3 ms·
That's not true, there are idealizations of ideal analog computers, such as the field computer model of analog computation†. We already have analog computations
by ethn 8y ago
That's not true, there are idealizations of ideal analog computers, such as the field computer model of analog computation†. We already have analog computations using continuous-time digital that can solve 32nd order differential equations in less than a millisecond††. We are also unaware of even the theoretical possibility of computation in QM. The noise and sampling problem hasn't been settled (see Kalai for a convincing argument); given the Quantum Threshold needed it becomes suspect when you have the equivalent of 1,000 CPU's for every individual CPU for just a .1% probability of error.
Given your same line of reasoning, we are able to measure real numbers, in fact you can derive discrete numbers from real numbers while the converse is not true. Intuitively, discrete numbers don't exist and everything ultimately becomes real numbers. This is obviously a correct following of the stimulating rhetoric yet completely untrue. The ability of derivation from an axiom has nothing to do with the validity of the derivative representations.
† https://www.eetimes.com/document.asp?doc_id=1138111 https://www.eetimes.com/document.asp?doc_id=1138111
†† https://ieeexplore.ieee.org/document/7463004/ https://ieeexplore.ieee.org/document/7463004/
- remcob 8y agoMy argument was purely theoretical. I fully agree that analog computers currently have more practically attainable advantages over digital computers. I'm also less confident than most people of quantum computers ever overcoming the practical problems, some of which you mentioned. But I do not doubt that the physics itself offers superior computation, even if we may never access it. > we are able to measure real numbers I disagree with you here. I like to believe in the Church-Turing-Deutsch thesis, which implies that reality is ultimately discrete and real numbers are nonphysical. The example you give, time, is indeed a real number in our best models of physics. But this is mostly because we don't know how to quantize it yet. It's one of the biggest open problems in physics. That said, the outcome could indeed be that it is a real number and CTD is wrong.