Alter (2004), Robert, The Five Books of Moses: A Translation with Commentary, W W Norton 2004 Through a distinguished career of critical scholarship and translation, Robert Alter has equipped us to read the Hebrew Bible as a powerful cohesive work of literature. In this landmark work, Alter's masterly translation and probing commentary combine to give contemporary readers the definitive edition of The Five Books of Moses. 
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Brown (2025), Bob, Defiance: Stories from Nature and its Defenders, Black Inc 2025 ' This book is a poweful reminder that the arc of the moral universe bends towards justice only if brave people make the effort to bend it.' Geraldine Brooks)
' Our unifying purpose ought to be safeguarding life on Earth, honouring happiness and securing humanity for its future int he universe. Far more than money, this simple and obvious pursuit offers us meaning to life on our brilliant little planet.' 
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Khinchin (1960, 1998), Aleksandr Yakovlevich, The Mathematical Foundations of Quantum Statistics, Dover 1998 'In the area of quantum statistics, I show that a rigorous mathematical basis of the computational formulas of statistical physics . . . may be obtained from an elementary application of the well-developed limit theorems of the theory of probability.' 
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Nicholls (2025), Jeffrey, Cognitive Cosmogenesis: a systematic integration of theology and physics, Austin Macauley 2025 ' The core idea of the top down theology devised by the Christian bishops for the Emperor Constantine is that the omnipotent and omniscient creator totally controls every moment of every event in the world. The imperial picture. Here we work from the bottom up. A key to the connection of physics and theology is symmetry with respect to complexity.
Although the difference in scale between fundamental particles and the people of an ideal democratic polity is immense, they are formally quite similar. Both democratic politics and quantum electrodynamics work in Hilbert space. Voting is linear, a form of superposition distributed by parties. Individuals and political parties are characterized by their directions in political space which may be modelled by vectors in a Hilbert space.
We may imagine a space with a basis vector for every person. Their sums in various combinations present us with a comprehensive picture of the political directions in an electorate. Such ideal democratic political systems have natural quantum mechanical support which gives us insight into the nature of the world.' 
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Amin Saikal (2025_10_27), The leader most capable of governing a future Palestinian state is languishing in an Israeli jail , 'As the future of Gaza hangs in the balance, the Palestinian Authority (PA) needs renewal if it’s to eventually govern the strip and play a key role in making the two-state solution a reality.
The PA has not proved effective under Mahmoud Abbas, the heavily criticised, unpopular 89-year-old leader. [. . .]
Under the circumstances, no one fits the bill better than Marwan Barghouti who has been languishing in Israeli jails since 2002.
Marwan Barghouti was a member of the Palestinian Legislative Council in the West Bank in the late 1990s and had established many close relationships with Israeli politicians and members of the peace movement.
During the Second Intifada from 2000–05, he became a leader of the street protests against Israeli occupation. In 2002, he was jailed for allegedly orchestrating attacks against Israelis and was convicted of murdering five people. He was sentenced to five consecutive life terms. [. . .]
Nearly 20 years later, he remains relevant. In a recent poll of Palestinians in the West Bank and Gaza, Barghouti would win a presidential election against two other leading candidates, Hamas leader Khaled Mashal and Abbas.
Among those who said they would vote, Barghouti got 50% of the support, followed by Mashal at 35% and Abbas at just 11%.
Hamas included Marwan, now 66, in its list of Palestinians to be freed from Israeli jails in exchange for the remaining Israeli hostages held by the group. Israel, however, refused to release him. [. . .]
If the Israeli and American leadership really wants the Gaza ceasefire to hold and lead to the implementation of the second and third stages of Trump’s 20-point peace plan, Marwan needs to be freed.
Viewed by the Palestinian people as a Nelson Mandela-like figure, he is the one most capable of reforming the Palestinian Authority and enabling it to govern for all Palestinians.
And among all potential future Palestinian leaders, he stands out as the one who can deliver on the peace plan and move to the eventual, internationally backed two-state solution.
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Ben Doherty (2025_10_27), A remote spy base and a ‘criminal’ blockade raise questions about Australia’s complicity in Gaza war, ' Straight and bare, Hatt Road runs south-west from Mparntwe-Alice Springs before it suddenly swings north through a narrow gap in the MacDonnell Ranges.
It is what lies beyond that draws protesters here time and time again.
Hatt Road – unremarkable save for the fierce signs insisting “No Photography From This Point On” and demanding drivers “Turn Around Now” – is the main route into Pine Gap, the highly secretive joint Australian-US satellite communications and signals intelligence surveillance base.
Twenty hectares and heavily guarded, “the base” – as it’s known locally – sits in a secluded, narrow valley, flanked by the sparse hills of the ranges. Little is officially confirmed about its operations but through leaked documents and whistleblower disclosures its criticality to US global-intelligence gathering is uncontested.
Ostensibly, the “joint defence facility” established by the CIA in 1966 is controlled by both Australia and the US. But Pine Gap has been described as America’s most valuable intelligence site outside US soil.
On 9 October two activists from Mparntwe for Falastin locked themselves to a concrete-filled barrel, blocking Hatt Road for nine hours and preventing Pine Gap workers from accessing the base. Flanking their protest were two boats, representing the aid flotilla then approaching the occupied territory of Gaza from the Mediterranean.
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Brouwer fixed point theorem - Wikipedia, Brouwer fixed point theorem - Wikipedia, the free encyclopedia, 'Among hundreds of fixed-point theorems] Brouwer's is particularly well known, due in part to its use across numerous fields of mathematics. In its original field, this result is one of the key theorems characterizing the topology of Euclidean spaces, along with the Jordan curve theorem, the hairy ball theorem, the invariance of dimension and the Borsuk–Ulam theorem. This gives it a place among the fundamental theorems of topology.' back

Evangelical counsels - Wikipedia, Evangelical counsels - Wikipedia, the free encyclopedia, ' In Christianity, the three evangelical counsels or counsels of perfection are chastity, poverty (or perfect charity), and obedience.As stated by Jesus in the canonical gospels, they are counsels for those who desire to become "perfect" (τελειος, teleios). The Catholic Church interprets this to mean that they are not binding upon all, and hence not necessary conditions to attain eternal life (heaven), but that they are "acts of supererogation" exceeding the minimum stipulated in the biblical commandments. Catholics who have made a public profession to order their life by the evangelical counsels, and confirmed this by public vows before their competent church authority (the act of religious commitment known as a profession), are recognised as members of the consecrated life.' back

Finn Brunton (2025_10_24), How a Fringe Movement of Gun Nuts, Backwoodsmen and Free Marketers Paved the Way for Autocracy, ' It was pitched as the world’s most exclusive invitation. Hundreds gathered at President Trump’s private country club in Virginia in May for a gala evening. Guests included Justin Sun, a cryptocurrency billionaire who, in the Biden administration, was under investigation for suspected financial crimes. He and the other attendees had won their seats by being the top buyers of $TRUMP memecoin, a form of crypto that benefits Mr. Trump’s family.
“There is a lot of common sense in crypto,” said Mr. Trump, as the room was served a meal accompanied by Trump-branded wine and water. “And we’re honored to be working on helping everybody here.” Mr. Sun later expressed gratitude and received an 18-karat-gold Trump Victory Tourbillon watch. And with that, cryptocurrency elided its dark past and ascended to the apex of American power. br> Cryptocurrency has found its hero in Mr. Trump. And in this unlikely moment of triumph, its most powerful proponent has laid bare the paradox at the heart of this brave new world of “new money.” Crypto was supposed to free us from the chains of government control, but now it is finally revealing what that freedom really means: removing all checks on the power of the wealthy to do what they want, discharged at last from law, supervision and civic obligation — even if the result is autocracy. Mr. Trump, with his thirst for money and power, has in one fell swoop both exposed and embraced the corruption at the heart of digital currencies — a corruption inherited from the libertarian ideals that created them. [. . .]
Libertarianism was always an elitist movement. Individual liberty and the destruction of the state’s authority would enable a new elite to take power over the population. Ayn Rand was libertarians’ favorite novelist, after all: Her rich, brilliant supermen despise everyone else, and their victory is the freedom to be in charge at last without rules or laws to restrain their self-interest.
In the 1990s, the internet revolution birthed an obscure technology that seemed almost purpose-built to fulfill a libertarian extremist’s visions: the blockchain. [. . .] The technology soon attracted a following of libertarians, the most extreme of whom had long dreamed of replacing government-regulated banks with a parallel financial infrastructure for untaxable, untraceable, borderless online-only cash. They used the technology to develop cryptocurrencies, the first of which was Bitcoin. [. . .]
Whether crypto was intended to replace the bank and its regulator down the street or to build new banking systems thousands of miles away, the goal was the same. Mr. Thiel and Mr. Andreessen had made big bets on creating their own financial system, one that could replace the existing one and earn them enormous returns. [. . .]
Both men focused on the legitimate prospects for cryptocurrency, rather than its deep links to the criminal economy. In 2013, the Drug Enforcement Administration’s analysis estimated that up to 90 percent of Bitcoin transactions that year were primarily used to facilitate illicit activity, including drug sales, blackmail, ransomware and illegal pornography. [. . .]
Mr. Trump and his Silicon Valley backers may have taken different journeys to get to their embrace of crypto, but they have ended up in the same place: The government, and the population, exists to serve the interests of their businesses, their enrichment, and their aggrandizement. So the trick of libertarianism wasn’t on them. It was on us.
Crypto is the most successful libertarian project in American history. A technology developed to escape the state is now at the political center of a global superpower. Crypto has become a machine for transferring control and wealth from the many to the few, a bribery-as-a-service platform for buying and selling influence among authoritarian oligarchs. It’s the perfect technological expression of the Trump moment: our country’s crypto era. back

Garrett C. Van Dyk (2025_10_29), How a ‘sewer socialism’ revival could see Zohran Mamdani become New York’s next mayor, ' Democratic candidate for mayor of New York City Zohran Mamdani looks increasingly like the one to beat at next week’s election. But he is up against more than the usual political challenges. US President Donald Trump has referred to him as “my little communist” and called his nomination “a rebellion”. More recently there have been calls for Mamdani’s citizenship to be investigated. Born in Uganda, and the first Muslim nominee for mayor of the biggest city in the US, the 34-year-old Mamdani is an obvious target. But it is his stance as a democratic socialist that has really invited the old-school “red-baiting”, aimed at discrediting him by invoking Cold War anxieties. In fact, Mamdani’s approach to democratic socialism is less about an abstract political ideology than it is about practical solutions. As he has put it: We want to showcase our ideals, not by lecturing people about how correct we are, but rather by delivering and letting that delivery be the argument itself. Because of this, he has also been described as an heir to the historical tradition of “sewer socialism”, a brand of left-wing thinking that favoured incremental, practical reform over revolutionary rhetoric.' back

Iain Boyd (11025_10_30), Nuclear-powered missiles: An aerospace engineer explains how they work – and what Russia’s claimed test means for global strategic stability, ' Russian President Vladimir Putin, dressed in a military uniform, announced on Oct. 26, 2025, that Russia had successfully tested a nuclear-powered missile. If true, such a weapon could provide Russia with a unique military capability that also has broader political implications.
The missile, called Burevestnik, was reportedly successfully tested over the Arctic Ocean after years of development and several earlier initial test flights, one of which resulted in the deaths of five nuclear scientists.
I am an engineer who studies defense systems. Here is how these weapons function, the advantages they present over conventional missile systems, and their potential to disrupt global strategic stability. [. . .]
Nuclear-powered missiles are a type of cruise missile. The designs are typically a form of scramjet. A thermal nuclear system uses fission of nuclear fuel to add energy to an airstream that is then accelerated through a nozzle to generate thrust. In this way, fission of nuclear material replaces chemical combustion of traditional cruise missile engines. [. . .]
The Russian military claims that the Burevestnik missile flew 8,700 miles at low altitude over a 15-hour period. For comparison, an airline flight from San Francisco to Boston covers 2,700 miles in six hours. While the Burevestnik vehicle is not flying particularly fast for a missile, it is likely maneuverable, which makes it difficult to defend against. [. . .]
Several developments threaten the current balance of power: better missile defense systems such as the U.S.’s planned Golden Dome and advances in highly maneuverable missiles. Missile defense systems have the potential to block a nuclear strike, and low-altitude maneuverable missiles have the potential to arrive without warning.
So, while much of the reaction to Russia’s announcement of its new nuclear-powered missile has focused on the challenges of defending against it, the more important concern may be its potential to completely disrupt global strategic stability.' back

Jeffrey Nicholls (25_10_30), Essay 16: Green theology: a path to heaven (2016), ' Abstract
We proceed here on the assumption that the Universe is divine. From this we conclude that the observable Universe is God's body. We assume that the Universe executes all the functions traditionally attributed to God: creator, sustainer and judge. Since we, too are agents of God, our actions are part of God's action. The premise of green theology is that life is, to a large degree, what we make it. Ancient religions promise heaven and hell in an afterlife. In reality we die. We experience heaven and hell in this life. The role of green theology is to guide us toward the experience of heaven and away from hell.' back

Karen Zraick & Lisa Friedman (2025_10_25), An E.P.A. Plan to Kill a Major Climate Rule Is Worrying Business Leaders, ' The Environmental Protection Agency is promising to erase a scientific finding that underpins climate regulations nationwide. But some business leaders said they are wary that the move could lead to a costly legal quagmire.
The rule, known as the “endangerment finding,” is the conclusion by the E.P.A. that greenhouse gases endanger public health and therefore must be regulated by the federal government. Lee Zeldin, the E.P.A. administrator, has said the agency would repeal the finding, claiming that the burden to industries of cutting greenhouse gas emissions is more harmful than a warming planet.
And yet carmakers, electric utilities and even the oil and gas industry have asked the E.P.A. to tread carefully. If the federal government were to stop regulating greenhouse gases, it could clear the way for states and municipalities to sue companies for damages from climate change. And it could spur individual states to come up with their own pollution limits, creating a patchwork of regulations. Environmental groups have also promised to sue the E.P.A. if it repeals the finding, leading to more uncertainty for businesses.
“This is something that the vast majority of industry didn’t ask for and doesn’t want,” said Zach Friedman, the senior director of federal policy at Ceres, a nonprofit group that submitted a letter from 59 companies and investors opposing the E.P.A. plan [. . .].
Ignoring that evidence, as the E.P.A. appears poised to do, Dr. Saleska said, “puts an exclamation point on the idea that science, as the best method the human species has ever come up with for discerning objective reality, has no role in this government". [. . .]
But other business groups supported removing the endangerment finding. The National Mining Association, which represents mining companies, and the Steel Manufacturers Association backed the agency, as did energy associations from several states, including coal and gas-rich Wyoming.' back

Kate Cowley (25_10_23), ‘We just have to be defiant’: irrepressible environmentalist Bob Brown reflects on a life of activism, Review: Defiance: Stories from Nature and Its Defenders – Bob Brown (Black Inc.
' Hobart’s Theatre Royal was packed to the rafters on a chilly October evening when the irrepressible nature warrior Bob Brown launched his latest book Defiance.
Given the state of the planet “we just have to be defiant”, Brown told the audience, as the image of activist Lisa Searle was projected onto the screen behind him.
Searle sat atop one of the world’s tallest flowering plants, a eucalyptus tree named Sentinel by its defenders, in Tasmania’s Styx Valley, perched there to prevent its destruction. [. . .]
Only defiant communal action, Brown argues, can keep the destruction of nature in check. If, as he writes, “materialism’s dream is of a virtual reality to replace the wild Earth”, we cannot stand by and do nothing. In Defiance, he evokes the great tradition of non-violent action, where “ordinary people take affairs into our own hands to overcome the power of corporate influence on governments”. [. . .]
There is no creeping conservatism about the octogenarian Brown; if anything, he is more infectiously defiant than ever. His book concludes with a series of odes to wild places that reveal his close, indeed transpersonal, connection with nature. He wants everyone to share how it feels to see a wedge-tailed eagle rise on thermals, or the sun break through the clouds and light up a patch of forest in a distant valley. “We need natural beauty,” he writes, because “our minds and bodies are made for wildness”.' back

Kyle E. Bradley & Judith A. Hubbard (2025_10_30), Mandalay earthquake pushes rupture limits, On 28 March 2025, a magnitude 7.7 earthquake struck the Sagaing Fault—a fracture in the Earth's crust that runs the north-to-south length of Myanma.r The earthquake kiled more than 4000 people and damaged a wide region, including the capital (Naypyidaw) and the country's second-largest city, (Mandalay). back

Lara Jakes (2025_10_24), A Tiny NATO Nation Is Cashing In on the Threat Next Door, back

Matthew Davis (2025_10_27), ‘The Rushmore story is hard to tell’: how an Indigenous park leader revealed the monument’s dark side, ' On 1 June 2004, Gerard Baker became the first Native American superintendent at Mount Rushmore national memorial, and his six years at the helm were both transformative and turbulent.
Mount Rushmore was first conceived by Doane Robinson, the South Dakota state historian, who wanted to build sculptures in the Black Hills that reflected the American west and attracted regional car tourists. When Robinson tasked the controversial artist Gutzon Borglum to lead the project, however, the idea metamorphosed from economics to politics, as Borglum decided to build a memorial to the American political system, which he deemed the apotheosis of western civilization. He envisioned portraits of four presidents who he called “empire makers”, and on 1 October 1925, Borglum held the memorial’s first dedication in front of over 3,000 spectators.
One hundred years later, the national memorial is a lightning rod of political and historical interpretation. In summer 2020, Donald Trump gave a speech at Rushmore that offered a narrow view of American history and the memorials and monuments meant to reflect that history. More recently, Rushmore has become a totem for Maga America, with legislation introduced to carve Trump into the granite. Yet the memorial stands on land that reflects the darker side of our nation’s past, a history the Trump administration is keen to erase.
The Black Hills, the Paha Sapa in Lakota, are sacred to the Lakota, and the US took the Paha Sapa from the Lakota Nation in early 1877, after the tribe had defeated George Armstrong Custer’s 7th Cavalry at the Battle of Little Bighorn the previous June. The Lakota call the Black Hills the Heart of Everything That Is, and when the US stole the landscape of ponderosa pine and granite, it broke the 1868 Treaty of Fort Laramie and began a process to erase Native American culture and history.' back

Money - Wikipedia, Money - Wikipedia, the free encyclopedia, ' Money is any item or verifiable record that is generally accepted as payment for goods and services and repayment of debts, such as taxes, in a particular country or socio-economic context.] The primary functions which distinguish money are: medium of exchange, a unit of account, a store of value and sometimes, a standard of deferred payment. Money was historically an emergent market phenomenon that possessed intrinsic value as a commodity; nearly all contemporary money systems are based on unbacked fiat money without use value. Its value is consequently derived by social convention, having been declared by a government or regulatory entity to be legal tender; that is, it must be accepted as a form of payment within the boundaries of the country, for "all debts, public and private", in the case of the United States dollar.' back

New Order, Blue Monday: (Live at the Alexandra Palace), ' As a club dj in the eighties, my fondest memory was the moment I could drop this masterpiece into my set. People would freak the fuck out, nearly tearing their clothes in an effort to get to the dance floor. I have never before and rarely since seen dancers experiencing such moments of total kinetic bliss. The word "floorgasm" was coined just to describe that scene. One of the highpoints of my 25+ years working as a DJ.' back

Renata Keller (2025_10_24)' Sixty-three years ago, President John F. Kennedy single-handedly brought the world back from the brink of nuclear war by staring down Soviet leader Nikita Khrushchev over the Cuban missile crisis. At least, so goes a standard U.S.-centric interpretation of events.
But despite the narrative of presidential strength and American resolve saving the day, the truth is more complicated – and involved a wider cast of continental characters.
On the evening of Oct. 22, 1962, Kennedy took to the airwaves and revealed to a live international audience that the Soviet Union had secretly placed nuclear-armed missiles in Cuba capable of reaching most of the mainland U.S. and Latin America. [. . .]
Most importantly, Mexican and Brazilian leaders changed their position in international organizations in response to the Cuban missile crisis. Prior to the crisis, these two countries had resisted all multilateral actions against Cuba and had abstained from Organization of American States votes that put sanctions on the island. But on Oct. 23, 1962, they changed their position and joined the unanimous vote to establish a quarantine around Cuba. The quarantine laid out a large zone where ships approaching the island could be intercepted and searched for offensive military equipment. The OAS action provided the legal foundations for the quarantine. Establishing the quarantine under the auspices of articles 6 and 8 of the Rio Treaty made it a multilateral “act of common defense.” Had the U.S. acted alone, interdicting ships in international waters would have legally been considered a “blockade,” or act of war. , The lost history of Latin America’s role in averting catastrophe during the Cuban missile crisis, ' Sixty-three years ago, President John F. Kennedy single-handedly brought the world back from the brink of nuclear war by staring down Soviet leader Nikita Khrushchev over the Cuban missile crisis. At least, so goes a standard U.S.-centric interpretation of events.
But despite the narrative of presidential strength and American resolve saving the day, the truth is more complicated – and involved a wider cast of continental characters.
On the evening of Oct. 22, 1962, Kennedy took to the airwaves and revealed to a live international audience that the Soviet Union had secretly placed nuclear-armed missiles in Cuba capable of reaching most of the mainland U.S. and Latin America.
Throughout his speech, Kennedy consistently emphasized that the missiles threatened the security not just of the U.S. but of the entire hemisphere. And because the missiles were a regional threat, they required a regional solution. Kennedy called upon the Organization of American States, a regional body created in 1948 to coordinate hemispheric affairs, including security, to invoke the 1947 Inter-American Treaty of Reciprocal Assistance “in support of all necessary action” to remove the missiles.[. . .]
Most importantly, Mexican and Brazilian leaders changed their position in international organizations in response to the Cuban missile crisis. Prior to the crisis, these two countries had resisted all multilateral actions against Cuba and had abstained from Organization of American States votes that put sanctions on the island. But on Oct. 23, 1962, they changed their position and joined the unanimous vote to establish a quarantine around Cuba. The quarantine laid out a large zone where ships approaching the island could be intercepted and searched for offensive military equipment. The OAS action provided the legal foundations for the quarantine. Establishing the quarantine under the auspices of articles 6 and 8 of the Rio Treaty made it a multilateral “act of common defense.” Had the U.S. acted alone, interdicting ships in international waters would have legally been considered a “blockade,” or act of war.' back

Sabrina Carpenter, Tears, Lyrics:
I get wet at the thought of you Being a responsible guy Treating me like you′re supposed to do Tears run down my thighs verse A little initiative can go a very long long way Baby just do the dishes I'll give you what you (what you), what you want A little communication yes that′s my ideal foreplay Assemble a chair from IKEA I'm like (uhhh) chorus I get wet at the thought of you Being a responsible guy Treating me like you're supposed to do Tears run down my thighs verse A little respect for women can get you very very far Remembering how to use your phone gets me Oh so, oh so, oh so hot Considering I have feelings I′m like, why are my clothes still on? Offering to do anything I′m like (oh my God) chorus I get wet at the thought of you Being a responsible guy Treating me like you're supposed to do Tears run down my thighs I get wet at the thought of you Being a responsible guy Treating me like you′re supposed to do Tears run down my thighs (Dance break) I get wet at the thought of you Being a responsible guy Treating me like you're supposed to do Tears run down my thighs Writer(s): John Henry Ryan, Amy Rose Allen, Sabrina Annlynn Carpenter back

The Green Institute, About The Green Institute, ' The Green Institute is cultivating ecological democracy through ideas, conversation and action. Founded in 2008, and supported by a grant-in-aid from the Commonwealth government as the official think-tank of The Australian Greens, the Institute has a national and international reputation for high-quality, exciting and influential research, and creating space for deep and rich discussion. Dedicated to the Global Greens’ four pillars of ecological sustainability, grassroots democracy, social and economic justice, and peace and nonviolence, the Institute has focussed its work on key points of intervention including the rights of nature and Earth-centred governance, participatory democracy, and universal basic income and the future of work, as well as over-arching discussions around ecological political theory and practice.' back

University of Cambridge: Millennium Mathematics Project, Maths in a Minute: Simplices – the atoms of topology, ' Two-dimensional triangles can be generalised to 0 dimensions, 1 dimension, 3 dimensions or indeed to any number of dimension. Such a generalisation is called a simplex. A 0-simplex is a point, 1-simplex is a line segment, a 2-simplex is a triangle, a 3-simplex is a tetrahedron, a 4-simplex is a pentatope (a four-dimensional object whose five faces are tetrahedrons – don't worry we can't visualise it either), and so on. And these simplices are used to describe and understand different mathematical spaces. back

Wee Kek Koon (2022_04_22), Reflections | Why Chinese Buddhists, Taoists and Confucians get along yet the world’s Christians, Muslims and Jews cannot, ' Followers of the Abrahamic faiths have clashed throughout history, but in China believers in Buddhism, Taoism and Confucianism have usually got along One reason is that these belief systems are not dogmatic; in the same Chinese temple one can offer devotions to Buddhist and Taoist deities and to Confucius back

Yashito Tanaka (2011_07_09), A Proof of Constructive Version of Brouwer′s Fixed Point Theorem with Uniform Sequential Continuity, ' It is often said that Brouwer′s fixed point theorem cannot be constructively proved. On the other hand, Sperner′s lemma, which is used to prove Brouwer′s theorem, can be constructively proved. Some authors have presented a constructive (or an approximate) version of Brouwer′s fixed point theorem using Sperner′s lemma. They, however, assume uniform continuity of functions. We consider uniform sequential continuity of functions. In classical mathematics, uniform continuity and uniform sequential continuity are equivalent. In constructive mathematics a la Bishop, however, uniform sequential continuity is weaker than uniform continuity. We will prove a constructive version of Brouwer′s fixed point theorem in an n-dimensional simplex for uniformly sequentially continuous functions. We follow the Bishop style constructive mathematics.' back