!* Game of geometry and cubism ↔ lines & abstract subjects A2
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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
The condor is one of the most spectacular geoglyphs on the Nazca site.
The Nazca Geoglyphs (or Nazca Lines) are large figures drawn on the ground, often stylized animals, sometimes mere lines several miles long, visible in the Nazca desert in southern Peru.
These geoglyphs were made by the Nazcas, a pre-Inca civilization that flourished between 300 BC AD and 800 AD. There are more than 800 geoglyphs registered.
The ground on which these geoglyphs are outlined is covered with pebbles that iron oxide stains red.
By removing them, the Nazcas brought out a grayish gypsum soil, thus cutting out the outlines of the figures they were tracing.
Several theories have been put forth to explain the existence of these geoglyphs.
Notably, the German mathematician Maria Reiche, who devoted most of her life to archaeological study and preservation of the site, claimed that these geoglyphs would form a huge astronomical calendar.
According to another theory, the geoglyphs represented places of worship and places of activity where the Nazcas walked during ritual processions.
In the trapeziums, the whole space was a processional space. In the linear figures, the Nazcas returned and followed the line to the exit at the other end.
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Le condor de Nazca
Le condor est un des géoglyphes les plus spectaculaires du site de Nazca.
Les géoglyphes de Nazca (ou lignes de Nazca), sont de grandes figures tracées sur le sol, souvent d'animaux stylisés, parfois de simples lignes longues de plusieurs kilomètres, visibles dans le désert de Nazca, dans le sud du Pérou.
Ces géoglyphes ont été réalisés par les Nazcas, une civilisation pré-inca qui se développa entre 300 av. J.-C. et 800 de notre ère. On en a recensé plus de 800.
Le sol sur lequel se dessinent ces géoglyphes est couvert de cailloux que l'oxyde de fer colore en rouge.
En les ôtant, les Nazcas ont fait apparaître un sol gypseux grisâtre, découpant ainsi les contours des figures qu'ils traçaient.
Plusieurs théories ont été émises pour expliquer l'existence de ces géoglyphes.
Notamment, la mathématicienne allemande Maria Reiche, qui a consacré la majeure partie de sa vie à l'étude archéologique et à la préservation du site, prétendait que ces géoglyphes formeraient un immense calendrier astronomique.
Selon une autre théorie, les géoglyphes représentaient des espaces cultuels et des lieux d'activité où les Nazcas marchaient, lors de processions rituelles.
Dans les trapèzes, l'ensemble de l'espace était un espace de procession. Dans les figures linéaires, les Nazcas rentraient et suivaient la ligne jusqu'à la sortie à l'autre extrémité.
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Nazca - Pérou /Peru
"Ooops ... I need to review the logarithms"
For Flickr group "Happy Caturday!", topics: "Our cats by numbers"
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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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:
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.
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.
Hannah Fry ~ Waterstones ~ St James's Church ~ Piccadilly ~ London ~ England ~ Thursday March 28th 2019.
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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?
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.
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..:)
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..:)
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
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.
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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)
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
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.
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 Mathematician" (detail) by Andrey Zakirzyanov
colored pencil on paper
57x 76 cm
1990
My animations & videoart here - www.youtube.com/view_play_list?p=F07F0FC9A199F76B
"The Mathematician" by Andrey Zakirzyanov
colored pencil on paper
57x 76 cm
1990
My animations & videoart here - www.youtube.com/view_play_list?p=F07F0FC9A199F76B
Bulgarian mathematician
Meyer-Optik Görlitz Oreston f/1.8 50mm
1/3200, f/1.8
Follow me on Instagram @evgenykoloskov
Bain News Service,, publisher.
Dr. Rikitaro Fujisawa
[between ca. 1920 and ca. 1925]
1 negative : glass ; 5 x 7 in. or smaller.
Notes:
Title from unverified data provided by the Bain News Service on the negatives or caption cards.
Forms part of: George Grantham Bain Collection (Library of Congress).
Format: Glass negatives.
Rights Info: No known restrictions on publication. For more information, see George Grantham Bain Collection - Rights and Restrictions Information www.loc.gov/rr/print/res/274_bain.html
Repository: Library of Congress, Prints and Photographs Division, Washington, D.C. 20540 USA, hdl.loc.gov/loc.pnp/pp.print
Part Of: Bain News Service photograph collection (DLC) 2005682517
General information about the George Grantham Bain Collection is available at hdl.loc.gov/loc.pnp/pp.ggbain
Higher resolution image is available (Persistent URL): hdl.loc.gov/loc.pnp/ggbain.34783
Call Number: LC-B2- 5808-14
“Cosmic Engine”, the greatest of all Chinese medieval clocks built by the astronomer Su Song in 1092. This device was an astronomical clock tower more than 10 metres high, like the previous one of Zhang.
Su Song’s tower was additionally equipped with a huge bronze power-driven astronomical instru¬ ment called an armillary sphere, with which one could observe the positions of the stars.In 727, the world’s first mechanical clock was constructed by the Chinese Tantric Buddhist monk and mathematician Yixing (683-727). It was also an astronomical instrument.
The Chinese invention of a mechanical clock that is considered to be the ‘most venerable of all escapement clocks’, predates the European mechanical clock by several centuries.
It’s worth mentioning that an escapement is the crucial component of a mechanical clock, that regulates the driving force of the timepiece and allows a rotating wheel to turn slowly, continuously, and with constant speed.Today no one doubts that the invention of the mechanical clock was one of the greatest scientific and technological achievements.
The clock is described in Robert Temple’s very interesting book The Genius of China: 3,000 Years of Science, Discovery, and Invention as follows:“[It] was made in the image of the round heavens and on it were shown the lunar mansions in their order, the equator and the degrees of the heavenly circumference....Water, flowing into scoops, turned a wheel automatically, rotating it one complete revolution in one day and night [24 hours].Besides this, there were two rings fitted around the celestial sphere outside, having the sun and moon threaded on them, and these were made to move in circling orbit… And they made a wooden casing the surface of which represented the horizon, since the instrument was half sunk in it.It permitted the exact determinations of the time of dawns and dusks, full and new moons, tarrying and hurrying. Moreover, there were two wooden jacks standing on the horizon surface, having one a bell and the other a drum in front of it, the bell being struck automatically to indicate the hours, and the drum being beaten automatically to indicate the quarters.
All these motions were brought about by machinery within the casing, each depending on wheels and shafts, hooks, pins and interlocking rods, stopping devices and locks checking mutually [i.e. the escapement]”.
Yixing’s clock was, like water clocks, subject to the vicissitudes of the weather. In order to keep the water in them from freezing, torches generally burnt beside them.
Therefore, in the next great and far more complex clock of which we have accounts in China, mercury was substituted for water because of the freezing problem, and one of the best examples is a much larger clock built by Zhang Sixun in 976 AD and described in this way:“… a tower of three storeys each over 3 metres in height, within which was concealed all the machinery. It was round at the top to symbolize the heavens and square at the bottom to symbolize the earth. Below there was set up the lower wheel, lower shaft, and the framework base.
There were also horizontal wheels, vertical wheels fixed sideways, and slanting wheels; bearings for fixing them in place; a central stopping device and a smaller stopping device [i.e. the escapement] with a main transmission shaft. Seven jacks rang bells on the left, struck a large bell on the right and beat a drum in the middle to indicate clearly the passing of the quarter-hours.
Each day and night [i.e. each 24 hours] the machinery made one complete revolution, and the seven luminaries moved their positions around the ecliptic. Twelve other wooden jacks were also made to come out at each of the doublehours, one after the other, bearing tablets indicating the time…”
Read more: www.messagetoeagle.com/ancient-chinese-ingenuity-created-...
Ancient Chinese .Astronomy... makes their work important to the development of the history of astronomy, and their ideas filtered down the Silk Road into the Middle East and Europe.Ancient chinese alchemy is often associated with the stories of turning base metal into gold.Chinese astronomy is fascinating in that it developed largely clear of the Indo-European sphere and developed its own particular methods and nuances. The Chinese were meticulous in keeping astronomical records, enabling modern historians to establish that Chinese astronomy remained largely unchanged from 1800 BCE onwards.Astronomy was very much a royal preserve, and emperors directly employed astronomers to chart the heavens and record phenomena, their main purpose being to record time accurately, something that they started to do with great accuracy.Unlike other cultures charting the stars at this period, astrologers were separate from astronomers and their job was to interpret occurrences and omens portended in the sky. As the astronomers began to chart regular events, such as lunar eclipses, these were removed from the realm of astrologers, who Emperors consulted before every major decision.As a result, the Chinese developed an extensive system of the zodiac designed to help guide the life of people on Earth. Their version of the zodiac was called the 'yellow path', a reference to the sun traveling along the ecliptic. As is the case with Western astrology, the Chinese had twelve houses along the yellow path, although the names they gave were different.The Chinese followed a calendar of twelve lunar months, and calculated the year to be 365.25 days long. They translated this 'magic' number into a unit of degrees, by setting the number of degrees in a circle equal to 365.25 (as compared to our use of 360 degrees). They also divided the sky into four quarters, with seven mansions in each, making 28 in total, and these were used to chart the position of the moon as it crossed the sky.The first Chinese records of astronomy are from about 3000 BC, and they used the circumpolar stars as their reference point for the heavens, unlike the Indo-Europeans who used observations based upon the rising and setting of celestial bodies on the ecliptic and the horizon.A tomb dating from about 4000 BCE contained bones and shells inscribed with the Plough and symbols for the Azure Dragon and White Tiger, two of the four regions, the black tortoise and the Vermillion bird being the others. A lacquered box, dating from before 433 BCE had the names of the 28 Mansions inscribed on the lid, showing that this system was in use for a long time.The main job of the Chinese astronomers was to chart time, announce the first day of every month and predict lunar eclipses. If they were wrong in their predictions, then they were often beheaded! To measure time, the Chinese divided the sky into 12 branches and 10 stems arranged around the ecliptic, to give a 60-year cycle. This particular system is believed to have been implemented by Emperor Huang Ti, whose reign began in about 2607 BCE. It is also stated that he built a great observatory and planetarium to help with accurate observations, although this is largely built upon tradition rather than hard evidence. In order to mark the passage of time and the seasons, the Chinese primarily used the orientation of the Big Dipper constellation relative to the pole star in early evening.The Chinese were meticulous in recording other astronomical phenomena, such as comets, sunspots, novas, and solar flares, long before any other culture made any such observations. They attempted to catalog every single star, defining their constellations by one major star, called the king, and surrounding it with princes.The astronomer Shi-Shen (4th Century BCE) is believed to have cataloged 809 stars in 122 constellations, although he took little interest in the planets, unlike the Greeks and Mesopotamians. He also made the earliest known observation of sunspots. Alongside his contemporary, Kan-Te, he is one of the most notable of the Chinese astronomers. To make such accurate measurements of position in the sky, the Chinese must have used an armillary sphere, a metal sphere consisting of intersecting scaled circles, which allowed the observer to give each star a coordinate.The first human record of an eclipse was made in 2136 B.C., and over hundreds of years of advanced sky watching, the Chinese became very adept at predicting lunar eclipses.One of the famous observations made by Chinese astronomers was that of a supernova in the year 1054. They referred to this phenomenon in records as a 'guest star', and mention that it remained bright for about a year before again becoming invisible. This supernova created what we see today as the Crab Nebula. The explosion itself in 1054 was also recorded by the Anasazi Indians of the American Southwest, but for some reason, there is no known record of this occurrence in European or any other cultures.The most important stage in the development of Chinese astronomy was between the 3rd and 6th centuries, when Chinese scholars and polymaths made many wonderful contributions to mathematics and astronomy, creating accurate measuring instruments. One of the leading astronomers of this particular period was Zu Chongzhi (429-500), a notable polymath. Using self-designed instruments, he proposed that the year was 365.24281481 days long, a measurement that is less than a minute different from modern measurements.He used this to design the Daming calendar, the most accurate lunisolar calendar available at that time. Other measurements included measuring the number of times that the sun and moon overlap, proposing 27.21223 times, which is very close to 27.21222 as we know today; using this number he successfully predicted an eclipse four times during 23 years (from 436 to 459).Yi Xing (683-727) was a monk who studied many of the methods and beliefs of Indian astronomy and mathematics, under the auspices of the Tang Dynasty. He was the first known astronomer to try to plot the length of a degree of the meridian line, stating that it was 123.7km, not far off the modern measurement of 111km. Yi Xing was the prime mover behind building an armillary sphere that moved in conjunction with the heavens.The Song Dynasty, 960-1279 saw the Chinese build a number of huge observatories, based upon a series of accurate star-maps, one of which was used to build a planetarium containing 1,434 stars and 28 constellations. At the end of this period emerged one of the greatest of Chinese astronomers, Guo Shoujing (1231-1316), responsible for creating a huge sundial, allowing him to calculate the length of a year to within less than 30 seconds, a monumental achievement. He also improved upon the armillary sphere, making it less complex but also more accurate.The Chinese astronomers have often been looked over in favor of the Greek, Indian, and Islamic contributions to the field, mainly because they use such different methods from the Eurocentric world. Their work tended to be more concerned with refining their observations and making ever more accurate measurements than developing theories but, in that respect, they were one of the leading ancient cultures.The Chinese astronomers generated fantastically accurate measurements of time and charted unusual cosmological phenomena, such as novae, comets and meteor showers. This makes their work important to the development of the history of astronomy, and their ideas filtered down the Silk Road into the Middle East and Europe.