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"
Jägermeister, archers, bowhunters, bowmen, dogs, dog trainers, fishing, forest workers, furriers, hunters, hunting, hunting dogs, huntsmen, inhabitants of the forest, machinists, mathematicians, metal workers, opticians, precision instrument makers, rabies victims, smelters, trappers, Saint-Lamberge, Belgium, diocese of Liege, Belgium and
against dog bite,
against hydrophobia.
against mad dogs and
against rabies.
A statue by artist and mathematician Rinus Roelofs at Hengelo railway station square, The Netherlands.
The interior designer Caroline tries to assemble a nonrepeating pattern discovered by the David Smith from Yorkshire. The shape is supposed to be a in a nonrepeating pattern a so called “einstein” or “one stone. Usually wallpaper or tiled floor are part of an infinite pattern that repeats periodically. An aperiodic tiling displays no such “translational symmetry,” and mathematicians have long sought a single shape that could tile the plane in such a fashion. This is known as the einstein problem.
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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St Paul's Cathedral and the Millennium Bridge
London, UK
July 2016
When I visited London in 2016, unfortunately, I did not step inside St Paul's. I only recently discovered one unique acoustic feature of St Paul's beautifully created dome that fascinated me. The Whispering Gallery is a circular walkway that is 257 steps up the dome from the cathedral floor, encircling the interior of the dome. At the Whispering Galley, a whisper against its curving walls is audible on the opposite side some 30 - 40 meters (on average, approximately 115 feet) away. How amazing! I am neither a physicist nor a mathematician. Based on what I have read, the late Lord Rayleigh discovered this phenomenon, that in a whispering gallery, the sound waves cling to the surface, creep horizontally along a relatively narrow belt around the circular shape of the wall, and travel to the other end of the gallery, thereby amplifying sound.
Copyright Rebecca Ang 2021. All Rights Reserved.
Do not copy, reproduce, download or use in any way without permission.
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:
Let's talk corrugated iron! I always assumed that the folded nature of this material helped the rain drain off my shed roof. Well it does but the corrugation of the "wrinkly tin" adds strength stopping it from sagging in the middle. This would happen to a flat piece of sheeting. I was ignorant of this until I listened to a "In Our Time" podcast this week on the life of German mathematician Carl Friedrich Gauss.I glazed over with some of the theories but apparently his maths prove that a sphere is less likely to collapse than a flat surface. OK, I have exhausted my knowledge on this subject now, so ask me no questions.Talking of podcasts, does anyone listen to the Martin Bailey podcasts. Clearly a knowledgeable photographer but I can't listen to him when I'm driving. Something about his voice is soporific-maybe just me!
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.
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...
Have a Fabulous Friday Y'all..:)
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.
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..:)
Hagia Sophia is a former Greek Orthodox patriarchal basilica (church), later an imperial mosque, and now a museum in Istanbul, Turkey. From the date of its construction in 537 until 1453, it served as an Eastern Orthodox cathedral and seat of the Patriarchate of Constantinople, except between 1204 and 1261, when it was converted to a Roman Catholic cathedral under the Latin Empire. The building was a mosque from 29 May 1453 until 1931. It was then secularized and opened as a museum on 1 February 1935.
The Church was dedicated to the Wisdom of God, the Logos, the second person of the Holy Trinity, its patronal feast taking place on 25 December, the commemoration of the Birth of the incarnation of the Logos in Christ. Although sometimes referred to as Sancta Sophia (as though it were named after Saint Sophia), sophia being the phonetic spelling in Latin of the Greek word for wisdom, its full name in Greek is Ναός τῆς Ἁγίας τοῦ Θεοῦ Σοφίας, "Shrine of the Holy Wisdom of God".Famous in particular for its massive dome, it is considered the epitome of Byzantine architecture and is said to have "changed the history of architecture." It remained the world's largest cathedral for nearly a thousand years, until Seville Cathedral was completed in 1520. The current building was originally constructed as a church between 532 and 537 on the orders of the Byzantine Emperor Justinian and was the third Church of the Holy Wisdom to occupy the site, the previous two having both been destroyed by rioters. It was designed by the Greek scientists Isidore of Miletus, a physicist, and Anthemius of Tralles, a mathematician.
The church contained a large collection of holy relics and featured, among other things, a 15-metre (49 ft) silver iconostasis. The focal point of the Eastern Orthodox Church for nearly one thousand years, the building witnessed the excommunication of Patriarch Michael I Cerularius on the part of Pope Leo IX in 1054, an act which is commonly considered the start of the Great Schism.
In 1453, Constantinople was conquered by the Ottoman Turks under Sultan Mehmed II. By this point, the Church had fallen into a state of disrepair. Nevertheless, the Christian cathedral made a strong impression on the new Ottoman rulers and they decided to convert it into a mosque.The bells, altar, iconostasis, and sacrificial vessels and other relics were removed and the mosaics depicting Jesus, his Mother Mary, Christian saints and angels were also removed or plastered over. Islamic features – such as the mihrab, minbar, and four minarets – were added. It remained a mosque until 1931 when it was closed to the public for four years. It was re-opened in 1935 as a museum by the Republic of Turkey.
Wiki
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)
These meandering tracks in the damp sand at low tide are more shallow and narrow than those of the periwinkles in the two photos posted below on my page, "Off to the Races" and "Periwinkle Road Map," and there were no critters in any of these. What creepy-crawly creature made them remains a mystery to me. They remind me that, as mathematicians know, a random walk tends to always return toward its starting point.
In his book, Dalla scienza alia fede, 10 the great mathematician, Francesco Severi, a very close friend of Einstein, proclaimed that the more he immersed himself in scientific research, the more evident it became to him that all that he discovered, as he proceeded step by step, was a function of an absolute “which set itself in opposition like an elastic barrier to its being overcome by cognitive means.” The more his investigation advanced, the more the particular horizon which he approached would point beyond to yet another, thus convincing him to perceive his victory as temporary, as merely something which would then urge him on towards another x, a “something” beyond the conditions in which he operated. Whenever the research would reach a certain end point, then the object of this operation, the “x,” would move further away again. The following illustration exemplifies this process: “r” is the inquisitive energy of human reason and freedom; and “x” is the temporary finish line which always points towards a further unknown. r → | … x → | … x → | x …
...By not admitting the existence of that incommensurable “x,” by not acknowledging the disproportionate gap between the ultimate horizon and human capacity, one eliminates the category of possibility, the supreme dimension of reason. This is so because only an incommensurable object can represent an unlimited invitation to the essential openness of a human being. Life is hunger, thirst, and passion for an ultimate object, which looms over the horizon, and yet always lies beyond it. When this is recognized, man becomes a tireless searcher.
--The Religious Sense, LUIGI GIUSSANI, pg. 50
The home of British codebreaking and a birthplace of modern information technology. It played a major role in World War Two, producing secret intelligence which had a direct and profound influence on the outcome of the conflict.
The key codebreakers were Alan Turing (Mathematician), Dilly Knox (British cryptographer), John Tiltman (British officer), Max Newman (Mathematician), Bill Tutte (Mathematician). In all there were over 10,000 people worked at Bletchley Park, Government Code and Cypher School.
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
A Northrop Grumman Antares rocket carrying a Cygnus resupply spacecraft is in the vertical launch position on the Mid-Atlantic Regional Spaceport’s Pad-0A, Tuesday, Feb. 16, 2021, at NASA's Wallops Flight Facility in Virginia. Northrop Grumman’s 15th contracted cargo resupply mission with NASA to the International Space Station will deliver about 8,000 pounds of science and research, crew supplies and vehicle hardware to the orbital laboratory and its crew. The CRS-15 Cygnus spacecraft is named after NASA mathematician, Katherine Johnson, a Black woman who time and again broke through barriers of gender and race. The launch is scheduled 12:36 p.m. EST, Feb. 20, 2021.
Photo Credit: NASA/Patrick Black
NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission.
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Prato della Valle.
Secondo le cronache, per la realizzazione dell'isola Memmia, dei ponti e della canaletta bastarono 44 giorni e senza aggravio per l'erario in quanto Andrea Memmo usò anche il suo denaro.
Il suo progetto, rimasto in parte incompiuto, è visibile in un'incisione su rame di Francesco Piranesi del 1785.
Sembra che Memmo avesse commissionato questa e altre rappresentazioni e le tenesse esposte a Palazzo Venezia, sede dell'ambasciata della Repubblica a Roma, nell'intento di ottenere il finanziamento per le statue ornamentali, proponendolo a persone notabili.
Le statue su piedistallo che adornano la piazza, 38 lungo l'anello interno all'Isola Memmia e 40 lungo quello esterno, furono scolpite in pietra di Costozza tra il 1775 e il 1883 da diversi artisti.
Esse rappresentano i più illustri figli della città, padovani di nascita o d'adozione, e ricordano professori e studenti che onorarono la città e lo Studio padovano.
Solo gli spazi dell'ingresso ai quattro ponti furono riservati a personaggi politici, a Dogi e Papi.
La statua numero 44 rappresenta Andrea Memmo e fu innalzata due anni dopo la sua morte, nel 1794, ad opera del padovano Felice Chiereghin.
Valore artistico ha la numero 52 del giro interno, opera giovanile del celebre scultore Antonio Canova, di cui l'originale è oggi ai Musei Civici; essa rappresenta Giovanni Poleni, il matematico e fisico veneziano che a soli 25 anni fu insegnante di astronomia e fisica presso la nostra università.
Tra le atre statue ricordiamo quelle di Antenore, Torquato Tasso, Pietro D'Abano, Andrea Mantegna, Ludovico Ariosto, Francesco Petrarca, Galileo Galilei, Giovanni Dondi dell'Orologio, Antonio Canova stesso e Antenore, che, secondo il mito, fu il fondatore di Padova.
(Comune di Padova)
Prato della Valle.
According to the chronicles, the construction of Memmia Island, the bridges, and the canal took just 44 days, and there was no burden on the treasury, as Andrea Memmo also used his own money.
His project, which remained partially unfinished, is visible in a copper engraving by Francesco Piranesi from 1785.
It seems that Memmo commissioned this and other representations and displayed them in Palazzo Venezia, the seat of the Republic's embassy in Rome, in an attempt to secure funding for the ornamental statues by offering them to notables.
The statues on pedestals that adorn the square—38 along the inner ring of Memmia Island and 40 along the outer ring—were sculpted in Costozza stone between 1775 and 1883 by various artists.
They represent the city's most illustrious sons, Paduans by birth or adoption, and commemorate professors and students who honored the city and the University of Padua.
Only the spaces at the entrance to the four bridges were reserved for political figures, Doges, and Popes.
Statue number 44 represents Andrea Memmo and was erected two years after his death, in 1794, by the Paduan Felice Chiereghin.
Statue number 52 on the inner circle is of artistic value, an early work by the famous sculptor Antonio Canova, the original of which is now in the Civic Museums; it depicts Giovanni Poleni, the Venetian mathematician and physicist who, at just 25 years old, taught astronomy and physics at our university.
Among the other statues are those of Antenor, Torquato Tasso, Pietro D'Abano, Andrea Mantegna, Ludovico Ariosto, Francesco Petrarca, Galileo Galilei, Giovanni Dondi dell'Orologio, Antonio Canova himself, and Antenor, who, according to myth, was the founder of Padua.
(Municipality of Padua)
IMG20250505103215m
Albrecht Dürer (Nuremberg, 21 May 1471 - Nuremberg, 6 April 1528) - Portrait of Frederick the Wise (1463–1525) (1497) - Gemäldegalerie, Berlin
Federico il Saggio protesse Martin Lutero dal papa, ospitandolo nel suo castello di Wartburg dopo le decisioni della Dieta di Worms di mettere le tesi luterane al bando dall'Impero.
Frederick the Wise protected Martin Luther from the pope by hosting him in his Wartburg castle after the Worms Diet decisions to ban Lutheran theses from the Empire.
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.