On 9/15/2012 4:11 AM, Russell Standish wrote:

On Sat, Sep 15, 2012 at 02:55:17AM -0400, Stephen P. King wrote:Dear Bruno,Could you elaborate on what your definition of "a digital machine" is?Anything Turing emulable.Dear Bruno, OK. But you do understand that this assumes an unnecessary restrictive definition of computation. I define computation as "any transformation of information" and Information is defined as "the difference between a pair that makes a difference to a third".

Hi Russell,

That is far too inclusive a definition of computation.

`Not really, it only requires some way of representing the`

`information such that it can be transformed. The integers are not the`

`only kind of number that we can represent numbers (or any other`

`mathematical object) with. IMHO, we are naive to think that Nature is`

`hobbled to only use integers to perform her Computations. We must never`

`project our deficiencies on Nature.`

A map from i in N to the ith decimal place of Chaitin's number Omega would satisfy you definition of transformation of information, yet the posession of such an "algorithm" would render oneself omniscient.

`That is exactly my point! I am forcing the issue of the implication`

`of Universal Turing Machines, they are implicitly omniscient unless they`

`are restricted in some way. Turing et al, considered the case of`

`computations via NxN -> N functions but abstracted away the resource`

`requirements and we get very smart people, like Bruno, taking this as to`

`means that we can completely ignore the possibility of actually`

`implementing a computation and not jsut reasoning about some abstract`

`object in our minds. The Ultrafinitists and Intuitionist (like Normal`

`Wildberger <http://en.wikipedia.org/wiki/Rational_trigonometry> for`

`instance) have a valid critique but forget that they too are fallible`

`and project their limitations on Nature. I am trying very hard to to do`

`that!`

You can answer any question posable in a formal language by means of running this algorithm for the correct decimal place. See Li and Vitanyi, page 218 for a discussion, or the reference they give: Bennett & Gardiner, (1979) Scientific American, 241, 20-34.

`Sure, but you are missing the point that I am trying to make.`

`Unless there is at least the possibility in principle for a given`

`computation to be implemented somehow, even if it is in the form of some`

`pattern of chalk marks on a board or pattern of neurons firing in a`

`brain, there is no "reality" to a abstraction such as a Universal Turing`

`Machine. I am arguing against Immaterialism (and Materialism!) of any`

`kind and for a dual aspect monism (like that which David Chalmers`

`discusses and argues for in his book <http://consc.net/book/tcm.html>).`

-- Onward! Stephen http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.