Index
- Extract
- Relativity of the economic concepts, a reflection on the
mathematical logic applied to the economy
- Usefulness of the mathematical abstractions, the infinitesimal
calculus
- Conclusions
1.
Extract
The
mathematical logic is employed to justify some behaviors in the real life; for
example, the mathematical logic is used in economy to demonstrate why it is
necessary a balance between income and spending of the states. That
mathematical premise is employed currently by the European Central Bank and the
International Monetary Fund to maintain its economic policy in Europe.
In
the first part of this work it is demonstrated that the mathematical logic is
not always the right way. In the second part it is developed a concrete example
which prove how the mathematical abstractions sometimes neither can be used
effectively in the real world.
2.
Relativity
of the economic concepts, a reflection on the mathematical logic applied to the
economy
European
countries like Spain, Italy, Portugal, Ireland and Greece suffer severe
economic restrictions that are affecting the life of millions of people. The
cause of those restrictions is the wrong belief that austerity is the right way
that the economies must follow. The desideratum of that belief is that balanced
budgets are the ideal objective for the construction of healthy economies. But
that rational and logic concept is not truth in all the cases. The fiscal and
financial deficit is not always something bad. For a people or for a private
enterprise the lack of financial resources is a sign of weakness or peril of
insolvency but for the governments no. The fiscal and financial deficit of the
states reveals that the economy as a whole is growing and therefore the
resources are insufficient. It
demonstrate also that the private investment is not enough and that it is
necessary the help of the state for assuring the normal economic development of
the countries. The states, the governments, moreover, have an advantage that does
not have the personas neither the private enterprises: the governments have the
sovereign capacity to print money; therefore they can solve their internal
financial necessities printing more money. What the governments cannot do is to
print the money of other countries, in this case, international means of
payment, like the U.S. dollar or the euro. The unique institutions that can
issue U.S. dollars and euro are the U.S. government and the European Central
Bank, respectively. All this is a proof of the economic concepts
relativity: the scarcity of financial resources is not ever something bad, it
depends on who is the actor; if the actor is the public sector the financial
deficit is different than if the actor is a person or a private enterprise.
The
European economic crisis has its origin in the fact that the states members of
the European Union resigned to its sovereign capacity to issue its own national
currencies to create a new common currency, the euro. But now they are trapped
in the hands of the European Central Bank and the International Monetary Fund,
which impose their criteria of austerity. How much time more will resist those
countries the impositions?
The
problem is that some economists have employed mathematics for intending to give
a character of exact science to the economy, but in some cases that pretension
of the economists has generated more damages than benefits, like demonstrate
the application of rigid and logic mathematical concepts of austerity in
Europe.
3. Usefulness of the mathematical abstractions, the infinitesimal calculus
In
this part of the work it is developed a reflection on one of the most important
mathematical issues, the infinitesimal calculus. So I want to ratify that the
mathematical exactitude not always is exact; it is relative. Therefore, the
application of mathematical concepts in the economy is not always a warranty of
success.
Begin:
Is
it possible the infinite division of the numbers?
Isaac
Newton and Gottfried Leibniz taught that it is possible the infinite division
of the numbers through the infinitesimal calculus.
But
what is the infinitesimal numbers?
The
infinitesimal numbers are considered the most reduced amount that the human
mind can conceive; it means the numbers nearest to cero. This answer reveals
the abstraction of some mathematical concepts.
The infinitesimal numbers should be the most reduced amount that can be
measured in the real world and not an abstract conception on the infinite
division of the numbers. Numbers are representation of the amounts of matter;
numbers do not exist like entities with own life. What exists is the unit. The
essence of one thing is different to the essence of other thing and this is the
cause of the diversity of things in nature. Therefore the unique number that
exists is the number one, which represents the essence and diversity of the
things; the other numbers that we know are only additions or fractions of one. For
example, two is two times one; nine is nine times one. One half or a quarter is
too in essence one unit.
Matter
is also one unity. Matter has the same properties of the numbers; this means
that matter can be added, subtracted, multiplied and divided. The atomic
fission is the proof of this assertion. If numbers are a representation of
matter then we can to make the following question:
What
is the most reduced amount of matter?
According
to the concepts accepted by science molecule is the lesser amount of matter; in
turn, molecule is integrated by atoms and these are composed by subatomic
particles, neutrons, protons and electrons; each one of them is a different
unit.
If
this is truth, then the infinite division of matter in the real world has a
limit; the limit of the division of matter is the atom and their components; if
the former idea is truth then the infinitesimal calculus is an abstraction that
can be only partially verified in the reality.
The
most reduced infinitesimal particle is always one unit and, on the contrary,
the biggest amount of matter is always one unit integrated by an addition of
unities. But, in the real world, we arrive ever to a point when we cannot to
reduce or to divide more the matter. So far, that point is when we arrive to
the molecule, the atom and their components.
Nanotechnology
is a new discipline that intends to manipulate the molecular and atomic
composition of matter.
Is
it possible for nanotechnology to create new unites of measures different to molecule
and atoms?
In
other words, would be possible to divide more the components of atom?
That
is an important question because if new unit of measure different to molecule
and atoms are created then the limit of measures of the matter would also
change.
The
speed of light is the other limited measure that exists in nature hitherto.
Would
be possible for science to discover that the speed of light is other and not
the measure that has been reveled until now?
If
this is so, then a new door toward the infinitude of the numbers division might
be opened.
But
while the molecule and atom remain like the most reduced amount of matter and
the speed of light remain like the maximum speed that man knows, the
possibility of infinite division of the numbers will be restricted. Atoms are
the limits of the division of matter and the speed of light the limit of the
speed in nature; in consequence, that is the lesser amount of matter that exists
in the real world and the maximum amount of speed by man known. If this is so,
then the philosophic concept of the infinitesimal calculus like infinite
division of the numbers would be only one abstraction. The division of the
numbers in the real world has a limit and that limit is the lesser amount of matter
and the speed of light; in any case that number is one; the lesser amount of
matter, the lesser infinitesimal fraction is itself one unit.
The
ideas expressed in this epigraph reveals that not always the mathematical
abstractions are absolute truths and that, in consequence, not ever may be
considered indisputable truths.
The
infinite does not end; only God, space and time are infinite and eternal; but
the material things always can be measured. The numbers, which are a
representation of the material things, also have a limit.
4.
Conclusions
-
The application of rationalist
mathematical conceptions has caused a big damage to millions of people in the
entire world. In Latin America, during the decade of the ninety years of the 20th
century was applied the same economic program that is being developed now in
Europe. The philosophical inspiration of that program is the austerity which
main base is the logical assumption of the balance between income and spending.
In Latin America the results of that policy was the instauration of leftists and/or
nationalists governments in 12 countries, including the big economies like
Argentina and Brazil and in nations like Venezuela, Ecuador, Uruguay, Bolivia,
Nicaragua, Honduras, El Salvador, Jamaica, Peru and the strengthening of the
leftist movement in Mexico.
-
Mathematics is relative, it is not an
exact science; it is a result of the imagination, of the capacity of abstraction
of man; therefore in many cases do not have true base in the real world.
-
Mathematics is a hermetic discipline,
incomprehensible for the most people. The mathematicians maintain its
discipline closed, inaccessible to the majorities. The day that mathematics is
simplified and the most people understand their fundaments, that day
mathematics will not be more a knowledge exclusive for erudite.
-
The application of the mathematical
logic is not a warranty of success in the economic practice.
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