**Nulla va perduto. L'esperienza di Pavel Florenskij**

*Movie @*

**http://youtu.be/NKVsZFkQnPk**

"*Pure mathematics is, in its way, the poetry of logical ideas*"

(Albert Einstein)

(Albert Einstein)

Apparently the sequences introduced in the Fibonacci Quarterly paper by Greg Back and myself have been discussed in the RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR (Neil J. A. Sloane's presentation was on February 17, 2011; for the abstract go to the *Archive of Speakers and Talks - 2011*).

The ONU-SOLVE problem group has been recognized in the November 2011 issue of the Fibonacci Quarterly for a solution to B-1078 - **http://www.fq.math.ca/Problems/ElemProbNOV2011.pdf**

(21 - 25 March, 2012,

via

(still,

No revolution (yet):

My review of David Berlinski's "One, Two, Three: Absolutely Elementary Mathematics" appeared in the Journal of the ACMS (Sept. 2011) -

**http://www.acmsonline.org/journal/2010_2011/Caragiu_Review_of_Berlinski.pdf**

Cotidianul LUMINA - 17 August 2011

**Oamenii de lângă noi**

de Monica Patriche

În memoria**Prof. Univ. Dr. Constantin Tudor**

de Monica Patriche

În memoria

“Un model de modestie şi de viaţă trăită din plin, împlinită prin faptul că nu a îngropat talantul primit, ci dimpotrivă. Numai gânduri bune pentru cel care aşteaptă din parte-ne ceva pozitiv. Şi-mi aduc aminte cum povestea părintele Galeriu că la înmormântarea părintelui Stăniloae vorbea cu acesta ca şi când ar fi fost în viaţă, cu convingerea că este auzit. Aceasta este, cu siguranţă, ceea ce e bine să facem şi noi.”

Some relevant links on Jorge Luis Borges and Mathematics:

Unthinking Thinking: Jorge Luis Borges, Mathematics and the New Physics by Floyd Merrell (Purdue University Press, 1991);

The Unimaginable Mathematics of Borges' Library of Babel by William Goldbloom Bloch (Oxford University Press, 2008);

From Borges y la matemática by Guillermo Martínez (Buenos Aires: Seix Barral, 2007).

Unthinking Thinking: Jorge Luis Borges, Mathematics and the New Physics by Floyd Merrell (Purdue University Press, 1991);

The Unimaginable Mathematics of Borges' Library of Babel by William Goldbloom Bloch (Oxford University Press, 2008);

From Borges y la matemática by Guillermo Martínez (Buenos Aires: Seix Barral, 2007).

The solution to FQ-B1074, provided by the ONU-Solve problem group was published in the "Elementary Problems and Solutions" section of the August 2011 Issue of the Fibonacci Quarterly.

From a review that I wrote for "One, Two, Three / Absolutely Elementary Mathematics" by David Berlinski, that I recently wrote (and submitted):

Image source (Hubble Deep Field (full mosaic) released by NASA on January 15, 1996)

Personally, I believe this is a particularly nice way to look at the “deep field” of mathematics: that’s a whole lot of treasure stuff out there (actually more abundant than the one in the physical world, as the author notices), enough for the unfolding, in complete Cantorian freedom, of the process of self-discovery of every human person. That may apply for the “deep field” of the arts and, why not, for that of physical/cosmological reality itself. Ultimately, such a reading of the mathematical experience in a phenomenological key may prove to be truly beneficial.

Image source (Hubble Deep Field (full mosaic) released by NASA on January 15, 1996)

(Pierre de Fermat;

Applications of finite fields (3/3) - Dickson polynomials and discrete logarithms. Older lecture notes from a notebook which I don't want to lose (unfortunately it is in danger of falling apart...)

Applications of finite fields to Latin squares, combinatorial designs, Hadammard matrices. Older lecture notes from a notebook which I don't want to lose (unfortunately it is in danger of falling apart...)

Applications of finite fields to Costas arrays. Older lecture notes from a notebook which I don't want to lose (unfortunately it is in danger of falling apart...)

În gândirea grecească, pe lângă ordine şi cosmos, logosul a fost o altă noţiune, cu dublu statut, obiectiv şi subiectiv. Logosul există atât în om, cât şi în lucruri. Cosmosul şi ordinea lui se opun unui aşa-numit haos iniţial şi sunt inseparabile de ideea de inteligibilitate, de logos. Pitagora, cel dintâi, a numit cuprinderea tuturor lucrurilor kosmos, din pricina rânduielii ce domnea în cuprinsul lor. Cosmosul era universul ordonat, altfel spus, normat. O altă proprietate fundamentală a kosmosului pitagoreic, pe lângă caracterul lui ordonat, este aceea a caracterului finit. Grecii, s-a spus, se temeau de infinit. Ei asociau valoarea binelui cu finitul şi, implicit, cu cognoscibilul. Pentru ei, infinitul era ceva de ordin iraţional, dăunător eticii. De altfel, esenţa învăţăturii pitagoreice e conceptul de număr în explicarea lumii. (Desigur, pe acea vreme, conceptul de număr era foarte primitiv, legat de ilustrări practice, cu pietricele sau din puncte.) Pitagora e ultimul punct nodal al sistemului încă nedivizat al imaginii lumii mitice, în centrul învăţăturilor sale aflându-se, într-un tot unitar, muzica, matematica, astronomia şi ritul. Există o mistică a numerelor pitagoreice care şi-a atins apogeul în şcoala neopitagoreicilor, în aşa-numitele teologii aritmetice ş. a. Se stabileau corelaţii între numere şi alte concepte matematice, numere şi muzică, numere şi morală, numere şi corpul uman, numere şi elementele universului.

E interesant de urmărit întâlnirea dintre poezie şi matematică în acest punct de convergenţă generală care este mitul, unde funcţiile spiritului nu sunt încă diferenţiate în discipline autonome, şi unde gnoseologicul şi ontologicul, cunoaşterea şi existenţa se suprapun. De altfel, suprapunerea dintre existenţă şi cunoaştere este o temă fundamentală a gândirii antice, şi care, de altfel, a cunoscut revalorificări interesante în modernitate. Parmenide afirma, de exemplu, că „acelaşi lucru este a cunoaşte şi a fi”. Cu alte cuvinte, există o identitate de natură între intelect şi restul existenţei, care face posibilă cunoaşterea. Ajungem, astfel, la ideea importantă de reflexivitate a gândirii, la ceea ce s-a numit, în legătură cu gândirea greacă şi nu numai, critica gândirii, cunoaşterea cunoaşterii.

În dialogul „Timaios”, Platon se referea la cele cinci poliedre regulate, spunând că sunt figuri cosmice la intersecţia dintre raţional şi iraţional, şi corespund treptelor universului său. Teoria lui Platon corespunde în mare măsură principiului economiei, în sensul folosirii unui număr minim de elemente pentru redarea diversităţii fenomenelor naturii, ca şi dezideratelor raţiunii, regularităţii şi ordinii de care e pătrunsă gândirea greacă. Existenţa ascultă de acelaşi logos ca şi intelectul [1].

A discussion of the paper "The Greatest Prime Factor and Related Sequences" (JP Journal of Algebra, Number Theory and Applications 6(2), 403-409 (2006), by Mihai Caragiu and Lisa Scheckelhoff), with neat pictures, can be found **here** (Mathematical Oddities Thread - The Something Awful Forums)

But Assembly expected to kill bill

by Mihai Caragiu and Ashley Risch

abstract -

March 18, 2004 (Univ. of Colorado, Boulder)

by

(

______________

image details

Dr. **Monica Patriche** în cotidianul LUMINA - Opinii, Miercuri, 25 Mai 2011

Ca la carte :

Matematica şi poezia

The **Council on Undergraduate Research** defines it as follows:

*A=B* to "discover" that *2A=2B*, or something like that), or trivial derivations in existent or made-up ad hoc formal systems. The original contribution to the discipline must also go through a rigorous, __external__, peer-review process. Ideally, a rigorous, solid peer-review is a process which does not accept works simply because they are formally correct, indeed it demonstrates a pattern of rejecting a significant percentage of logically correct but otherwise not interesting enough (as judged by the reviewers) works. Also, note that being "peer-reviewed" is not the same with "being made public/disseminated" (a confusion that is still circulating). A valuable original contribution will be able to generate 'participative waves', engaging others in the area. Thus, when it comes to goals and assessment, 'undergraduate research' is not (and shouldn't be, in my opinion) different from good old 'research'. So it is a serious matter, and competitive universities recognize that. I found interesting the following straight-to-the-point **statement** (due to Jim Coleman, vice chancellor for research and professor of biology at the University of Missouri) on the central place of undergraduate research in the life of a good university:

*their own* involvement and demonstrated proficiency in research. Indeed the undergraduate research is driven, after all, by faculty research. Or, if you want, *faculty research is a necessary condition for undergraduate research*. One may ask, is it also a sufficient condition? This is not true, mainly because *the student is a person*, not a machine or a notebook on which the faculty mentor writes a paper. In the end, note that the complexities of (undergraduate) research that even an otherwise well prepared academic (mentor) faces, ultimately *point to* *persons* (as in *real persons*, and not ``*the idea* of a person''), and their *participative experience*.

The word "original" is very important. An original contribution to knowledge rules out works of a severely expository or textbook nature, results that follow immediately from previous work (as in... use the previously obtained``An inquiry or investigation conducted by an undergraduate student that makes an original intellectual or creative contribution to the discipline.''

``Integrating the research/scholarship into the undergraduate life is a challenging enterprise. There are no clear recipes, since there are students and students. Each individual case is unique and interesting in itself. The faculty's essential asset isThere is nothing more central to the mission of a university than activities associated with discovery, creation, innovation and scholarship. So, I think that what defines a great university is the integration of these activities into the entire fabric of the undergraduate experience.''

Solution to FQ-B1078 (Fibonacci Quarterly 48 (2010), no. 4, 367) submited on May 9, 2011 by the ONU-SOLVE problem group (faculty advisor - Mihai Caragiu).

Solution to AMM 11537 (The American Mathematical Monthly 117 (2010), no. 10, p. 929), written by Mihai Caragiu and submitted on April 21, 2011.

Solution to AMM 11536 (The American Mathematical Monthly 117 (9), November 2010, p. 835) written by Mihai Caragiu and submitted on March 30, 2011.

Solution to AMM 11527 (The American Mathematical Monthly 117 (2010), no. 8, 742) written by Mihai Caragiu and submitted on February 28, 2011.

Solution to FQ-B1074 (Fibonacci Quarterly 48 (2010), no. 3, p. 278) submited on February 10, 2011 by the ONU-SOLVE problem group (faculty advisor Mihai Caragiu)

A linear algebra classroom snippet: symmetric matrices... with nice numbers. A grab bag of symmetric matrices

MGPF - multidimensional greatest prime factor sequences

**The MGPF conjecture: all MGPF sequences are ultimately periodic.**

**An-MGPF-Path-Towards-a-Fixed-Point**

Forthcoming (Far East Journal of Mathematical Sciences) - *An Euler-Fibonacci Sequence*

by Mihai Caragiu and Ashley Risch

(some raw data -**here**)

by Mihai Caragiu and Ashley Risch

(some raw data -

From the Online Encyclopedia of Integer Sequences:

G. Back and M. Caragiu,

The greatest prime factor and recurrent sequences,

Fib. Q., 48 (2010), 358-362.

Photo © Mihai Caragiu

The process of pure mathematical thought and the engagement with ever-surprising, profound new statements and their proofs (fulfillable mathematical intentions) reveals, alongside with a never-ending, other-worldly depth of pure mathematical discovery, the true meaning of Cantor's words,Russell W. Howell

Prof. of Mathematics, Westmont College - Santa Barbara, California

July 28, 2005

'Through thatthe essence of mathematics lies in its freedom'

(

Part 1 - http://www.youtube.com/watch?v=z9WdE7Ucc_Q

Part 2 - http://www.youtube.com/watch?v=Gb3C1Cfx2TU

Part 3 - http://www.youtube.com/watch?v=KU9mKnuLMF4

http://www.youtube.com/watch?v=lNLKcq6JjYk

Dreyfus's critique of artificial intelligence (AI) concerns what he considers to be the four primary assumptions of AI research. The first two assumptions he criticizes are what he calls the "biological" and "psychological" assumptions. The biological assumption is that the brain is analogous to computer hardware and the mind is analogous to computer software. The psychological assumption is that the mind works by performing discrete computations (in the form of algorithmic rules) on discrete representations or symbols.

Dreyfus claims that the plausibility of the psychological assumption rests on two others: the epistemological and ontological assumptions. The epistemological assumption is that all activity (either by animate or inanimate objects) can be formalised (mathematically) in the form of predictive rules or laws. The ontological assumption is that reality consists entirely of a set of mutually independent, atomic (indivisible) facts. It's because of the epistemological assumption that workers in the field argue that intelligence is the same as formal rule-following, and it's because of the ontological one that they argue that human knowledge consists entirely of internal representations of reality.

On the basis of these two assumptions, workers in the field claim that cognition is the manipulation of internal symbols by internal rules, and that, therefore, human behaviour is, to a large extent, context free (see contextualism). Therefore a truly scientific psychology is possible, which will detail the 'internal' rules of the human mind, in the same way the laws of physics detail the 'external' laws of the physical world. But it is this key assumption that Dreyfus denies. In other words, he argues that we cannot now (and never will) be able to understand our own behavior in the same way as we understand objects in, for example, physics or chemistry: that is, by considering ourselves as things whose behaviour can be predicted via 'objective', context free scientific laws. According to Dreyfus, a context free psychology is a contradiction in terms.

Dreyfus's arguments against this position are taken from the phenomenological and hermeneutical tradition (especially the work of Martin Heidegger). Heidegger argued that, contrary to the cognitivist views on which AI is based, our being is in fact highly context bound, which is why the two context-free assumptions are false. Dreyfus doesn't deny that we can choose to see human (or any) activity as being 'law governed', in the same way that we can choose to see reality as consisting of indivisible atomic facts...if we wish. But it is a huge leap from that to state that because we want to or can see things in this way that it is therefore an objective fact that they are the case. In fact, Dreyfus argues that they are not (necessarily) the case, and that, therefore, any research program that assumes they are will quickly run into profound theoretical and practical problems. Therefore the current efforts of workers in the field are doomed to failure.

__Source__: *Hubert Dreyfus - Wikipedia - *http://en.wikipedia.org/wiki/Hubert_Dreyfus

*Hubert Dreyfus on Husserl and Heidegger*

**Section 1 - http://www.youtube.com/watch?v=aaGk6S1qhz0**

**Section 2 - http://www.youtube.com/watch?v=ylKnb6WtYqU**

**Section 3 - http://www.youtube.com/watch?v=LgUDaml7ZJY**

**Section 4 - http://www.youtube.com/watch?v=QzAqfzWJTq4**

**Section 5 - http://www.youtube.com/watch?v=VfsKTSM5Sns**

Dreyfus claims that the plausibility of the psychological assumption rests on two others: the epistemological and ontological assumptions. The epistemological assumption is that all activity (either by animate or inanimate objects) can be formalised (mathematically) in the form of predictive rules or laws. The ontological assumption is that reality consists entirely of a set of mutually independent, atomic (indivisible) facts. It's because of the epistemological assumption that workers in the field argue that intelligence is the same as formal rule-following, and it's because of the ontological one that they argue that human knowledge consists entirely of internal representations of reality.

On the basis of these two assumptions, workers in the field claim that cognition is the manipulation of internal symbols by internal rules, and that, therefore, human behaviour is, to a large extent, context free (see contextualism). Therefore a truly scientific psychology is possible, which will detail the 'internal' rules of the human mind, in the same way the laws of physics detail the 'external' laws of the physical world. But it is this key assumption that Dreyfus denies. In other words, he argues that we cannot now (and never will) be able to understand our own behavior in the same way as we understand objects in, for example, physics or chemistry: that is, by considering ourselves as things whose behaviour can be predicted via 'objective', context free scientific laws. According to Dreyfus, a context free psychology is a contradiction in terms.

Dreyfus's arguments against this position are taken from the phenomenological and hermeneutical tradition (especially the work of Martin Heidegger). Heidegger argued that, contrary to the cognitivist views on which AI is based, our being is in fact highly context bound, which is why the two context-free assumptions are false. Dreyfus doesn't deny that we can choose to see human (or any) activity as being 'law governed', in the same way that we can choose to see reality as consisting of indivisible atomic facts...if we wish. But it is a huge leap from that to state that because we want to or can see things in this way that it is therefore an objective fact that they are the case. In fact, Dreyfus argues that they are not (necessarily) the case, and that, therefore, any research program that assumes they are will quickly run into profound theoretical and practical problems. Therefore the current efforts of workers in the field are doomed to failure.

“That grand myth which I asked you to admire a few minutes ago is not for me a hostile novelty breaking in on my traditional beliefs. On the contrary, that cosmology is what I started from. Deepening distrust and final abandonment of it long preceded my conversion to Christianity. Long before I believed Theology to be true I had already decided that the popular scientific picture at any rate was false. One absolutely central inconsistency ruins it; it is the one we touched on a fortnight ago. The whole picture professes to depend on inferences from observed facts. Unless inference is valid, the whole picture disappears. Unless we can be sure that reality in the remotest nebula or the remotest part obeys the thought--laws of the human scientist here and now in his laboratory-in other words, unless Reason is an absolute--all is in ruins. Yet those who ask me to believe this world picture also ask me to believe that Reason is simply the unforeseen and unintended by-product of mindless matter at one stage of its endless and aimless becoming. Here is flat contradiction. They ask me at the same moment to accept a conclusion and to discredit the only testimony on which that conclusion can be based. The difficulty is to me a fatal one; and the fact that when you put it to many scientists, far from having an answer, they seem not even to understand what the difficulty is, assures me that I have not found a mare's nest but detected a radical disease in their whole mode of thought from the very beginning. The man who has once understood the situation is compelled henceforth to regard the scientific cosmology as being, in principle, a myth; though no doubt a great many true particulars have been worked into it.”(

Image source: http://en.wikipedia.org/wiki/File:Hubble_-_infant_galaxy.jpg

Argument from Reason- Wikipedia.

C. S. Lewis'The cardinal difficulty of naturalism

An interesting paper:

by SAMOILĂ Gheorghe Ştefan,

Aplimat – Journal of Applied Mathematics, Vol. 2 (2009), No. 1, 227-234.

A recent major breakthrough is announced

Image

A relevant video - Ken Ono talk (Emory University YT Channel):

This 'being captured by the truth' is echoed, in a sense, in mathematical research (and in science as well). It's as if a certain picture of the world (visible/physical or invisible/mathematical) progressively unfolds inside us, acquiring in the process a 'pointing beyond', iconic feature, that lifts ourselves.The truth is a trap: you can not get it without it getting you; you cannot get the truth by capturing it, only by its capturing you.(Søren Kierkegaard)

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