So within reason talks about Recursive Automorphism ---citing and earlier claim that
the infinite is the quality of being eternally recursive..
We've got to take note of the Infinite Reflections in the Mirror Project.
Simply ... its a collection of pictures taken with digital cameras (mostly, I think) and mirrors .. to .... guess what ... generate Infinite Reflections. Neat!
and there are a lot of other neat projects there.
really ... what about Paul Cohen, Cantor and Godel?
Really need to understand this Axiom of Choice thing ...
W. Hugh Woodin for example writes about .... The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal
What about Transfinite Numbers ....
the record costliest Transfinite -- not transexual --- are:
L V Kantorovich: Selected Works by Vsevolod L Kantorovich, S.S. Kutateladze, and J.V. Romanovsky and Kronecker's Jugendtraum and Modular Functions by S. G. Vladut .... you could probably go crazy just thinking about the price ... let alone the Ein-Sof ian infinities.
of course ... you can't possibly be serious unless you read Cohen's Set Theory and the Continuum Hypothesis (Paul J. Cohen (Author) )
This is really interesting -- a map of online communities
gives you a sense of what's really going on ...
Of course STRANGE MAPS has a really extensive collection of interesting maps worth visiting often
that's the question raised by Information Week .... read the answere here
The swimoff is between Vista and Ubuntu and the results are fascinating
certainly worth keeping an eye on this unfolding story
Not Even Wrong alerts us to several new string theory books ... Peter finds String Theory and M-Theory: A Modern Introduction [by Katrin Becker, Melanie Becker, John H. Schwarz] "The most complete of the three books" -- however, he cautions the aspiring grad student 'Any student who chooses to follow this path will need to devote many years to mastering this material ...There’s no particular reason to believe that this kind of training is one that will lead to a solid background in techniques that are likely to have more success in the future."
If that doesn't make you think twice ... or more ... you might just like the punishment. So in other words ... its as fine an ivory tower you can find if someone is willing to pay your way ... and you really don't care to accomplish much ... Maybe I am just reading too much into this. Of course you could just retire as a monk and crossbreed peas ...
Its incredible ... looking at the SM ... its been going exponential ...if you look over the past 60 years ... that means the value of the money is probaly declining exponentially .... Well it seems like its hard to tell ... the real question is what is the deflated value per capita ... (or indexed value PerCapita ...)
Actually, Archimedes was mostly right ... but his explanations, according to Ernst Mach, were circular in some cases ... and unless you were at an intellectual level of Mach ... you probably wouldn't notice it. However, if you understood and appreciated Mach ... you might have been in the Einstein League ...
find more information on:
Archimedes, and
Mach
"Browse through 85 billion web pages archived from 1996 to a few months ago." - that's what it says over at Internet Archive
Wow! but what about now ... how Do they decide when to cut off the archive ... when recent is recent and needs no archiving? maybe something will slip through the cracks ...
Really, if universities have been around for so long, why are we so behind? In understanding what we need to do ...
Italy seemed to have a pretty good head start ... No Bologna here ... actually UB looks to have been the first European University .... hats off to Bologna ...
Wikipedia has an interesting list of oldest continuously operating universities. The abridged list is reproudced below:
[year founded, location, name, name details]
859 Fes, Morocco University of Al Karaouine -- Considered to be the "oldest existing educational institution in the world". (Note --Shishi Middle School, China, claims to have been formed in 143 BC and so would be the longest running educational instituion, making the University of Al Karaouine the oldest University in the world.)
988 Cairo, Egypt Al-Azhar University -- Considered by most Sunni Muslims to be the most prestigious school of Islamic learning
1088 Bologna, Italy University of Bologna
1150 Paris, France University of Paris Now split among several autonomous universities
1167 Oxford, England University of Oxford Exact date uncertain, founded before 1167
1175 Modena, Italy University of Modena
1209 Cambridge, England University of Cambridge
1212 Valladolid, Spain University of Valladolid Claims continuity with University of Palencia, founded in 1212 in Palencia [1]
1218 Salamanca, Spain University of Salamanca
1220 Montpellier, France University of Montpellier
1222 Padua, Italy University of Padua
1224 Naples, Italy University of Naples Federico II
1229 Toulouse, France University of Toulouse
1240 Siena, Italy University of Siena
1290 Coimbra, Portugal University of Coimbra Founded in Lisbon
1303 Rome, Italy University of Rome La Sapienza
1308 Perugia, Italy University of Perugia
1336 Camerino, Italy University of Camerino
1343 Pisa, Italy University of Pisa
1348 Prague, Czech Republic Charles University of Prague
1361 Pavia, Italy University of Pavia
1364 Kraków, Poland Jagiellonian University
1365 Vienna, Austria University of Vienna
1367 Pécs, Hungary University of Pécs
1386 Heidelberg, Germany Ruprecht Karls University of Heidelberg
1391 Ferrara, Italy University of Ferrara
1402 Würzburg, Germany University of Würzburg
1404 Turin, Italy University of Turin
1409 Germany Leipzig, Germany University of Leipzig
1412 Scotland St. Andrews, Scotland University of St. Andrews
1419 Germany Rostock, Germany University of Rostock
1425 Belgium Leuven, Belgium Catholic University of Leuven Now split between the French-speaking Université catholique de Louvain, Louvain-la-Neuve and the Dutch-speaking Katholieke Universiteit Leuven, still at Leuven
1431 France Poitiers, France University of Poitiers
1434 Catania, Italy University of Catania
1451 Glasgow, Scotland University of Glasgow
1456 Greifswald, Germany Ernst Moritz Arndt University of Greifswald
1457 Freiburg, Germany Albert Ludwigs University of Freiburg
1460 Basel, Switzerland Basel University
1465 Bratislava, Slovakia Academia Istropolitana
1472 Munich, Germany Ludwig Maximilians University of Munich
1473 Trier, Germany University of Trier
1477 Uppsala, Sweden Uppsala University
1477 Tübingen, Germany Eberhard Karls University of Tübingen
1477 Mainz, Germany Johannes Gutenberg University of Mainz
1479 Copenhagen, Denmark University of Copenhagen
1481 Italy Genoa, Italy University of Genoa
1495 Aberdeen, Scotland University of Aberdeen King's College was founded in 1495 and Marischal College in 1593; they merged in 1860
1495 Santiago de Compostela, Spain University of Santiago de Compostela
1499 Madrid, Spain Complutense University of Madrid Claims continuity with Estudio de Escuelas Generales de Alcalá, founded in 1293 in Alcalá de Henares
1499 Valencia, Spain University of Valencia
Post-1500, oldest universities by country or region
* Algeria: University of Algiers, 1909
* Americas: Universidad Autonoma de Santo Domingo, Dominican Republic, 1538
* Argentina: Universidad Nacional de Córdoba, 1610
* Armenia: Yerevan State University , 1919
* Australia: University of Sydney, 1850
* Azerbaijan: Baku State University, 1919
* Baltic States: Vilnius University, 1579, twice closed and reopened
* Bangladesh: University of Dhaka, 1921
* Bosnia-Herzegovina: University of Sarajevo, 1940, successor to the Sharia Law School founded in 1531
* Brazil: Universidade Federal do Paraná, 1921 (note: the oldest institution of higher learning in Brazil, though not a university, is the Instituto Militar de Engenharia, founded under the name of Academia Real Militar 1811).
* Bulgaria: University of Sofia, 1888
* Canada: Université Laval, 1663; University of New Brunswick is the oldest English language university in Canada, founded in 1785
* Chile: Universidad de Chile, 1622, 19 August, as Santo Tomás de Aquino
* China:
o Nanking University, the first school officially called university in English in China, 1888. It's also the first to offer doctoral education in China, 1913.
o Beiyang University, the first school called 大學堂(Daxuetang or Daxue, today's Chinese translation of university), 1896. Beijing University to be the second, 1898.
o St. John's University, Shanghai, the first school granting bachelor's degree in China, 1907.
* Colombia: Universidad del Rosario, 1653
* Croatia: University of Zagreb, 1669
* Cuba: Universidad de La Habana, 1728
* East Timor: National University of Timor-Leste, 2000
* Estonia: University of Tartu, 1802, successor to Academia Gustaviana (1632-1710)
* Finland: University of Helsinki, 1640, originally the Academy of Turku, but moved to Helsinki in 1827
* Georgia: Tbilisi State University, 1918
* Greece: University of Athens, 1837
* Hong Kong: University of Hong Kong, 1912, evolved from the Hong Kong College of Medicine, founded in 1887
* India: University of Calcutta, 1857, the oldest full fledged university in South Asia
o Serampore College with university status (though not a university), 1818
* Indonesia: Institut Teknologi Bandung, 1920, founded as the Technische Hogeschool te Bandoeng
* Iran: University of Tehran, 1934
* Iraq: University of Baghdad, 1956 - Although the Iraqi Royal College of Medicine was established in 1928.
* Ireland: Trinity College, Dublin, 1592
* Israel: Technion, 1924
* Japan: University of Tokyo, 1877
* Korea: Korea University, 1905
* Lebanon: American University of Beirut, 1866
* Lithuania: University of Vilnius, 1579, successory to the Vilnius Academy 1570
* Malaysia: University of Malaya, 1905
* Malta: University of Malta, 1769, successory to Collegium Melitense 1592
* Mexico: National Autonomous University of Mexico, 1551 (or 1910 [2])
* Myanmar: Rangoon University,1878
* Netherlands: University of Leiden, 1575
* New Zealand: University of Otago, 1869
* North America: National Autonomous University of Mexico, 1551 (or 1910 [3])
* Norway: University of Oslo, 1811
* Spain:University of Oviedo,1608 [4]
* Pakistan: University of the Punjab, 1882
* Peru: National University of San Marcos, 1551
* Philippines: Disputed by two universities:
o University of San Carlos, established as the Colegio de San Ildefonso 1595 by the Jesuits, closed in 1769, reopened in 1783 by the local bishop, transferred ownership to the Dominicans (1852), then to the Vincentians (1867), and finally to the Society of the Divine Word fathers on 1935. Closed on 1941 during World War II; opened again on 1945. Received university charter in 1948.
o University of Santo Tomas, established as the Colegio de Nuestra Señora del Santísimo Rosario on 1611, received university charter in 1645, closed during World War II, reopened during post-war rebuilding. Owned by the Dominicans in its entirety of existence.
* Romania: Alexandru Ioan Cuza University, Iasi, 1860
* Russia: either Moscow State University, 1755 or Saint Petersburg State University (1724-1803, 1819) or Kant Russian State University (1544-1945, 1967)
* Serbia: Belgrade University, 1905, successor to the Great School, 1808; Orthodox Christian Academy in 1794; Teacher's college in 1778
* Singapore: National University of Singapore, 1905
* Slovenia: University of Ljubljana, 1810
* South America: National University of San Marcos, Peru, 1551
* South Africa: University of Cape Town, 1829
* Thailand: Chulalongkorn University, 1917
* Turkey: Istanbul Technical University (1773)
* Ukraine: University of Lviv, 1661
* Venezuela: Central University of Venezuela, 1721
American Universities have little debate underway [though non can claim being really old]... right now the discussion basically comes down to:
(In alphabetical order by full institutional name):
* The College of William and Mary's website states, "The College of William and Mary was the first college to become a university (1779)."
* Educational historian Frederick Rudolph once said Cornell University was "the first American university" [3]. However, Rudolph did not mean that Cornell was the first university in America, but rather that it was in the vanguard of sweeping changes brought about by the Land Grant movement which created a characteristically American style of institution: coeducational, nonsectarian, egalitarian, and with a curriculum not focused on the Latin and Greek classics.[citation needed]
* Harvard University itself claims only to be "the oldest institution of higher education in the United States". The claim of being "the first university" has been made on its behalf by others, e.g., the title of a book published in 1886: Bush, George Gary (1886). Harvard, the First American University. Cupples, Upham and Company, Boston.
* Johns Hopkins University says, "The Johns Hopkins University was the first research university in the United States." Johns Hopkins claim is based on its adherence to the German university model that stresses research as the primary function of a university.
* University of Pennsylvania makes claim on their website of being "America's First University". The university has published a book about being the first university in America: (2000) Building America's First University: An Historical and Architectural Guide to the University of Pennsylvania;
* Georgetown University claims that Jesuit teaching began on the same site where the university still stands in 1634, which, if taken to be the founding date of the university, would make it the oldest in the United States. However, formal construction of the current campus began in 1788 which is why many accept 1789 as its true founding date.
[edit] Facts that have been used to support claims of being "the first university in the United States"
So I was watching Peter Higgs' 'My life as a Boson' lecture over at the Michigan Theoretical Physics website ... first ... this Good Will Hunting for the Higgs Bosons will really have to end one day ... the more more i read and watch these things ... the more I am convinced that its really time to move on to other topics .... second ... the Einstein-Bohr issue hasn't really been solved to any degree of satisfaction ... roll back the film please.
[you do know there's actually a Higgs Hunter's Guide ... but what about a String Hunter's Guide] and that's no Hip-Hop/Hop-Hip
In case you're wondering what's really happening at the edge of the edge [like right t the perimeter ;-) ]... or were curious here eternity fits in ... Joy's got it figured out! In the the arxiv preprint Joy Christian of the Perimeter Institute writes "Contrary to our immediate and vivid sensation of past, present, and future as continually shifting non-relational modalities, time remains as tenseless and relational as space in all of the established theories of fundamental physics." -- the way to find out if this is really the case is to examine "the oscillating flavor ratios of ultrahigh energy cosmic neutrinos, or of altering pulse rates of extreme energy binary pulsars."
some where in the paper, Joy tracks back to the Eleatics who "argued that change is nothing but an illusion, thereby rejecting the prevalent view, expounded by Heraclitus, that becoming is all there is." maybe reflections of reflections just don;t exist [kidding of course ... they'e just tightly entangled].
in any case probably a must read .. so I'll read it ... but i alrady probably readit/didn't read it ... since nothing changes ...
-- in any case if this kind of stuff interests you ... you probably should look at Appleby's "Concerning Dice and Divinity" discussion about physical realism.
NO - its really not a B movie ... its more like an F- for civilization. Apparently honeybee colonies are dying off ... with dire ramifications in tow .... Reported in hte NY Times [via the Volokh Conspiracy] .. this is particularly distressing if you like flowers and fruits and things that need to be pollinated ...
a propos nothing:
De arte logistica Joannis Naperi Merchistonii baronis libri qui supersunt By John Napier -- mentions that around 1544 Michael Stifel publishes Arithmetica integra introduces the notation: +, -, √. [Note ... per U. ST. ANDREWS Math Chronology Stifel's integra also contains discussion of binomial coefficients]
-- it also mentions Robert Recorde's [1557] The Whetstone of Witte which introduces = (the equals sign) into mathematics.
--- so in a short span of time we have: +, -, √, = symbols and Logarithms ... and this allows incredible jumps in mathematical thinking and calculations (not to speak of, but also worth of mention is the understanding of the importance of zero and its position power]
--
A) Rousseau's Dog: Two Great Thinkers at War in the Age of Enlightenment by David Edmonds, John Eidinow
B) Google engEDU videos of course we'll need to add some more filters
[right now watching Google Tech Talks April 9, 2007 by Craig Mello who was awarded the Nobel Prize in Physiology or Medicine in 2006-- he's talking about RNAi and C. elegans. Mello and colleague Andrew Fire [Carnegie Institution of Washington], discovered RNAi, a natural but previously unrecognized process by which a certain form of RNA can be manipulated to silence—or interfere with—the expression of a selected gene.] pretty interesting ... worth following up
Bigeometric Calculus: A System With a Scale-free Derivative By Michael Grossman is pretty interesting --- it has a lot if interesting references ... not quite sure if the subject matter is useful ... but the quotes and citations are likely to be of high value.
[random path along the search for Jacques Hadamard's Psychology of Innovation in the Mathematical Field]
{the GoogleBook version of Bigeometrric Calculus is here
Everything is just SUPER for SUPERQUARK Man Murray Gell-Mann .. quite an elementary yet entertaining talk (On Getting Creative Ideas) for the Google Tech Crowd. The G-Man views himself the patron of superstrings (before they were popular)... the main talk was about aspects of creative ideas .. and there some interesting anecdotes ... clearly ... he likes to pronounce people's names as they would sound in their home tongue ...
In the Q&A lots of discussion about ... superstrings -> supersymmetry ... breaking of the symmetry ... superpartners ... When asked about the little that superstring has produced to date he credits superstring theory with retrodiction of the general theory of relativity. About the debate ... he says its all a question of money ... that those that feel string theory is getting more money that it deserves - are essentially unhappy that string theory is crowding other areas out ...
I probably didn't capture it all precisely ... but there's some of the wild quantumal in me ... its just that uncertainty has to rule ... ;-0
One wonders what his take would be about woit's Not Even Wrong perspective.
Is the Univese Infinite? The evidence points against it ... but ...
What does general relativity have to say on the topic? cosmology?
Where would the energy come from?
Prime Causes?
Are there infinite numbers of questions? Good Questions?
No Vacation here!
So here's a path to the edge ... search for Concept of Infinity
Google scholar reports 642 links today ... the first interesting hit suggests is ERIC # EJ436607
The Conceptual Evolution of Actual Mathematical Infinity - by Authors: Moreno A., Luis E.; Waldegg, Guillermina in Educational Studies in Mathematics, v22 n3 p211-31 Jun 1991 [Abstract: Analyzed are the different stages in the conceptual evolution of infinity as developed historically through the work of Bolzano and Cantor. Results of a study of 18 to 20 year old's concept of infinity prior to instruction produced aspects of the passage between conceptual levels of infinity].
Interesting youtubevid "teaching the machine" {actually its Web2.0 digital ethanography [via Beyond Real Time] }
One wonders what's going on right at the edge of infinity - right now?
It would appear there was a lot of excitement around the Cantor Era ... but its not clear that the same excitement and vitality is there (here?) today.
Google Scholar has a number of citations for Dauben: His Mathematics and Philosophy of the Infinite [here] [like Jourdain's review of Set Theory]
see the real time Technorati stats "Georg Cantor" per day for the last 30 days.
Get your own chart!
Leibniz is very important fellow to understand ... here's another character that cast intense illumination and generated many interesting ideas ... to be continued.
