The Thing and I continues.
"… the Quantum Realm wouldn’t really become a 'thing'
in Marvel’s comic book mythology until the end of that
decade [the 1970s], and the arrival of a toy license at
the publisher."
— Graeme McMillan in The Hollywood Reporter Saturday
Continued from yesterday's 9 PM (ET) post.
Here KR stands for Knowledge Representation .
See also some ontology remarks by Marissa Mayer.
Kate felt quite dizzy. She didn't know exactly what it was
that had just happened, but she felt pretty damn certain that
it was the sort of experience that her mother would not have
approved of on a first date.
"Is this all part of what we have to do to go to Asgard?"
she said. "Or are you just fooling around?"
"We will go to Asgard...now," he said.
At that moment he raised his hand as if to pluck an apple,
but instead of plucking he made a tiny, sharp turning movement.
The effect was as if he had twisted the entire world through a
billionth part of a billionth part of a degree. Everything
shifted, was for a moment minutely out of focus, and then
snapped back again as a suddenly different world.
— Douglas Adams, The Long Dark Tea-Time of the Soul
|
Overarching Symmetries, Theory Change, and Ontology "Overarching symmetries help us to determine which new theories should replace older, falsified theories. Typically, when an earlier theory has been rejected and physicists are searching for a new theory to replace it, physicists don't just start from scratch. They assume that many of the features of the old theory were, in fact, correct, assuming the theory in question had a history of empirical successes. The old theory must have gotten something right to be successful, so since new theories should be strictly better than the theories they replace, we need a way to identify those successful features of our old theories and carry those features over into our new theories. Successful features of older theories can thus constrain what good candidates for these theories' replacements should look like." — Daniel Peterson, "Physical Symmetries, Overarching Symmetries, and Consistency" |
|
You, Xi-lin; Zhang, Peter. "Interality in Heidegger."
The term "interology" is meant as an interventional alternative to traditional Western ontology. The idea is to help shift people's attention and preoccupation from subjects, objects, and entities to the interzones, intervals, voids, constitutive grounds, relational fields, interpellative assemblages, rhizomes, and nothingness that lie between, outside, or beyond the so-called subjects, objects, and entities; from being to nothing, interbeing, and becoming; from self-identicalness to relationality, chance encounters, and new possibilities of life; from "to be" to "and … and … and …" (to borrow Deleuze's language); from the actual to the virtual; and so on. As such, the term wills nothing short of a paradigm shift. Unlike other "logoi," which have their "objects of study," interology studies interality, which is a non-object, a no-thing that in-forms and constitutes the objects and things studied by other logoi. |
Some remarks from this journal on April 1, 2015 —
Manifest O
|
| 83-06-21 | An invariance of symmetry The diamond theorem on a 4x4x4 cube, and a sketch of the proof. |
| 83-10-01 | Portrait of O A table of the octahedral group O using the 24 patterns from the 2×2 case of the diamond theorem. |
| 83-10-16 | Study of O A different way of looking at the octahedral group, using cubes that illustrate the 2x2x2 case of the diamond theorem. |
| 84-09-15 | Diamonds and whirls Block designs of a different sort — graphic figures on cubes. See also the University of Exeter page on the octahedral group O. |
The above site, finitegeometry.org/sc, illustrates how the symmetry
of various visual patterns is explained by what Zhang calls "interality."
Friday March 31, 2006
|
See also mentions of Justin E. H. Smith in this journal, including . . .
“… Western academic philosophy will likely come to appear
utterly parochial in the coming years if it does not find a way
to approach non-Western traditions that is much more rigorous
and respectful than the tokenism that reigns at present.”
— Justin E. H. Smith in the New York Times philosophy
column “The Stone” yesterday
For example—
The phrase "ontological secret" is from 1927 —
" Beauty is thus 'a flashing of intelligence…
on a matter intelligibly arranged' or, as Maritain
adds in the 1927 edition of Art and Scholasticism ,
it is 'the ontological secret that [things] bear within
them[selves], their spiritual being, their operating
mystery.' "
— John G. Trapani, Jr., "'Radiance': The Metaphysical Foundations
of Maritain's Aesthetics," pp. 11-19 in Beauty, Art, and the Polis ,
ed. by Alice Ramos, publ. by American Maritain Association, 2000.
This 1927 phrase may be the source of McLuhan's 1944
"ontological secret" —
From a search in this journal for "Object of Beauty" —
“She never looked up while her mind rotated the facts,
trying to see them from all sides, trying to piece them
together into theory. All she could think was that she
was flunking an IQ test.”
— Steve Martin, An Object of Beauty
"There was an idea . . ." — Nick Fury in 2012
". . . a calm and objective work that has no special
dance excitement and whips up no vehement
audience reaction. Its beauty, however, is extraordinary.
It’s possible to trace in it terms of arithmetic, geometry,
dualism, epistemology and ontology, and it acts as
a demonstration of art and as a reflection of
life, philosophy and death."
— New York Times dance critic Alastair Macaulay,
quoted here in a post of August 20, 2011.
Illustration from that post —
See "Imagination and Layered Ontology in Greek Mathematics,"
by Reviel Netz, at
See also …
Some background — Posts now tagged Noesis.
"Though realism is excellent rhetoric, maybe the best,
in a purely technical or instrumental sense,
that cannot be an adequate reason to accept it
as a serious intellectual position. In its tropes of
Death and Furniture we see a rhetoric that refuses
to acknowledge its own existence; a politics that
can claim a critical-radical credibility only by
the selective use of its opponents' analytic tools;
and a theology which is deeply conservative and
seeks nothing less than the death of disruptive,
disturbing inquiry. While tedium, good taste, political
and moral sensibility will properly determine what
sorts of given realities are thought worthy of inquiry,
those considerations are no grounds for promoting
a realist ontology for social science, nor any other
science, nor for rejecting relativism. On the contrary,
relativism is social science par excellence . . . ."
Loughborough University
— Edwards, D., Ashmore, M., and Potter, J. (1995),
"Death and furniture: The rhetoric, politics and theology
of bottom line arguments against relativism,"
History of the Human Sciences , 8, 25-49.
Related material:
Platonic realism in this journal, yesterday's post Ripples, and …
Gravity's Shadow , 2004 —
Gravity's Ghost , 2010 —
See also an "Inception"-related object —
The dateline from a slide at a string-theory conference:
See also this journal on that date.
A related "string theory," for those who like to compare and contrast:
A paper on the late Michael Weinstein by Robert L. Oprisko —
"Strings: A Political Theory of Multi-Dimensional Reality."*
From the abstract:
"An 'unfaithful' interpretation of Michael Weinstein's oeuvre
illuminates a complex, interpenetrative system of realities
that reflects the lived experience of his vitalist ontology."
* Theoria & Praxis: International Journal of Interdisciplinary Thought ,
Vol 2, No 2 (2014): On the Concept of Globality.
"I CAN TELL you about my friend Andrew,
the cognitive scientist. But it’s not pretty."
— Opening of Andrew's Brain: A Novel by
E. L. Doctorow, Random House, Jan. 14, 2014*
"…whirligig consciousness…."
—The New York Times Book Review
See also Inside the White Square (Log 24, Feb. 15, 2015):
.
* Cf. Log24 on that date.
Continued from remarks of Marissa Mayer at Davos last year —
Related material — This evening's NY lottery…
… and Log24 post number 1424 —
The premiere of the Lily Collins film Abduction
(see previous post) was reportedly in Sydney, Australia,
on August 23, 2011.
From that date in this journal—
For the eight-limbed star at the top of the quaternion array above, She drew from her handbag a pale grey gleaming implement that looked by quick turns to me like a knife, a gun, a slim sceptre, and a delicate branding iron—especially when its tip sprouted an eight-limbed star of silver wire. “The test?” I faltered, staring at the thing. “Yes, to determine whether you can live in the fourth dimension or only die in it.” — Fritz Leiber, short story, 1959 |
Related material from Wikipedia, suggested by the reference quoted
in this morning's post to "a four-dimensionalist (perdurantist) ontology"—
"… perdurantism also applies if one believes there are temporal
but non-spatial abstract entities (like immaterial souls…)."
Margalit Fox in The New York Times this evening—
Judith Daniels, the founding editor in chief of Savvy ,
the first glossy magazine aimed at executive women,
died on Sunday at her home in Union, Me. She was 74….
“Savvy will not tell you how to be a good secretary,”
one of its early promotional fliers read. “Savvy will tell you
how to hire a good secretary— and how to fire.”
From the date of Daniels' death: The Crossword Omen.
See, too, Vogue in this journal and Ontology.
From a post of January 26, 2013—
Sally in the 2013 film Oblivion : "Are you an effective team?"
Related material: "universe of discourse"—
Excerpt from an essay cached nine years ago:
"The current dominant conceptual framework
which pictures the self as an inner entity
is slowly breaking up. And I am convinced that
some, if not all, of the approaches to the self
sketched here will form the basis for a new
conceptual framework…."
Context for the essay:
A journal issue titled "The Opening of Narrative Space" (pdf, 475 KB)
For one sort of narrative space, see Giordano Bruno in this journal.
See also Nine Years.
"… Western academic philosophy will likely come to appear
utterly parochial in the coming years if it does not find a way
to approach non-Western traditions that is much more rigorous
and respectful than the tokenism that reigns at present."
— Justin E. H. Smith in the New York Times philosophy
column "The Stone" yesterday
For example—
“… Which makes it a gilt-edged priority that one of us
gets into that Krell lab and takes that brain boost.”
— American adaptation of Shakespeare's Tempest , 1956
From "The Onto-theological Origin of Play:
Heraclitus and Plato," by Yücel Dursun, in
Lingua ac Communitas Vol 17 (October 2007)—
"Heraclitus’s Aion and His Transformations
The saying is as follows:
αἰὼν παῖς ἐστι παίζων, πεττεύων·
παιδὸς ἡ βασιληίη
(Aion is a child playing draughts;
the kingship is the child’s)
(Krell 1972: 64).*
* KRELL, David Farrell.
“Towards an Ontology of Play:
Eugen Fink’s Notion of Spiel,”
Research in Phenomemology ,
2, 1972: 63-93.
This is the translation of the fragment in Greek by Krell.
There are many versions of the translation of the fragment….."
See also Child's Play and Froebel's Magic Box.
Update of May 5— For some background
from the date May 4 seven years ago, see
The Fano Plane Revisualized.
For some background on the word "aion,"
see that word in this journal.
Happy birthday to Amy Adams
(actress from Castle Rock, Colorado)
"The metaphor for metamorphosis…" —Endgame
Related material:
"The idea that reality consists of multiple 'levels,' each mirroring all others in some fashion, is a diagnostic feature of premodern cosmologies in general…."
— Scholarly paper on "Correlative Cosmologies"
"How many layers are there to human thought? Sometimes in art, just as in people’s conversations, we’re aware of only one at a time. On other occasions, though, we realize just how many layers can be in simultaneous action, and we’re given a sense of both revelation and mystery. When a choreographer responds to music— when one artist reacts in detail to another— the sensation of multilayering can affect us as an insight not just into dance but into the regions of the mind.
The triple bill by the Mark Morris Dance Group at the Rose Theater, presented on Thursday night as part of the Mostly Mozart Festival, moves from simple to complex, and from plain entertainment to an astonishingly beautiful and intricate demonstration of genius….
'Socrates' (2010), which closed the program, is a calm and objective work that has no special dance excitement and whips up no vehement audience reaction. Its beauty, however, is extraordinary. It’s possible to trace in it terms of arithmetic, geometry, dualism, epistemology and ontology, and it acts as a demonstration of art and as a reflection of life, philosophy and death."
— Alastair Macaulay in today's New York Times
SOCRATES: Let us turn off the road a little….
— Libretto for Mark Morris's 'Socrates'
See also Amy Adams's new film "On the Road"
in a story from Aug. 5, 2010 as well as a different story,
Eightgate, from that same date:
The above reference to "metamorphosis" may be seen,
if one likes, as a reference to the group of all projectivities
and correlations in the finite projective space PG(3,2)—
a group isomorphic to the 40,320 transformations of S8
acting on the above eight-part figure.
See also The Moore Correspondence from last year
on today's date, August 20.
For some background, see a book by Peter J. Cameron,
who has figured in several recent Log24 posts—
"At the still point, there the dance is."
— Four Quartets
"Of course, the aesthetic program
of cultural modernism
has long been summed up
by the maxim épater la bourgeoisie."
— The New York Times
Sunday Book Review, July 17
Examples:
"This Extreme and Difficult Sense of Spectacular Representation:
Antonin Artaud's Ontology of 'Live'," by Deborah Levitt
of the New School (See the noon post of July 13), as well as…
and, from mathematician Ellen Gethner's home page—
See also Sunday Dinner, A Link for Sunrise, and Inside CBS News.
"Eighteenth century theories of language were often presented as genealogies; instead of looking to the functions or operations of language to describe its 'nature,' they appealed to the story of its origins (with more or less literalist intentions.) The interest in an original 'revealed' language began much earlier, however. Leibniz, for example, searched for a primitive root-language which he felt could be discovered through research into etymology, and asserted that this ur-text, whether its signifiers were natural or conventional, would be composed of rational relations worthy of its original author, or Author, that is, God. He also toyed with the notion that hieroglyphics might be a philosophical language, a kind of meaningful mathematics, whose revelations would be exact and necessary. The debate over the origins of language— and the status of hieroglyphics— as it played out in the eighteenth century was linked to a dispute over metaphor, conceived as a 'primitive' mode of expression which preceded and was less nuanced and precise than the 'arbitrary' modern European languages. What is essential here is not the specifics of the debate on the origins of language (although this would certainly add much to the present inquiry) but rather the link that was thus constituted between hieroglyphics, the primitive ('the savage and the poet speak only in hieroglyphics') and the idea of an archaic language as an original archive of meanings which pre-exists Man and his derivative or arbitrary tongues."
— "This Extreme and Difficult Sense of Spectacular Representation: Antonin Artaud's Ontology of 'Live'," by Deborah Levitt
^
"In several programming languages, such as C, C++, C#, Java, Perl, and Python, a caret (^) is used to denote the bitwise XOR operator. This is not used outside of programming contexts because it is too easily confused with other uses of the caret." —Wikipedia article on Exclusive Or
See also the above date, July 7, 2010, in this journal.
Philip K. Dick, author of the novel
on which the Harrison Ford film
"Blade Runner" (1982) was based.
"You'd never know it, but buddy
I'm a kind of poet."
Project Management at Villanova
Yesterday's noon post, "Lying Forth," linked to a passage by Walter A. Brogan, Professor of Philosophy at Villanova University.
A related Brogan remark for Harrison Ford's birthday—
"The last few pages of the text 'Différance' [an essay by Derrida] are a refutation of the nostalgia and hope involved in Heidegger's ontology, a rejection of the quest for the lost origin and final word."
Walter A. Brogan, "The Original Difference," pp. 31-40 in Derrida and Différance, ed. by David C. Wood and Robert Bernasconi (Northwestern University Press, 1988), p. 32
See, too, "Make a Différance."
"Rosemary Desjardins argues boldly and brilliantly that the Theaetetus contains not only an answer to the question of the character of knowledge, but considerably more besides — an outline of a Platonic ontology. That ontology is neither materialist nor idealist (it is not a theory of forms), but like the twentieth century theory known as generative emergence holds that beings are particular interactive combinations of material elements. On this view, while wholes (for example, words, to use a Platonic model) may be analyzed into their elemental parts (letters), each whole has a property or quality separate from the aggregated properties of its parts."
— Stephen G. Salkever, 1991 review of The Rational Enterprise : Logos in Plato's Theaetetus (SUNY Press, 1990)
See also "strong emergence" in this journal.
Death of a Nominalist
“All our words from loose using have lost their edge.” –Ernest Hemingway
(The Hemingway quotation is from the AP’s “Today in History” on July 21, 2007; for the context, see Death in the Afternoon.)
Today seems as good a day as any for noting the death of an author previously discussed in Log24 on January 29, 2007, and January 31, 2007.
Joseph Goguen died on July 3, 2006. (I learned of his death only after the entries of January 2007 were written. They still hold.)
Goguen’s death may be viewed in the context of the ongoing war between the realism of Plato and the nominalism of the sophists. (See, for instance, Log24 on August 10-15, 2004, and on July 3-5, 2007.)
Joseph A. Goguen, “Ontology, Society, and Ontotheology” (pdf):
“Before introducing algebraic semiotics and structural blending, it is good to be clear about their philosophical orientation. The reason for taking special care with this is that, in Western culture, mathematical formalisms are often given a status beyond what they deserve. For example, Euclid wrote, ‘The laws of nature are but the mathematical thoughts of God.’ Similarly, the ‘situations’ in the situation semantics of Barwise and Perry, which resemble conceptual spaces (but are more sophisticated– perhaps too sophisticated), are considered to be actually existing, real entities [23], even though they may include what are normally considered judgements.5 The classical semiotics of Charles Sanders Peirce [24] also tends towards a Platonist view of signs. The viewpoint of this paper is that all formalisms are constructed in the course of some task, such as scientific study or engineering design, for the heuristic purpose of facilitating consideration of certain issues in that task. Under this view, all theories are situated social entities, mathematical theories no less than others; of course, this does not mean that they are not useful.”
5 The “types” of situation theory are even further removed from concrete reality.
[23] Jon Barwise and John Perry. Situations and Attitudes. MIT (Bradford), 1983.
[24] Charles Sanders Peirce. Collected Papers. Harvard, 1965. In 6 volumes; see especially Volume 2: Elements of Logic.
From Log24 on the date of Goguen’s death:
Requiem for a clown:
“At times, bullshit can only be
countered with superior bullshit.”
This same Mailer aphorism was quoted, along with an excerpt from the Goguen passage above, in Log24 this year on the date of Norman Mailer’s birth. Also quoted on that date:
Sophia. Then these thoughts of Nature are also thoughts of God.
Alfred. Undoubtedly so, but however valuable the expression may be, I would rather that we should not make use of it till we are convinced that our investigation leads to a view of Nature, which is also the contemplation of God. We shall then feel justified by a different and more perfect knowledge to call the thoughts of Nature those of God….
Whether the above excerpt– from Hans Christian Oersted‘s The Soul in Nature (1852)– is superior to the similar remark of Goguen, the reader may decide.
On the ABC-conjecture in number theory:
“We hope to elucidate the beautiful connections between elliptic curves, modular forms and the ABC–conjecture.” —Dorian Goldfeld (pdf)
An Edinburgh postgraduate student on the conjecture:
“… abc brings us full circle to Fermat’s Last Theorem….” —Graeme Taylor at Everything2.com
I regret I can add nothing to Taylor’s admirable exposition and to Goldfeld’s “beautiful connections” except the following observation of a rather ugly connection.
The previous Log24 entry, from yesterday afternoon, related the May 18 “details” entry to Friday’s PA evening lottery number, 005. A followup seems (if only to honor the madcap tradition of John Nash) to be called for. The PA evening number yesterday evening, Saturday, was 443. Nash, in his younger days, might have been pleased to note that this number is associated (if only by coincidence) with a topic Woit mentioned earlier yesterday– Fermat’s famed conjecture:
in The Annals of Mathematics,
2nd Ser., Vol. 141, No. 3 (May, 1995)
This is the first page of a rather
famous paper by Andrew Wiles.
“At times, bullshit can only be
countered with superior bullshit.”
— Norman Mailer
“It may be that universal history is the
history of the different intonations
given a handful of metaphors.”
— Jorge Luis Borges (1951),
“The Fearful Sphere of Pascal,”
in Labyrinths, New Directions, 1962
— Joseph A. Goguen, “Ontology, Society, and Ontotheology” (pdf)
Goguen does not give a source for this alleged “thoughts of God” statement.
A Web search for the source leads only to A Mathematical Journey, by Stanley Gudder, who apparently also attributes the saying to Euclid.
Neither Goguen nor Gudder seems to have had any interest in the accuracy of the Euclid attribution.
Talk of “nature” and “God” seems unlikely from Euclid, a pre-Christian Greek whose pure mathematics has (as G. H. Hardy might be happy to point out) little to do with either.
Loose talk about God’s thoughts has also been attributed to Kepler and Einstein… and we all know about Stephen Hawking.
Gudder may have been misquoting some other author’s blather about Kepler. Another possible source of the “thoughts of God” phrase is Hans Christian Oersted. The following is from Oersted’s The Soul in Nature—
“Sophia. Nothing of importance; though indeed I had one question on my lips when the conversion took the last turn. When you alluded to the idea, that the Reason manifested in Nature is infallible, while ours is fallible, should you not rather have said, that our Reason accords with that of Nature, as that in the voice of Nature with ours?
Alfred. Each of these interpretations may be justified by the idea to which it applies, whether we start from ourselves or external nature. There are yet other ways of expressing it; for instance, the laws of Nature are the thoughts of Nature.
Sophia. Then these thoughts of Nature are also thoughts of God.
Alfred. Undoubtedly so, but however valuable the expression may be, I would rather that we should not make use of it till we are convinced that our investigation leads to a view of Nature, which is also the contemplation of God. We shall then feel justified by a different and more perfect knowledge to call the thoughts of Nature those of God; I therefore beg you will not proceed to [sic] fast.”
Oersted also allegedly said that “The Universe is a manifestation of an Infinite Reason and the laws of Nature are the thoughts of God.” This remark was found (via Google book search) in an obscure journal that does not give a precise source for the words it attributes to Oersted.
Semantic Transparency
"… semantic transparency … would allow disparate systems to share some understanding of the actual concepts that are represented…"
— IBM Developer Works on October 7, 2003
"There is no neutral ground
that can serve as
a means of translating between
specialized (lower) ontologies."
There is, however,
"the field of reason"–
the 3×3 grid:
Click on grid
for details.
From a Log24 entry of January 7, 2007:
"One of the primary critiques of modernism that Learning from Las Vegas was engaged in, as Frederic [sic] Jameson clearly noted, was the dialectic between inside and outside and the assumption that the outside expressed the interior. Let's call this the modernist drive for 'expressive transparency.'"
— Aron Vinegar of Ohio State U., "Skepticism and the Ordinary: From Burnt Norton to Las Vegas"
From this week's New Yorker (issue dated Jan. 22, 2007)–
"A Life," by Zbigniew Herbert
(translated from the Polish by Alissa Vales):
I was a quiet boy a little sleepy and–amazingly–
unlike my peers–who were fond of adventures–
I didn't expect much–didn't look out the window
At school more diligent than able–docile stable
For the rest of the poem, click here.
From the Wikipedia article on Zbigniew Herbert:
"In modern poetry, Herbert advocated semantic transparence. In a talk given at a conference organized by the journal Odra he said: 'So not having pretensions to infallibility, but stating only my predilections, I would like to say that in contemporary poetry the poems that appeal to me the most are those in which I discern something I would call a quality of semantic transparency (a term borrowed from Husserl's logic). This semantic transparency is the characteristic of a sign consisting in this: that during the time when the sign is used, attention is directed towards the object denoted, and the sign itself does not hold the attention. The word is a window onto reality.'"
(Wikipedia cites as the source–
Herbert's talk at the meeting "Poet in face of the present day," organized by the "Odra" journal. Print version: Preface to: Zbigniew Herbert "Poezje," Panstwowy Instytut Wydawniczy, Warszawa 1998, ISBN 83-06-02667-5.)
Fom Nabokov's Transparent Things (pdf):
"Its ultimate vision was the incandescence of a book or a box grown completely transparent and hollow. This is, I believe, it: not the crude anguish of physical death but the incomparable pangs of the mysterious mental maneuver needed to pass from one state of being to another. Easy, you know, does it, son."
Related material:
(continued from
January 9, 2003)
George Balanchine
|
"What on earth is
a concrete universal?"
— Robert M. Pirsig
Review:
From Wikipedia's
"Upper Ontology"
and
Epiphany 2007:
"There is no neutral ground
that can serve as
a means of translating between
specialized (lower) ontologies."
There is, however,
"the field of reason"–
the 3×3 grid:
Click on grid
for details.
As Rosalind Krauss
has noted, some artists
regard the grid as
"a staircase to
the Universal."
Other artists regard
Epiphany itself as an
approach to
the Universal:
— Richard Kearney, 2005,
in The New Arcadia Review
Kearney (right) with
Martin Scorsese (left)
and Gregory Peck
in 1997.
— Richard Kearney, interview (pdf) in The Leuven Philosophy Newsletter, Vol. 14, 2005-2006
For more on "the possible," see Kearney's The God Who May Be, Diamonds Are Forever, and the conclusion of Mathematics and Narrative:
|
"We symbolize
logical necessity with the box  )and logical possibility with the diamond  )."
"The possibilia that exist,
— Michael Sudduth, |
An Epiphany
for the Birthday
of E. L. Doctorow,
Author of
City of God
(Doctorow wrote about
New York. A city more
closely associated with
God is Jerusalem.)
On the morning of January 2 this year, inspired by Sambin’s “basic picture,” I considered an entry dealing with Galois lattices (pdf). This train of thought was halted by news of the death earlier that morning of Teddy Kollek, 95, a founder of the Israeli intelligence service and six-term mayor of Jerusalem. (This led later to the entry “Damnation Morning“– a reference to the Fritz Leiber short story.)
This morning’s entry reboards the Galois train of thought.
Here are some relevant links:
Galois Connections (a French weblog entry providing an brief overview of Galois theory and an introduction to the use of Galois lattices in “formal concept analysis“)
Ontology (an introduction to formal concept analysis linked to on 3/31/06)
One motive for resuming consideration of Galois lattices today is to honor the late A. Richard Newton, a pioneer in engineering design who died at 55– also on Tuesday, Jan. 2, the date of Kollek’s death. Today’s New York Times obituary for Newton says that “most recently, Professor Newton championed the study of synthetic biology.”
A check of syntheticbiology.org leads to a web page on– again– ontology.
For the relationship between ontology (in the semantic-web sense) and Galois lattices, see (for instance)
“Knowledge Organisation and Information Retrieval Using Galois Lattices” (ps) and its references.
An epiphany within all this that Doctorow might appreciate is the following from Wikipedia, found by following a link to “upper ontology” in the syntheticbiology.org ontology page:
- There is no self-evident way of dividing the world up into concepts.
- There is no neutral ground that can serve as a means of translating between specialized (lower) ontologies.
- Human language itself is already an arbitrary approximation of just one among many possible conceptual maps. To draw any necessary correlation between English words and any number of intellectual concepts we might like to represent in our ontologies is just asking for trouble.
Related material:
The intellectual concepts
mentioned by Richard Powers
at the end of tomorrow’s
New York Times Book Review.
(See the links on these concepts
in yesterday’s “Goldberg Variation.”)
See also Old School Tie.
Augustine of Hippo, who is said to
have died on this date in 430 A.D.
"He is, after all, not merely taking over a Neoplatonic ontology, but he is attempting to combine it with a scriptural tradition of a rather different sort, one wherein the divine attributes most prized in the Greek tradition (e.g. necessity, immutability, and atemporal eternity) must somehow be combined with the personal attributes (e.g. will, justice, and historical purpose) of the God of Abraham, Isaac, and Jacob."
— Stanford Encyclopedia of Philosophy on Augustine
Here is a rather different attempt
to combine the eternal with the temporal:
|
The Eternal
Symbol of necessity,
For details, see |
The Temporal
Symbol of the
For details, see |
|
The eternal
combined with the temporal:
|
|
Related material:
— Opening sentence of
Martha Cooley’s The Archivist
“Frere Jacques, Cuernavaca,
ach du lieber August.”
— John O’Hara, Hope of Heaven, 1938
Mathematics and Narrative
continued…
“Now, at the urging of the UC Berkeley cognitive linguist George Lakoff, liberal America’s guru of the moment, progressive Democrats are practicing to get their own reluctant mouths around some magical new vocabulary, in the hope of surviving and eventually overcoming the age of Bush.”
— Marc Cooper in The Atlantic Monthly, April 2005, “Thinking of Jackasses: The Grand Delusions of the Democratic Party”
Cooper’s “now” is apparently still valid. In today’s New York Times, the leftist Stanley Fish reviews Talking Right, by leftist Geoffrey Nunberg:
“… the right’s language is now the default language for everyone.
On the way to proposing a counterstrategy (it never really arrives), Nunberg pauses to engage in a polite disagreement with his fellow linguist George Lakoff, who has provided a rival account of the conservative ascendancy. Lakoff argues that Republicans have articulated– first for themselves and then for others– a conceptual framework that allows them to unite apparently disparate issues in a single coherent worldview … woven together not in a philosophically consistent framework but in a narrative ‘that creates an illusion of coherence.’
Once again, the Republicans have such a narrative– ‘declining patriotism and moral standards, the out-of-touch media and the self-righteous liberal elite … minorities demanding special privileges … disrespect for religious faith, a swollen government’– but ‘Democrats and liberals have not offered compelling narratives that could compete’ with it. Eighty pages later he is still saying the same thing. ‘The Democrats need a compelling narrative of their own.'”
Lakoff is the co-author of a book on the philosophy of mathematics, Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being. From Wikipedia’s article on Lakoff:
“According to Lakoff, even mathematics itself is subjective to the human species and its cultures: thus ‘any question of math’s being inherent in physical reality is moot, since there is no way to know whether or not it is.’ Lakoff and Rafael E. Nunez (2000) argue at length that mathematical and philosophical ideas are best understood in light of the embodied mind. The philosophy of mathematics ought therefore to look to the current scientific understanding of the human body as a foundation ontology, and abandon self-referential attempts to ground the operational components of mathematics in anything other than ‘meat.'”
For a long list of related leftist philosophy, see The Thinking Meat Project.
Democrats seeking narratives may also consult The Carlin Code and The Prime Cut Gospel.
— Rebecca Goldstein,
Mathematics and
the Character of Tragedy
The winning numbers
for Tuesday, May 2–
the feast of
St. Athanasius:
“You gotta be true to your code”
— Sinatra (see previous entry)
| Dewey Decimal Code:
703 The Arts: Related material: For the arts, see |
“All persons living and dead are purely coincidental….”– Kurt Vonnegut, epigraph to Bagombo Snuff Box
* For instance,
David Auburn in Proof,
which also involves
Dewey decimal numbers
Women's History Month continues…
Ontology Alignment
"He had with him a small red book of Mao's poems, and as he talked he squared it on the table, aligned it with the table edge first vertically and then horizontally. To understand who Michael Laski is you must have a feeling for that kind of compulsion."
— Joan Didion in the
Saturday Evening Post,
Nov. 18, 1967 (reprinted in
Slouching Towards Bethlehem)
"Or were you," I said.
He said nothing.
"Raised a Catholic," I said.
He aligned a square crystal paperweight with the edge of his desk blotter.
— Joan Didion in
The Last Thing He Wanted,
Knopf, 1996
"It was Plato who best expressed– who veritably embodied– the tension between the narrative arts and mathematics….
Plato clearly loved them both, both mathematics and poetry. But he approved of mathematics, and heartily, if conflictedly, disapproved of poetry. Engraved above the entrance to his Academy, the first European university, was the admonition: Oudeis ageometretos eiseto. Let none ignorant of geometry enter. This is an expression of high approval indeed, and the symbolism could not have been more perfect, since mathematics was, for Plato, the very gateway for all future knowledge. Mathematics ushers one into the realm of abstraction and universality, grasped only through pure reason. Mathematics is the threshold we cross to pass into the ideal, the truly real."
— Rebecca Goldstein,
Mathematics and
the Character of Tragedy
"We symbolize logical necessity
with the box )
and logical possibility
with the diamond ).
— Keith Allen Korcz,
(Log24.net, 1/25/05)
And what do we
symbolize by 
?
On the Lapis Philosophorum,
the Philosophers' Stone –
"'What is this Stone?' Chloe asked….
'…It is told that, when the Merciful One
made the worlds, first of all He created
that Stone and gave it to the Divine One
whom the Jews call Shekinah,
and as she gazed upon it
the universes arose and had being.'"
– Many Dimensions,
by Charles Williams, 1931
(Eerdmans paperback,
April 1979, pp. 43-44)
"The lapis was thought of as a unity
and therefore often stands for
the prima materia in general."
– Aion, by C. G. Jung, 1951
(Princeton paperback,
1979, p. 236)
"Its discoverer was of the opinion that
he had produced the equivalent of
the primordial protomatter
which exploded into the Universe."
– The Stars My Destination,
by Alfred Bester, 1956
(Vintage hardcover,
July 1996, p. 216)
"The possibilia that exist,
and out of which
the Universe arose,
are located in
a necessary being…."
— Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)
See also
The Diamond Archetype.
For more on modal theology, see
Kurt Gödel's Ontological Argument
and
The Ontological Argument
from Anselm to Gödel.
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