NON-CLASSICAL ONTOLOGY. I THINK, THEREFORE THOUGHT EXISTS!

Poluyan Pavel Vadimovich, Director of Neosintez Research Centre, 660049, Krasnoyarsk city, post office box 19589, (391) 212-07-53, e-mail: polyan2002@mail.ru

"I think, therefore I am" - is the phrase by Rene Descartes, which became a foundation of Western philosophy. Moreover, it can be logically followed with: "I think, therefore I am - therefore thought exists". Having admitted this inevitable conclusion we inevitably face the question whether thought existence is the existence we imply speculating of the being of things and processes in the Universe. Yes, that is true. The progress in the sphere of information technology has shown that one cannot deny the objective nature of information processes as well as the objectiveness of information existence as such. It was the global computerization that made us look at the world from a different angle. "What if the whole of the Universe is a single huge superpowerful self-adaptive computer?" There are certain grounds for this kind of hypothesis. Firstly, electromagnetic waves record and transfer information quite naturally. The eye and the brain work together like a scanner, which enables us to see. Secondly, every atom has several discreet states and can be considered as the initial logical element, a cell in a global information structure. Thus, one should admit that we say "Thought exists!" because we realize the fact of its subjective being. Still we trace thought existence because it is the part of objective information reality. As everyone is aware that thought exists in his mind he analogically concludes thought exists in the mind of the other. Now it is high time we admitted that generally this OTHER one is the WHOLE WORLD!
Nevertheless, even if you admit indisputable cogency of all this reasoning, you will remain in the sphere of philosophical metaphysics. To fall outside the limits one needs to find the means of expressing new ontology in the language of universally acknowledged scientific theories. This is what we will attempt to do in the suggested piece of writing.
Russian philosophy of XX century defined and developed the idea of IMYASLAVIE [from Russian  glorifying the name'], vividly expressed in the works of Pavel Florensky and later in the works of Alexey Losev. It is alleged that NAME should be understood not as an assigned notation to the object but as something ontologically rooted. Following this theory the author specified the ontological name's equivalent with the help of mathematical means in his work Financial Quantum and Quantity of Name in the materials of international conference NonStandard Methods and Applications in Mathematics (Italy, University of Pisa, May 25-31, 2006. Abstracts of International Congress - http://www.dm.unipi.it/~nsm2006/abstracts.html)

Can the amount of money be indefinitely small? Supposing one is offered to distribute 100 euros into three equal bank deposits. The quantity of money on each of the three accounts will equal 33,333+ - with a nonterminating trail. Thus, the notion of the infinitesimal helps to determine the exact quantity of money.

However, in reality there exists the limit of decrease. Real amount of money is anyhow a SIGN, the production of which costs money. Just imagine printing a banknote the production of which costs as much as it signifies. Similarly does changing of a single figure in a computer file, showing the amount of money on a bank account, involves certain expenses. Then it should be admitted that the lengthening of the trail of a decimal fraction must be ceased as the bank expenses to introduce the changes will become equivalent to changeable figures. The expenditures referred to the client will not result in the money increase on his account.

The above described situation copies the peculiarities of quantum dimension where the measurement process itself leads to the change in quantitative parameter being measured. In the sphere of money calculus there appear numerical figures summing up of which cannot but lead to the actual money increase.

A hundred years ago Henri Poincare called non-Archimedean geometries which were built by Giuseppe Veronese and David Hilbert strange. Can we assert that people have got used to non-Archimedean property by now? From our point of view non-Archimedean property is understood as non-standard due to the fact that it is traditionally connected with geometric interpretation of quantity viz. with extension. Still the infinitesimal of non-standard kind is naturally discovered in the situation where a new notion serves an object for determination. We suggest calling this notion the QUANTITY OF NAME. In the given example it is vivid that the SIGN can be measured with the measure it denotes. In our opinion what it reflects is not the specific character of money, but common algebraic property of measurable quantities.

What does A=B express? We are saying that two quantities are equal, though they are ascribed different names. In mathematical sense the names seem to be unimportant, playing a service role. Well, it is really true when we speak about equaling the fragmentons situated in different points of space. Discrimination between them is done with the help of coordinates with their literal notation being really unimportant. However, we have a different situation when it comes to equaling the quantities thought to be out of any space either real or abstract one. Then the task is set in a paradoxical way. We must distinguish between the objects of equal quantity, thus the quantity is the only parameter taken into consideration while discriminating.

Discrimination between the objects can be made by putting a mark, which is measured in the same way as the quantity itself. Let's give a simplified example; we can distinguish between two similar weights by marking one of them. But marking one of them will lead to changing its weight. So, the weight of the mark must be negligibly small. This is how we naturally formulate the algebraic conception of the infinitesimal which is not connected with geometric extension. Assuming that NAME will exist only if we can mark infinite aggregate of similar objects in such a way that summing up the quantities of names should not lead to appearance of appreciable difference in objects' quantities. Thus, summing up qualities of names must have non-Archimedean character.

In conclusion let's outline the main points. We have discovered that algebra implicitly gets use of the notion about the names which lets us discriminate between equated quantities. This means that traditional letter symbols are not conventional signs created for making mental operations more convenient but the true expression of a fundamental fact. The congruent quantities do have their own names in reality. Consequently, it is not accidental that a very important part in quantum statistics is played by the notions of equality and discriminability of particles. So signs-names invented by us really have their ontological originals. And the main philosophical conclusion to be made is that we discover the ontological basis for giving names to quantities. Even in the ordinary equation A=B the discrimination between the names appears not through subjective choice of different denominating letters but through the discrimination of the equated quantities to vitally infinitely small share which serves the objective equivalent of subjective notion of NAME. The mark itself, infinitely small compared to the marked quantity, is an ontological original of name. Moving further in this direction we will be able to find the fundamental basis of objective information existence too.

Another side to it is how to understand the existence of information processes within space-time structure. It was described by the author of the work Numbers in Space partially presented in the materials of international scientific conference Quantum Mind 2003, the University of Arizona, Tucson, USA. ("Quantum Mind 2003. Consciousness, Quantum Physics and the Brain". (March 15-19, 2003, The University of Arizona, Tucson. Abstracts - Pavel V. Poluyan, Numbers in Space: Transformation of four-dimensional space-time into quaternion time-space. http://www.quantumbrain.org/Abstract2003.html)
It is possible to coordinate vector's name but not for an isolated point as all three axis of standard Euclidean space are equivalent to each other (x can be renamed to y). The definition of Euclidean space lacks the possibility of discerning between and ascribing names to the axes - the set of three coordinates permit permutation. But it is still possible to create mathematical space when every axis acquires its own immanent NAME and we take imaginary units for measurement.

Let's specify the material coordinate for time and present three spatial coordinates as imaginary i, j and k with time dimension. Then, Minkowsky's four-dimensional pseudo-euclidean continuum will transform into some unusual variety which we shall call "Quaternized time-space".

Here we have a special S coefficient specified with [sec/m] dimension to transfer the spatial coordinates dimension into the one characteristic of time. As a result we have got a usual C constant (speed dimension) which lets us present time in length units in four-dimension space-time continuum and has additional S coefficient. Their multiplication in its turn gives us non-dimensional constant. Quaternized time-space is a logically necessary addition to four-dimensional space-time. As quaternized time-space is  formed' not with geometrical points but with something like micro vectors (dipoles, domains, spins, angular momentums)  it can be presented as REALLY EXISTING mathematical variety with information processes taking place independent from our conscience.

The mathematical construction of  reverse side' of geometrical space was described by Pavel Florenskiy. Many spoke of special space of meanings but mathematician Vasiliy Nalimov tried to outline its contours. Thus, research in the field can be perspective. Yet it has not been well comprehended from philosophical point of view, as this new ontology highlights instead of two substances or two attributes of a substance - duality of space-time varifold. Whether this hypothesis is true will be shown by future development of science and philosophy.

Summing it all up, let us point out that information processes are somehow ingrained in the very basis of the matter. This is already evident at present time. However, scientific realization of the fact requires from us not only the developing of new ontology, but also working out new unusual but functional scientific cognition methods. We suppose that the term  information' denotes a wide range of phenomena which does not yield in its scale to the notion of  energy'. And we are just at the very beginning of our way to cognize this objective constituent of our being.

Poluyan Pavel Vadimovich, Director of Neosintez Research Centre, 660049, Krasnoyarsk city, post office box 19589, (391) 212-07-53, e-mail: polyan2002@mail.ru