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 <[email protected]<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. >
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 [email protected]<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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
