From Future to Past and Back


Both RNA and DNA strands are linear structures with each base having two neighbors, except the first and the last that are with one neighbor. In some earlier papers there is a proposition/algorithm how to convert these linear  structures into 2D. The idea was to use the three position sequence(codon) as one parameter and four bases as the another that led to the 3×4 matrix, as the smallest 2D structure within which it would be possible to place a sequence of twelve positions(Fig.1). Within this matrix there are four elements with two neighbors, six elements with three neighbors and two elements with four neighbors.(Fig.2)



There are various ways to place this kind of linear structure into 3×4 matrix out of which the two seems to be the simplest. One, in which a sequence is placed inside the matrix as unbreakable linear structure in a snake like manner. Here the continual line  will go in opposite directions in the neighboring horizontal sequences and the vertical distance between the bases will vary from 1, 3 to 6.(Fig.3a) Another possibility would be to cut the sequence in four segments of three positions(codon) and place them one below another. Here the vertical distance between neighboring bases will be 3, the same for all the bases(Fig.3b). In further analysis we will adopt this second method as it was done in my previous papers.



There are two ways to organize a longer sequence within 3×4 matrix. One     is static in which first 12 positions are placed in one box, next 12 in another box, and so on. The question that emerges here is how to organize these matrices into a larger structure. And there are a few possibilities, including introduction of Cartesian coordinates, that will be presented in the Appendex 2 at the end of this paper.(Fig.4)



Another possibility would be to have a linear “frame” of 12 positions that moves along the sequence, one base at the time. Something similar to a film camera moving horizontally from left to right. Here it is 1D frame  that is converted into 3×4 matrices where each of the matrices would be like one film frame.(Fig.5).



These matrices will be organized in a film like  linear structure thus enabling introduction of the notions change/time. In this kind of translation of a linear sequence into a series of images, in each frame the first (upper left)base is leaving the frame in the next step, while simultaneously a new base is entering the picture in the low right corner. After moving the frame through 12 positions all the bases from the first (initial) image will leave the picture(Fig.6).



In order to observe how bases are moving through a picture representing the present we will divide the 3×4 matrix in four horizontal lines(codons): 1, 2, 3 and 4, and in three vertical lines: I, II and III.(Fig.7). Vertical line I in which is the position(1, I) from where a base always leaves the picture we will name the past, while the line III in which is the position(12, III) where a base enters the picture we will call the future, while the line in the middle(II) will be the present. One way to interpret the entire picture is that it represents the Present in a broader sense with past, present and future sections as its components. In other words each picture generated in this way represents an instance of the Present.



As the frame is moving one base at the time, it is interesting to observe how each move is changing the configuration within the picture. While the first base is leaving the picture, the last base in the position 12 is moving to the position 11 and the new base enters the picture on the position 12. Meanwhile the entire vertical line II(present) moves to the line I(past) while the line III(future) move to the center(II) and becomes new present. Finally, the three lower levels of the past line(I) moves to the upper section of the new future, as if some parts of the past will come back as(from) the future. What makes this interpretation a bit unusual is not that future becomes present and present becomes the past, but that a section from the past will move to the future and from there comes back to the present. A simple process like an interval(linear frame) moving along a linear sequence one position at the time, becomes a complex process within a pictures represented by 3×4 matrices. It is not the entire past that goes back to the future, since each time one its base leaves the frame, and it doesn’t cover the entire future since one new base always enters the picture in the position(12) that belongs to the future vertical. As if part of the past is being remembered and as a kind of memory appears from the future. Since each of the vertical sections have four parts/stages, then each base will  move three times from the past to the future and back to the past section before finally moving out of the picture.At this point it is hard to tell to what degree, if at all, this interpretation reflects some actual phenomena characteristic for life in general, like: what is/are the picture(s) of the “world” encoded and thus remembered by the living matter?

These images might be the most rudimentary ways how the early life forms have perceived its environment, interpreted and memorized it, in order to increase their chances to survive.


Gregor Mobius                                                                   August 28, 2019



Appendix 1







Appendix 2











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