Thank you very very very much, but that was too much said: it is not
so wonderful, but a better version is being prepared. (01)
The relevance of the the topic of infinity is quite clear to ontology:
It simplifies things a lot if _transfinity_ is identified as a sign
that something is wrong. Especially transfinity, not infinity in all
respects. For example, Relativity implies transfinity at least in the
form of singularities where space is curved transfinitely. This must
be taken solely as a sign that Relativistic equations loose their
applicability after certain limits. This is the view of many great
physicists: (02)
We believe that the initial state of Universe in cosmology’s standard-
and inflatory models, which entails infinite [should say transfinite]
energy, density and temperature, more likely indicates that the theory
is false than the actual physical conditions that prevailed in the
initial state. [1, p.388]: (03)
Cosmologists understand that this infinity [should say transfinity]
indicates a mathematical breakdown and that Einstein’s theory of
gravity has to be replaced by new physical laws. [2, p.52-53]. (04)
...while calculations assuming pointlike particles and gravitons give
nonsensical, infinite [should say transfinite] answers, calculations
for stringy particles and loopy gravitons produce sensible, finite
results. Although not designed for the purpose, string theory appears
to automatically incorporate a theory of quantum gravity without
infinities [should say transfinities]. [2, p.124]. (05)
The reason string theory works where the [point-like] particle
description of quantum field theory fails can be explained by single
geometry. If two pointlike particles collide, their energy is
concentrated at a point. Such pileups of energy cause a large
gravitational field, curving space and drawing even more energy into
the region. A runaway process ensues in which space curls up
irretrievably into a tinier and tinier knot: a singularity. This
catastrophe leads to mathematical infinities [transfinities]
signalling a breakdown of the theory. On the other hand, if particles
are tiny vibrating strings, their energy is spread out. If a collision
causes a momentarily pileup of energy, the string rapidly wriggles
away and spreads out the energy, preventing the gravitational
distortion from concentrating in one spot. Calculations of what
happens when two bits of string collide, join, and break apart again
give sensible, finite results. There are no singularities, and no
infinities [transfinities].” [2, p.125-126]. (06)
These passages testify that the only use of transfinity in physics is
exactly as an indicator that a physical theory does not apply when the
results are transfinite, and that considering it possible to have
something that exists to be of a zero size point-like, drives one into
the transfinities. When it is said that e.g. an infinite gravitational
force is supposed to affect on some point, then the force should be
called transfinite, and not just infinite, since if the force is
infinite and affects a single point as a totality, then the force is
transfinite. Transfinity=infinity as a completed totality. Cantor has
to be credited for defining exactly what _cannot_ be :) Luckily, there
are ways to formally define infinity, in the way that does not produce
anything transfinite. (07)
[1] Brian Greene: Kätketyt Ulottuvuudet. Supersäikeet, ajan halkeamat
ja maailmaselityksen haaste. Tammi, 2000. Translated into Finnish by
Mikko Vänttinen and inspected by Claus Montonen. Originally appeared
as The Elegant Universe. Superstrings, Hidden dimensions, and the
Quest for the Ultimate Theory, Brockmann Inc., 1999. (08)
[2] Paul J. Steinhardt and Neil Turok: Endless Universe. Doubleday, 2007. (09)
-Avril (010)
Lainaus "ravi sharma" <drravisharma@xxxxxxxxx>: (011)
> Paola, Avril
> Here are my observations on this wonderful paper by Avril:
>
>
>
>
>
>
> Brief Comments Dated - Jan 24, 2010 by Ravi Sharma on Wonderful Paper on
> Infinity: published by Avril Styrman.
>
>
>
> Finitist Critique on Transfinity: An Investigation of Infinity, Collection
> Theory and Continuum by Avril Styrman Licentiate of Science Thesis Helsinki
> 23.1.2009
>
>
>http://www.cs.helsinki.fi/u/astyrman/set.pdfhttp://www.cs.helsinki.fi/u/astyrman/set.pdf<http://www.cs.helsinki.fi/u/astyrman/set.pdfhttp:/www.cs.helsinki.fi/u/astyrman/set.pdf>
>
>
>
> Wonderful single source and very praiseworthy publication that covers lot of
> knowledge base – author’s deep understanding of metaphysics, philosophy,
> mathematics and ontology and of course concepts related to INFINITY.
>
>
>
> Some Observations different from those expressed in the paper:
>
>
>
> Largely drawn from Eastern Background and learning that does not regard
> Aristotle as absolute reference but refers to concepts earlier than those
> documented by Aristotle (the Great Western Philosopher of few hundred BC).
>
>
>
> I am doing my best to express these in English.
>
>
>
> Concept of infinite and especially transfinite is only comprehensible by
> mind consciousness which is of course all pervading
> (manas+Buddhi+THAT=INFINITE) meaning that which is beyond but inclusive of
> mind, intellect and THAT (implying beyond connotations).
>
>
>
> Everything physical, such as Universe is, by definition, finite or
> innumerable (Asankhya) and therefore: NOT INFINITE but included in Infinite.
>
>
>
> Infinite (Anantha) includes all i.e. innumerable (transfinite) and finite.
>
>
>
> Even the Concept of Whole Number required by 1+1=2 is rooted in the
> cognition of innumerable asymptotically leading to infinite or at least
> transfinite.
>
>
>
> For mereology, or part of, or set of, please refer to a different way of
> thinking parts of: by referring to Upanishads – especially the concept of
> PURNA = Whole or Complete (approximately translated) – part – taken from
>the
> Complete still remains Complete - exemplifies not only transfinite but
> infinite.
>
>
>
> Some other parts of the paper that deal with ontology are rich and require
> further analysis – more homework for me.
>
>
>
> However one thing to keep in mind – new knowledge about this physical
> universe (really new conceptual knowledge not necessarily the utilitarian
> one) may well come from transfinite areas and examples are
> Tensorial-characteristics of General Relativity, multidimensional symmetry
> and charge spin parity of Quarks and Gluons, and perhaps unified forces and
> dark matter and energy.
>
>
>
> The other knowledge that goes beyond the finite is the knowledge based on
> realization of Consciousness and is called Self-knowledge.
>
>
>
> P.S. Comment: The bibliography does not include origin of concept of
> Infinity and Whole – completeness - these are found in 4-Vedas and about 108
> Major-Upanishads originally spoken and written in Sanskrit but translated at
> various times in past in English (often poorly translated).
>
>
>
> There is still a lot in this wonderful paper that I have to learn and absorb
> that would help us in understanding the basis of Ontology. In the pursuits
> of understanding Infinity, it would be nice to publish a sequel (paper) on
> what additional valuable concepts of relevance to ontology can be found in a
> deeper analysis of Eastern Philosophies and Vedic Mathematics (Arithmetic).
> Thanks Avril
> Ravi
>
>
>
> Paula
>
> - thanks for unearthing the wonderful paper by Avril.
>
> I copied your questions relating to infinity to me under this thread, hope
> you do not mind.
> I still have to address your specific questions given below, as these
> observations were made earlier while reading the paper.
> ______________
> from Paula:
> Ravi
>
> i am not sure what is the official position of science on 'infinity'
>
> Was it Avril working on it? Avril please enlighten us:
>
> If I remember correctly, EMC2 formula ended with an implication that
> resulted in an assertion of infinity,
> that however is not a subject that science has been able to define.neasure
> therefore
> it results at false (go figure) or ignored
>
> (apologies for the trivialization of the paraphrased argument, please
> correct the above if you know how
> it goes)
>
>
> I have seen papers published about the replication of random sets techniques
> and that makes me think (uhm> common sense would suggest it doesnt sound
> right)
>
>
> re, intellectual freedom, maybe it should be 'ontological freedom' for the
> purpose of this forum
>
> I understand that both science and religion try to provide some certainties
> so that people dont too astray in this world,
> but the amount of misinformation that goes around is massive, even in
> universities
>
> PDM
>
> On Sun, Jan 24, 2010 at 12:49 PM, Paola Di Maio
> <paola.dimaio@xxxxxxxxx>wrote:
>
>> Avril
>>
>> I found your paper on Infinity, of which I think you circulated to this
>> list before
>>
>> http://www.cs.helsinki.fi/u/astyrman/set.pdf
>>
>> I dont have the capacity to study in detail, wonder if you could provide a
>> plain english synopsis with your main conclusion for the
>> layperson, and maybe one straight answer from your pov
>>
>> can we say that infinity does not exist because our equations prove
>> otheriwse
>>
>> or
>>
>> could it be that the equation we are trying to measure infinity with is not
>> adequate to the task
>>
>> or...
>>
>>
>> I assume infinity complexity and the measures of randomness are related
>>
>> P
>>
>>
>> P
>>
>> --
>> Paola Di Maio
>> **************************************************
>> “Logic will get you from A to B. Imagination will take you everywhere.”
>> Albert Einstein
>> **************************************************
>>
>>
>>
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>
>
>
> --
> Thanks.
> Ravi
> (Dr. Ravi Sharma)
> 313 204 1740 Mobile
> (012)
--
Always forward towards the supreme maxim of scientific philosophizing (013)
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