On Thursday, May 2, 2019 at 10:18:33 AM UTC-5, Bruno Marchal wrote:
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> On 1 May 2019, at 19:58, [email protected] <javascript:> wrote:
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> On Wednesday, May 1, 2019 at 11:30:20 AM UTC-5, Bruno Marchal wrote:
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>> On 1 May 2019, at 10:56, [email protected] wrote:
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>> By "heat" I just mean it as one studies it as a subject in a physics 
>> class, for example.
>> - https://en.wikipedia.org/wiki/Heat
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>> *Does all computation generate heat?*
>>
>> (Should be a simple enough question, I think.)
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>>
>> Hmm… Not that simple. In the 1950s, Hao Wang has given the first proof 
>> that there exist universal machine working in a completely reversible way, 
>> without any erasing of information. Wang was a mathematical logicien, and 
>> his result was ignored. 
>>
>> In 1961, Landauer, a physicist, working on the Maxwell Daemon problem, 
>> discovered that the only computational process that generates heat is the 
>> erasure. To erase 1 bit of information Landauer shows that you need to 
>> dissipate at least kTln(2) energy, with k the Boltzman constant and T the 
>> temperature. 
>>
>> So, in principle, given Hao Wang + Landauer, we can build a machine doing 
>> computation without using, nor dissipating any energy, except for the start 
>> and ending of the computation.
>>
>> Then, most algorithm in quantum computing require full reversibility, and 
>> should work with very few amount of energy, except similarly for the local 
>> read and write, or starting vs stopping behaviour. 
>>
>> Both from mechanism and physics, I conjecture that there is a core 
>> physical reality which is a BCI algebra, which means no erasure of 
>> information, and no duplication of information. This CANNOT be Turing 
>> universal, and it is unclear to me which of erasure and duplication can be 
>> truly physical. It is just well above the scope of the present knowledge of 
>> the machine’s physics to answer this, and among physicians, this leads to 
>> discussion of black hole, non cloning theorem, etc. Open problem for me.
>>
>> Of course, in arithmetic, no computation at all use energy, given that 
>> they use only the arithmetical truth, which are out of time and space, and 
>> any physical category. The physics emerge from this, as an invariant 
>> pattern for all Turing universal observation, defined by a sort of bet on 
>> first person experiences. Energy should be retrieved from that Core 
>> physics. I speculate that the Monster Group plays a role here.
>>
>> Bruno
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>> - @philipthrift
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> In the curious case of quantum computation, it seems it may be the case 
> that there is no heat generated until a "measurement" is made.
>
> Is that right?
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> That is right, unless you are using a special quantum algorithm which does 
> “measurement” during the computation. But if not, then the computation 
> corresponds to a unitary, completely reversible, process, and no heat is 
> generated.
>
> Bruno
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A related question to my original ("Does all computation generate heat?"):

Does consciousness generate heat?

@philipthrift

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