On Infinities



How can the past and future be, when the past no longer is, and the future is not yet? As for the present, if it were always present and never moved on to become the past, it would not be time, but eternity.  St. Augustine

-Infinity exists only as a word, sign/symbol or a notion/concept, but it doesn’t exist as such, since in the time based infinity called eternity(timelessness), nothing could exist. There is no existence “there”.

-If from infinity it is not possible to define a finite state while from the finity it is possible to define (imagine) infinity, then the finity is meta in relation to infinity. In other words, from infinity it is not possible to “see” finity, while from the finite state we could “see” infinity. Thus, conceptually, finity is meta-infinity.

-It means that infinity “exists” only as a (finite) word or symbol (∞) since there is no phenomenon that could be(have properties of) infinity as such. Any attempt to implement the notion of infinity on the real (physical) world leads to absurd conclusions-aporia(Zeno).  The only meaningful and practical use of notions “infinite large” or “infinite small” seems to be in cases of extremely large or small quantities of a certain property in relation to a referential, thus finite, quantity of the same property.

-Another possibility to represent infinity related notions (infinite large or infinite small) could be values on the gray-scale:  “black” and “white”. Let’s say that value “black” represents infinite large (∞) and value “white” is infinite small (0).  Unlike the numeric or verbal expressions of these notions, this visual one has some interesting properties. Since values “black” and “white” relate to each other as positive-negative it would indicate that these two infinities relates to each other in the same way: infinite large is negative of infinite small, and vice versa. Another interesting relationship is a mixture of equal amounts of “black” and “white” which is a new value – “gray”. “Gray” is not only “half way”  between  “black “ and “white”, but also an interesting property  of “gray” is that its negative is also “gray”.  It seems value “gray” could be interpreted as representation of finity,  and not any finite, but referential finity which verbal expression is “one” and numeric: “1”. However,  other kind of finities, like finite large marked as “x” and finite small as “1/x” relate to each other as positive-negative if represented with corresponding values on the gray scale: x=dark gray and 1/x =light gray.


-An observer is changeable and limited in time and space. There is no infinite or eternal observer. Any kind of infinity would be beyond the reach of the observer since there is no change in the infinity of time called eternity.Eternity is timeless and its synonyms are god and death. God cannot exist since existing is time based phenomenon. Observer is changeable, never remains the same (Heraclitus). For any observer the past is its birth and death is its future.

– All kinds of infinity (infinite large, infinite small, eternity, infinite sets) are conceptual, not actual. They could not exist and for any observer they would be unreachable, at best asymptotically approachable (crossing of parallel lines, Riemann Sphere).

-There is no time-flow unless there is a change. Where there is no change,      there is no time. It is change that could have direction and be irreversible.  That irreversiblity is property of the (referential) observer. There is no unchangeable (timeless or eternal) observer. It seems that this changeability of the observer is projected/reflected on what is being observed (environment, world). Eternity is beyond and out of reach for any observer including human. No observer is eternal. To an observer it appears that world is changing.  It is because the observer is changing.  From the position of change/time it is possible to “see” eternity, but from eternity it is not possible to “see” change/time. We could conclude that time is meta-eternity, or that change is meta-nonchange .  We could “see” both reversible and irreversible change from the position of an (irreversible) observer. But could a reversible observer (if possible) “see” an irreversible process? And what about memory without which there seems cannot be any observer? Memory cannot be reversible although it can be erased or lost(end of observer, death). But there has to be another(referential) observer that would notice/observe this.

-Memory is reflected picture(interpretation) of the surrounding (environment) impressed on living matter. There is no living matter without memory. It is living matter where memory, life, chaos, entropy, death, eternity meets. Entropy is connected with eternity through living matter. Acquiring memory is anti-entropic process while erasing memory (memory loss) is entropy.

-It is in fact memory that gives us the sense of time-flow and not entropy.In order to observe change we have to remember the previous states, and thus recognize the direction of change. It is the nature of memory process that gives a sense of the direction of time and its irreversibility. By moving through orders of magnitude, from a living cell to a water molecule, we are moving from living to non-living matter, from life to death, but also, if going “up” it will be transition from dead to alive. It seems that the state of entropy is not necessarily the final state, like in case of DNA/RNA strands.



According to Gregor Mobius,  first it was some kind of proto-RNA molecule that was both the observer and the memory/picture of the observed/world. Later this role took the coding strand of DNA that in fact became the observer (positive) and template would be its negative, while corresponding RNA, as a picture of the coding DNA strand, would represent what is being observed. Proto-RNA was also a proto-observer. It was a reflection of its environment but was not separated from it. It was DNA that became both the observer and the reflection of the environment and thus enabled establishing the observer that became separated from the environment, thus establishing a binary relationship: observer- observed.

Argos Panopty                                                      New York, October 2018

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