> On 1 May 2019, at 10:56, cloudver...@gmail.com wrote:
> 
> 
> 
> 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 <https://en.wikipedia.org/wiki/Heat>
> 
> Does all computation generate heat?
> 
> (Should be a simple enough question, I think.)

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



> 
> - @philipthrift
> 
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