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European Journal of Applied Sciences – Vol. 11, No. 3
Publication Date: June 25, 2023
DOI:10.14738/aivp.113.14767.
Doepp, M. (2023). The Secret of the Exponential Function in View of Mankind. European Journal of Applied Sciences, Vol - 11(3).
214-217.
Services for Science and Education – United Kingdom
The Secret of the Exponential Function in View of Mankind
Doepp, Manfred
Holistic Center, 13 Haupt St., Abtwil 9030, Switzerland
ABSTRACT
We have become accustomed to the fact that the economy in the individual
countries and in the world needs continuous growth rates in order to ensure our
prosperity. This is understandable, but mathematically wrong. Because regular
quantitative growth means that exponential growth is created, which must lead to
catastrophe. The exponential function implies that the average quantity must
remain in a dynamic and sustainable equilibrium if disaster is not to occur. Not
affected by this are changes in quality, as they occur in nature. If humanity does not
change its purely quantitative objectives of production and gross social products, it
can be predicted that it will not be able to persist.
Keywords: World economics, interest system, exponential growth, disaster ahead,
capitalism
INTRODUCTION
We humans are used to thinking in linear terms, where past, present and future are linked
linearly. Logarithmic or exponential behavior and corresponding developments obviously
contradict our imagination. However, they are more often present in nature than linearity. For
example, if our sense organs were linear, we would not be able to hear soft sounds, very loud
sounds would overstrain our ears, we would not be able to see in the dark, and lightning would
blind our eyes. This is what we call the Weber-Fechner law. The Weber-Fechner law (1,2) is the
formulation of a psychophysical relationship in sensory physiology and states that a linear
increase in the (psychically) subjectively perceived strength of sensory impressions is equal to
the logarithm of the increase in the (physically) objectively measurable intensity of the
stimulus.
Hereby, Weber's relation - that the difference amount sufficient for a just perceptible difference
of the intensity of stimuli is in a constant relation to the stimulus strength - is extended to
Fechner's relation by the theoretical assumption that, due to the same relative difference
thresholds, a scale of sensation strength is to be defined with respect to the absolute threshold.
This is applicable for different sensory modalities in the range of medium stimulus intensities.
However, there is a sensation threshold and a saturation threshold (4). For medium and high
sound pressures, the perceived loudness does not follow the Weber-Fechner law, but Stevens'
power law (3) with k ≈ 0.6: an increase of the sound pressure by a factor of root of 10 (10 dB)
causes a doubling of the subjective loudness. We have become accustomed to these
relationships without being aware of them. Unfortunately, this unconsciousness leads to the
fact that even in economics we have no idea that the exponential function contains a secret,
namely that it leads to infinity, and this infinity is a disaster (figure 1).
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Doepp, M. (2023). The Secret of the Exponential Function in View of Mankind. European Journal of Applied Sciences, Vol - 11(3). 214-217.
URL: http://dx.doi.org/10.14738/aivp.113.14767.
Fig. 1 : graph of the exponential function y=e^x (red) with the tangent (light blue dashed line)
through the point 0/1 ( linear abscissa and ordinate) (4).
THE INTEREST SYSTEM
Let's take the compound interest system as an example. In Islam, taking interest is forbidden,
possibly a wise decision. The political insight of Aristotle, that the taking of interest destroys a
community in the long run, is explicitly confirmed in the Qur'an (5).
In Islam, interest is considered harmful to society from an economic, social and ethical
perspective. For this reason, Allah, the Exalted, forbids the taking and giving of interest. As
background information, it is useful to know that the holistic approach to life that Islam imposes
on every believer also determines the methods of business and financial activities. The essential
principles of Shariah, the part of Islamic law that establishes practices and activities, dictate
that investors must not engage in transactions that are speculative in nature, involve interest
payments, or contain contractual uncertainties. In addition, all transactions must be secured by
assets.
Islamic Finance consistently takes into account the completely different way of thinking in
Islamic finance. Western capitalism, for example, is based primarily on the profit motive of
individuals who can steadily increase their capital through interest income. Islamic finance is
different: It also recognizes private property, the market and competition, but focuses on the
additional benefits that a certain product creates for the common economy. This understanding
of economics goes back to the Prophet Muhammad, who expressly forbade Arab merchants to
pay or accept interest. This prohibition of interest is recorded in the Qur'an. In the Torah, an
interest rate of 3% is considered acceptable. If you are a customer of a credit card company
today, you will be amazed at interest rates of e.g. 12 to 23% (6). This used to be called usury.
But we are used to it.
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European Journal of Applied Sciences (EJAS) Vol. 11, Issue 3, June-2023
What makes this system exponential? It is the interest on the interest rate. An exponential
process is a process in which a quantity increases exponentially. The increase is proportional
to the currently existing value. Such a system must lead to a catastrophe. This is shown in the
financial system by the fact that crash situations occur at regular intervals. And it is not rare
that weak currencies are terminated because of inflation and replaced by new currencies.
THE WORLD ECONOMY
In the area of currencies, individual countries are affected, which can help and possibly save
themselves by introducing a stronger currency. But what is to be said in the field of
macroeconomics? Here, the dogma of the necessity of an uninterrupted increase of the gross
social product prevails. Remaining the same is called stagnation. An inflation rate of 2% is
targeted and considered normal, as is an increase in production of at least 2%. In China, an
annual growth rate of 6% was considered the minimum. According to the law of the exponential
function, this must lead to a catastrophe.
One could now ask whether one could not orient oneself to nature. Nature knows an
exponential development only in the initial stage, after some time a dynamic equilibrium
develops regularly. Thereby decreases and increases are approximately equal. This equilibrium
is only minimally unstable, it is very adaptable and stable in the long term. Even after natural
catastrophes such as earthquakes or volcanic eruptions, a new equilibrium emerges after a few
years. This is natural and this is good. It is compatible with a qualitative growth. Why is man
not willing - or able ? - to take this as an example ? Why does man think that a quantitative
growth is necessary ?
OUR SITUATION
A lack of quantitative growth is curiously called zero growth and considered a danger. On the
other hand, if industrial production continues to increase (also as a result of the use of robots,
computers and artificial intelligence), but the sales and consumption of the world population
have reached a limit, this alone will lead to a world economic crisis. The solution so far has been
a war or several wars, which led to a destruction of the prosperity of the people and created a
new demand. This is apparently a law of capitalism, especially of turbo-capitalism.
As a positive example, consider a tree: it grows continuously until it reaches a size
predetermined by its genes. Then the quantitative growth ends and it changes to a qualitative
growth, i.e. an improvement of the foliage and the roots in order to be more resistant to negative
influences. The same is true for the virgin forest: growth and degeneration or loss are in
dynamic equilibrium. Such a system is stable overall. The present economic system of mankind
is not.
CONCLUSION
In contrast to the current reality, the taking of interest was declared problematic and rejected
in ancient cultures. Also the permanent quantitative growth in the economy was considered
unnatural. This is logically quite correct. A permanent growth of the production and of the gross
social product leads, through the law of the exponential function, to a collapse and a disaster
(concretely: to wars). Acceptable and in accordance with nature is only a qualitative growth, i.e.
a replacement of inadequate methods and means by better, more sustainable and more
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Doepp, M. (2023). The Secret of the Exponential Function in View of Mankind. European Journal of Applied Sciences, Vol - 11(3). 214-217.
URL: http://dx.doi.org/10.14738/aivp.113.14767.
advanced products. The quantity and the value of the products remain thereby on an identical
level. This should be strived for in order to spare mankind a catastrophe.
References
1. https://de.wikipedia.org/wiki/Weber-Fechner-Gesetz
2. https://elmer-herzig.de/wp-content/uploads/2012/03/Hoppe-posthum1.pdf
3. https://de.wikipedia.org/wiki/Stevenssche_Potenzfunktion
4. Lisa Lorentzen, Haakon Waadeland: A.2.2 The exponential function. In: Continued Fractions – Convergence
Theory (= Atlantis Studies in Mathematics for Engineering and Science. Vol 1). Atlantis Press, 2008, ISBN
978-94-91216-37-4, ISSN 1875-7642
5. https://zinsfrei.de/islam-zinsen/
6. Own expériences