scholarly journals From the four-color theorem to a generalizing “four-letter theorem”: A sketch for “human proof” and the philosophical interpretation

2020 ◽  
Author(s):  
Vasil Dinev Penchev

The “four-color” theorem seems to be generalizable as follows. The four-letter alphabet is sufficient to encode unambiguously any set of well-orderings including a geographical map or the “map” of any logic and thus that of all logics or the DNA (RNA) plan(s) of any (all) alive being(s).Then the corresponding maximally generalizing conjecture would state: anything in the universe or mind can be encoded unambiguously by four letters.That admits to be formulated as a “four-letter theorem”, and thus one can search for a properly mathematical proof of the statement.It would imply the “four colour theorem”, the proof of which many philosophers and mathematicians believe not to be entirely satisfactory for it is not a “human proof”, but intermediated by computers unavoidably since the necessary calculations exceed the human capabilities fundamentally. It is furthermore rather unsatisfactory because it consists in enumerating and proving all cases one by one.Sometimes, a more general theorem turns out to be much easier for proving including a general “human” method, and the particular and too difficult for proving theorem to be implied as a corollary in certain simple conditions.The same approach will be followed as to the four colour theorem, i.e. to be deduced more or less trivially from the “four-letter theorem” if the latter is proved. References are only classical and thus very well-known papers: their complete bibliographic description is omitted.

2019 ◽  
Vol 09 (03) ◽  
pp. 410-413
Author(s):  
山中 邹

2021 ◽  
Author(s):  
Alessandro Capurso

The following essay would like to elaborate on a possible “philosophy of efficiency” connected to the “Engineering of a toy model of the universe based on information and memory from an ICT perspective” (a more technical paper from the same author proposing a framework for Quantum Gravity). The insights derived from the interpretation of spacetime considered focus on causality, free will and efficiency, and promote collaboration, empathy and trust. Even if some of the concepts presented are common to several human cultures at different level of conceptual abstraction, this paper does not pretend to have scientific value nor suppose any reference to religion. The scope is just to draft a high level parallel between the description of the Universe proposed in the scientific contribution and a more philosophical interpretation of life, inspired by efficiency and based on the memory of a common beat.


Author(s):  
Ikrom B. Mirzaev ◽  

The article analyzes the heritage of Avesto from a philosophical point of view and gives a philosophical interpretation of the role of myths. At the same time, special attention is paid to the perception of the structure of the world. The ideas and philosophy of Avesto that have come down to us show that our ancestors who lived in the Zoroastrian era had a high level of worldview and thinking. Even in these distant times, our ancestors are struck by the fact that the deepest thinking, attitude to nature, existence, integrity and integrity of the universe, nature and human dignity, as well as the preservation of the Motherland are the main tasks of mankind.


2020 ◽  
pp. 1-4
Author(s):  
Joseph Edward Brierly ◽  

2N-Color Theorem This article gives a standard proof of the famous Four-Color theorem and generalizes it be the 2N-Color problem. The article gives a number of possible applications of the 2N-Color problem that is the essence of orientation. Orientation is fundamental to many fields of scientific knowledge. The Fourcolor theorem applies to map making by the knowledge that only four colors are necessary to color a planar map. The Six-color theorem applies to three dimensional space implying that a space station could be ideally designed to have six compartments adjacent to one another allowing a door from any one of the compartments to the other five. The 2N-color generalization applies to the physical reality of quantum physics. Bubble chamber investigations suggest that the universe is four or more dimensions. Thus the 2N-color theorem applies to the N dimensional universe. At this time string theorists have suggested that the universe could be greater than four dimensions. Physics has not as of yet proven the exact dimension of the universe that could even be infinite as a possibility


2021 ◽  
Vol 5 (1) ◽  
pp. 32-46
Author(s):  
Gennady Petrovich Andreev ◽  

Rabbi Moshe ben Maimon (Maimonides) in the Second part of his main philosophical treatise The Guide for Perplexed analyzes geocentric cosmology which was for his epoch as paradigm. Also there he considers peripatetic ideas on Pre-eternity of the Universe and concept of multitude of worlds. He challenges and queries Post-Ptolemaic concept of epicycles what is so indistinctive for 12th century. Also two Medieval Jewish mysterious doctrines named Ma’ase Bereshit (Action of Creation) and Ma’ase Merqava (Action of Charriot) are analyzed by him in light of popular for Jewish High Middle Age interpretation as Physics and Metaphysics respectively. Mystical Talmudic teaching on Kise ha-Kavod (the Throne of [Divine] Glory) is interpreted as Peripatetic view on superlunary world. In The Epistle to the Sages of Marseille Maimonides sets some criteria up for rational faith and regards fundamental arguments against astrology by dividing pre-scientific cosmology and superstitions. He considers concept of rea’ya brura (pure viewing or clear proof) in epistemological and ontological sense. To rabbi Moshe logic of mathematical proof (and Pre-Scientific Knowledge at all) and sensual perception have got more weight than Biblical prophets literary words.


2021 ◽  
Vol 4 (1) ◽  
pp. 69-86
Author(s):  
Dmitry Koshlakov

The key term for the scientific discourse of Alexander von Humboldt is “Kosmos”. The paper interprets the term in connection with an idea, which is widespread in modern Russian philosophy, that conception as a special epistemic object is an alternative to the logical concept. This study substantiates the statement according to which Alexander von Humboldt in his widely known work Cosmos: A Sketch of a Physical Description of the Universe combines scientific and aesthetic perception of reality. The author makes an assumption that the term “Kosmos” encodes an epistemic object that combines the properties of concept and image and is a conception. For its investigation, the author discusses a few interpretations of the conception as a phenomenon: 1) the equivocalist interpretation, which sees conception as an ambiguous semantic formation, combining transcendent and immanent meanings; 2) the imaginistic interpretation, which considers conception as a semantic entity that has not evolved to an abstract concept; 3) the emotive interpretation, which interprets conception as an emotional semantic entity; this entity is object of thinking and object of emotional experience; 4) the linguo-philosophical interpretation, which considers conception as an element of the conceptual framework of language and thinking. The paper demonstrates that each of indicated interpretations of the conception corresponds to the sense of Humboldt’s term “Kosmos”.


1980 ◽  
Vol 77 (12) ◽  
pp. 803 ◽  
Author(s):  
Michael Detlefsen ◽  
Mark Luker

2017 ◽  
Vol 73 (3) ◽  
Author(s):  
Gideon J. Kühn

The essence of number was regarded by the ancient Greeks as the root cause of the existence of the universe, but it was only towards the end of the 19th century that mathematicians initiated an in-depth study of the nature of numbers. The resulting unavoidable actuality of infinities in the number system led mathematicians to rigorously investigate the foundations of mathematics. The formalist approach to establish mathematical proof was found to be inconclusive: Gödel showed that there existed true propositions that could not be proved to be true within the natural number universe. This result weighed heavily on proposals in the mid-20th century for digital models of the universe, inspired by the emergence of the programmable digital computer, giving rise to the branch of philosophy recognised as digital philosophy. In this article, the models of the universe presented by physicists, mathematicians and theoretical computer scientists are reviewed and their relation to the natural numbers is investigated. A quantum theory view that at the deepest level time and space may be discrete suggests a profound relation between natural numbers and reality of the cosmos. The conclusion is that our perception of reality may ultimately be traced to the ontology and epistemology of the natural numbers.


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