simple to solve using the "usual" methods (i.e., thinking about waves and using the Schrodinger equation) can become intractable math nightmares with Feynman's path integral. I'm sure there are problems for which the reverse is true, too.
Most people who work with QM seem to take a very pragmatic approach when dealing with problems outside the foundations of QM: use whatever works for you for the problem at hand. Peter Shor (the guy who invented the quantum algorithm to factor numbers in polynomial time) once wrote:
Interpretations of quantum mechanics, unlike Gods, are not jealous, and thus it is safe to believe in more than one at the same time. So if the many-worlds interpretation makes it easier to think about the research you’re doing in April, and the Copenhagen interpretation makes it easier to think about the research you’re doing in June, the Copenhagen interpretation is not going to smite you for praying to the many-worlds interpretation.
(Source)
And I agree that people should read QED: it's very easy to read, and it's great.
This discussion is mixing two different things: the decimal expansion of irrational numbers and infinite random sequences.
I won't argue about random sequences, but Hatta is right about irrational numbers in general (an pi in particular). It's perfectly possible (as far as we know today) that the decimal expansion of pi does not contain, for example, any "1"s after the n-th digit (for some n).
Considering that pi represented as a decimal number is infinitely long, it would eventually contain the encoding for every song in existence.
Actually, that does not necessarily follow.
It's not known whether pi contains every finite-length sequence in its decimal expansion (although most people believe it to be true). In fact, our knowledge is even worse than that (from Wikipedia):
It is for instance unknown whether sqrt(2), pi, ln(2) or e is normal (but all of them are strongly conjectured to be normal, because of some empirical evidence). It is not even known whether all digits occur infinitely often in the decimal expansions of those constants.
Here's some more discussion about that: http://math.stackexchange.com/questions/96632/do-the-digits-of-pi-contain-every-possible-finite-length-digit-sequence
Sure, precognition ("beyond our current, assumed capabilities", as you said) may not be completely ruled out in our current understanding of the universe, I'm not disputing that.
My whole point, again, is that determinism doesn't have all that much to do with that.
I showed limits (under the currently known laws of physics) on precognition even under a completely deterministic universe (note that it's even possible, and even likely, that precognition is completely ruled out under determinism, we just don't know yet).
Conversely, it might be the case that limited precognition ("beyond our current, assumed capabilities") is allowed even if there is indeterminism in the universe. That is: it might be the case that for some types of phenomena, indeterminism (of the kind we know might exist according to quantum mechanics) could never affect the future of a system -- and so precognition is not ruled out even if the universe is not deterministic.
And yes, "as we know them", insofar as it's ever valid to claim as an absolute what "we know".
Well, I'm assuming what "we know", so my arguments might be invalidated if what we know changes. But if we don't base the discussion in what we know, then anything might be possible (it might be possible that precognition has nothing to do with determinism, who could tell?)
The point is that determinism is not a free pass for precognition: even assuming that the laws of physics are deterministic, unrestricted precognition violates at least one pretty basic law of physics (i.e., there exists at least one -- "arbitrary" -- phenomenon that violates a law).
Another way to understand this is to realize that Laplace's demon can't be implemented in the real world, with the laws of physics as we know them.
Indeed, things like precognition overtly violate so very many physical laws...
Not really, if you posit those physical laws are deterministic.
I don't think that's quite enough. You have to remember that the person with precognition must him/herself work under the laws of physics.
Under this reasoning -- disregarding any computational requirements -- for a person to have precognition over arbitrary phenomena (and not just phenomena under his/her complete control), he/she must have access to information about anything that could influence this phenomena. Further, this information must be acquired in a finite amount of time, that is, before the phenomena happens. This means that the person must be able to either:
Our current understanding of physics says that (A) violates the Bekenstein bound and (B) violates special relativity.
You do realize Non-locality of Mind has already been proven, right?
No, it hasn't, despite what one or a few physicists might be saying.
First of all, some interpretations of Quantum Mechanics don't even accept non-locality (e.g., many-worlds).
Second, and more importantly, most interpretations don't attribute any special role to the mind. The "mind" doesn't even appear in the description of the most accepted interpretations, from Copenhagen to many-worlds to Bohm's to consistent histories.
Perhaps you are thinking of this in a purely theoretical sense. In that case then yes, if you can harvest 100% of the energy stored when changing a value, then no additional energy is required.
That's the whole point of IBM's experiment and Landauer's principle: even in a purely theoretical sense, if you erase information when you're changing the state of a bit, you necessarily spend a minimum amount of energy. You can't, even theoretically, harvest 100% of the energy back. I was showing that there are other useful ways to change the state of a bit (e.g. in reversible computing) that do not incur in this purely theoretical energy cost, where you could theoretically harvest 100% of the energy back.
Sure. But the whole point is that the *computation* itself doesn't need to spend energy[1]. The only time you have to spend energy, in principle, is when preparing the computation and when measuring -- the computation itself could run for years and no energy would be necessary (if the system is sufficiently isolated from the environment). In contrast, with "normal" irreversible computation, every time you irreversible flip a bit (e.g., when you apply an AND gate) you must spend energy.
[1] in the "quantum world", that's very easy to see: if you set things up so that the computation evolves with a time-independent Hamiltonian, the energy is necessarily conserved.