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1 INTRODUCTION

The extraordinary achievements and acceleration of

science (and therefore technology) began essentially in

the 17th century with the introduction of the

mathematical-empirical method by I. Newton. The

extremely rapid development of science was caused by

methodological self-limitation: philosophical

questions of "why" were no longer asked; scientists

were only interested in "how" (with mathematical

description). This self-limitation is imperceptible if we

are far from the borders of science (I mean engineering

sciences). The development of science has led to the

creation of extremely powerful tools that approximate

reality, which have been called "artificial intelligence".

The AI tool can be used in applications close to the

classical borders of technical sciences. For this reason,

it seems worth considering the basics of this field of

science, especially since its application may affect

safety. One application of artificial intelligence may be

the introduction and improvement of autonomous

shipping. However, the safety of navigation depends

on the accuracy of the predictions – approximations of

the adopted mathematical model. The analysed

phenomena should be simplified as much as possible,

but in such a way that the resulting models give correct

predictions of experimental results. A scientist or

engineer should be aware of the limitations and scope

of application of a given model. Modelling of processes

and physical phenomena is so common in engineering

practice that it is often unnoticeable. Fully realizing

that the most accurate model is not a physical reality -

it has its limitations - is extremely important when

analysing various engineering issues. The comparison

of a photo of a real ship under construction (Fig. 1) with

its exact model for calculating the global vibrations of

the hull and superstructure of the ship (Fig. 2) shows

the fundamental differences between a physical object

and its model. In many cases, the complete

computation process from modelling a physical object

Autonomous Navigation Safety in the Light

of the Limitations of Necessary AI-based Predictions

L. Murawski

Gdynia Maritime University, Gdynia, Poland

ABSTRACT: The development of science has led to the creation of powerful tools that approximate reality, which

have been called "artificial intelligence". One application of AI may be the introduction and improvement of

autonomous shipping. The safety of navigation depends on the accuracy of the predictions – approximations of

the adopted mathematical model. This paper presents the basic threats related to the approximation used by AI

and the lack of distinction between interpolation and extrapolation. Selected barriers in modelling physical objects

related to the basic assumptions of our science, which commonly uses infinities and continuity of mathematical

functions, were also considered. The extensiveness of necessary, further research that should be conducted was

signalled, the aim of which should be to precisely identify the limitations of the extremely powerful and useful

tool that is artificial intelligence. The safety of the processes (e.g. autonomous shipping) to which it will be applied

depends on this.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 19

Number 3

September 2025

DOI: 10.12716/1001.19.03.11

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through a mathematical model to numerical

calculations is not fully understood. At each stage of

this process we introduce some approximations –

inaccuracies; even when we use a tool for

approximation that has been (rather unfortunately)

called artificial intelligence (the first computers were

called electronic brains).

Figure 1. Container ship with a capacity of 2000 TEU [1]

Figure 2. FEM model of a container ship with a capacity of

2000 TEU based on Patran-Nastran software [1]

This paper presents the basic threats related to the

approximation used by AI and the lack of distinction

between interpolation and extrapolation (especially in

dynamic and nonlinear processes). Selected barriers in

modelling physical objects related to the basic

assumptions of our science, which commonly uses

infinities (e.g. infinitesimal numbers – differential

calculus) and continuity of mathematical functions,

were also considered. The limitations of the extremely

powerful and useful tool that is artificial intelligence

should be identified. The safety of the processes to

which it will be applied depends on this; our area of

interest is autonomous shipping.

2 CRITICISM IN SCIENTIFIC RESEARCH

METHODS

Criticism is necessary to break the existing scientific

certainties - constant questions about the basics of

science (or "only" about the basics of one, analysed

issue). Leibniz's question is still open: "why is there

something rather than nothing?". Why does physics

(mechanics) exist and why can it be described with

such simple mathematical formulas (why is the world

mathematical)? In physics, the principle of least action

is a fundamental law of nature. In engineering and

technical sciences, a similar principle should be apply,

but mainly for methodological reasons. The analysed

phenomena should be simplified as much as possible.

Only humans can creatively determine the scope of

applicability of a given theory, its limitations, and its

expected errors. For example, the vast majority of

engineering analyses are based on a model of the world

in which the earth is motionless and flat (!). Because in

most cases we do not take into account the forces

associated with the movement of the earth (sun,

galaxy, local galactic cluster...) such as gyroscopic or

centrifugal forces. The assumption of earth flatness

results from the assumption of parallel forces of gravity

of individual parts of the body, while determining its

centre of gravity. It can be said with some exaggeration

that the Copernican revolution did not reach

engineering. It is definitely a correct (optimal)

approach (simplification) but the engineer cannot

forget that he uses only the model of reality, which has

its limitations - the scope of applicability.

Mathematical - empirical research method is the

inseparable whole [2, 3]. It is not possible to separate

individual parts from it, we can only talk about the

mathematical and empirical aspect of a given method

with some simplification. The mathematical aspect

seems to be connected with our mental cognition,

while the measuring aspect with our sensual cognition.

However, it is a simplification, because there are

numerous correlations between both aspects. After all,

in the simplest measurement (e.g. the diameter of a

shaft with the use of a caliper) it is necessary to process

it mentally. There is a common belief among engineers,

which is well expressed by the travesty of Albert

Einstein's saying: “No one believes in calculations

except the person who made it, everyone believes in

measurements except the person who made it”. In the

light of the analysis of the methodology of modern

science this belief should be verified. Not only

computational analyses are burdened with a number

of errors, but also measurement research is not free of

them. What is more, if we have a wrong theory

(hypothesis), the experiment will "search" for

quantities that do not exist.... and will often find them

(if we don't approach it critically enough). Limited

trust (criticism) should be the basis of every engineer's

work, but not artificial intelligence. In all types of

research, it should be remembered that the quality of a

given mathematical model is not an absolute quantity.

It depends on the purpose for which the model is to be

used. For example, a crankshaft model for calculating

torsional vibration is useless for assessing its strength.

3 APPROXIMATIONS IN ENGINEERING

In the light of modern research, the physical world is

non-linear and dynamic in states far from being

balanced. However, most engineering problems are

linearly modelled as static or quasi-static phenomena.

This approach is useful and optimal, but the limitations

of such models must not be forgotten. One way to

avoid thick modelling errors in dynamic and/or non-

linear phenomena by linear systems is to use a

sentence: “Extrapolation should be prohibited in

engineering research, only interpolation is allowed”.

This is certainly way too much simplification.

Nevertheless, it is worth remembering it in order to use

the extrapolation of the obtained results (especially the

measurement results) with great caution (e.g. unusual

maritime events during autonomous navigation).

Let us assume that we are researching a certain

physical phenomenon about which we do not have too

strong theoretical foundations (the mathematical

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model is poorly developed). But according to Einstein's

saying, a good measurement should be enough to

recognize the problem. Let us additionally assume that

we are able to carry out measurement tests with a very

small, almost negligible measurement error. Let's

assume that vibrations of a given object are a problem.

So we carry out a series of measurements of amplitudes

(displacements, velocities or accelerations) of

vibrations as a function of the forces frequency. The

results of such measurements are marked with red

stars in Fig. 3 (all further simulations were performed

in Matlab). In order to predict the behaviour of the

object for the frequency of excitation different from the

measurement (it is impossible to carry out

measurements for all frequencies, because it is

impossible to carry out infinite number of

measurements) it is necessary to introduce some

mathematical model. If we are interested in the

response of the structure to extortion with a frequency

within the measured area (1-7 Hz), then the simplest

mathematical model is to use interpolation of the

measurement results. It can be observed that even the

simplest linear interpolation gives predictions with

acceptable errors in relation to the "real" behaviour of

the object (black colour - an exact mathematical model).

The higher the degree of the interpolation curve, the

lower the error rate. Despite this, it should be

emphasized that even carrying out "error-free"

measurements gives results with a certain dispersion.

Figure 3. Interpolation of measurement data

If we believe uncritically in measurements, we can

say that as a result of conducting extremely accurate

empirical research we know everything about the

dynamic behavior of the object. Let us assume that we

are interested in the behavior of the object for the

frequency of forces outside the measurement range: for

10 and 15 Hz. Wanting to rely only on "reality" - on

measurements (without the mathematical part of the

method) we use extrapolation of results of empirical

tests. Fig. 4 shows the extrapolation with different

methods against the background of the behavior of the

object resulting from the commonly known

mathematical model. The resonance curve (continuous

black color) is a well-known phenomenon, well known

on the basis of the mathematical-empirical method. It

can be observed that in case of correct interpolation of

measurement results (within the measurement range)

the errors should not exceed 10%. As a result of

extrapolation, in our example, the errors significantly

exceed even 1000%. At 10 Hz the vibration amplitude

is about 10 mm/s (black line), and the extrapolation

results in values of 2-4 mm/s. However, at 15 Hz the

vibration amplitude is about 1 mm/s, and from

extrapolation we obtain values of the order of 3-13

mm/s. The result of such a measurement (without the

mathematical part of the method) is useless. Moreover,

the error rate is not correlated with the degree of

extrapolation polynomial - a higher degree of

polynomial does not necessarily lead to smaller errors.

This may be the justification for saying that

extrapolation is not allowed for an engineer. It cannot

be assumed that the measured values give us an

absolute truth about the phenomenon. Already at the

level of "pure" empirical measurements some

mathematical model of the phenomenon is necessary.

An engineer must be aware of the fact that he always

uses a given mathematical model, and that each of

them has its own assumptions - limitations. An

example of the lack of common and sufficient

knowledge of the mathematical-empirical method is

the use of genetic algorithms in the so-called artificial

intelligence. From the fact that genetic algorithms to

some extent (rather less than more!) reflect the

evolution and behaviour of the human mind, many

people draw a conclusion about their perfection.

However, these algorithms are a bit more advanced

way of interpolation (acceptable) and extrapolation

(acceptable with great caution) of measurement data.

Figure 4. Extrapolation of measurement data

On the basis of the previous considerations it could

be concluded that if we avoid extrapolation, empirical

research will have an advantage over mathematical

modelling of reality. So it is enough only to extend the

measuring range? Fig. 5 shows the measurement

research in the range of the resonance curve we are

interested in. It was assumed that the measurement

studies are still carried out with extraordinary

accuracy, which makes it possible to ignore

measurement errors. If the resonance curve (marked

with an axial line) describes the torsional vibrations of

the ship's power transmission system, we must be

aware of the fact that most often the continuous

operation of the system in the resonance is

unacceptable (the range of closed revolutions) due to

the strength of the power transmission system. During

measurements the researcher may be subjected to

pressure from engineers - exploiters to leave the

resonance area as soon as possible (limiting the number

of measurement points). For this reason, the number of

measurement points (red stars) shown in Fig. 5 is

realistic. It can be observed that interpolations with

polynomials do not work very well in this type of

physical phenomena. Very often linear interpolation is

used (connection of individual measurement points

with straight lines) - red lines in Fig. 5. Interpolation

with more precise curves (e.g. spline) will not give

much more information. The frequency of occurrence

of vibration resonance will be determined on the basis

of measurements, as equal to 9.5 Hz. While in "reality"

(in the mathematical model) is 10 Hz. The error of very

accurate measurements in this case is 5%. This error

rate is significant when determining the natural

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vibration frequency. The frequency of resonant

vibrations determined by interpolation of

measurements with polynomials and spline lines gives

more accurate results in the case under consideration,

but it is rather a matter of chance. The error rate is not

possible to estimate without the knowledge of physics

of the phenomenon, i.e. the mathematical model.

Figure 5. Measurement data and their interpretation

4 CONFIDENCE LEVEL IN MEASUREMENTS

Until now, unavoidable measurement errors have not

been taken into account. In the case under

consideration, both the natural frequency (abscissa

axis) and the amplitude of the vibrations (ordinate axis)

are determined with some error. For this reason, the

confidence level of measurement studies (used for AI

decision-making, e.g. in autonomous shipping) is

limited. Usually, the vibration frequency is determined

with greater accuracy than the vibration amplitude, as

shown in Fig. 6. From a basic mathematics course it is

known that three points are enough to uniquely

determine a quadratic curve. For the analysis, three

points (the first, fifth and sixth point) of the

measurements presented in Fig. 5 were used, with

additional accepted measurement errors. These errors

were taking at a relatively high level in order to better

illustrate the problem. The measuring points were

connected by a second degree polynomial. The first,

red and continuous curve was determined for the

measurement points without taking into account

measurement errors. Subsequent curves (green, point

and blue, intermittent) were determined for the same

measurement points with randomly selected deviation

values. It can be observed that in engineering practice

(in which it cannot be assumed that there are no

measurement errors) to determine the second degree

curve realistically it is necessary to know at least four

measurement points (!). In the case under

consideration, the measurement of vibration

amplitudes for frequencies of about 5 Hz would define

much more unambiguously the approximation curve

of measurement quantities.

Figure 6. Approximation of research including measurement

errors

After introducing to the research the values of

measurement errors presented in Fig. 5, we obtain a set

of measurement points presented in red in Fig. 7.

Subsequent interpolations made with the use of the

spline function are presented in different colors. The

violet line represents the interpolation with zero

measurement errors, while the green and blue curves

were created for the same measurement points, but

with randomly selected errors. Despite the large

number of measurement points, a large dispersion of

curves can be observed - the results of measurements

in which "everyone believes, except for the measuring

person". Moreover, all these curves are outlying from

the reality (especially around resonance) represented

by the mathematical model as shown in Fig. 7 by the

axial line. Moreover, the measurements may "reveal"

some characteristics of the tested object, which are not

really there! For example, when analysing the blue line

that interpolates the measurement research, we can see

four resonance frequencies. Despite the fact that we

know that we are analysing a system with one degree

of freedom! This phenomenon occurs despite the fact

that all measurement points lie exactly on the

considered resonance curve. In the considered

examples, some phenomena have been consciously

overestimated for teaching purposes, but all the

described errors appear in the measurement practice.

Figure 7. Results of resonance curve research including

measurement errors

5 INFINITIES AS A BARRIERS IN MODELING

PHYSICAL OBJECTS ON THE EXAMPLE OF

PREDICTING THE POSITION OF THE

CRANKSHAFT CRANKS

In our mind, the world is modeled (i.e. approximated,

very often in a linear way) by numbers (mathematical

method), which by their nature are infinite and

continuous. We operate with functions that are almost

universally applied to engineering as continuous

functions. The vast majority of real numbers (infinitely

many times more) have infinite long expansions in the

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decimal system of number writing. In practice, it is

impossible to use infinity (in any sense). For an

engineer to say that an object is 4 m long is not the same

as to say that it is 4.00 m long. The first information says

that the object is between 3.5 m and 4.4 m long, and the

second information gives the information that the

object is 3.995-4.004 long. The accuracy of both

information can of course be developed theoretically

infinitely. This fact, often not realized by an engineer,

has its deep consequences. Even in the nineteenth

century it was assumed that if the laws governing the

world are deterministic, everything (!) is determined

(the problem of free will of man). If we know these laws

and initial conditions, we can determine the state of a

given object, at any past or future moment, with any

accuracy. It is the so-called Laplace's postulate [4, 5]:

"An intellect which at a certain moment would know

all forces that set nature in motion, and all positions of

all items of which nature is composed, if this intellect

were also vast enough to submit these data to analysis,

it would embrace in a single formula the movements of

the greatest bodies of the universe and those of the

tiniest atom; for such an intellect nothing would be

uncertain and the future just like the past would be

present before its eyes..." This reasoning assumes by

default the possibility to determine the initial

conditions in an infinitely precise manner (infinite

expansion of the numbers determining the initial

conditions).

The starting point for Albert Einstein's

revolutionary theory was a statement about the

finiteness of the speed of light (in a simplified way).

The consequences of this simple assumption were

extremely rich (special theory of relativity). Also in the

theory of quantums we find limitations concerning

infinitely small quantities or infinitely precise

determination of physical parameters. Under the

pressure of experimental data, contemporary physics,

both the theory of quantum and the theory of relativity,

resigns from infinity [6]. The smallest and the biggest

sizes of the universe are finite. But for the human the

size of the universe and the smallness of elementary

particles exceeds the capabilities of its mind. The world

in which man lives is suspended between two practical

infinites. Einstein joked: "Two things are infinite: the

universe and human stupidity; but I'm not sure about

the universe." Many years of engineering practice,

along with philosophical considerations, led the author

to make the hypothesis that: “In the physical world,

infinity does not exist in any form”. Which does not

contradict the thesis that mathematics with its infinity

is extremely useful. But it serves only/until to model

the world - an approximate representation of its

structure and phenomena. There are many types of

infinity. Examples of types of infinity, important from

the point of view of modelling in mechanics, are:

− infinity of time

− limitlessness of space

− continuity

− infinite divisibility

− infinite speed

− infinity in mathematics (infinitely small and large

numbers, continuity, real numbers and their infinite

development, the concept of functions, etc.)

An interesting example is the infinity of the

expansion of real numbers, the consequences of which

are presented below – crankshaft position analysis. The

whole differential (and therefore integral) calculation

also contains infinity - infinitesimally small quantities,

e.g.: t →0. It is known from quantum physics that

time cannot approach zero infinitely. Therefore the

differential calculus is only a rough approximation. It

means that a model of reality to be used with some

caution. An attempt at infinitely precise determination

of the state of the elementary particle (e.g. momentum

and position) encountered the resistance of the basic

nature. Mathematics is now the language of physics

and all sciences. In mathematics, most of the basic

functions can be illustrated by graphs with a curve line

or a set of points (one argument corresponds to one and

only one value of the curve). And yet both a point and

a line contain infinity (infinitely small size or infinitely

small width or continuity). In the physical world, one

argument corresponds to one value, but with a certain

dispersion - the error level. Drawing the function

should be done by means of a line of finite thickness.

What is more, if the argument of the function is time,

and this cannot be infinitely small, then the function

consists of individual points (fuzzy and not infinitely

small) and not a continuous line. Physical space-time is

then distinguishable only with a certain

approximation.

Let us consider the movement of a simple

mechanical object: the rotation of the engine

crankshaft. In the case under consideration, it is the

crankshaft of a 10-cylinder ship's slow-speed engine:

10K98 from MAN B&W. Its FEM model is shown in

Fig. 8. We are interested in the position of a given crank

shaft (Fig. 9) at any time.

Figure 8. Crankshaft of 10-cylinder marine low-speed engine

Figure 9. Position of crankshaft crank

The crankshaft crank are evenly distributed; the

ignition sequence determines the order of the relative

rotation of the throws. In a 10-cylinder engine, the

throws are spaced every 36 degree. We assume that the

shaft speed, which is constant, is known with infinite

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accuracy. Also, time is in the first assumption infinitely

determinable. In this case, the relative position of the

crank is determined by a fully deterministic

relationship: the speed multiplied by time gives the

angle of rotation of the shaft. In order to know the

position of a given throw at any time, we still need to

know the initial conditions: the angle  (Fig. 9) at the

t=0 moment. Let us assume, that the initial position of

the crankshaft was determined extremely precisely:

0=36.001°. Such a record means that the initial angle of

rotation of the throw has been determined to an

accuracy of ±0.001°. The actual angular position may be

=36.00149...° or =36.00050...°. The initial angular

position of the shaft can be written in a form:

0=36.001nnnnn...°. Where "n" stands for an unknown

number. After ten ignitions (in each cylinder) the throw

will rotate by 10x36°, it is enough to multiply the

number 0 by ten. In the decimal system it is reduced

to moving the point one position to the right. As a

result of this operation we will obtain:

10=360.01nnnnn...° = 0.01nnnnn...°. The precise

knowledge of the throw position is still high (±0,01°)

but has decreased tenfold! After a thousand ignitions

our knowledge of the crankpin position is reduced to

±1° because: 1000=36001.nnnnn...° = 1.nnnnn...°.

It can be observed that after 10 thousand ignitions

the accuracy of the crank position drops to the value of

±100°, i.e. in practice it is unknown (theoretically a

completely undetermined position occurs after 100

thousand ignitions). It should be stressed that having

ideally deterministic dependencies (with infinitely

accurate parameters of time and rotational speed) we

are not able to determine the searched value after a

sufficient number of cycles of work. If the rotational

speed of the considered engine is n=100 rpm, then for a

10-cylinder engine 100 thousand ignitions will occur

after 10 thousand revolutions, i.e. after 100 minutes.

After about an hour and a half it is impossible to

determine the position of the crank despite the

determination of its initial conditions with a

remarkable accuracy of 0.001. In practice, the situation

of the researcher is even more difficult, because the

engine speed can be determined only with a finite

accuracy, and what is more, the assumption of a

constant speed is also a certain (often coarse)

approximation. Only the error of time determination

can be ignored in engineering practice, because of the

possibility of obtaining a very high accuracy of its

determination.

In order to graphically illustrate the described

phenomenon, a simple procedure of crankshaft crank

position calculation was performed. It was assumed

that the starting throw position, equal to 10°, is

determined with the accuracy of ±0.01°. The next

position is obtained by multiplying the previous

angular position by 10 (due to the ease of operation in

the decimal system) - the subsequent cycles of work are

a tenfold increase in the angle describing the throw

position. Of course, the results obtained above 360° are

reduced to the range of 0-360°. As already shown in the

previous paragraph, each new cycle is a tenfold

reduction in the accuracy of the throw position

determination. The subsequent numerical values of the

angular positions are calculated deterministically, but

their final values have a random scattering equal to the

accuracy of the position determination for the given

calculation cycle. For example, in the second

calculation cycle we have the angular position 100°

with the dispersion of ±0.1°; so for further calculations

the number 99.9° or e.g. the number 100.05° can be

used. Fig. 10 shows an exemplary (due to randomness,

each subsequent calculation will give a different

course) course of changes in the position of throw of

the crankshaft. In order to make the drawing easier to

read, the crank position (navy blue line) is given for

every tenth calculation cycle, while the size of the

position error (red line) is given for every hundredth

calculation cycle. It can be observed that after 2,000

cycles the error rate covers the entire 0-360° range. This

means that the throw position is undetermined.

Figure 10. Position of the crank and its dispersion in

subsequent calculation cycles

The sensitivity of the system to initial conditions is

shown in Fig. 11. The position of the throw of a shaft of

the crankshaft for three starting values has been

calculated. The initial throw position was determined

as 10.00° (continuous blue line), 9.99° (dotted green

line) and 10.01° (dotted brown line). It should be noted

that all lines start from practically the same point, while

the course of throw position changes is random and

drastically different for each initial condition. For

example, for cycle no. 1801 the throw can be deflected

from the vertical by 56° or 286° (for 0=9,99°)) or 114°

(for 0=10,01°).

Figure 11. Sensitivity to the determination of the crank

position to initial conditions

The determination of the throw of a shaft position

with any finite accuracy will not permit the

determination of its angular position after a sufficiently

long time. It should be noted that the above examples

have been prepared for the simplest way of modeling -

linear models. In case of the occurrence of non-

linearities (e.g. geometrical, material), describing

physical phenomena becomes very complicated. In the

descriptions there are bifurcations (jumping change of

properties of a mathematical model with a small

change of its parameters), which lead to the formation

of completely different families of solutions passing

through bifurcation points. The whole of these

phenomena is defined by the term deterministic chaos

[7]. Generally, hypersensitivity to initial conditions

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leads to deterministic chaos, and as it has been shown

it is impossible to determine initial conditions with

infinite accuracy. The difficulty or even impossibility of

predicting the weather forecast for a longer period of

time is caused by deterministic chaos; and in this case

the use of increasingly powerful computers will not

help us. An engineer must remember that despite the

deterministic (expressed in strict mathematical

formulas) laws of nature, the researched and "tamed"

world is not fully determined; many phenomena can

be determined only with a certain (deterministic!)

probability. The non-linear, dynamic world in states far

from equilibrium must, however, be characterized by a

certain order of complexity - a certain self-

organization. In the most complex systems, certain

quantities must be measurable. Otherwise, the

existence of strict sciences would be impossible. It

should be remembered that not always and not all

phenomena can be modelled linearly. The most

complex phenomena are dealt with by such branches

of physics as the theory of dynamic systems,

deterministic chaos or nonlinear thermodynamics.

6 CONCLUSIONS

The aim of this paper is not to systematically present

all measurement errors, confidence levels and/or all

limitations of AI-based predictions. The target is to

make the reader aware of the fact that an engineer

(scientist) operates only a model of reality constructed

with the mathematical-empirical method, in which one

should always be critical (to have a limited level of

trust). The mathematical-empirical method has two, in

principle inseparable members. Both measurements

and calculations can be a source of significant errors

with incomplete understanding of the phenomenon

and errors made during its modelling.

The limitations of our predictions (both empirical

and theoretical) are also evidenced by Gödel's proven

theorem, which was a shock to the 20th century

scientific community. These are basically several

interlinked statements, the most important of which for

our considerations are the non-conflictability claim and

the inconclusive claim. In a simplification, it can be

summarized as follows: "If the system (rich at least like

arithmetic) is complete, it is contradictory, and if it is

not contradictory, it is incomplete". The world

described by physics (mechanics) is certainly richer

than arithmetic. So any model of the world will be

incomplete. An engineer must be aware that not

everything knows. Never, in any even the most

complicated model, we describe the entire physical

phenomena. The aim of further research on

autonomous shipping should precisely identify the

limitations of the extremely powerful and useful tool

that is artificial intelligence. The safety of the processes

to which it will be applied depends on this.

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Technologii Eksploatacji Wydawnictwo Naukowe, 2020.

[2] M. Heller, Filozofia i Wszechświat. TAiWPN Universitas,

2006.

[3] M. Heller, Fizyka Ruchu i Czasoprzestrzeni.

Wydawnictwo Naukowe PWN, 1993.

[4] R. Kotowski, P. Tronczyk, Modelowanie i Symulacje

Komputerowe. Wydawnictwo Uniwersytetu Kazimierza

Wielkiego, 2009.

[5] V. Mityushev, Computer Modeling and Simulations. Crc

Pr Inc, 2024.

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