On Monday, April 22, 2013 10:23:04 PM UTC-4, Russell Standish wrote: > > On Mon, Apr 22, 2013 at 08:06:29PM +0200, Telmo Menezes wrote: > > > > > > On 22 avr. 2013, at 19:14, Craig Weinberg <whats...@gmail.com<javascript:>> > wrote: > > > > > A quote from someone on Facebook. Any comments? > > > > > > "Computers can only do computations for rational numbers, not for real > numbers. Every number in a computer is represented as rational. No computer > can represent pi or any other real number... So even when consciousness can > be explained by computations, no computer can actually simulate it." > > > > Of course it can, the same way it represents the letter A, as some > sequence of bits. And it can perform symbolic computations with it. It can > calculate pi/2 + pi/2 = pi and so on. > > > > > > To expand a bit on Telmo's comment, the computer represents pi, e, > sqrt(2) and so on as a set of properties, or algorithms. Computers can > happily compute exactly with any computable number (which are of > measure zero in the reals). They cannot represent nondescribable > numbers, and cannot compute with noncomputable numbers (such as > Chaitin's Omega). > > Also, computers do not compute with rational numbers, they compute > with integers (often of fixed word size, but that restriction can > easily be lifted, at the cost of performance). Rational numbers can > obviously be represented as a pair of integers. What are called "real" > numbers in some computer languages, or more accurately "float" numbers > in other computer languages, are actually integers that have been > mapped in a non-uniform way onto subsets of the real number > line. Their properties are such that they efficiently generate > adequate approximations to continuous mathematical models. There is a > whole branch of mathematics devoted to determining what "adequate" > means in this context. >

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I think there are some clues there as to why computation can never generate awareness. While a computer can approximate the reals to an arbitrary degree of precision, we must delimit that degree programmatically. A machine has no preference about what is adequate, and can compute decimal places for a thousand years without coming any closer to conceiving of the particular significance of pi to circle geometry. I'll paste the next comment from the OP of the first. I think it's interesting that he also has noticed the connection between biological origins in the single cell and non-computability, but he is looking at it from QM perspective. My view is to focus on the single cell origin as a single autopoietic event origin...an event which lasts an entire lifetime. "If you think about your own vision, you can see millions of pixels > constantly, you are aware of the full picture, but a computer can't do > that, the cpu can only know about 32 or 64 pixels, eventually multiplied by > number of kernels, but it see them as single bit's so in reality the can't > be conscious of a full picture, not even of the full color at a single > pixel. > > This is simply a HW problem you can't get around with the current > technology. With Quantum Computing it may be possible to make large models > where all pixels are part of one structure build on entanglement. > > Man comes from a single cell and that means that entanglement could bind > the cells together, icluding our cells dedicated to building the internal > cinema. But it is still not enough to create the necessary understanding of > the picture. > > Gödels theorem states than there are problems that are unsolvable within > the system, that you need something from without the system, and computers > are fully within the system and as man can solve these problems he must > have something from without this system. This understanding you wouldn't > get if you don't use Gödels theorem, so you put fences up and around you > hindering your expansion of your understanding. > > BTW I am a computer scientist educated at Datalogical Institute at the > University of Copenhagen, and have worked with Artificial Intelligence, > Numerical Analysis and Combinatorial Optimization, all ways to bring pseudo > intelligence to computers." Craig > > Cheers > > -- > > ---------------------------------------------------------------------------- > > Prof Russell Standish Phone 0425 253119 (mobile) > Principal, High Performance Coders > Visiting Professor of Mathematics hpc...@hpcoders.com.au<javascript:> > University of New South Wales http://www.hpcoders.com.au > ---------------------------------------------------------------------------- > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out.