The following message verges on science fiction, but I just can't help myself.
A few days ago, I read an article in the October, 1995 Scientific American called "Quantum-Mechanical Computers" by Seth Lloyd. The author describes the construction of a quantum mechanical computer which makes use of the Heisenburg uncertainty principle to solve difficult problems in combinatorial mathematics--a super fast factoring algorithm, for example. The quantum computer would use particle energy state/positions to encode information. I can't pretend to understand all the details yet, but if this really works is could be the scientific breakthrough of the century, IMHO.
A day or so later I read Brian's post on psychoacoustics, and was struck by the idea that the brain might be a quantum mechanical computer. This would explain many anomalies about how such an apparently slow system could consistently outperform silicon which seemingly operates hundreds or thousands of times faster. It could also mean that far from a simple on/off coding for each neuron, that each exchange of an ion between two neurons could encode a multibit packet of information.
If you've read this far, remember that I tried to warn you.
Marion
Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 30 Sep 1995 17:21 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id IAA11855; Sat, 30 Sep 1995 08:21:12 -0700 Date: Sat, 30 Sep 1995 08:21:12 -0700 Message-Id: <9509300820.aa01733@cyber.cyber.net> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu
Marion says: > It seems to me that for any finite number of integers, there are an infinity > of generating functions.
To the contrary. As I said a generating function does NOT have the numbers of the sequence as a result. It depends on the numbers. It is similar to the Z-transform. The generating function is unique, for a finite or infinite number of integers. Of course a function can be notated in an infinite number of ways but that doesn't alter the function.
Manuel Op de Coul coul@ezh.nl
Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 26 Jul 1996 19:18 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id KAA01817; Fri, 26 Jul 1996 10:18:53 -0700 Date: Fri, 26 Jul 1996 10:18:53 -0700 Message-Id: <1.5.4b12.32.19950726170952.0067fc38@interlinx.qc.ca> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu