Abstract
The mathematical talent of Paul Erdös, in search for
the hidden Proofs from The Big Book, teaches us about the soulful
world journey of the scientific mind towards patterns of eternity.
This magic of numbers reveals that N is more than a number and that
one is the beginning of all human reasoning about natural or physical
reality. Creative tools (numbers, letters) of the human spirit have
shaped our developmental history and help us to detect the concealed
vibrations and frequencies of the universe we live in via the
perfection of cultural techniques.
Key terms: one; mathetics; proofs; The Big Book; eternal patterns; unified
force.
Írta:
Stephen I. Ternyik
Magan
valalkozo/tudos (1985 ota)
StephenJehucal@web.de
It is now well known that we live in the technological age of electronic social media,
communication networks and automated informationprocessing;
free informatics design, open source and knowledge working
are definitely future trends of human productivity. Evolutionary and
anthropological limits of humankind cannot be erased by these
technical motions, but human communicative culture will be changed
forever.
Concerning these future events, Paul Erdös/Erdös
Pal (19131996) was a brilliant trendsetter or role model; this
mathematical genius came out of a Hungarian group of scientific
researchers (e.g. Polya G/18871985; Neumann Jv/19031957; Turan
P/19101976) who were all ‘spiritual children’ of Fejer Lipot
(18801959). Behind this kind of mathematical science worked the
hidden paradigm that the blueprint of reality is concealed in numbers
and can be revealed by the scientific soul/mind of the
logical/empirical researcher.
At that time, a ‘perfected’ scientific
infrastructure for free mathematical research did exist already in
Hungary, for example regular Journals with price questions, nationwide
contests and loose formation of study groups at the university level
where mentors/topics could be chosen via voluntary choice. Of course,
these were not yeshivas or laboratories, but communicative study
partnerships (‘give me a study partner or death’, an old Hebrew
saying).
The cosmopolitan spirit of Paul Erdös, dedicated to
empirical mathematical ‘revelation’, made him a role model of the
future scientist; his permanent research into the Proofs from The Book
and deep need for humane communication are the motivational driving
factors of his scientific life. Despite all horrific setbacks and
experiences, he found a way to mystically survive by inquiring into
universal unity (oneness) for aesthetic reasons and intellectual
beauty, i.e. his mathematical mind tried to grasp the spiritual
essence of the physical order of this world, we may call it
‘mathematical redemption’ or ‘intuitive reconciliation’ of the human
mind.
For a deeply religious person of ethical monotheist
faith this looks like a real and Ersatz human link towards the
creative divine order of the eternal upper force; however, science is
factually the psychological metamorphosis of religion and philosophy
at another stage of human development, i.e. the human mind tries to
better and more exactly understand the deeper layers (laws/principles)
of the natural process order or: Gd has the Big Book, the beautiful
proofs of mathematical theorems are listed here ( a saying attributed
to Paul Erdös).
Among the quantitative record of 1525 mathematical
articles from Erdös are 511 research papers with direct coauthors; he
visited these colleagues constantly throughout the world, lived out of
a suitcase, had very few possessions, donated his scarce money to
needy researchers and ‘turned coffee into theorems’ (A.Renyi). Erdös’
scientific network had no hierarchies, was not organized, of informal
nature, and he was the central knot of all hubs and connections. It
was surely not a random network, but a probability network of
potential communicators where knowledge working was focused on
creative problemsolving. Human and scientific networks of this kind
are a social phenomenon and economically very efficient: A) the costs
of knowledge ‘transactions’ are very low, and B) they work better
without a formal structure, in legal and monetary terms. Motivation
and creativity are more valued than mechanical efficiency, i.e. it is
quite the opposite interaction model of the current economization and
commercialization of academia where intellectual property rights have
become somehow paramount. Such an open source model is based on
brilliant ideas (ideals), factual or empirical performance
(experience) and real problemsolving (results); it resembles as
communicative ensemble a Jazz band (create and reset) and not a labor
hierarchy (command and control), i.e. human interaction follows the
quality principle of optional growth, in quantitative terms: the
ethical imperative is to reduce complexity via small steps, circular
feedbacks and process strategy, i.e. a variable dependency of
independent elements via a specific temporal content is at work, e.g.
only variety can create variety.
The Erdös collaboration technique of scientific
communication is a prototype of Jewish epistemology or learning
process how Jews gain knowledge; a much solidified body of knowledge
and skills is slowly being extended by thematic human communication
and permanent exchange. Not an academic homo clausus is the ideal of
knowing, but a serious knowledge worker who socially cooperates,
shares and cares about the scientific results of the research
discipline; professional and biographical background are minors and
the topic of investigation becomes the major priority. In this case,
the magic of numbers (not Hebrew letters which are actually also
numbers, according to the religious science of Kabballah) in
spacetime and timespace drives the permanent and perennial research
for the eternal patterns of universal force as a temporal moment of
being here in this world. From this point of view, mathematical
genealogy is a scientific approach to decipher the historical journeys
of the human mind via the discovery route of the natural working
order, i.e. it is mathetics, the science of learning. In addition,
Erdös was very good at didactics and promoted a lot of mathematical
talents (e.g. B.Bollobas, J.Kruskal, L.Lovasz, and T.Tao).
Travelling with a Hungarian passport, being
officially affiliated with the Hebrew University of Jerusalem and the
Hungarian Academy of Sciences, researching at several prominent
American and British universities, and visiting scientific conferences
globally ( in 25 countries), Paul Erdös was a true world citizen,
incorporating humane science and peace in times of the cold war.
Approaching a first conclusion:
The essentially Jewish epistemology of Erdös made
him an original cosmopolitan knowledge worker in the research field of
mathematical science who was well ahead of today’s open source, social
media networks and communication culture. His lifelong research into
the concealed number magic of Proofs from the Big Book reveals a real
and Ersatz human link to the eternal upper and unified force of all
proofs.
We could stop here and point to reference
resources, conferences, scientific problems and research methodologies
of modern contemporary mathematics as related to Paul Erdös, i.e. the
pure intellectual legacy of a continuous searcher for elegant proof
methods. Of course, we have also to do some homework and to understand
the underlying math and the abstract scientific value of the Erdös
methodical problemsolving strategy which was a social product of
really applied creativity and human ingenuity. In other words, the
mathematical world that average inhabitants of this planet normally
experience is an earthly mixture of daily accounting techniques,
general school memories and continuous number applications; this was
definitely not the Erdös world. However, infinite calculus and
continuous analysis, basic technological tools of engineering,
computation and other applied natural sciences, were also not his
ballpark or if you want cognitive playground.
The discrete or finite world that Paul Erdös
mathematically explored (inhabited) was the scientific foundation of
the digital age and the majority of research contributions, concerning
sets and graphs, were basic inquiries into the computability of
theorems via intuitive proofs. As a scientific consequence, this
intuitive work developed fundamental computational patterns of human
exact thought for the technical age of automated
informationprocessing or informatics as we know it today. So, this is
not the formal mathematics of the modern technician, engineer or
applied scientist, but the profound exploration of the deeper layers
of structural and functional reality patterns of this physical world,
working by energy and matter in discrete terms.
The research into N is definitely more than a
scientific exploration of number symbols; it is the quest for discrete
patterns of energy and the information flow. As a result of this
spiritual way of thinking, mathematics is a science of the human mind
as related to rationality; rationality is consequently about efficient
human reasoning while morality is about ethical human action, both
systems of reasoning fall under the categorical dichotomy of false or
right. The globalization of mathematical thought (since about 1900 )of
which Paul Erdös was a vital and pioneering part, has to be better and
deeper understood, and not only for the explanation of the many
successful applications in modern (quantum) physics. It was a decisive
historical process and the most important single elements (sparks) for
grasping modern complexity methodically were such spirits or human
minds like Erdös who was dynamically interconnecting to any possible
willing source of mathematical interaction, i.e. the mutual
continuity and dependency of this spiritual work in math is an
original chain of human ideas, dating 4000 years back to the Abrahamic
times of Sumer and Mesopotamia, and it was translated via discrete
mathematical thought into computational modernity.
As we want to deeper and better understand the
epistemological and ontological heritage of Paul Erdös, concerning
Hungarian Jewry, scientific ingenuity and cosmopolitan world culture,
it is crucial to delve into the biographical and professional details
of the Erdös cosmos; this will be on one side social psychology
indepth ( as related to critical life events and interaction
patterns) and on the other side a fresh look into mathematics as
globalized discipline (after having coped successfully with a basic
cognitive crisis, in terms of scientific and technological history,
i.e. formalism vs. intuitivism).
If both of your parents are mathematicians,
physicists and teachers, the probability of getting professionally
also involved in one of the above mentioned vocational directions is
well above 80%; however, this is no proof for mathematical talent and
a matter of circumstances: Intellectual ‘capital’ can get lost as life
goes on and many talented people walked into lethal detours. The
deeper look into the biographical process of Paul Erdös reveals a very
protective behavior from side of his parents, an early detected strong
mathematical talent and an upbringing in a rational culture of free
thought; his intuitive scientific formation was via homeschooling,
KöMal (Közepiskolai Matematikai es Fizikai Lapok/math and physics
sheets for young students) and he received his PhD fast track
(19301934) from Budapest University (today ELTE). The magic numbers
of the discrete world captured his soul/mind at the developmental
stage of early youth, saved surely his life and built the rational
‘rock of life’. Manchester, Princeton and Jerusalem were important
locations of his voyage, but
Budapest remained his
spiritual root center of cosmopolitan gravity.
We can detect a strong interest in politics (to
avoid politics), a cordial sociability (human connectedness), and
celibacy for scientific reasons, skeptical humor and a permanent
ambition to creative mathematical problemsolving until his physical
death in Warszaw at a scientific conference. Intuitive rationality may
be the best words to describe the overall attitude or life style of
Paul Erdös; intuitive rationality is a continuous combination of
internal meditation and external concentration, but in this case, not
focused on holy texts or divine hermeneutics. The Erdös reverence was
done by deep immersion into the discrete and combinatory mystical
magic of proofs; it resembles the kabalistic interpretation of the
physical world via mathematical and numerological means. This constant
research into eternal patterns is ultimately very similar to
religious activity, i.e. knowing and experiencing more about the
concealed harmony of universal force; the intuitivism (‘fruit’) of
deeds (proofs) counts more than the formality (‘shell’) of creed
(theory). Here lies the intersection between mathematics and theology
or religion and science; formality and intuition are complementary
forces of human inquiry and philosophically intersect where standard
knowledge meets learning by faith, i.e. formal religion did interfere
with Erdös’ faith in intuitive proofs and his own life experiences did
rationally not confirm the formal statements of any official faith.
Consequently, he concluded that hidden proofs from The Big Book can be
researched via intuitive rationality; this lead to an ‘irrational’
merger of a wanderlust life style and a communicative scientific
method, in terms of practicalities and coping with everyday tasks.
Also the scientific genius is rooted to the earth and the fruits of
his work remain earthly products, even though they are pointing to
patterns of eternity and higher force.
Approaching a second conclusion:
Hungarian Jewry and scientists have played a central and vital role in
the globalization of the mathematical discipline in the 20^{th} century and its physical applications in natural science, e.g.
computers; networking capacity, economic generosity and mathematical
creativity have made of Paul Erdös a role model for the cosmopolitan
scientific researcher. Knowledge networking, sociability and humane
creativity are surely the key traits of future scientists and
advancing globalization humanely will be driven by this intellectual
epistemology. Erdös anticipated this trend of the next scientific
stage of human cooperation by almost 100 years via a creative
technique of survivalist rationality and morality.
The epistemological heritage and intellectual
legacy of Paul Erdös was molded by three distinct cultural factors: A)
Mathematical problemsolving; B) Hungarian reflective mind; C) Jewish
learning techniques. Scientific vagabondery has reinforced this
molding of intellectual cultures into a cosmopolitan epistemological
framework of caseoriented (proofs) and interpersonal research
communication (networking). Erdös was not very much interested in
mathematical theorybuilding; he stayed in the formal and intuitive
system of traditional mathematical thought, developing it further by a
discrete combination of puzzling and communicating via a world wide
web of connections.
The theoretical statement of mathematician L.
Kronecker (18231891) that ‘Gd made the integers, all else is the
work of man’ bears fundamental importance for understanding the
psychological consequences of mathematical (human) and natural
science. As it has been explained many times, the lack of
communication between the natural and human sciences, including its
applied intersections like math, is a cultural tragedy (CP. Snow,
1959); the malapplications and malinterpretations of math and
physics in the social sciences (e.g. global financial economics) are
one part of this cultural dilemma, i.e. the two mathematical
approaches of theoretical precision and proof practice are not
reconciled. Letters and numbers are cognitive tools to better and
deeper understand the construction principles/laws of the natural
world order, but it is not wise to attribute divinity to cultural
tools and techniques of the human mind. A clear physical distinction
between the human mind and eternal patterns does exist, concerning
lifetime priorities, meaning and free choice. In any case, Erdös
believed in the discovery of the hidden proofs from The Big Book; this
is truly a real and Ersatz human link to the above mentioned
statement.
Paul Erdös was bad at recognizing faces and names,
but when he came to know the telephone number of a colleague then he
immediately could connect name and research topic. This goes to show
that his memory of contacts was based on numerical processing even in
interpersonal relationships which illustrates the intellectual and
epistemological merger of human lifestyle and science; the limits of
the mathematical method as ‘linguistic tool’ are set by the human mind
itself. Erdös was fascinated by the creativity and beauty of
mathematical proofs and this kept him breathing for 83 years; you can
find his grave at Kozma Street Jewish Cemetery, Budapest
(plot:17A629).
Approaching a summary and third conclusion:
The lifespan of Paul Erdös covers the end of the
AustroHungarian Empire (of which his father Lajos was a soldier and
prisoner of war in Russia/19141920), WW1 and WW2, the Shoah, the
Israeli war of
Independence, the Iron Curtain/
Cold War and the fall of the Berlin wall, and …more. This
is quite a lot for a mortal human being and can only be done by a
survival strategy. Consequently, Erdös’ brain/mind was trained to
decipher the mathematical structures of this world by numbers,
researching into the hidden proofs from The Big Book which Gd has
concealed for humankind to discover. His open source approach was more
than futuristic, pointing to a new kind of scientific research
cooperation, based on a deep knowledge base, social connectivity and
physical relocation; he was primarily a problemsolver and not a
theorybuilder. Mother Anna was the most important woman in his life
and she nurtured also his mathematical talent by educating him to a
high level by private means. The mystery and magic of numbers, the
deep immersion into theoretical proofs and intuitive rationality were
his cultural tools of human survival and meaning; it is also reported
that he enjoyed dining out in a good restaurant. The intellectual
heritage of Erdös’ epistemology is to search for meaning not only in
the purity of theoretical proofs, but to socially connect/communicate
in an open source manner about scientific problems and to investigate
as creatively as possible. A humanization of the scientific discourse
is a rational and moral imperative in our times of economic
overcompetition, knowledge overspecialization and interpersonal
alienation. N is definitely more than a number and Aleph is definitely
more than a letter; beyond being cultural tools of human survivalist
rationality and morality, they serve a higher purpose, i.e. the
detection of eternal patters, unified force and spiritual unity. Zero
and One are the most important numbers while Aleph and Beth are the
most important letters; the true purpose of science is most probably
to provide a vehicle for the perception and observation of Gdliness
in the worldly order of natural processes/systems. Science is not the
view from above, but the empirical view from below. When empirical
science will become true science then will theoretical practice reveal
the unity of this world as the simple unity of the eternal upper
force. Science is a relative reference system of the absolute, if it
is performed in a balanced manner of rationality and morality; this is
also the solution of the paradox that Erdös Pal sought: Gd made the
integers, all else is made by man like him.
Literature/Links:
Aigner
M/Ziegler G. 1988. Proofs from The Book. Heidelberg: Springer.
Atiyah M. 2007.
Siamo tutti matematici. Roma: Di Renzo.
Blau L. 1898
(2005). Ozsido Büveszet. BP: Gabbiano (reprint).
Graham R. et
al. 2013. The Mathematics of Paul Erdös (2 Volumes). NY: Springer.
Lovasz L. 2012.
Large Networks and Graph Limits. Providence/RI: AMS.
Rosenzweig F.
1925. Die Bauleute. Berlin:
Philo.
Schlechter B.
2000. My Brain is Open. NY: Simon & Schuster.
Sznaider N.
2011. Jewish Memory and the Cosmopolitan Order. Cambridge/UK: Polity.
Venetianer L. 1922. A Magyar Zsidosag Törtenete. BP: Fövarosi Nyomda.
http://www.fulbright.hu/book5/craigwebster.pdf
http://www.renyi.hu/
(Archive/Paul Erdös/Papers)
http://fqxi.org/community/forum/topic/2302
http://www.elliottsharp.com/recent_compositions.html
