•  391
    Georg Cantor was the genuine discoverer of the Mathematical Infinity, and whatever he claimed, suggested, or even surmised should be taken seriously -- albeit not necessary at its face value. Because alongside his exquisite in beauty ordinal construction and his fundamental powerset description of the continuum, Cantor has also left to us his obsessive presumption that the universe of sets should be subjected to laws similar to those governing the set of natural numbers, including the universal …Read more
  •  261
    The original purpose of the present study, 2011, started with a preprint «On the Probable Failure of the Uncountable Power Set Axiom», 1988, is to save from the transfinite deadlock of higher set theory the jewel of mathematical Continuum — this genuine, even if mostly forgotten today raison d’être of all traditional set-theoretical enterprises to Infinity and beyond, from Georg Cantor to David Hilbert to Kurt Gödel to W. Hugh Woodin to Buzz Lightyear.
  •  52
    In the search of new approaches to the problem of emergence and evolution of natural languages, Mathematics, Theoretical Computer Science, as well as Molecular Biology and Neuroscience, both deeply penetrated and profoundly inspired by concepts originated in Mathematics and Computer Science, represent today the richest pools of formal concepts, structures, and methods to borrow and to adapt.
  •  72
    In the search of new approaches to the problem of emergence and evolution of natural languages, Mathematics, Theoretical Computer Science, as well as Molecular Biology and Neuroscience, both deeply penetrated and profoundly inspired by concepts originated in Mathematics and Computer Science, represent today the richest pools of formal concepts, structures, and methods to borrow and to adapt.
  •  113
    Walking Cautiously Into the Collatz Wilderness: Algorithmically, Number Theoretically, Randomly
    with Maurice Mignotte
    Discrete Mathematics and Theoretical Computer Science. 2006.
    Building on theoretical insights and rich experimental data of our preprints, we present here new theoretical and experimental results in three interrelated approaches to the Collatz problem and its generalizations: algorithmic decidability, random behavior, and Diophantine representation of related discrete dynamical systems, and their cyclic and divergent properties.
  •  302
    The enigma of the Emergence of Natural Languages, coupled or not with the closely related problem of their Evolution is perceived today as one of the most important scientific problems. The purpose of the present study is actually to outline such a solution to our problem which is epistemologically consonant with the Big Bang solution of the problem of the Emergence of the Universe}. Such an outline, however, becomes articulable, understandable, and workable only in a drastically extended episte…Read more
  •  546
    What is so special and mysterious about the Continuum, this ancient, always topical, and alongside the concept of integers, most intuitively transparent and omnipresent conceptual and formal medium for mathematical constructions and the battle field of mathematical inquiries ? And why it resists the century long siege by best mathematical minds of all times committed to penetrate once and for all its set-theoretical enigma ? The double-edged purpose of the present study is to save from the tran…Read more
  •  135
    "The definitive clarification of the nature of the infinite has become necessary, not merely for the special interests of the individual sciences, but rather for the honour of the human understanding itself. The infinite has always stirred the emotions of mankind more deeply than any other question; the infinite has stimulated and fertilized reason as few other ideas have ; but also the infinite, more than other notion, is in need of clarification." (David Hilbert 1925)
  •  173
    Scientific enterprise is a part and parcel of the contemporaneous to it general human cultural and, even more general, existential endeavor. Thus, the fundamental for us notion of evolution, in the modern sense of this characteristically Occidental term, appeared in the 19-th century, with its everything pervading, irreversible cultural and technological change and the existential turmoil. Similarly, a formerly relatively recherché word emergence, became a widely used scientific term only in the…Read more
  •  70
    Biblical Hebrew, BH, could be seen as primarily a verbal language [1], with an average verse of the Hebrew Bible containing no less than three verbs and with the biggest part of its vocabulary representing morphological derivations from verbal roots, almost entirely triliteral, or triconsonantal, – the feature BH shares with all Semitic and a few other Afro- Asiatic languages. The unique peculiarity of this triconsonantal morphological pervasiveness did not completely escape the attention of pre…Read more
  •  280
    We present here a biblical exegesis of the value of Pi, PI_{Hebrew} = 3.141509 ..., from the well known verse 1 Kings 7:23. This verse is then compared to 2 Chronicles 4:2; the comparison provides independent supporting evidence for the exegesis.
  •  130
    Discerning the Historical Source of Human Language
    Faith Magazine 41 (5): 10-12. 2009.
    The problem of the emergence and evolution of natural languages is seen today by many specialists as one of the most difficult problems in the cognitive sciences. We believe that a key to unravelling this enigma is the close relationship of language to mathematics.
  •  314
    Guessing the outcome of iterations of even most simple arithmetical functions could be an extremely hazardous experience. Not less harder, if at all possible, might be to prove the veracity of even a "sure" guess concerning iterations : this is the case of the famous 3x+1 conjecture. Our purpose here is to study and conceptualize some intuitive insights related to the ultimate (un)solvability of this conjecture.