On Sat, Sep 16, 2017 at 12:44:20PM +1200, Lawrence D'Oliveiro wrote:
On Sat, 16 Sep 2017 12:04:27 +1200, Michael Cree wrote:
On Fri, Sep 15, 2017 at 10:34:14PM +1200, Lawrence D'Oliveiro wrote:
The essence of analog computing is that physical quantities are represented by physical quantities.
Huh? I'm not sure what you are trying to say here as what you state is just a tautology.
It’s the difference between analog and digital computers: in an analog computer, a scalar physical quantity in the model being solved is represented by a scalar physical quantity in the machine.
Oh, that's what you meant.
In a digital computer, each scalar physical quantity in the machine is just a digit of a number (hence “digital”);
And is only true of the abstract idealisation (the digital model). But in a real implementation (the machine) each physical quantity is represented by an electric potential, a scalar physical quantity. (I hear you say that there is only two values of the electric potential used but that is most certainly not true of real computers.)
Thus, physical limitations in the construction of digital machines don’t constrain the accuracy with which we can do calculations, only their speed;
Only in some limited regime; ultimately the fact the underlying architecture of a modern digital computer is analogue takes over and limits both accuracy (as logic highs are confused with logic lows) and speed (as it takes time for the electric potential to continuously propagate from a logic low to a logic high and vice versa). Pack more transistors into the same space on an IC and the heat generated will lead to thermal fluctuations which leads to a loss of accuracy in calculation even at the same speed. Also the EM coupling between signals increases again leading to a degradation of signal integrity, which appears as a loss of accuracy (i.e. incorrect calculation or processing). These are major problems in implementing dense high-speed digital systems. I think that when you characterise traditional computer architecture as "digital" you judge it by the model and ignore the failings of the machine, and when you characterise quantum computers as "analogue" you judge it by the failings of the machine but ignore the model. Cheers Michael.