Semiotics and Prerogative

Given signs and their denotations, a language represents relations between signs and also perhaps between signs and niches of the real world.

Gödel has proven that any fixed formal system is incomplete.  A successful formal system requires an organic nexus to assess and introduce new signs.

————— —————— ——

Victoria University of Wellington has successfully proven the failure of the Victorian headless system.

Rugby

Given the nature of quantum mechanics, how does a puny geek seal a point?

How would one prevent the impossible?

Purely positive republics.      15 July 2009

The Chaotic Pendulum

Matter, coming in discrete quantities, in certain configurations, can demonstrate ‘chaotic’ behaviour, such as in the undergraduate physics experiment of the chaotic pendulum. There are no fractions of a molecule.

cp :: Prime a => a -> a -> [Integer]
-- x y relatively prime sufficient
cp x y
| y > x = cp' x y [y-x]
| otherwise = cp' y x [x-y]

cp' x y zs@(z:_)
| z > x = cp' x y ((z-x):zs)
| otherwise = cp' x y ((z+y-x):zs)


Intelligent Design

The recent fad of ‘intelligent design,’ a dressed up rehash of the creationist fallacy, is nothing but a curse on the developing and evolving world of post-enlightenment man. Through logical, energetic, and social arguments, I shall attempt to convince that I personally do not hold intelligent design one shred of respect.

Cooperation and the Golden Ratio

A little book that I have published, Learning and Behaviour, has provided an example of another lesson to be learned at educational institutions, namely, one should read the references.

I have attempted to enlist the aid of a renowned expert on Evolution and Game Theory, Martin Nowak, at the Program for Evolutionary Dynamics at Harvard University.

The Semantic Universe

Through deed, word, then thought, entities can establish communication. No matter what words are used, there is a difference between the letter and the spirit.

Though we all have but one life, our children may work towards keeping us in their existence.

In the spirit of openness, the attached proposal is here to sketch a concept, however, the implementation requires dedication and time.  The bona in fidele agreement of course would allow academic competition, but for any party to either acquire the source illegally or illicitly, or to use the document in a manner that would result in loss of income to OM Consulting Limited is, de natura, fidele in non bona.

Korero

[Addendum 25 05 2009]

After having been recommended to UBS NZ Limited by UBS AG in Basel, I, as Executive Director of OM Consulting Limited, approached their office in Auckland.  A month after not receiving a reply to my mail I went to their office, where the receptionist informed me that the proposal had been looked at and they would probably not be interested.

Alas, I shall have to establish the company in New York or Edinburgh.  Hopefully UBS AG has an office in Scotland or the willingness to appoint someone to run the company from Scotland or New York.  Unfortunately, with the standard of language and care in the United States Armed Services [read friendly fire incidents] I am currently unable to hire anyone not in the RNZAF or RAF.

Perfect Fair Subsequences

Definition [The Naturals]

Given the λ-calculus [Church] and Haskell [www.haskell.org],

data Zero = Zero
data One = ZeroSucc Zero
data Nat = One One
              | Succ Nat

The Naturals () are clearly merely the Nat.

Theorem [Perfect Fair Subsequences]

Suppose the completeness of the Reals and their construction via Cauchy sequences.
Let be a Cauchy sequence in .
has a subsequence such that .

Proof

.

Now, let be the sequence such that and
.

By construction, is such a subsequence.

Theorem [Perfect Fair Rational Subsequences]

Suppose the existence of the rationals. Every real sequence has a perfect fair rational subsequence.

Theorem [Constructive Rational Calculus]

There exists a constructive rational calculus of infinitessimals.

Thus allowing for discrete space quantum algebra.

Exercise

Consider the natural (or prime) number indexes of such sequences.

Analytic Signals and Synchrony

The Hilbert Transform, , of a real-valued signal, , can be used to generate an analytic signal, .

where , the impulse response of a Hilbert Filter and is the convolution operator.