Simulation: digital vs analogue
in [Theory]
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From: Tim Tyler on 26 Jan 2008 15:10 ``We should keep in mind as well that you digital computing can be functionally equivalent to analog computing - that is we can perform any of the functions of a hybrid digital-analog network with an all digital computer. The reverse is not true: we can't simulate all of the functions of the digital computer with an analogue one.'' - The Singularity is Near, Ray Kurzweil, page 130 What?!? Both can do universal computation - and so can simulate any other type of system with an arbitrary degree of precision. -- __________ |im |yler http://timtyler.org/ tim(a)tt1lock.org Remove lock to reply.
From: A.G.McDowell on 27 Jan 2008 01:08 In article <DsMmj.283013$S37.84001(a)fe3.news.blueyonder.co.uk>, Tim Tyler <seemysig(a)cyberspace.org> writes >``We should keep in mind as well that you digital computing > can be functionally equivalent to analog computing - that > is we can perform any of the functions of a hybrid > digital-analog network with an all digital computer. > The reverse is not true: we can't simulate all of the > functions of the digital computer with an analogue one.'' > > - The Singularity is Near, Ray Kurzweil, page 130 > >What?!? > >Both can do universal computation - and so can simulate >any other type of system with an arbitrary degree of >precision. Quantum computing is being investigated precisely because it cannot be simulated efficiently with traditional digital computers, so, quoted out of context, Kurzweil appears to be 180 degrees wrong. But if his context identifies analog computing with consensus models of neurones he may be practically correct; very few people believe that neurones are exploiting quantum computing, and they appear to be suffer too much from noise and general irreproducibility to make it practical to use them as building blocks for general purpose digital computing. While there are theoretical schemes for building reliable digital computers from unreliable components, in practice the cost is high and the payoff low. Systems faced with this problem (e.g. satellite electronics, which face radiation-induced errors) tend to put a lot of effort into physical hardening to stop the problem at source, leaving them with fairly simple dual redundancy schemes for the main computer, backed up with a core of hardwired electronics sufficient to reboot and reload the computer under orders from the ground if necessary. Even where dual redundancy is used, some very small part of the control logic usually remains a single point of failure. -- A.G.McDowell
From: Tim Tyler on 27 Jan 2008 05:32 A.G.McDowell wrote: > In article <DsMmj.283013$S37.84001(a)fe3.news.blueyonder.co.uk>, Tim Tyler >> ``We should keep in mind as well that you digital computing >> can be functionally equivalent to analog computing - that >> is we can perform any of the functions of a hybrid >> digital-analog network with an all digital computer. >> The reverse is not true: we can't simulate all of the >> functions of the digital computer with an analogue one.'' >> >> - The Singularity is Near, Ray Kurzweil, page 130 Oops - I mean page 149. >> What?!? >> >> Both can do universal computation - and so can simulate >> any other type of system with an arbitrary degree of >> precision. > Quantum computing is being investigated precisely because it cannot be > simulated efficiently with traditional digital computers, so, quoted out > of context, Kurzweil appears to be 180 degrees wrong. Quantum computing doesn't seem to crop up in the context - and even that can be simulated on ordinary digital computers, just rather slowly. > But if his context identifies analog computing with consensus models of > neurones he may be practically correct; very few people believe that > neurones are exploiting quantum computing, and they appear to be suffer > too much from noise and general irreproducibility to make it practical > to use them as building blocks for general purpose digital computing. He doesn't mention efficiency. He says it's impossible: ``we can't simulate all of the functions of the digital computer with an analogue one.'' I reckon the most parsimonious explanation is a bad day, and a lack of proof reading. > While there are theoretical schemes for building reliable digital > computers from unreliable components, in practice the cost is high and > the payoff low. Systems faced with this problem (e.g. satellite > electronics, which face radiation-induced errors) tend to put a lot of > effort into physical hardening to stop the problem at source, leaving > them with fairly simple dual redundancy schemes for the main computer, > backed up with a core of hardwired electronics sufficient to reboot and > reload the computer under orders from the ground if necessary. IMO, the prevalance of hardware error correction doesn't mean it's a good engineering solution. Indeed, I rate it as an engineering roadblock - since self-assembled nano-scale computing crystals *will* have simple non-error correcting units which are vulnerable to noise, cosmic rays, etc - so low-level software engineers will *need* to get to grips with dealing with systems with unreliable components - and at the moment, they are being lulled into thinking that this is a problem for the hardware guys. -- __________ |im |yler http://timtyler.org/ tim(a)tt1lock.org Remove lock to reply.
From: Chris F Clark on 27 Jan 2008 09:57 A.G.McDowell wrote: >> While there are theoretical schemes for building reliable digital >> computers from unreliable components, in practice the cost is high and >> the payoff low. Systems faced with this problem (e.g. satellite >> electronics, which face radiation-induced errors) tend to put a lot of >> effort into physical hardening to stop the problem at source, leaving >> them with fairly simple dual redundancy schemes for the main computer, >> backed up with a core of hardwired electronics sufficient to reboot and >> reload the computer under orders from the ground if necessary. I can't talk to Kurzweil's point, but we are already facing unreliable digital hardware. Intel already keeps track of soft-error rates (circuits that compute the wrong answer occasionally due to radiation etc.) in how their chips work and minimizes its impact on the actual functioning of the chip to maintain the illusion of a deterministic digital computer. It is, however, an illusion, not just in exotic environments either, in your desktop, laptop, pda, and cell phone. Moore's law with its attendant shrinking of transitors is only going to make the problem continue to get worse.
From: Paul E. Black on 28 Jan 2008 13:25
On Saturday 26 January 2008 15:10, Tim Tyler wrote: > ``We should keep in mind as well that you digital computing > can be functionally equivalent to analog computing - that > is we can perform any of the functions of a hybrid > digital-analog network with an all digital computer. > The reverse is not true: we can't simulate all of the > functions of the digital computer with an analogue one.'' > > - The Singularity is Near, Ray Kurzweil, page 130 > > What?!? > > Both can do universal computation - and so can simulate > any other type of system with an arbitrary degree of > precision. True analog computation doesn't have an arbitrary degree of precision. A slide rule is an analog computer which can multiply two numbers. It is limited to three, maybe four significant figures. A digital computer are routinely programmed to multiply number thousands of digits long, for example in encryption schemes. Even a rigid slide rule the size of the galaxy with atomic resolution could only manage about 35 digits of accuracy. -paul- |