Proposed Approach

How does one actually verify in a simple experiment that packets do exist: a filtering mind game or a manifestation of order in chaos?

The author believes that the optimum approach to resolution of this fundamental problem consists of studying the correlations between events that are spread out over a period of time. For example, should there be a relationship between successive occurrences on a roulette wheel in a casino? (We are not talking about instances of deception or the underhanded methods used by owners). We all think that there should not be any relationship, because the roulette wheel is a system that cannot remember is previous occurrences. Of course, there was not a professional roulette wheel among the physical systems studied; however, they are all similar to it as far as their operating principle. The author called the physical systems studied RWAs for short – roulette wheel analogs.

We will examine a physical system, exemplified by a roulette wheel, on which we will perform trials. We will assume that a roulette wheel has 10 possible states: 1,2,..9,10. After it is spun, the roulette wheel is in motion and searches through its states, for example: 1,2,3….9,10 (this is the first cycle), then 1,2,3…9,10 again (the second cycle), and so forth until it comes to a full stop. Then moment that it stops, the roulette wheel provides a result, for example, 7. We could not predict the result of this individual trial due to the fact that the available information was insufficient to make such a prediction. However, if we run many trials in a row, we can then make predictions based on the probability theory.

The probability theory does not go into the details of each individual trial, but rather is based on the generalized concept of “probability”. In order to apply this theory to the roulette wheel under consideration, it must be assumed that we are able to bring the roulette wheel to a certain identical initial state the necessary number of times. And, which is especially important to us in the context of the work at hand, it must be assumed that no mechanism exists by means of which the roulette wheel could remember its previous occurrences. Only in this instance can the probability theory be used to describe successive roulette wheel trials.

We will assume that everything has been done correctly and that the roulette wheel actually does not have a memory mechanism. Probability theory techniques can then be used to analyze the successive occurrences of the roulette wheel.

All the classical physical systems studied in the work at hand are similar to a roulette wheel as far as their operating principle; however, differences exist that are important to us. Take, for example, RWA1 (a roulette wheel analog) – this is how we have designated our first “roulette wheel”. These systems operated in the following manner: a simple cyclic program, written in the Qbasic language, was launched and halted by pressing a key on a keyboard.

CLS

DIM nn(100) AS DOUBLE

DIM n(10, 10) AS DOUBLE

CONST True = -1, False = 0

DIM EOJ AS INTEGER, EOC AS INTEGER, i AS INTEGER

DIM IK AS STRING

i = 0

DO WHILE NOT EOJ

LOCATE 3, 1

PRINT "Press a key... "

EOC = False

DO

IF i >= 100 THEN i = 0 ELSE EOC = False

i = i + 1

IF INKEY$ = "" THEN EOC = False ELSE EOC = True

LOOP UNTIL EOC,

LOCATE 1, 1

PRINT i

LOCATE 3, 1

PRINT "SPACE – continue, Esc - escape"

DO

IK = INKEY$

LOOP UNTIL IK <> ""

IF IK = CHR$(27) THEN EOJ = True

LOOP

END

When the program is launched, the i variable begins to search through the values 1,2,3…99,100, 1,2,3…99,100, etc., stopping on each value for roughly 25 microseconds. When the program shuts down, the current i value is displayed on the screen. Thus, there is an important difference from the classical casino roulette wheel, for which the velocity continuously decreases until it equals zero. RWA1 searches through the i values at a constant rate up to a full stop. This is important to us, because it means that when moving at a constant velocity, RWA1 loses information on its past occurrences.

Does this mean that during a given series, RWA1 has no mechanism by means of which the system could remember its previous occurrences? When RWA1 is in motion, information is forgotten, this we already know. The final stage remains – cycle shutdown. We need a way to shut the program down with a fairly large error. That is to say, complex objects must be involved in the shutdown process that increase the uncertainty of the exact moment in time of shutdown.

Intuitively, it’s probably clear what we are talking about; however, let’s formulate a quantitative criterion. Let’s assume that we perform successive RWA1 trials with an approximate frequency of 2 seconds; that is to say, we have a time interval sequence of t(i), with an average value of <t(i)> = 2 seconds (sec). We can compute the magnitude of the standard deviation, Δt, for the t(i) sequence. As we previously stated, RWA1 is stopped manually from a keyboard. The participation of a human hand, as well as a keyboard and all the other “hardware”, makes it possible to achieve quite high Δt standard deviation values, or more precisely, Δt = 0.05 sec.

Thereafter, let’s assume that the RWA performs a single cycle over a time frame of T, called a period. For example, RWA1 runs through the values 1,2,3…99,100 over a time frame of T = 2.5 milliseconds (25 microseconds multiplied by 100). We will now call the ratio of the standard deviation, Δt, to the T period,, , the randomness factor. It is reasonable to assume that information on past occurrences at  cannot be retained during the RWA shutdown process. Why? Because we are in no position to stop a very crude tool, for example, an RWA1 cycle, at a specific value.

In practice, as we see it, there is no need to strive for high randomness factor values. It is sufficient if  equals 2 or 3.

We will now return to RWA1. The computation of the randomness factor yields . Thus, RWA1 can be trusted in the sense that there should be no memory mechanism in RWA1.

All the classical physical systems studied are presented in Table 0-1. The interesting results the author obtained required the verification of different “hardware” in order to give the work a certain legitimacy.

Table 0-1. Classical physical systems studied (they will hereinafter be referred to by the abbreviation RWA – roulette wheel analogs)

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