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Design+ Modern interpretations of probability

different physical natures show that the hypothesis of ideal giving it the role of a measure of our ignorance regarding a
statistical stability is not confirmed. Statistical estimates phenomenon, event, process, and case at a given moment
formed on relatively small intervals of observations of time of their manifestation.
have relative stability, that is, with an increasing volume Events, phenomena, and the world itself are hyper-
of statistical data, estimate value fluctuations decrease. random. The category “hyper-randomness” parameterizes
However, starting from some critical volume, with the “past” as a forerunner, a precursor of the future, but
increasing quantitative data, the fluctuations practically with a share of hyper-randomness. The past and the future
do not change, and sometimes increase. The violation of are linked by the phenomenon of “probability,” or, more
statistical stability in the real world means that the concept precisely, “hyper-probability.” It is these categories that,
of probability has no physical interpretation.
in a general sense, determine predictions for the future
Probability is a mathematical abstraction. The causes of in any sphere of science or human existence. If we know
violation of statistical stability can originate from various the past reliably, with what degree of probability (hyper-
processes, for example, the inflow into an open system probability) is it possible to predict the future?
from external “substance,” energy, and information, which By the concept of “past,” we understand a continuum
feed unsteady processes.
of events, each of which had its past, present, and future,
The study of violations of statistical stability and the hence the continuum character of the category “past” itself,
search for effective means of an adequate description of real its discreteness, and, at the same time, continuity. Each
phenomena of the surrounding world, taking into account event of this continuum, probable for its past, is in some
these violations, led to the creation of a new physical and regular and probabilistic way transformed into the present.
mathematical theory of hyper-random phenomena by the We should understand it as an animated (or animated)
Ukrainian scientist Igor Illich Gorban. 9-11 concrete realization out of a set of unrealized possible
It is possible to describe hyper-random phenomena variants about which nothing will ever be known in the
using the triad (Ω, Ψ, ϔ, and P). Ω is the space of present or, even more so, in the future.
elementary phenomena, ω ϵ Ω, Ψ is the Borel field, ϔ is Thus, each event, the phenomenon of modernity, is the
the set of conditions g ϵ ϔ, and P is a probability measure result of choice from a real set of their possible variants
g
of subsets of events that depend on conditions g. in the past, and each of the latter, in turn, is “chosen”
A hyper-random event A can be interpreted as an event from another subset of variants of the even deeper past,
whose frequency of occurrence P (A) does not stabilize and so “infinitely” back in time. In other words, each
N
with increasing number of experiments N and has no phenomenon, the event of modernity, is preceded by an
boundary (limit) at N → ∞. In this case, the frequency “infinite” series of its variants that did not come true in the
of events does not have statistical stability. For example, past. It is “it,” one specific one, chosen by-laws, cases, and
if a random variable X is completely characterized by a fate unknown to us, that has reached us.
probability distribution F(x), then a hyper-random variable Hence, the phenomenon of hyper-probability,
X = [X/g ϵ ϔ] is characterized by a set of conditional underlying the existence of the world and its attributes,
distribution functions F (x/g), g ϵ ϔ. explains the fact of our unsatisfactory forecasts, which
The isolation of a new class of random processes, predicted future under stochastic causes of its occurrence
hyper-random variables, allows us to expand the list of (and in separate cases of phenomena, events, and
metrics for practical use significantly and bridges the gap processes, including their individual properties, qualities,
from the formal-mathematical axiomatic interpretation characteristics, and parameters). That is, we do not know
of the concept of probability to the construction of a all the reasons for the event.
new physical and mathematical theory of hyper-random After all, when we flip a coin, we can predict with an
phenomena. According to Gorban, this theory is based on average probability of 50% the appearance of “heads” or
a more general “statistical instability” phenomenon than “tails.” At the same time, we, living in the 21 century,
st
the alternative “statistical stability” phenomenon, which cannot analytically describe the motion of the hand tossing
may be only a partial variant of the former. the coin, taking into account force, speed, mass, distance,
The phenomenon of the hyper-random hypothesis and acceleration, air resistance, and many other things, with
its feature – limited statistical stability – creates the basis sufficient accuracy, which would determine not probable,
for accepting the concept of the world structure on hyper- but deterministic behavior of the coin. Of course, there
random principles. The mentioned limitation emphasizes are reasons for such behavior of the coin, but they are not
the emergent nature of the key concept of probability, known to us now.

Volume 2 Issue 2 (2025) 9 doi: 10.36922/dp.6387