Atmosphere of The Derby Epsom Downs
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The inflorescence of Romanesco broccoli or Romanesque cauliflower. Each bud is composed of a series of smaller buds, each arranged in a logarithmic spiral. Mathematicians use the term fractal to describe a curve or geometrical figure, each part of which has the same statistical character as the whole. In Romanesco broccoli, the pattern is only an approximate fractal since the pattern eventually terminates when the feature is sufficiently small. For more information see: en.wikipedia.org/wiki/Romanesco_broccoli
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I am very grateful for the very kind comments and faves. Thanks for visiting.
There is a colour photo (shallower dof) in the first comment.
f/32 1.6sec ISO 800 Pentax 100mm Pentax K-1
Taken on the dark and rainy Nottingham Light Night 2021.
More information about the mill and the mathematician can be found here:
"Ooops ... I need to review the logarithms"
For Flickr group "Happy Caturday!", topics: "Our cats by numbers"
Here's a pretty scene in a favorite garden of mine in Kuala Lumpur. The shrub on the right is the Toothbrush Tree. It was first described (1790) for the West by that indefatigable Portuguese Jesuit priest, João de Loureiro (1717-1791). He worked in Cochinchina as a missionary, of course, but primarily as a mathematician and naturalist often in the service of local royalty.
Twigs of this shrub were 'frayed' at their ends and served as instruments to clean teeth. Apparenly there's some biochemical reaction as well in that process. The tooth white of the bridge is an apt reminder of that remedy.
The Frederick Douglass Centre, Newcastle University, UK.
The story and importance of Frederick Douglass can be found here:
www.ncl.ac.uk/who-we-are/frederick-douglass/
Design (2019): Sheppard Robson.
The auditorium uses a cladding system inspired by the Newcastle-born mathematician Louis Fry Richardson whose pioneering work defined modern methods of weather forecasting. Fry Richardson’s work, which subdivided the planet into hexagonal zones, has been expressed in expanded aluminium mesh on the external elevations of the auditorium. A pattern has been created by the changing the orientation of the mesh, varying the opacity of the material.
Desde fuera, Santa Sofía no intenta seducir. Es un bloque imponente, reforzado por contrafuertes, que parece más preocupado por resistir que por impresionar. Pero basta con cruzar sus puertas para que el tiempo se diluya y el asombro se imponga. Su grandeza no está en las proporciones externas, sino en el espacio que contiene: un interior que desafía, incluso hoy, la lógica de lo posible.
Inaugurada en el año 537, esta es la tercera versión del templo. Las dos anteriores sucumbieron a las revueltas populares, pero la versión 3.0 no solo resistió, sino que cambió la historia de la arquitectura. Para concebir semejante prodigio hicieron falta un físico y un matemático: Isidoro de Mileto y Antemio de Tralles. No se limitaron a diseñar un edificio; imaginaron lo inconcebible para su época.
Los innumerables terremotos que ha sufrido Estambul han intentado derribarla, pero ahí sigue. Y su cúpula sigue siendo el prodigio más evidente: 31,87 metros de diámetro, suspendida a 56,6 metros de altura, flotando como por arte de magia sobre un anillo de ventanas. Durante casi mil años, Santa Sofía fue el edificio religioso más grande del mundo. Lo más asombroso es que, pese a sus dimensiones, no abruma. Todo en ella —la luz, las proporciones, la acústica— está pensado para elevar, no para aplastar.
Para su construcción se emplearon algunos de los materiales más preciosos del mundo antiguo, y todavía se percibe. Columnas de mármol traídas de Éfeso, pórfido de Egipto, piedra verde de Tesalia, ónice de Frigia... Un catálogo de imperios antiguos al servicio de la nueva Roma. Todo fue elegido para deslumbrar.
Y si algo detiene el paso, son los mosaicos. Dorados, delicados, suspendidos en el tiempo, sobreviven como fragmentos de una gloria que fue bizantina, que fue cristiana, que fue imperial. Algunos permanecen cubiertos; otros asoman tímidamente entre yesos y restauraciones. Todos hablan un idioma que mezcla fe, arte y poder. Es imposible no quedarse en silencio ante el Cristo Pantocrátor o la emperatriz Zoe ofreciendo sus dones celestiales.
Hoy, tras su reconversión en mezquita, ya no se puede visitar libremente la planta baja. Y eso significa que uno de los rincones más curiosos ha quedado fuera del alcance de los visitantes: la famosa “columna que llora”, siempre húmeda, envuelta en leyendas. Se dice que si introduces el dedo en su orificio y este sale mojado, tus deseos serán cumplidos. Otros creen que sus aguas tienen poderes curativos. Según la tradición, la columna llora de pena por el sultán Vedud y fue creada, nada menos, con la saliva del profeta Mahoma.
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From the outside, Hagia Sophia doesn’t try to seduce. It’s an imposing mass, reinforced with buttresses, more concerned with endurance than with display. But step through its doors, and time dissolves. Awe takes over. Its greatness doesn’t lie in its outer proportions, but in the space it holds within—a space that, even today, defies the logic of what should be possible.
Inaugurated in 537, this is the third version of the building. The two previous ones fell victim to popular uprisings, but version 3.0 not only survived—it changed the course of architectural history. It took a physicist and a mathematician to conceive such a marvel: Isidore of Miletus and Anthemius of Tralles. They didn’t just design a building; they imagined the unimaginable.
The many earthquakes that have shaken Istanbul tried to bring it down, but Hagia Sophia still stands. And its dome remains its most extraordinary feature: 31.87 meters in diameter, suspended 56.6 meters above the ground, seemingly floating on a ring of windows. For nearly a thousand years, it was the largest religious building in the world. What’s most astonishing is that, despite its scale, it doesn’t overwhelm. Everything—its light, proportions, and acoustics—seems designed to uplift rather than oppress.
The materials used in its construction were among the most precious of the ancient world, and that richness is still felt. Marble columns from Ephesus, porphyry from Egypt, green stone from Thessaly, onyx from Phrygia... a catalogue of ancient empires placed at the service of the new Rome. Every detail was chosen to dazzle.
And if anything stops you in your tracks, it’s the mosaics. Golden, delicate, suspended in time—they survive as fragments of a glory that was Byzantine, Christian, imperial. Some remain covered, others peek out timidly from beneath plaster and restorations. They speak a language of faith, art, and power. It’s impossible not to fall silent before the image of Christ Pantocrator, or Empress Zoe offering her celestial gifts to the Redeemer.
Today, since its reconversion into a mosque, the ground floor is no longer freely accessible. That means one of the building’s most curious features is now out of reach: the famous “weeping column,” always moist, wrapped in legend. It’s said that if you insert your finger into the hole and it comes out wet, your wishes will come true. Others believe its waters have healing powers. According to tradition, the column weeps in sorrow for Sultan Vedud, and was created using the saliva of the Prophet Muhammad.
Leider verschlechterten sich die Wetterbedingungen am Nachmittag des 27. Mai 2016. Bei nicht mehr ganz optimalen Lichtverhältnissen passierte der SLGAG 47895 von Hagen-Kabel nach Ljubljana meinen Standpunkt bei Sulzau. Trotzdem war mir der Zug eine Aufnahme wert - war doch die frisch gewaschene 193 831 der SETG an der Spitze. Diese trägt eine Seiten-Beklebung, die an den österreichischen Mathematiker und Physiker Christian Doppler erinnert. Zweite Lok des Tandems war die 193 814.
Unfortunately the weather-conditions got worse in the afternoon of the 27th of May 2016. Nevertheless I took a picture when freight train SLAG 47895 from Hagen in Germany to Ljubljana in Slovenia passed my photo-spot. SETG's 193 831 was washed completely in recent time. On its side it shows a foil remembering Austrian physician and mathematician Christian Doppler. Second engine working on this Tandem was 193 814.
The Mathematician
The Father of Computer Science and Artificial Intelligence
The Logician
The Cryptanalyst
The Philosopher
The Genius
The Saver of Lives
One of the Greatest Persons of the 20th Century
One of the Greatest Ever Britons
.... and the victim of a cruel society.
Alan Turing
Read: 10 Facts About Enigma Codebreaker Alan Turing
Read: Alan Turing
Artwork ©jackiecrossley
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Taken 20 metres from The City of Nottingham Skyline photos during the same week..
Green's Windmill in Sneinton was built by the father of notable scientist and mathematician George Green in 1807. Today the working Mill is a popular museum and science centre, which teaches new generations of children about the valuable work of George Green.
Sadly, the mill was badly damaged by a fire in 1947, but was later restored by Nottingham City Council in the 1980's. The windmill began milling again in December 1986 and the giant sails can still be seen working to this day.
long stories shortened... (discarded and abandoned and intertwined short stories) well..actually they are chunks and fragmets and notes of stories that never made it
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a young PhD math candidate writing his dissertation on an obscure arab mathematician from the middle ages who specialized in cycles and periods in infinite series and develops a process to determine prime number density in a large number space. (which is all and good) except this makes it an excellent tool to decrypting military grade encryption, which is based on the computational difficulty of factoring large numbers into their prime components
the arab mathematician was ultimately censured by the religious mullahs for developing tools to rationalize the infinite, which is of course the nature of Allah and for man to attempt to place Allah into a human scale is blasphemy
so the arab mathematician disappears and the young phd candidate finds that his dissertation has been suspended pending review but cant get any information on who is reviewing it
finally another young mathematician approaches him and starts a long discussion on math and the nature of numbers and the mathematicians love of the underlying structure of reality that math represents. the phd candidate is leary of this mathematician cause he wont answer what he does or where he went to school or how he knows so many cutting edge fields in math
eventually, the young mathematician offers the phd candidate a position with the NSA, National Security Agency, (where all the big crypto and high math goes on) but explains that if he accepts that he will essentially disappear from his current world. his work will be classified, he will not be able to publish in academic journals or speak in public, or talk about his work to his friends on the outside, but the compensation is that he
would be able to work unfettered with the greatest math minds in the country, totally funded, free to explore any field or fancy he thought. after a few moments of thought, the phd accepts.
then the story will go back to the arab mathematician who is also approached my a young beared mullah, who offers him a position within his group of thinkers who do ponder and explore the nature of nature reality and Allah through mathematics, but that by joining them he would need to disappear from the world, after a few minutes of thought, he too accepts...
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Daniel sipped his 6th coffee (colloidal suspension for caffeine transport) while his batch jobs on ramanet, the Indian supergrid, finished their checksum verification. His chin, a bit stubbly, itched. His eyes, a bit red, were sore. The goa trance shoutcast feed had mushed into a fast cadence drone. The flat screen monitor warped and bulged with the oscillating fan blowing on Daniel's face
'O' glamorous larval life of a PhD student...' he jotted and doodle-circled on his notepad.
Daniel cracked his neck and jutted his jaw, stretching out the accumulation of kinks, as RamaNet finished the final integrity check on his dataset. this two hour round of processing on the Indian supergrid would cost about $130 out of his precious grant fund, but you couldnt beat the bargain. 120 minutes times 150,000 PCs in the RamaNet processing collective = 1,080,000,000 seconds or 18,000,000 minutes or 300,000 hours or 12500 days or 34.25 years of processing time for the price of a video game. Calculation was commoditized now. You uploaded your pre-fromatted dataset to RamaNet. the data was packeted and sent to out to 150,000 Indians who lent a few percents of never-to-be missed CPU cycles off their systems for background processing. when their alotted package was completed it was sent back to RamaNet for re-assembly into something coherent for the buyer. in return the Indians got a rebate on their net access charges or access to premier bollywood galleries or credit towards their own processing charges. a good deal all the way around. Daniel's dataset, an anthology of complex proofs from a long-dead arab mathematician, was queued with amateur weather forecast modeling, home-brewed digital CGI for indie movies, chaos theory-based currency trading algorithms, etc. the really high end, confidential jobs, like protein folding analysis or big pharm drug trials were more likely handled by the huge western collectives of several million collaborative systems, usually high-performance machines in dedicated corporate server farms. the cost there was out of Daniel's range, but you got a faster return and better promises of encryption for your buck.
Daniel scratched his scalp and flexed his fingers. 'two months from today i will be a doctor of mathematics...and no job. damnit. i need to find something fast.' Daniel calculated in his mind how quickly the student loans repayments would kick in and completely wipe him out. RamaNet would have done it in nanoseconds, ha! he laughed to himself. Daniel had avoided the rounds of job interviews and recommendations that passed his way. he was too absorbed in his research to look ahead, and perhaps a bit intimidated by the idea of the job hunt flea market. flexing his CV, getting a monkey suit, trying to explain his research to recruiters, who were often the same finger-counting business majors in college that made his skin crawl. Daniel always felt a bit embarrassed when he announced he was math PhD candidate. folks would immediately glaze over,
tsk tsk out a 'that's interesting', and swiftly change the subject. something will come up, he mantra'd to himself over and over, something will come up. stick with ali, there is something real in there, just a bit deeper. the real problem was his thesis advisor. dr. fuentes was not returning his calls, his secretary was not taking appointments from Daniel. he had submitted his finished draft of his thesis two weeks ago, but hadnt heard back since, except for a cryptic email saying that the review committee was having some issues with his paper and that Daniel would be hearing from him shortly. Daniel was rerunning his calculations on RamaNet to assuage the gnawing doubt that he completely botched some component of his argument and that the review committee was debating some manner of telling him to redo the entire effort. no PhD and no job. that would ice the cake. Daniel started calculating his body mass and general aerodynamic resistance relative to the height of the school cathedral to figure out if he had time to reach a terminal velocity before impact...only a failed math PhD would attempt to determine at what speed his body would smack concrete, he morbidly thought to himself.
ali ja'far muhammed ibn abdullah al-farisi slipped meditatively on his cup of water, thinking about his proof. he dipped a finger in the cup and held up a droplet of water under his fingertip, watching the sunlight prisimatically splay out on the mouth of the cup. 'praise be Allah and his wonderous bounty' he mumured to himself.
the elders had been in conference all day over his proof. though the heavy doors to their chamber were closed, he would occasionally hear muffled but distinctly angry shouts. ali sat on a divan in the anteroom, served numerous cups of tea by an obviously nervous secretary. ali knew there was deep resistance to his research, but for the life of him he couldnt figure out why. he was a simple mathematician. he came up with some unique observations. he wanted to share them with his peers...
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Overview: biotech researcher discovers a new life-extension technology and is murdered. He is cryogenically frozen for 150 years. When he is
revived he must stop a dark corporate conspiracy – and find his murderer.
Summer 2015 - Hot genius free-lance biotech researcher unravels the key component of a radical life-extension gene therapy that will ensure 300 years of robust life to its recipients. The researcher is murdered shortly after he hides the critical component. His distraught friend has him cryogenically frozen. 150 years later, the researcher is revived by the same major bio-med corporation for which he had originally been working.
Quickly he realizes that their motives are less than altruistic: his modification of the gene therapy is needed to resolve an unforeseen debilitation now creeping up in the recipients of the life-extension process. The recipients, now nearing 125 years off added life, are decompensating into psychotics. The researcher at first tries to remember and reconstruct what he did with the hidden critical component, but stops in disgust when he learns that in the past 150 years the life-extension therapy has been reserved solely for the ultra-affluent and has created an extreme and cruel global gerontocratic elite. He voices his disgust to his corporate minders, who cease being beneficent and show their true colors as trying to gain control of this critical technology in order to control the elites.
In the process of dealing with the corporation, he learns about his murder and begins investigating.As he comes closer to the identity of his murderer, he uncovers a wider conspiracy and is the target of more murder attempts.
He was killed by a friend in 2015. The friend was the CEO of a small bio-gen firm that the researcher was doing the LET work for. The CEO, a biz-head with a genetics academic background, took the researcher’s work and exploited it as his own, in the process growing his small firm into a bio-med powerhouse and him into one of the world’s wealthiest individuals.
The CEO also was the first recipient of the LET and is now 190 years old, but doesn’t look a day over 45. Smart, urbane, ruthless, the CEO used his wealth and position to start the cabal of Ultras. It is a faction of the top 50 smartest and wealthiest people in the world who have ‘ascended from the world’ (faked their demise) and control the global economy with their vast coordinated wealth. Perhaps they will call themselves ‘The Ascended’. We need to decide how the cabal lives. Are they sequestered on a luxurious island compound, or do they live in the open, surgically re-sculpted after each faked death, or do they live in the open.
Also we need to figure out what the world will look and feel like in 150 years.
As the ultras decompensate into psychosis, the CEO orders the researcher to be revived in order to find a cure. The CEO had the researcher’s lab notes decrypted and figured that the he was close if not successful in finding the missing component to stabilize the LET.
Tiberius Syndrome: the decline into cruel psychosis experienced by the ultras, named after the roman emperor Tiberius’ degenerate behavior after he sequestered himself on Capri.
The ironic twist might be that there is no cure, no stabilization. The psychosis is not the result of the LET alone, but also due in part to the unfettered ego/wills of the ultras. Absolute power corrupts…
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a brazilian hacking syndicate was subcontracted by a st petersberg crew to run interference on a hit on SWIFT, the global currency clearinghouse notification network. The UniFavela clan was going to run a multi-flank raid. They specialized in fast propagating virii and had created a custom mail-in virus that exploited a few microsoft vulnerabilities that they had discovered and kept mum. Their target was a Latin American PR spokesman listed on the corporate web site for press queries. The PR flak would be just the sleepy guard on the wall for their virus to slip past. 30 minutes after opening an inocuous spoofed email from a French e-trade publication requesting clarification on the SWIFT-Indentrus partnership. the virus would port scan and map its entire site LAN, salmoning its way up the router paths till it found the deep waters of the main corporate campus network in Brussels. Shortly, the internal LAN at Brussels would be suffering switch and router buffer overflows and traffic would gasp, ack, and sputter. UniFavela would then towel whip out a vanilla DDOS on the main company web site, any INTERNIC-registered addresses, and any other system in the IP block reserved for SWIFT that had previously port scanned as interesting, or ,even, as nothing. Mongols charging the village gates and tossing flaming torches on thatched roofs. IT Operations would be running to and fro, trying to figure out the internal bandwidth crunch and if there was a bleedout causing the external net problems.
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The Post-Human Story of Minos:
the CEO of a powerful commercial combine is bore an illegitimate son by his indiscreet wife in retaliation for his own dalliances. the son has a hideous deformity but is fantastically brilliant - brilliant enough for the father overcome his own repulsion of the child - as a bastard and a freak. the father sequesters the child in an elaborate virtual domain. the child, a hacker savant, is used to breach competitor nets. but as his power in the digital realm expands, the child transforms into the tyrant-monster. using the nets, he lashes out at people who have caused him pain, then evolves into enjoying the taste of terror and fear. He becomes the Minotaur.
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'there was a mad scramble amongst all the big spook governments, dark side corporations, and the privacy maccabees once it was determined that quantum computation had left the tidal pool of academia, grown legs and air-breathing lungs, and was headed for the nat sec intel highlands. all previous encryption models were rendered obsolete, and worse, exposed. QC became an undefiable xray spotlight, laying bare any encrypted secret with a ease of opening a mathematical candy wrapper. And for a while it swung the advantage back to the state in the digital Boer War against the freecon partisans.'
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The Oort, to the Intras, looked as one people. Extra-stellar hillbillies, ekeing out a subsistance existence on extracted organics from the frozen crud comets and other planetesimals of the Oort Cloud that slung around the solar system in a 1K AU circuit. To the Oort there was no Oort. Each station, each kampong was distinct and seperate. Seperate dialects, traditions, norms, goals. Some were scientific collectives, some were tired mining operations, some were intense sectarian cults - they shared little between themselves beyond necessary trade links for scarce commodities.
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A young prince is disgraced in an internal court scandal and sent into a quasi-exile on a worthless mission. On his travels he builds the wisdom and learns the skills necessary to be a just and effective leader.
His exile was a gambit by his patriarch to remove Genji from the arena of pointless court intrigues and develop him as a real leader. The patriarch dispatched a team of loyal praetorians to discreetly follow and protect Genji on his odyssey.
Genji was sent as an emissary to the Oort system. He must pass through the Martian-Saturnine corridor, populated with industrial trading guilds and their private militias.
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Genealogy becomes paramount in a closed culture; hierarchy by heredity. Reference the roman patrician class’ death-grip obsession with lineage, or the medieval Japanese imperial court’s strict intra-elite caste system.
But in an era of extreme genetic engineering, how can bloodlines retain their importance? Perhaps this is the wrong question. Perhaps in an era of extreme genetic engineering, authentic bloodlines can only retain their importance. The longevity of an unchanged gene line demonstrates success in evolutionary competition. Over time however, the fitness of a rigidly enforced and ‘sequestered’ gene line will degrade. Consider the hemophilia of the European royal strata.
I would not want the imperial court of the inner system to be pure blue bloods, eschewing genetic manipulation. Rather I would have them take the opposite tack – and embrace genetic engineering in the pursuit of perfecting particular socially valued or distinctive attributes; a roman nose, elongated refined fingers, even the possession of certain ‘noble’ afflictions (for ex., the aforementioned hemophilia as a sign of noble lineage).
The elites should pursue genealogy with the same passion and gusto as horse breeders; studs and mares and percentages of bloodlines, enforced and suppressed gene expressions, surrogates, and gene modes des saisons.
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a bum finds a the wallet and keys of a man who jumped from a bridge
he goes to his townhouse to find something to eat or steal
is impressed and overwhelmed with the man's townhouse
showers, eats, gets cleaned up, finds some clothes
is ready to leave when he helps a woman wrestling with groceries at her door
she thanks him, but looks stunned.
‘are you the man in #560? umm..i have lived here for 3 years and have never actually seen you. you seem to leave so early in the morning and get
home so late and keep to yourself.’
they spend 30 minutes talking, having a generally warm friendly encounter.
‘well, I am so glad to have finally met you. Hope to see you soon.’ As she closes her door, the bum turns to leave but pauses and thinks for a moment, then goes back into the man's townhouse
he pours through the man's papers and keepsakes and learns that the man has no family that he speaks with, no friends, lives off a well-endowed trust fund
and
the bum moves in and takes over the mans identity
he brings warmth and sincerity to the man's identity
what makes a hermit tick? what lengths do they go to to remove themselves from society? does it become a game to avoid contact, trying to become a shadow, a phantom? does society dissolve away as a mental force in their thoughts, atrophy away or does it become an amputated impression?
what divsion line stands between a hermit and convict in solitary? the hermit, by and large, chooses their isolation, the convict has it enforced upon them. at what point does the human need for society or socialization collapse? is there anything left that we can inspect and evaluate? a hermit, however, is able to maintain walls against the Great Other, which would imply that they are seeking refuge from the world. a schizo or an autistic will be physically surrounded by others but unable or incapable of making contact.
when does the will to contact die? what is left over? do humans require contact to retain our humanity? can you love and sacrifice in a vacuum?
what defines humanity? oooh, a big question...
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genetic engineering will continue to deconstruct the human species
there will be catastrophic disasters: gene sequence specific viruses engineered to attack 'types' of people. Der Genkampf
petroleum will be replaced- hydrogen-powered locomotion and green power (in the wealthy states). the poor states will continue to be held hostage to oil politics
(cultures and civilizations do not move forward uneringly. they spasticly jerk forward and fro, in clumps andgrains, never ever as a lemming death drive.)
developed economies will be netized. a new state structure will be needed to manage and dsitribute resources. the corporate structure, the commercial backbone of the capitalist democracy, will replace the republic. it is flexible to markets and political forces, insistent on accountability, it provides a sufficient compromise between individual representation and republican government. they will begin their political evolution as projects in community development. assurances of an educated workforce by charter education. assurances of uninterrupted utilities by running their own power/water etc. net-based marketplaces create corporate agoras. employees are in fact de facto citizens of the corporation. citizenship, or regular employment, will be a reward for merit, stock shares will count towards suffrage.
great corporate collectives will arise. housing, education, security...all the needs of the middle class will be absorbed in the corporate state. the tradtional state will cede roles and responsibilities to the corporate state as their resources dwindle. a few isolated violent reactions (military or legal)by the republics against the corporate states, but they will fail over time. against, or more so, in conjunction with the homogenized corporatsists wil be the diasporae, non-corporates will glom to other modes of networked alignment, ethnic allegiance will become stronger over time - as the chinese, indian, and jewish disporaestrengthen as a formula for a successful competition against/with the corporates.
the american state, succored by its overwhelming techo-military supremancy, loses its mission, its vision - substitutes will to dominate for will to excel - and falls into the deep narcotic, insulated slumber of the unassailable. GE, nano, and the banknote net weaken the mythic cohesion of the american spirit. we are no longer united by common experience (mass-mediated or otherwise) the promise of science to make us stronger, smarter, near immortal is held like a manifest destiny or a divine IOU for services rendered to humanity.
Galileo Galilei was an important Italian scientist, physicist, mathematician, astronomer and philosopher. His scientific contribution started a new era in the history of astronomy, he was the first astronomer to access new knowledge using the telescope. He defended the concept that the Earth was not the center of the universe.
Galileo Galilei was born in Pisa, Italy, on February 15, 1564, son of Vincenzo Galilei and Julia Ammannati. His parents noticed Galilei's great intelligence and special aptitudes from an early age. The boy showed an interest in the arts and performed excellent paintings, demonstrating manual skill and creativity to manufacture toys and contraptions. He played the organ and zither with aplomb. Thus, Galilei excelled in studies at the Sunday school in Vallombrosa and planned to enter the monastery, but his father did not agree with the idea and enrolled him to study medicine at the University of Pisa. Two years after joining, he dropped out of the course and went to dedicate himself to the study of mathematics. The move did not please his father, and Galilei ended up dropping out of the University in 1585. He did not complete any degrees, but in the same year he went to Florence and began giving private lessons to support himself. He stood out for his research in geometry and continued with his mathematical studies.
It was at this time that he invented the hydrostatic balance, a mechanism that would be published in a detailed treatise in the year 1644. In 1589, in recognition of his scientific contributions and brilliant reasoning, he was appointed to the chair of mathematics at the University of Pisa. He was not welcomed by teachers, as he was only 25 years old, had incomplete academic training and publicly discredited Aristotle's established theories. In 1590 Galilei published a treatise on the motion of bodies. In 1591 he was removed from the professorship, after succumbing to intrigues and disputes with Aristotle's supporters. In 1592 he was appointed by the Senate of Venice to teach mathematics at the University of Padua, a position he would hold for 18 years. In 1609 he built a telescope based on the one previously invented by Hans Lippershey in Holland. Galilei made meticulous observations of the sky and incredible discoveries: he located the four largest moons of Jupiter and the mountains and craters on the Moon's surface. And when he detected spots present on the Sun's surface, the discovery helped to prove his theory that the star rotated on an axis. He investigated Saturn and observed what appeared to be two fixed moons, which were the edges of Saturn's ring system, but Galilei's telescope was not accurate enough to determine exactly what those points were.
His findings were collected and published in March 1610 in the book “The Messenger of the Stars”. The work was acclaimed and also generated much controversy, as Galilei publicly defended Nicolaus Copernicus' theory that the Sun was the center of our Solar System, not the Earth. At that time, the Catholic Church fully controlled science and held the opposite view, that the center was the Earth.
In 1616 Galilei was cornered by the authorities of the Inquisition and threatened with the death penalty if he did not publicly deny the scientific truths he had proved. He was expressly prohibited from teaching and propagating ideas that were contrary to the position of the Church. Even so, in 1632 he published the "Dialogue Concerning the Two Greatest Systems of the Universe", causing the Church's total rejection and intolerance. Prevented from continuing with his research and theories, the scientist retired to his castle located in Arcetri, a village near Florence, where he dedicated himself to pursuing his experiments alone.
Galileo Galilei died on January 8, 1642 in Arcetri, Italy. He was almost blinded by the observation of sunspots done without adequate protection for decades. Three hundred and fifty years later, through Pope John Paul II, on October 31, 1992, the Catholic Church formally recognized the legitimacy of Galilei's theories.
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He is reburied here:
Hannah Fry ~ Waterstones ~ St James's Church ~ Piccadilly ~ London ~ England ~ Thursday March 28th 2019.
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You can also buy my WWT card here (The Otter image) or in the shop at the Wetland Centre in Barnes ~ London ~ www.wwt.org.uk/shop/shop/wwt-greeting-cards/european-otte...
Have a Fabulous Friday Y'all..:)
Secret #26: Having a degree in maths does not mean I can count! Seriously, I can prove theorems like "i to the power of i is a great number of real distinct numbers"... but I suck at splitting the restaurant bill.
If you are not a mathematician, you are unlikely to know of a gentleman named August Ferdinand Möbius, who was a professor of Mathematics and Astronomy at the University of Leipzig. Despite being outlandishly talented, the good professor didn’t exactly blaze through academic ranks because he was unable to attract paying students to take his class and would advertise his lectures as ‘free’ to get adequate enrollment. However, the absentminded professor considered mathematics to be poetic, and ended up defining and lending his name to one of the most enigmatic two-dimensional structures: the Möbius band (or, Möbius strip).
Yes, all of us have seen a Möbius band: the recycling sign on plastic or the infinity sign are great examples of Möbius band. To make a Möbius strip of your own, find yourself a rectangular strip of paper and glue both ends of the strip together after half-twisting the paper (by 180 degrees). Many things are extremely remarkable about this structure. Most uniquely, this two-dimensional structure has one surface. Don’t believe? Find yourself a ink pen and mark your initials anywhere on the surface. Now, with your finger tip, travel away from your initials along the central line of the strip surface. Keep going without lifting your finger from the paper. When you will have traveled the whole strip twice, you will find your fingers back on your initials –– convinced, that’s only one surface?
This 'one surface' property leads to another unintuitive – almost tantalizing – nature of this unique structure where the laterally inverted (mirror image) form of any physical point exists on the same surface! In a regular piece of paper, your initials and its mirror image (bleed-through the paper) would be on two different surfaces; To travel between them, you will have to switch surfaces. But in your personal paper Möbius strip, it is now possible to start from your initials, and without altering surfaces, reach their bleed-through mirror image, which is apparently on the other side of the surface from your initials! Also, one could keep walking on the only surface of the strip forever without ever needing to turn around – if you didn’t already, now you know why the infinity sign looks as it does!
Finally, the most unintuitive signature of Mobius structures is that they are unorientable. What’s that, right? Points on orientable things, like a ball or a bat, can be ‘inward’ and ‘outward’ or ‘upward’ and ‘downward’. No matter how you rotate the ball, an ‘outward’ point will always remain outward. But on a Möbius band, a point can slide from an ‘outward’ to an ‘inward’ orientation by rotating the strip. Simply put, the Möbius band has no ‘sidedness’. Here, every point and its mirror-image have collapsed on the same surface. It is as if, all dichotomies have disappeared and dimensions have warped-up somewhere!
Do Möbius bands exist in nature? Yes, they do. Despite the illusory visual of being so, the famous namesake arch in Alabama hills, CA is geometrically not a Möbius band. But, non-fictitious Möbius bands exist in nature elsewhere. Crystals of certain chemical compounds (e.g., niobium and selenium, NbSe3) display Möbius structures. In quantum physics, waveforms for fermions (not bosons) curiously reminds one of the Möbius pattern. Now, imagine how nice would it be if we had Möbius roller coasters or freeways in our perceivable world? We could then hop on them to simultaneously be ourselves and our mirror image – our alter ago – thereby drawing a closure to all our dichotomies. Wouldn’t it be nice if that happened?
Let me close with a crazy thought. What if, Möbius bands come into existence somewhere in those ten dimensions (M-theory) around us somewhen during magical times of the day, but due to limitations of our perceptual faculties, we are unable to acknowledge their presence?
Melba Roy Mouton (1929-1990) was a mathematician and computer programmer in NASA’s Trajectory and Geodynamics Division, acting as the Assistant Chief of Research Programs. Mouton worked at NASA’s Goddard Space Flight Center, coding computer programs to calculate the trajectories and locations of various aircraft. She also led the group of "human computers," who tracked the Echo satellites. Roy and her team's computations helped produce the orbital element timetables by which millions could view the satellite from Earth as it passed overhead.
Image Credit: NASA
#nasa #NASAmarshall #history #blackhistorymonth #BHM
This Group become a mathematicians today at a University of Szeged . Found them drinking vodka ,beer and other good stuff at side of the fountain ! two of them had math hat !
Rachel Riley ~ Trolled ~ Kingspace ~ Kings Cross ~ London ~ England ~ Sunday September 15th 2019.
www.flickriver.com/photos/kevenlaw/popular-interesting/ Click here to see My most interesting images
Purchase some of my images here ~ www.saatchiart.com/account/artworks/24360 ~ Should you so desire...go on, make me rich..lol...Oh...and if you see any of the images in my stream that you would like and are not there, then let me know and I'll add them to the site for you..:))
You can also buy my WWT card here (The Otter image) or in the shop at the Wetland Centre in Barnes ~ London ~ www.wwt.org.uk/shop/shop/wwt-greeting-cards/european-otte...
Well, I had the absolute awesome pleasure of seeing & meeting the always gorgeous Mathematician & TV Presenter Rachel Riley at the @kingsplacelondon in #london for a live #podcast of #trolled Both, she, Tracy Ann Oberman & Nick Cohen were as awesome as you'd expect on the difficult subject of "On line" abuse!!! 😊
Have a great Monday Y'all..:)
In 1961, mathematician Edward Lorenz from the Institute of Technology in Boston was running simulations on a computer about the evolution of the climate of a certain region and discovered that small perturbations in the initial conditions of the system generated significant divergences over time. It was nothing more and nothing less than the birth of the famous phrase "A butterfly's flap of wings could cause a hurricane" and, with it, the beginnings of Chaos Theory. Over the years, mathematicians such as Mitchell Feigenbaum, David Ruelle, Floris Takens, and even Benoit Mandelbrot (father of fractal geometry) were working on the theory.
Towards the end of the 1980s, G. J. Sussman, J. Wisdom, and J. Laskar used powerful computers to perform a numerical simulation of the behavior of the outer and inner planets and discovered that, after a significant number of years, their orbits exhibited chaotic behavior. In particular, the orbital motion of the Earth and with it the Moon, was unstable after ten million years.
For now, regardless of changes, scientific advances, our finitude and contingency, and the fragile flutter of a butterfly, the planets and their moons remain there, within reach of our telescopes, beyond chaos and order in the bowels of disorder.
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From left to right: Ganymede, Europa, Jupiter and Io.
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Maksutov Cassegrain Telescope "Explore Scientific" 127, f/15.
Player One Ceres-C Camera.
Jupiter captured with Barlow Celestron X-Cell LX, 2x.
Moons captured without barlow for the final composition.
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December 24, 2023, 00:35 UT. Rural area, Concordia, Entre Ríos, Argentina.
Rachel Riley ~ Trolled ~ Kingspace ~ Kings Cross ~ London ~ England ~ Sunday September 15th 2019.
www.flickriver.com/photos/kevenlaw/popular-interesting/ Click here to see My most interesting images
Purchase some of my images here ~ www.saatchiart.com/account/artworks/24360 ~ Should you so desire...go on, make me rich..lol...Oh...and if you see any of the images in my stream that you would like and are not there, then let me know and I'll add them to the site for you..:))
You can also buy my WWT card here (The Otter image) or in the shop at the Wetland Centre in Barnes ~ London ~ www.wwt.org.uk/shop/shop/wwt-greeting-cards/european-otte...
Well, I had the absolute awesome pleasure of seeing & meeting the always gorgeous Mathematician & TV Presenter Rachel Riley at the @kingsplacelondon in #london for a live #podcast of #trolled Both, she, Tracy Ann Oberman & Nick Cohen were as awesome as you'd expect on the difficult subject of "On line" abuse!!! 😊
Have a great Hump Day Wednesday Y'all..:)
Srinivasa Ramanujan FRS was an Indian mathematician who l had almost no formal training in pure mathematics. He made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable. Ramanujan initially developed his own mathematical research in isolation. Seeking mathematicians who could better understand his work, in 1913 he began a postal partnership with the English mathematician G. H. Hardy at the University of Cambridge, England. Recognizing Ramanujan's work as extraordinary, Hardy arranged for him to travel to Cambridge. In his notes, Ramanujan had produced groundbreaking new theorems, including some that Hardy said had "defeated him and his colleagues completely", in addition to rediscovering recently proven but highly advanced results.
Foto, Weil der Stadt, 18.2.2017
Johannes Kepler, Philosoph, Mathematiker, Astronom (Keplersche Planeten-Gesetze), geboren in Weil der Stadt bei Stuttgart
Johannes Kepler, philosopher, mathematician, astronomer (Kepler's Planet - laws), born in Weil der Stadt near Stuttgart
Otton Nikodym and Stefan Banach who were sitting here in Cracow in October 1916 and met another famous mathematicial - prof. Hugo Steinhaus;
commemorative monument - the author Stefan Dousa; financed by the Astor company; October 2016; Poland
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I'm stampolina and I love to take photos of stamps. Thanks for visiting this pages on flickr.
I'm neither a typical collector of stamps, nor a stamp dealer. I'm only a stamp photograph. I'm fascinated of the fine close-up structures which are hidden in this small stamp-pictures. Please don't ask of the worth of these stamps - the most ones have a worth of a few cents or still less.
By the way, I wanna say thank you to all flickr users who have sent me stamps! Great! Thank you! Someone sent me 3 or 5 stamps, another one sent me more than 20 stamps in a letter. It's everytime a great surprise for me and I'm everytime happy to get letters with stamps inside from you!
thx, stampolina
For the case you wanna send also stamps - it is possible. (...I'm pretty sure you'll see these stamps on this photostream on flickr :) thx!
stampolina68
Mühlenweg 3/2
3244 Ruprechtshofen
Austria - Europe
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great stamp Helvetia 40c Celestial globe, Himmelsglobus, Globus coelestis (by Jost Bürgi, 1552-1632, swiss mathematician, watchmaker and astronomer; Globe céleste, Звёздный глобус, 天球仪)
Albrecht Dürer (Nuremberg, May 21, 1471 - Nuremberg, April 6, 1528) - Paumgartner Altar (1496-1504) - oil on lime wood, dimensions 155x126 cm, the central compartment - 157x61 each of the side panels - Alte Pinakothek Monaco
È la più grande pala d'altare dell'artista. Il pannello centrale mostra l'Adorazione del Bambino, affiancata da due pannelli di santi cavalieri a tutta figura: a sinistra San Giorgio, col vessillo crociato e con il drago dalla testa mozza, a destra Sant'Eustachio, nella cui bandiera si vede la miracolosa apparizione a cui assistette durante una caccia, un crocifisso tra le corna di un cervo.
I committenti, come accade frequentemente in area tedesca, sono rappresentati minuscoli ai lati in primo piano del pannello centrale, con scudi araldici che ne chiariscano l'identificazione. A sinistra si vedono Martin Paumgartner con i figli Lukas e Stephan; a destra la moglie Barbara Volkamer con le figlie Maria e Barbara. Inoltre nei volti dei santi laterali, secondo un'antica tradizione, dovrebbero essere raffigurati rispettivamente Stephan e Lukas Paumgartner.
It is the largest altarpiece of the artist. The central panel shows the Adoration of the Child, flanked by two panels of full-length knight saints: on the left Saint George, with the crusader banner and the dragon with the severed head, on the right St. Eustachius, in whose flag you see the miraculous apparition he witnessed during a hunt, a crucifix in the horns of a deer.
The clients, as frequently happens in the German area, are represented minuscule on the foreground sides of the central panel, with heraldic shields that clarify their identification. On the left we see Martin Paumgartner with his sons Lukas and Stephan; on the right his wife Barbara Volkamer with his daughters Maria and Barbara. Furthermore, according to an ancient tradition, the faces of the lateral saints should be represented respectively by Stephan and Lukas Paumgartner.
Egnazio Danti (Perugia 1536 - Alatri 1586)
Mathematician, astronomer, Dominican friar and even cosmographer.
In 1567 or so, Cosimo I de Medici, Duke of Tuscany summoned him in his court to develop and share the mathematical and astronomical studies in the territory of his competence.
He became soon a Grand Ducal cosmographer working hard on the maps that are still decorating the Hall of Charts in Palazzo Vecchio.
During his permanence in Florence Danti lived at the convent of Santa Maria Novella assembling the armillary sphere, the gnomon and the gnomonic holes on the façade.
The armillary sphere, installed it on the building in 1574, is on the left side of the front of the church and was used to determine the time of the vernal or Spring equinox by the shadow of the sun on its equatorial ring.
It was with this instrument that Fra' Egnazio Danti established that the calendar was 10 days late. He presented his plan to the pope who approved it. Thus was born the Gregorian calendar which is also ours, jumping from 4 to 14 October
Hypatia of Alexandria was born in Alexandria, Egypt, then part of the Roman Empire, around 355 CE. She was the daughter of Theon of Alexandria, a mathematician and astronomer associated with the Museum and the scholarly traditions that followed the legacy of the great Hellenistic centers of learning. Unlike most women of her time, Hypatia received a rigorous scientific and philosophical education. Under her father’s guidance she studied mathematics, astronomy, geometry, and philosophy, eventually surpassing many of her contemporaries in reputation and intellectual authority.
She became the head of the Neoplatonic school of Alexandria, where she taught philosophy in the Platonic tradition, along with advanced mathematics and astronomy. Her students included both pagans and Christians, some of whom later occupied high public offices. Hypatia wrote or edited commentaries on key scientific works, including Diophantus’ “Arithmetica” and Ptolemy’s “Almagest,” contributing to the preservation and transmission of classical scientific knowledge. Ancient sources also associate her with the construction or refinement of scientific instruments such as the astrolabe and hydrometer, reinforcing her practical as well as theoretical engagement with science.
Hypatia was not only a scholar but a respected public intellectual. She moved freely in civic life and was known for her integrity, independence, and rhetorical skill. She advised Orestes, the Roman prefect of Alexandria, during a period of intense political and religious tension in the city. Alexandria in the early fifth century was marked by escalating conflict between imperial civil authority and the growing power of the Christian episcopate under Bishop Cyril. As a pagan philosopher of high status, intellectually influential and politically connected, Hypatia became a symbolic figure within this struggle.
According to ancient sources such as Socrates Scholasticus, in March 415 CE a mob of Christian extremists, reportedly led by a church reader named Peter and associated with radical factions linked to the bishop’s circle, intercepted her carriage as she was returning home. She was dragged into the Caesareum, which had been converted into a church, stripped, and brutally killed using ostraka—sharp pottery shards or tiles. Her body was dismembered, and the remains were burned outside the city. The killing was widely recognized even by some Christian historians as a disgraceful act. There is no clear evidence of formal punishment for those directly responsible. Her murder stands as a documented case of politically charged religious violence directed against an independent intellectual woman whose authority crossed boundaries of belief and power.
Hypatia’s death has come to represent the violent suppression of philosophical inquiry and scientific freedom in a period of profound transformation within the Roman world. She embodied intellectual autonomy, female authority in public life, and commitment to rational discourse in a polarized society. Her life and death continue to be studied not as legend, but as a historically grounded episode revealing how knowledge, influence, and gender could become threats in times of ideological consolidation.
I publish this series to remember that freedom, dignity, knowledge, and justice are never abstract ideals but realities defended by real people who often paid with their lives. Behind every right there are names, faces, biographies, and violent ruptures. I publish these works to oppose the normalization of political and religious violence, to speak to younger generations, and to affirm that silence always benefits unchecked power. This is not passive commemoration; it is active memory, a conscious choice, and a form of resistance.
The image used for this work is based on artistic representations of Hypatia found in historical paintings and later visual interpretations, given the absence of authentic contemporary portraits due to the antiquity of the period.
Mathematician, navigator, and first mate of the Henri, Myles Bowditch is signing up for Eslandola and the East Trade Wind Company! For gold and country! - and the ETWC.
My sig-fig for Brethren of the Brick Seas. Check it out here!
Jack Hale. Plenary talk on the International Conference on Dynamical Systems And Applications in Atlanta (GE), 2007.
Still life with caustics in Buenos Aires.
Nikon FM2 + Voigtländer Nokton 58mm f/1.4 SLII + Kodak Vision 3 250D.
Monument to the Italian physicist and mathematician, best known for his invention of the barometer.
By Alessandro Tomba 1864.
In Faenza.
Strobist: AB800 with HOBD-W, 15 degree grid, overhead, 45 degrees. AB1600 with 60X39 softbox overhead right, AB800 with Softlighter II camera left. Triggered by Cybersync.
The School of Athens (Italian: Scuola di Atene) is a fresco by the Italian Renaissance artist Raphael. The fresco was painted between 1509 and 1511 as a part of Raphael's commission to decorate the rooms now known as the Stanze di Raffaello, in the Apostolic Palace in the Vatican. It depicts a congregation of philosophers, mathematicians, and scientists from Ancient Greece, including Plato, Aristotle, Pythagoras, Archimedes, and Heraclitus. The Italian artists Leonardo da Vinci and Michelangelo are also featured in the painting, shown as Plato and Heraclitus respectively.
The School of Athens is regarded as one of Raphael's best known works, and has been described as "Raphael's masterpiece and the perfect embodiment of the classical spirit of the Renaissance". The Stanza della Segnatura was the first of the rooms to be decorated, and The School of Athens, representing philosophy, is believed to be the third painting to be finished there, after La Disputa (Theology) on the opposite wall, and the Parnassus (Literature).
The School of Athens is one of a group of four main frescoes on the walls of the Stanza (those on either side centrally interrupted by windows) that depict distinct branches of knowledge. Each theme is identified above by a separate tondo containing a majestic female figure seated in the clouds, with putti bearing the phrases: "Seek Knowledge of Causes", "Divine Inspiration", "Knowledge of Things Divine" (Disputa), "To Each What Is Due". Accordingly, the figures on the walls below exemplify philosophy, poetry (including music), theology, and justice. The traditional title is not Raphael's. The subject of the painting is actually philosophy, or at least ancient Greek philosophy, and its overhead tondo-label, "Causarum Cognitio", tells us what kind, as it appears to echo Aristotle's emphasis on wisdom as knowing why, hence knowing the causes, in Metaphysics Book I and Physics Book II. Indeed, Plato and Aristotle appear to be the central figures in the scene. However, many of the philosophers depicted sought knowledge of first causes. Many lived before Plato and Aristotle, and hardly a third were Athenians. The architecture contains Roman elements, but the general semi-circular setting having Plato and Aristotle at its centre might be alluding to Pythagoras' monad.
Aspects of the fresco other than the identities of the figures have also been variously interpreted, but few such interpretations are unanimously accepted among scholars. That the rhetorical gestures of Plato and Aristotle are kinds of pointing (to the heavens, and down to earth) is popularly accepted as likely. However, Plato's Timaeus – which is the book Raphael places in his hand – was a sophisticated treatment of space, time, and change, including the Earth, which guided mathematical sciences for over a millennium. Aristotle, with his four-elements theory, held that all change on Earth was owing to motions of the heavens. In the painting Aristotle carries his Ethics, which he denied could be reduced to a mathematical science. It is not certain how much the young Raphael knew of ancient philosophy, what guidance he might have had from people such as Bramante and whether a detailed program was dictated by his sponsor, Pope Julius II.
The identities of some of the philosophers in the picture, such as Plato and Aristotle, are certain. Beyond that, identifications of Raphael's figures have always been hypothetical. To complicate matters, beginning from Vasari's efforts, some have received multiple identifications, not only as ancients but also as figures contemporary with Raphael. Vasari mentions portraits of the young Federico II Gonzaga, Duke of Mantua, leaning over Bramante with his hands raised near the bottom right, and Raphael himself.
Central figures (14 and 15)
An elder Plato walks alongside a younger Aristotle
In the center of the fresco, at its architecture's central vanishing point, are the two undisputed main subjects: Plato on the left and Aristotle, his student, on the right. Both figures hold contemporary (of the time), bound copies of their books in their left hands, while gesturing with their right. Plato holds Timaeus and Aristotle holds his Nicomachean Ethics. Plato is depicted as old, grey, and bare-foot. By contrast, Aristotle, slightly ahead of him, is in mature manhood, wearing sandals and gold-trimmed robes, and the youth about them seem to look his way. In addition, these two central figures gesture along different dimensions: Plato vertically, upward along the picture-plane, into the vault above; Aristotle on the horizontal plane at right-angles to the picture-plane (hence in strong foreshortening), initiating a flow of space toward viewers.
It is popularly thought that their gestures indicate central aspects of their philosophies, for Plato, his Theory of Forms, and for Aristotle, an emphasis on concrete particulars. Many interpret the painting to show a divergence of the two philosophical schools. Plato argues a sense of timelessness whilst Aristotle looks into the physicality of life and the present realm.