I don't know if it would do any good to repeat the conclusion that
there is no lower geometric limit no more than there is an upper
geometric limit.
> > otherwise the choice is to conclude that the Pi value is
> > periodic.
>
> Pi = circumference/diameter = fixed ratio
>
> What is meant by a periodic value?
Well that is a little more involved and I don't know if you can see
where I am coming from.A Penrose tiling pattern is non-periodic
meaning that it is neither entirely ordered or disordered so that the
arrangement of tiles acts like a geometric form of the non-periodic
arrangement of the decimals in the Pi and Phi proportions,the tiling
patterns reflect a 2d version of what exists in reality as
quasicrystals and their growth -
http://en.wikipedia.org/wiki/Quasicrystal
It does raise the issue of fundamentally defining things such as time
and space which are essentially limitless in extent but with readers
here so wound up with other things,it is difficult for the genuinely
curios and innovative to focus on such things as the background
conditions which allow quasicrystals to grow and many forms,both
animate and inanimate,to tend towards the Phi proportion in matters of
natural efficiency.It does appear to indicate that some type of
electromagnetic background is involved in quasicrystal growth as they
have to follow some prescribed path in maintaining a balance between
periodic and random so that should be tempting for those of an
intuitive temperament who are not too concerned about
definitions,axioms and so on.It is ,of course,a wider issue on how to
approach natural and celestial phenomena but at least there are
historical precepts to go on in cutting loose from the one-size-fits-
all 'scientific method' -
"The reason, therefore, that some intuitive minds are not mathematical
is that they cannot at all turn their attention to the principles of
mathematics. But the reason that mathematicians are not intuitive is
that they do not see what is before them, and that, accustomed to the
exact and plain principles of mathematics, and not reasoning till they
have well inspected and arranged their principles, they are lost in
matters of intuition where the principles do not allow of such
arrangement. They are scarcely seen; they are felt rather than seen;
there is the greatest difficulty in making them felt by those who do
not of themselves perceive them. These principles are so fine and so
numerous that a very delicate and very clear sense is needed to
perceive them, and to judge rightly and justly when they are
perceived, without for the most part being able to demonstrate them in
order as in mathematics, because the principles are not known to us in
the same way, and because it would be an endless matter to undertake
it. We must see the matter at once, at one glance, and not by a
process of reasoning, at least to a certain degree. And thus it is
rare that mathematicians are intuitive and that men of intuition are
mathematicians, because mathematicians wish to treat matters of
intuition mathematically and make themselves ridiculous, wishing to
begin with definitions and then with axioms, which is not the way to
proceed in this kind of reasoning." Pascal
> >Start off with a Planck length as a diameter and you should
> > draw the only possible conclusion that such an entity has as much
> > relevance as determining a meter is the smallest length possible.
>
> > > Since:
>
> > > All succeeding Wavelengths, Phi, circumference, Fibonacci numbers,
> > > Science has claimed to be Integers (No fractions) of Planck units.
>
> > Both Pi and Phi reflect quasi-periodic decimals in that the sequence
>
> I explained bad:
>
> Phi and Fibonacci numbers in computation demonstrate that succeeding
> Wavelength's are integers(meaning multiples) of preceding
> wavelengths.
>
The Phi proportion which reflects relationships between geometry and
sequential mathematics exists as a tempting mystery to those who
encounter it in natural at whatever level and there are numerous
excellent websites expressing its prevalence,in short,it is fun.
>
>
>
>
>
>
> > of numbers are neither ordered nor disordered but finely balanced
> > between the two.There is an incredible amount of information contained
> > in quasi-periodicity and not least when there is a hideous perspective
> > floating out there in terms of the 'no center/no circumference'
> > ideologies of 'black hole and big bang'.In short,this really does
> > matter.
>
> > > Therefore:
>
> > > It still seems the smallest Planck Wavelength can also have only one
> > > Planck Amplitude??
I am afraid I do not have so much regard for those men in the early
20th century who tried to set limits where there are really
none,whatever advantage it appears to give a person
mathematically,geometrically it shuts off a different approach that is
infinitely more productive.The rise of geometric anomalies like 'big
bang' and 'black hole' are tied to this issue so while appearing very
simple at first glance,it becomes rapidly complicated with further
investigation.