# Re: Rationals vs Reals in Comp

```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:
> >
> > >
> > > "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
>
> 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
> ----------------------------------------------------------------------------
>
>

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