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Monastery - Nilova Hermitage. Tver region. Russia.
The monastery dates back to 1528, from the moment of the arrival of the Monk Nile on the island of Stolobny, on Lake Seliger.
A few years later, after the presentation of the Monk Nil of Stolobensky, in 1594, a Blessing was given for the opening of the monastery of the Nilov Pustyn.
In the 18-19 centuries, the Nilova Pustyn Monastery was one of the largest cultural centers in Russia, with a huge library, educational institutions, with its own large production of goods and products.
It was in the Nilova desert that Leonty Magnitsky, a mathematician and teacher, studied under whom, later, the Great Lomonosov studied. Nilova Hermitage was visited by many great people, including Emperor Alexander I and Russian President Vladimir Putin.
After the blasphemous looting and partial destruction of the monastery by the Bolsheviks, the buildings were used as a colony for minors, as a prisoner of war camp, as a military hospital, as a camp site. When all the buildings of the monastery fell into disrepair and could no longer be used, without major repairs, by the Council of Ministers of the RSFSR, in 1990, the monastery complex was transferred to the Moscow Patriarchate of the Russian Orthodox Church.
2016 marks the 25th anniversary of the revival of the Nilo-Stolobensky Monastery. Ahead, there are still colossal works to restore the former splendor of the holy monastery. But already now, the Nilo-Stolobenskaya hermitage is the pearl of the Tver diocese. Even in spite of all the destruction that befell from the godless power, this monastery with all this lies before us in all its beauty and grandeur of the genius of architecture, the pious ancestors of the Russian land.
Today, the monastery, thanks to the governor Archimandrite Arkady (Gubanov), is being successfully restored by the brethren and already has its own autonomous production of products, which is in great demand among pilgrims and local residents.
The screw thread is believed to have been invented around 400 BCE, by Archytas of Tarentum, a Greek philosopher sometimes called “the father of mechanics.” The general principle of the screw was applied early on, in cities like Pompeii, to extract olive oil and grape juice. It was further developed the Greek mathematician Archimedes to alter water levels. The water screw, first mentioned in Mechanica of Heron of Alexandria, was made from wood and aided farm irrigation and rid ships of bilge water.
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:
The conifer forests of the Mediterranean Basin have been subjected to overuse by humans since ancient times. Some species have survived in inaccessible refuges. Abies pinsapo is surviving in only three enclaves in southern Spain and two in northern Morocco. Until the mid 20th century Abies pinsapo forests were under constant threat from intensive grazing and the use of their timber for construction, firewood and charcoal making. The limited area occupied by these forests makes them highly vulnerable to disturbance. The small male cones seen in the photo are found only on the lower branches. Abies pinsapo was first described in 1838 by Swiss botanist, explorer and mathematician Pierre Edmond Boissier.
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
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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:
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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Leica M8, Voigtlaender NC 35/1.4. Stephen Kettle's slate sculpture of Alan Turing at Bletchley Park, Buckinghamshire. Bletchley Park during WWII was Britain's codebreaking and intelligence centre. Turing was an extremely gifted mathematician, cryptanalyst and one of the fathers of computer science and AI. During the war years, he worked at Bletchley Park, improved the (pre-war) Polish Bomba decryption computer and, in 1941, was responsible for breaking the encryption of the German Enigma machine (seen here as part of the sculpture) that was used by the German navy.
Secret #26: Having a degree in maths does not mean I can count! Seriously, I can prove theorems like "i to the power of i is a great number of real distinct numbers"... but I suck at splitting the restaurant bill.
If you are not a mathematician, you are unlikely to know of a gentleman named August Ferdinand Möbius, who was a professor of Mathematics and Astronomy at the University of Leipzig. Despite being outlandishly talented, the good professor didn’t exactly blaze through academic ranks because he was unable to attract paying students to take his class and would advertise his lectures as ‘free’ to get adequate enrollment. However, the absentminded professor considered mathematics to be poetic, and ended up defining and lending his name to one of the most enigmatic two-dimensional structures: the Möbius band (or, Möbius strip).
Yes, all of us have seen a Möbius band: the recycling sign on plastic or the infinity sign are great examples of Möbius band. To make a Möbius strip of your own, find yourself a rectangular strip of paper and glue both ends of the strip together after half-twisting the paper (by 180 degrees). Many things are extremely remarkable about this structure. Most uniquely, this two-dimensional structure has one surface. Don’t believe? Find yourself a ink pen and mark your initials anywhere on the surface. Now, with your finger tip, travel away from your initials along the central line of the strip surface. Keep going without lifting your finger from the paper. When you will have traveled the whole strip twice, you will find your fingers back on your initials –– convinced, that’s only one surface?
This 'one surface' property leads to another unintuitive – almost tantalizing – nature of this unique structure where the laterally inverted (mirror image) form of any physical point exists on the same surface! In a regular piece of paper, your initials and its mirror image (bleed-through the paper) would be on two different surfaces; To travel between them, you will have to switch surfaces. But in your personal paper Möbius strip, it is now possible to start from your initials, and without altering surfaces, reach their bleed-through mirror image, which is apparently on the other side of the surface from your initials! Also, one could keep walking on the only surface of the strip forever without ever needing to turn around – if you didn’t already, now you know why the infinity sign looks as it does!
Finally, the most unintuitive signature of Mobius structures is that they are unorientable. What’s that, right? Points on orientable things, like a ball or a bat, can be ‘inward’ and ‘outward’ or ‘upward’ and ‘downward’. No matter how you rotate the ball, an ‘outward’ point will always remain outward. But on a Möbius band, a point can slide from an ‘outward’ to an ‘inward’ orientation by rotating the strip. Simply put, the Möbius band has no ‘sidedness’. Here, every point and its mirror-image have collapsed on the same surface. It is as if, all dichotomies have disappeared and dimensions have warped-up somewhere!
Do Möbius bands exist in nature? Yes, they do. Despite the illusory visual of being so, the famous namesake arch in Alabama hills, CA is geometrically not a Möbius band. But, non-fictitious Möbius bands exist in nature elsewhere. Crystals of certain chemical compounds (e.g., niobium and selenium, NbSe3) display Möbius structures. In quantum physics, waveforms for fermions (not bosons) curiously reminds one of the Möbius pattern. Now, imagine how nice would it be if we had Möbius roller coasters or freeways in our perceivable world? We could then hop on them to simultaneously be ourselves and our mirror image – our alter ago – thereby drawing a closure to all our dichotomies. Wouldn’t it be nice if that happened?
Let me close with a crazy thought. What if, Möbius bands come into existence somewhere in those ten dimensions (M-theory) around us somewhen during magical times of the day, but due to limitations of our perceptual faculties, we are unable to acknowledge their presence?
Syracuse is a historic city on the Italian island of Sicily, the capital of the Italian province of Syracuse. The city is notable for its rich Greek and Roman history, culture, amphitheatres, architecture, and as the birthplace and home of the pre-eminent mathematician and engineer Archimedes. This 2,700-year-old city played a key role in ancient times, when it was one of the major powers of the Mediterranean world. Syracuse is located in the southeast corner of the island of Sicily, next to the Gulf of Syracuse beside the Ionian Sea.
UNESCO World Heritage site.
Like a mathematician of colours
in his laboratory of wavelenghts,
subtraction after subtraction
I've reached a perfect formula
to render an electromagnetic final
description of you:
green - the distilled measured joy
of your Mona Lisa smile;
white - the lightness
of your supernatural being, everchanging
like wind-driven summer clouds;
and blue - the sky-looking ocean
of your unbounding peaceful restless
soul.
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
In 1961, mathematician Edward Lorenz from the Institute of Technology in Boston was running simulations on a computer about the evolution of the climate of a certain region and discovered that small perturbations in the initial conditions of the system generated significant divergences over time. It was nothing more and nothing less than the birth of the famous phrase "A butterfly's flap of wings could cause a hurricane" and, with it, the beginnings of Chaos Theory. Over the years, mathematicians such as Mitchell Feigenbaum, David Ruelle, Floris Takens, and even Benoit Mandelbrot (father of fractal geometry) were working on the theory.
Towards the end of the 1980s, G. J. Sussman, J. Wisdom, and J. Laskar used powerful computers to perform a numerical simulation of the behavior of the outer and inner planets and discovered that, after a significant number of years, their orbits exhibited chaotic behavior. In particular, the orbital motion of the Earth and with it the Moon, was unstable after ten million years.
For now, regardless of changes, scientific advances, our finitude and contingency, and the fragile flutter of a butterfly, the planets and their moons remain there, within reach of our telescopes, beyond chaos and order in the bowels of disorder.
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From left to right: Ganymede, Europa, Jupiter and Io.
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Maksutov Cassegrain Telescope "Explore Scientific" 127, f/15.
Player One Ceres-C Camera.
Jupiter captured with Barlow Celestron X-Cell LX, 2x.
Moons captured without barlow for the final composition.
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December 24, 2023, 00:35 UT. Rural area, Concordia, Entre Ríos, Argentina.
Rachel Riley ~ Trolled ~ Kingspace ~ Kings Cross ~ London ~ England ~ Sunday September 15th 2019.
www.flickriver.com/photos/kevenlaw/popular-interesting/ Click here to see My most interesting images
Purchase some of my images here ~ www.saatchiart.com/account/artworks/24360 ~ Should you so desire...go on, make me rich..lol...Oh...and if you see any of the images in my stream that you would like and are not there, then let me know and I'll add them to the site for you..:))
You can also buy my WWT card here (The Otter image) or in the shop at the Wetland Centre in Barnes ~ London ~ www.wwt.org.uk/shop/shop/wwt-greeting-cards/european-otte...
Well, I had the absolute awesome pleasure of seeing & meeting the always gorgeous Mathematician & TV Presenter Rachel Riley at the @kingsplacelondon in #london for a live #podcast of #trolled Both, she, Tracy Ann Oberman & Nick Cohen were as awesome as you'd expect on the difficult subject of "On line" abuse!!! 😊
Have a great Monday Y'all..:)
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 !
Bernkastel-Kues, Germany.
The first settlements date back to the time of the Linear Pottery culture, some 5000 years ago. The present town developed in the Middles Ages. Bernkastel was granted town status by King Rudolph of Habsburg in 1291. Bernkastel literally means "bear castle".
In 1905, Bernkastel, on the right bank, was merged with the village of Kues, on the left bank. They were joined by the villages of Andel and Wehlen in 1970.
Kues was the birthplace of Cardinal Nicholas of Cusa ("Nikolaus von Kues" in German, 1401-1464), a philosopher, jurist, mathematician, and astronomer, who is regarded as one of the greatest geniuses and polymaths of the 15th century.
For video, please visit youtu.be/fOJxngF7z2k
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..:)
Northamptonshire is sometimes known as "the county of spires and squires" on account of the number of beautiful church spires and numerous country estates with grand houses.
This Grade II*-listed house, which is now a hotel, dates from 1693 and is actually a former rectory. The original house on this site was built by John Palmer (the rector of Ecton 1641–79) but rebuilt in its present "William & Mary" style in 1693 by his eldest son, also called John Palmer (though a further source credits his grandson Eyre Whalley - another rector - as the builder).
A further grandson, confusingly also known as John Palmer, erected a ‘school for poor children’ off the High Street in Ecton in 1752.
As well as being rector of Ecton, the older John Palmer was promoted to Archdeacon of Northampton in 1665. He is acknowledged as a celebrated mathematician, astronomer and linguist, publishing a number of works including The Planisphere.
Pythagoreio (Πυθαγόρειο) is a municipality on the island of Samos, Samos Prefecture, Greece. Population 9,003 (2001). Also known as Pythagoreion and Pythagorio.
The capital of the municipality is the town of Pythagoreio, formerly known as Tigani. The town was renamed in 1955 to honour the local-born mathematician and philosopher Pythagoras. The port of the town is considered to be the oldest man-made port of the Mediterranean Sea. (from Wikipedia)
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.
Otton Nikodym and Stefan Banach who were sitting here in Cracow in October 1916 and met another famous mathematicial - prof. Hugo Steinhaus;
commemorative monument - the author Stefan Dousa; financed by the Astor company; October 2016; Poland
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I'm stampolina and I love to take photos of stamps. Thanks for visiting this pages on flickr.
I'm neither a typical collector of stamps, nor a stamp dealer. I'm only a stamp photograph. I'm fascinated of the fine close-up structures which are hidden in this small stamp-pictures. Please don't ask of the worth of these stamps - the most ones have a worth of a few cents or still less.
By the way, I wanna say thank you to all flickr users who have sent me stamps! Great! Thank you! Someone sent me 3 or 5 stamps, another one sent me more than 20 stamps in a letter. It's everytime a great surprise for me and I'm everytime happy to get letters with stamps inside from you!
thx, stampolina
For the case you wanna send also stamps - it is possible. (...I'm pretty sure you'll see these stamps on this photostream on flickr :) thx!
stampolina68
Mühlenweg 3/2
3244 Ruprechtshofen
Austria - Europe
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great stamp Helvetia 40c Celestial globe, Himmelsglobus, Globus coelestis (by Jost Bürgi, 1552-1632, swiss mathematician, watchmaker and astronomer; Globe céleste, Звёздный глобус, 天球仪)
... and "do Sal" means "of salt" - literally, Fortress of Salt :)
The Castle of Alcácer do Sal overlooks the City Hall building (on the right-hand side of the photo). The square takes its name from the local mathematician Pedro Nunes, whose statue sits at the centre.
Alcácer do Sal, Setúbal - Portugal
O Castelo de Alcácer do Sal no topo da colina (por curiosidade, "alcácer" é sinónimo de fortaleza, castelo), com vista para a Praça Pedro Nunes, onde foi colocada uma estátua do matemático, em frente à Câmara Municipal de Alcácer do Sal (à direita, na imagem).
Do you realise that the symbol used to represent pi….you know, that horrible 3.141….thing you had to learn about at school in maths for calculating the circumference or area of a circle….., originated in North Wales?
The first calculation of pi was made by Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world, but it was a much less famous man called William Jones who introduced that symbol ‘π’ which until then was just a Greek letter.
William Jones was born sometime around 1675 on the island Anglesey in the parish of Llanfihangel Tre’r Beirdd, about four miles west of the town which is now Benllech. He had a humble up-bringing and was raised on a small farmstead by his parents Siôn Siôr (John George Jones) and Elizabeth Rowland. However his talent for mathematics quickly became apparent when he attended a charity school at Llanfechell. It was to be his only formal education. His aptitude for the subject ensured that he would not follow in the family footsteps. A local squire and landlord of the distinguished Bulkeley family, heard of his skill and took him under their patronage. They arranged for him to work in a merchant’s counting house in London.
It was only the first of many journeys. Between 1695 and 1702 he served in the Royal Navy, sailing to the West Indies during which time he taught mathematics on board a man-of-war, en-route learning about navigation. He was present at the battle of Vigo in October 1702 when the English successfully captured the Spanish treasure fleet as it was returning to the port in north-west Spain under French escort. Ignoring the obvious riches of silver to be had, he went in search of other booty according to an 1807 memoir by Baron Teignmouth, ‘... literary treasures were the sole plunder that he coveted.’
On his return he published A New Compendium of the Whole Art of Navigation which he dedicated to a benefactor John Harris, a writer, scientist and Anglican priest who had taken him under his wing. Back in the capital, his voyages over, he became a mathematics teacher in coffee houses and as a private tutor to the son of the future Earl of Macclesfield. He also became tutor to Philip Yorke, later 1st Earl of Hardwicke (1690-1764), who became Lord Chancellor and provided an invaluable source of introductions for his tutor.
In those circles, Isaac Newton had already mentioned to the Admiralty the benefit of sending mathematicians to sea. So inevitably it was only a matter of time before Jones came to the attention of Newton after reading “Jones’s Synopsis”, in which the younger man explained Newton’s methods for calculus as well as other mathematical innovations. It was in this book that Jones first used the Greek symbol ‘π’ to denote the pi. More significantly he used it as a constant number - 3.141...
Before Jones, approximations such as 22/7 and 355/113 had also been used to express the ratio. Explaining its use, he wrote: ‘... the exact proportion between the diameter and the circumference can never be expressed in numbers...’. Hence, a symbol was required to represent an ideal that can be approached but never reached. For this Jones recognised that only a pure platonic symbol would suffice.
In 1708 Jones was able to acquire an extensive library and archive, which contained several of Newton’s letters and papers written in the 1670s. The following year he applied for the mastership of Christ’s Hospital Mathematical School, despite references from Newton and Edmund Halley (the astronomer who calculated the orbit of the comet, now named after him) but he was turned down. Jones went back into private teaching but thanks to the papers he had acquired he was able to help his old mentor Newton resolving a dispute with German mathematician Gottfried Leibniz, over which of the men first invented calculus.
In 1712 Jones joined the committee set up by the Royal Society to determine which of them invented calculus. He was now firmly in the mathematical establishment.
He married twice, firstly the widow of his counting-house employer, whose property he inherited on her death.He remarried in 1731, to Mary, the 22-year-old daughter (30 years his junior) of cabinet-maker George Nix, with whom he had three children.
And therein lies the story of ‘π’ and it’s origins in North Wales. My photo is actually of part of some derelict structure of the Penmaenmawr quarry, the quarry that has removed the top one third of this granite mountain. But I thought it looked like ‘π’ standing high above the North Wales Expressway.
The Grade I listed Chesterton Windmill is one of Warwickshire's most famous landmarks. It stands on a hilltop overlooking the village of Chesterton, near the Roman Fosse Way, about five miles (8 km) south-east of Warwick. It was built around 1632–1633, probably by Sir Edward Peyto, who was Lord of the Chesterton Manor House. At this time John Stone, a pupil of Inigo Jones, was in Chesterton designing the new Manor House and he probably helped with the windmill as well. Sir Edward was a mathematician and astrologer and probably his own architect for the windmill, but although claims have been made that the tower was originally built as an observatory, the estate accounts now at Warwick Record Office show that it has always been a windmill, making it the earliest tower mill in England to retain any of its working parts.
Slate wall.
The Downing site is one of the two main city-centre sites for the University of Cambridge, housing predominantly biomedical science departments. I went there earlier in the year to attend one of over 400 free public lectures given as part of the University’s Science Festival.
The lecture, on "Playing Games like a Mathematician" was brilliant fun and given by Katie Steckles, a mad mathematician from Manchester University.
Did you know the record for completing Rubik’s cube from memory, one-handed, while blindfolded, is one minute 16 seconds? Well, feel your ignorance evapourate!
But I’m drifting as usual. The modern pedestrian entrance to the Downing site from the East is a staircase up from the lower street below. I noticed it had a curious and rather beautiful slate wall made of grey slates with thin layers of mortar between.
It strikes me as being a wildly inefficient way of making a wall. I can only assume it was done for architectural aesthetic reasons or perhaps as a way of reusing materials recovered from the buildings that occupied the site previously as a poignant memory of what went before - architects and planners like doing that in the UK it seems.
I had my trusty phone with me and I worked out that if I angled the lens in the right way I could get an image, not of flat layers, but of a star-burst of rays from one corner.
Hah! I thought. Such is the stuff... the making of a Sliders Sunday series.
And thus we have it…. This is the Sliders Sunday version. I’ll post the original in-camera image in the first comment, so you can see how far we came.
I’ve used the picture in various ways to make a short series of endpoints again, so you can see which you prefer (if any lol). I’m always interested to hear what other folk think.
I’ll also publish a black and white version done in Nik Silver Efex Pro as a straight rendition of the image.
Thank you for taking the time to look. I hope you enjoy the image. Happy Sliders Sunday!
[Handheld in daylight.
Processed as a black and white in Affinity Photo.
Taken into Topaz studio and used one of the AI Remix settings to create the colour and stripes.
Back into Photo and a simple single mirror in the distortion Mirror filter, playing about with different input and output angles and dragging the cursor around the image to find an interesting perspective.
Hues shifted a little using an HSL layer.
Sharpened using Unsharp Mask with that adjustment blended using Linear Light at reduced opacity.
Lighting filter with white light from top right and some texturing as well.
Frame formed by expanding the size of the canvas and having a dark blue fill layer underneath, then using Layer Fx to add a narrow white outline… then we are done.]
Egnazio Danti (Perugia 1536 - Alatri 1586)
Mathematician, astronomer, Dominican friar and even cosmographer.
In 1567 or so, Cosimo I de Medici, Duke of Tuscany summoned him in his court to develop and share the mathematical and astronomical studies in the territory of his competence.
He became soon a Grand Ducal cosmographer working hard on the maps that are still decorating the Hall of Charts in Palazzo Vecchio.
During his permanence in Florence Danti lived at the convent of Santa Maria Novella assembling the armillary sphere, the gnomon and the gnomonic holes on the façade.
The armillary sphere, installed it on the building in 1574, is on the left side of the front of the church and was used to determine the time of the vernal or Spring equinox by the shadow of the sun on its equatorial ring.
It was with this instrument that Fra' Egnazio Danti established that the calendar was 10 days late. He presented his plan to the pope who approved it. Thus was born the Gregorian calendar which is also ours, jumping from 4 to 14 October
Hypatia of Alexandria was born in Alexandria, Egypt, then part of the Roman Empire, around 355 CE. She was the daughter of Theon of Alexandria, a mathematician and astronomer associated with the Museum and the scholarly traditions that followed the legacy of the great Hellenistic centers of learning. Unlike most women of her time, Hypatia received a rigorous scientific and philosophical education. Under her father’s guidance she studied mathematics, astronomy, geometry, and philosophy, eventually surpassing many of her contemporaries in reputation and intellectual authority.
She became the head of the Neoplatonic school of Alexandria, where she taught philosophy in the Platonic tradition, along with advanced mathematics and astronomy. Her students included both pagans and Christians, some of whom later occupied high public offices. Hypatia wrote or edited commentaries on key scientific works, including Diophantus’ “Arithmetica” and Ptolemy’s “Almagest,” contributing to the preservation and transmission of classical scientific knowledge. Ancient sources also associate her with the construction or refinement of scientific instruments such as the astrolabe and hydrometer, reinforcing her practical as well as theoretical engagement with science.
Hypatia was not only a scholar but a respected public intellectual. She moved freely in civic life and was known for her integrity, independence, and rhetorical skill. She advised Orestes, the Roman prefect of Alexandria, during a period of intense political and religious tension in the city. Alexandria in the early fifth century was marked by escalating conflict between imperial civil authority and the growing power of the Christian episcopate under Bishop Cyril. As a pagan philosopher of high status, intellectually influential and politically connected, Hypatia became a symbolic figure within this struggle.
According to ancient sources such as Socrates Scholasticus, in March 415 CE a mob of Christian extremists, reportedly led by a church reader named Peter and associated with radical factions linked to the bishop’s circle, intercepted her carriage as she was returning home. She was dragged into the Caesareum, which had been converted into a church, stripped, and brutally killed using ostraka—sharp pottery shards or tiles. Her body was dismembered, and the remains were burned outside the city. The killing was widely recognized even by some Christian historians as a disgraceful act. There is no clear evidence of formal punishment for those directly responsible. Her murder stands as a documented case of politically charged religious violence directed against an independent intellectual woman whose authority crossed boundaries of belief and power.
Hypatia’s death has come to represent the violent suppression of philosophical inquiry and scientific freedom in a period of profound transformation within the Roman world. She embodied intellectual autonomy, female authority in public life, and commitment to rational discourse in a polarized society. Her life and death continue to be studied not as legend, but as a historically grounded episode revealing how knowledge, influence, and gender could become threats in times of ideological consolidation.
I publish this series to remember that freedom, dignity, knowledge, and justice are never abstract ideals but realities defended by real people who often paid with their lives. Behind every right there are names, faces, biographies, and violent ruptures. I publish these works to oppose the normalization of political and religious violence, to speak to younger generations, and to affirm that silence always benefits unchecked power. This is not passive commemoration; it is active memory, a conscious choice, and a form of resistance.
The image used for this work is based on artistic representations of Hypatia found in historical paintings and later visual interpretations, given the absence of authentic contemporary portraits due to the antiquity of the period.
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 over 10,000 people worked at Bletchley Park, Government Code and Cypher School.
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!
1. It was the tallest man-made structure until 1930
The Eiffel Tower reigned supreme as the tallest man-made structure in the world for about four decades. Without its antenna, the Eiffel Tower stood at a staggering 984 feet. From 1930 onwards, it was officially surpassed by the Chrysler Building and the Empire State Building in New York.
With a net worth of 400 billion euros today—six times that of the Colosseum in Rome and more than the Tower of London—the Eiffel Tower is no doubt a hallmark of engineering and modern architecture. Take a guided tour to learn more about this grand dame.
2. The Eiffel Tower was supposed to be demolished after 20 years
The Eiffel Tower was built to flaunt France’s industrial prowess at the 1889 World Fair. But when its permit expired in 1909, it was ready to be dismantled. To preserve this landmark, a radio antenna was erected atop the Eiffel Tower—and the plan worked. City officials felt that it was too valuable as a radio transmission tower and decided against tearing it down.
3. Believe it not, the Eiffel Tower was once yellow
Yellow Eiffel Tower in Paris
Made of wrought iron, the Eiffel Tower needed a protective coat to counteract any natural elements. During its official launch, it sported a copper-brown color. But after a decade, its metallic structure was coated in yellow paint instead.
From 1968 onwards, the signature “Eiffel Tower Brown” became the official color. The darkest shade was painted on top, and the lightest on the bottom—giving it a subtle ombre effect. Take a closer look at the paintwork as you make your way up the Eiffel Tower.
4. The Eiffel Tower can only be painted by hand
It takes a lot of primping to look fab at 133 years old. Here’s a fun fact about the Eiffel Tower: It’s painted the traditional way—mostly by hand. The Eiffel Tower is stripped of its color and repainted every seven years by 50 painters. To date, the tower has been repainted 19 times.
On average, at least 60 tons of paint are applied to the whole structure to prevent the iron exteriors from rusting. The Eiffel Tower has since undergone a sparkling golden makeover for the 2024 Paris Olympic Games.
5. The Eiffel Tower has a (not so) secret apartment
Architect Gustave Eiffel cleverly included a private apartment at his namesake tower—possibly the world’s most enviable address. Perched 1,000 feet above Champ de Mars, this space was used to conduct experiments and host impressive guests like Thomas Edison.
After being locked away for years, you can now view this hidden sanctuary, with much of the furnishing still in place. Maximize your time with skip-the-line tickets and bask in the aerial views from up here.
6. You’ll see 72 names engraved at the base
Names engraved at the bottom of the Eiffel Tower in Paris
Not known to many, the Eiffel Tower was practically a science lab. Inspect the tower’s details, and you’ll notice 72 names engraved on the edge of the first floor. These names were previously covered up, but restorative efforts made their golden letters visible again. It’s a symbolic way of paying homage to the scholars, scientists, and mathematicians who contributed tirelessly to the tower’s successful assembly.
7. There’s a tiny post office, too
If you’re thinking of a novel souvenir, swing by the Eiffel Tower’s post office on the first floor (at the south pillar). Pick a postcard and mail it back home. It’ll be delivered with an exclusive "Tour Eiffel Paris” stamp, something you can’t get anywhere else. Consider this a special memento to commemorate your trip, or send a surprise letter to a loved one back home.
8. The Eiffel Tower’s height changes with the seasons
Here’s another interesting fact about the Eiffel Tower: Its height changes with the seasons. If you’re visiting in summer, the tower is actually taller as the iron structure expands up to 7 inches when temperatures are as high as 104°F. In winter, the cold weather causes the tower to shrink up to 6 inches. Besides the seasonal changes, strong winds and bad weather can also cause the tower to sway.
9. To get to the top, you’ll have to climb 1,665 steps
eiffel tower paris
The Eiffel Tower comprises three sections. On the first level (189 feet high), you’ll find an observation area, souvenir shops, and Madame Brasserie, a chic restaurant. Challenge yourself to walk on the glass floor; it affords expansive views of the city beneath your feet.
The second level—at 379 feet—includes a Michelin-starred restaurant, Le Jules Verne, plus another observation deck. From up here, keep your eyes peeled for famous sights like the Louvre Museum, Arc de Triomphe, and Champs Élysées.
Unless your fear of heights gets in the way, head to the top floor which is 905 feet above the ground. Revel in panoramic views while sipping some rosé at Bar à Champagne. The climb (and all 1,665 steps) will be worth celebrating.
10. It’s actually illegal to publish photographs of the lit-up Eiffel Tower
During the daily illumination show, catch the Eiffel Tower twinkling in its full glory. The iron edifice sparkles after sunset thanks to the 20,000 light bulbs adorning it.
Before you get all excited to post on your newsfeed, remember: the light display is essentially an artwork protected by copyright. Capturing and sharing photos of the Eiffel Tower is fine for personal use, but not for commercial purposes. Don’t risk getting into trouble with the French authorities.