Tag: Science

Can you solve it? Are you smarter than a forester?

A puzzle about planting trees

Hello guzzlers,

Your mission today is to design an arrangement of trees on a desert island, like the one below.

An
An aerial view of five trees on an island.

When there is a single tree, no matter where you stand on the island you will always be able to see exactly one tree.

An
An island with a single tree. From each of the two black dots you can see a single tree.

With two trees, however, there are some places where you can see two trees, and there are some places where you can see only a single tree, since the other one is blocked from view.

Read more: https://www.theguardian.com/science/2017/jul/31/can-you-solve-it-are-you-smarter-than-a-forester

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The world has lost a great artist in mathematician Maryam Mirzakhani

She was the only woman to have won the Fields medal, maths equivalent of the Nobel prize

The mathematician Maryam Mirzakhani died two weeks ago. Shewas 40. I had never heard of her before reading about her death in the papers. Its a piercingly sad story: Iranian-born, and latterly a professor at Stanford University, Mirzakhani was the only woman to have won the Fields medal, the equivalent for a mathematician of the Nobel prize, and is survived, in newspaper-speak, by a husband and a daughter.

I always find the locution survived by too cruel to bear. So final the rupture, no room for error: shes gone, theyre left. And, in this case, how young the mother and the wife.

It is a sad story for other reasons, too, not least the intensity of Mirzakhanis expression in the photograph most of the papers used. There is a beauty that can onlybe described as that of the minds migration to the face, the transfiguring beauty of exceptional intelligence. So its a double loss: thepremature loss of a person and the premature loss of her genius.

I remember there being an unspoken qualitative distinction atschool between those who were good at maths and science the priests of numbers and symbols and the more poetical of us, whose medium, as Wordsworth had it, was the language of men talking to men. The assumption, at least on the part of us Wordsworthians, was that creativity was all on our side. I have since come to think the word creative has much to answer for. Among the freedoms it sometimes gave us was the freedom from structure, knowledge and the obligation to convince.

Mirzakhani, it is said, considered being a writer before turning to mathematics. It is unlikely she believed shed made a choice in favour of an inferior, or less artistic, discipline. And she expressed her immersion in mathematics in language every writer will recognise like being lost in a jungle and trying to use all the knowledge you can gather to come up with some new tricks, and with luck you might find a way out.

The luck, of course, is no such thing. Its the mystery Keats called negative capability, the trust that the work will do itself if only we dareto plunge without irritability orinsistence into the dark, not sure we will find a way out at all. The bestwriting happens in this way, unintended, unknowing, grateful and surprised. Such abnegation of will is what we mean by creativity. So the mathematician and the artist are companioned in the same dark, and do obeisance to the same gods. The pity of Mirzakhanis death will be felt by poets as well as mathematicians.

Read more: https://www.theguardian.com/science/2017/jul/29/maryam-mirzakhani-great-artist-mathematician-fields-medal-howard-jacobson

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Can you solve it? Are you smarter than an architect?

A puzzle that tests 3D thinking

Hi guzzlers,

Todays puzzle was sent in by a reader who remembers it from his days as an architecture student.

Draw a 3-dimensional picture of a shape that goes through each of these holes, exactly touching all sides as it passes through.

A
A triangle with sides 1 unit. A square with sides 1 unit. A circle with diameter 1 unit.

Architects will surely find the answer obvious. The heads of the rest of us will look rather like the house in the picture above, since it requires you to visualise an object in three dimensions, which is a challenge if your brain isnt trained to do it.

If you want to email me your answer, or post it on Twitter with the hashtag #MondayPuzzle, Ill send the author of my favourite image a copy of my puzzle book Can You Solve My Problems?

Ill be back at 5pm UK time with the solution.

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I set a puzzle here every two weeks on a Monday. Send me your email if you want me to alert you each time I post a new one. Im always on the look-out for great puzzles. If you would like to suggest one, email me.

My puzzle book Can You Solve My Problems? is just out in paperback.

Read more: https://www.theguardian.com/science/2017/jul/17/can-you-solve-it-are-you-smarter-than-an-architect

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Maryam Mirzakhani, first woman to win mathematics’ Fields medal, dies at 40

Stanford professor, who was awarded the prestigious prize in 2014, had suffered breast cancer

Maryam Mirzakhani, a Stanford University professor who was the first and only woman to win the prestigious Fields medal in mathematics, has died. She was 40.

Mirzakhani, who had breast cancer, died on Saturday, the university said. It did not indicate where she died.

In 2014, Mirzakhani was one of four winners of the Fields medal, which is presented every four years and is considered the mathematics equivalent of the Nobel prize. She was named for her work on complex geometry and dynamic systems.

Mirzakhani specialized in theoretical mathematics that read like a foreign language by those outside of mathematics: moduli spaces, Teichmller theory, hyperbolic geometry, Ergodic theory and symplectic geometry, the Stanford press announcement said.

Mastering these approaches allowed Mirzakhani to pursue her fascination for describing the geometric and dynamic complexities of curved surfaces spheres, doughnut shapes and even amoebas in as great detail as possible.

Her work had implications in fields ranging from cryptography to the theoretical physics of how the universe came to exist, the university said.

Mirzakhani was born in Tehran and studied there and at Harvard. She joined Stanford as a mathematics professor in 2008. Irans president, Hassan Rouhani, issued a statement praising Mirzakhani.

The grievous passing of Maryam Mirzakhani, the eminent Iranian and world-renowned mathematician, is very much heart-rending, Rouhani said in a message that was reported by the Tehran Times.

Irans foreign minister, Mohammad Javad Zarif, said her death pained all Iranians, the newspaper reported.

The news of young Iranian genius and math professor Maryam Mirzakhanis passing has brought a deep pang of sorrow to me and all Iranians who are proud of their eminent and distinguished scientists, Zarif posted in Farsi on his Instagram account.

I do offer my heartfelt condolences upon the passing of this lady scientist to all Iranians worldwide, her grieving family and the scientific community.

Mirzakhani originally dreamed of becoming a writer but then shifted to mathematics. When she was working, she would doodle on sheets of paper and scribble formulas on the edges of her drawings, leading her daughter to describe the work as painting, the Stanford statement said.

Mirzakhani once described her work as like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out.

Stanford president Marc Tessier-Lavigne said Mirzakhani was a brilliant theorist who made enduring contributions and inspired thousands of women to pursue math and science.

Mirzakhani is survived by her husband, Jan Vondrk, and daughter, Anahita.

Read more: https://www.theguardian.com/us-news/2017/jul/15/maryam-mirzakhani-mathematician-dies-40

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Can you solve it? Are you smarter than a cat?

Feline clever? This moggy mystery will mess with your mind

Hi guzzlers,

Todays puzzle requires you to demonstrate superior intelligence to a contrary cat.

A straight corridor has 7 doors along one side. Behind one of the doors sits a cat. Your mission is to find the cat by opening the correct door. Each day you can open only one door. If the cat is there, you win. You are officially smarter than a cat. If the cat is not there, the door closes, and you must wait until the next day before you can open a door again.

If the cat was always to sit behind the same door, you would be able to find it in at most seven days, by opening each door in turn. But this mischievous moggy is restless. Every night it moves one door either to the left or to the right.

How many days do you now need to make sure you can catch the cat?

A
A cat sits behind one of these doors. Whats the best strategy to find it?

(First some clarifications. The 7 doors are in a line, so if the cat is behind the first or the last door, it has only one option for where it can move during the night. Otherwise, each night it decides randomly whether to move to the left or to the right.)

I purr with delight at this puzzle. At first it appears almost impossible that you will be able to get your hands on the furtive feline. But if you begin by trying the puzzle with a smaller number of doors, you will hopefully be able to work out the correct strategy.

Ill get you started. If there are only THREE doors, then it is possible to catch the cat in two days:

  • Day 1: open the middle door.
  • Day 2: open the middle door.

This strategy guarantees you will get the cat, since if it is not behind the middle door on Day 1, then it must be behind either of the end doors. And if it is behind either of the end doors on Day 1, then in both cases it will move to behind the middle door on Day 2. Caught!

If there are FOUR doors, it is possible to catch the cat in four days. But now its up to you to work out how.

The cat puzzle originally appeared in the New York Times now defunct Numberplay column as The Princess Problem, where a prince was knocking on doors and a flighty princess moving from room to room. This version has become a staple problem for maths teachers in Singapore. Toh Pee Choon, of Singapores National Institute of Education, told me that the princess context had great effect in stirring up interests in young girls.

I rephrased the puzzle with a cat to make it non gender specific, and also because people on the internet like looking at pictures of cats.

NO SPOILERS PLEASE

Ill be back at 5pm with the solution.

UPDATE: Read the solution here.

I set a puzzle here every two weeks on a Monday. Send me your email if you want me to alert you each time I post a new one. Im always on the look-out for great puzzles. If you would like to suggest one, email me.

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My puzzle book Can You Solve My Problems is out in paperback this week. You can get it from the Guardian bookstore or other online retailers.

Thanks to Charlie Gilderdale from maths resource project NRICH for first alerting me to this puzzle.


Read more: https://www.theguardian.com/science/2017/jul/03/can-you-solve-it-are-you-smarter-than-a-cat

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Can you solve it? Pythagoras’s best puzzles

Three teasers from the vaults

Hi guzzlers,

The most famous theorem in maths is named after the Greek thinker Pythagoras. So is the most famous recreational mathematics publication in the Netherlands.

Pythagoras Magazine was founded in 1961, and to celebrate its half century it recently published a selection of its best brainteasers in English. Ive selected three of them here, in increasing order of difficulty.

1) Dollar bills. In a bag are 26 bills. If you take out 20 bills from the bag at random, you have at least one 1-dollar bill, two 2-dollar bills, and five 5-dollar bills. How much money was in the bag?

2) Yin and Yang. The Yin-Yang symbol is based on the figure below, bordered by three semi-circles. How can you divide this shape into two identical shapes?

Big
Big yin

3) Huge pie. A huge pie is divided among 100 guests. The first guest gets 1% of the pie. The second guest gets 2% of the remaining part. The third guest gets 3% of the rest, etc. The last guest gets 100% of the last part. Who gets the biggest piece?

Ill be back later today with the solutions.

NO SPOILERS PLEASE

I set a puzzle here every two weeks on a Monday. Send me your email if you want me to alert you each time I post a new one. Im always on the look-out for great puzzles. If you would like to suggest one, email me.

Thanks to the editors of Pythagoras Magazine for todays puzzles. You can check out more of them in Half a Century of Pythagoras Magazine.

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Football School, which I which I co-wrote with Ben Lyttleton, is a book for 7 to 13-year olds children that uses football to explain subjects like English, maths, physics, geography, philosophy and zoology. You (by which I mean any 7-13-year-olds you may know) can check out the Football School YouTube channel, in which Ben and I answer all questions about football and life. Submit your questions and subscribe!

Read more: https://www.theguardian.com/science/2017/jun/19/can-you-solve-it-pythagorass-best-puzzles

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Can you solve it? The incredible sponge puzzle

This brainteaser will wring out your brain

Hi guzzlers.

For todays puzzle, let me introduce you to the Menger sponge, a fascinating object first described by the Austrian mathematician Karl Menger in 1926. Well get to the problem as soon as I explain what the object is.

The Menger sponge is a cube with smaller cubes extracted from it, and is constructed as follows: Step A: Take a cube. Step B: Divide it into 27 smaller subcubes, so it looks just like a Rubiks cube.

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Step C: Remove the middle subcube in each side as well as the subcube at the centre of the cube, so if you looked through any hole you would see right through it. Step D: Repeat steps A to C for each of the remaining subcubes, that is, imagine that each subcube is made from 27 even smaller cubes and remove the middle one in each side and the central one.

We could carry on repeating steps A to C ad infinitum, on smaller and smaller subcubes, but here lets do it just once more:

Menger
Menger sponge. Illustration: Edmund Harriss/Visions of Numberland

Menger sponges are so loved within the maths community that building origami models of them out of business cards is a thing.

Menger
Menger sponge made as part of Matt Parker and Laura Taalmans MegaMenger project. Photograph: MegaMenger

There are lots* of reasons why Menger sponges are cool and one of them is illustrated by todays puzzle.

How
How to slice a cube in two.

On the left here is how you slice a cube in half such that the cross section is a hexagon.

When you slice a Menger sponge in two like this, what does the hexagonal slice look like?

This question is probably the most difficult one I have ever set in this column, as it requires phenomenal levels of spatial intuition. But I urge you to give it a go, even if just a basic sketch. Send me some images, or post them to me on social media. You may draw something along the right lines…

Please forgive me, though, for posing this toughie. The answer is jaw-droppingly amazing. In fact, I was told about the Menger slice by a respected geometer who told me it gave him probably his biggest wow moment in maths. Come back at 5pm BST and see for yourself.

NO SPOILERS PLEASE! Please talk about Karl Menger and origami instead.

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Photograph: Bloomsbury

Both the Menger sponge and the Menger slice are included in my latest book, Visions of Numberland: A Colouring Journey Through the Mysteries of Maths. The book is a gallery of the most spectacular images that Edmund Harriss, my co-author, and I could find in maths. You can colour them in, or just contemplate them in black and white.

I set a puzzle here every two weeks on a Monday. Send me your email if you want me to alert you each time I post a new one.

Im always on the look-out for great puzzles. If you would like to suggest one, email me.

* Here are a couple. 1) Each time you follow the iteration described in steps A to C you decrease the volume of the sponge, but increase its surface area. After an infinite number of iterations, you will have removed an infinite number of cubes. The sponge will then have zero volume and infinite surface area. 2) After an infinite number of iterations, the object is a fractal, that is, it contains parts that are identical to the whole thing.


Read more: https://www.theguardian.com/science/2017/apr/10/can-you-solve-it-the-incredible-sponge-puzzle

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Your animal life is over. Machine life has begun. The road to immortality

In California, radical scientists and billionaire backers think the technology to extend life by uploading minds to exist separately from the body is only a few years away

Heres what happens. You are lying on an operating table, fully conscious, but rendered otherwise insensible, otherwise incapable of movement. A humanoid machine appears at your side, bowing to its task with ceremonial formality. With a brisk sequence of motions, the machine removes a large panel of bone from the rear of your cranium, before carefully laying its fingers, fine and delicate as a spiders legs, on the viscid surface of your brain. You may be experiencing some misgivings about the procedure at this point. Put them aside, if you can.

Youre in pretty deep with this thing; theres no backing out now. With their high-resolution microscopic receptors, the machine fingers scan the chemical structure of your brain, transferring the data to a powerful computer on the other side of the operating table. They are sinking further into your cerebral matter now, these fingers, scanning deeper and deeper layers of neurons, building a three-dimensional map of their endlessly complex interrelations, all the while creating code to model this activity in the computers hardware. As thework proceeds, another mechanical appendage less delicate, less careful removes the scanned material to a biological waste container for later disposal. This is material you will no longer be needing.

At some point, you become aware that you are no longer present in your body. You observe with sadness, or horror, or detached curiosity the diminishing spasms of that body on the operating table, the last useless convulsions of a discontinued meat.

The animal life is over now. The machine life has begun.

This, more or less, is the scenario outlined by Hans Moravec, a professor of cognitive robotics at Carnegie Mellon, in his 1988 book Mind Children: The Future of Robot and Human Intelligence. It is Moravecs conviction that the future of the human species will involve a mass-scale desertion of our biological bodies, effected by procedures of this kind. Its a belief shared by many transhumanists, a movement whose aim is to improve our bodies and minds to the point where we become something other and better than the animals we are. Ray Kurzweil, for one, is a prominent advocate of the idea of mind-uploading. An emulation of the human brain running on an electronic system, he writes in The Singularity Is Near, would run much faster than our biological brains. Although human brains benefit from massive parallelism (on the order of 100 trillion interneuronal connections, all potentially operating simultaneously), the rest time of the connections is extremely slow compared to contemporary electronics. The technologies required for such an emulation sufficiently powerful and capacious computers and sufficiently advanced brainscanning techniques will be available, he announces, by the early 2030s.

And this, obviously, is no small claim. We are talking about not just radically extended life spans, but also radically expanded cognitive abilities. We are talking about endless copies and iterations of the self. Having undergone a procedure like this, you would exist to the extent you could meaningfully be said to exist at all as an entity of unbounded possibilities.

I was introduced to Randal Koene at a Bay Area transhumanist conference. He wasnt speaking at the conference, but had come along out of personal interest. A cheerfully reserved man in his early 40s, he spoke in the punctilious staccato of a non-native English speaker who had long mastered the language. As we parted, he handed me his business card and much later that evening Iremoved it from my wallet and had a proper look at it. The card was illustrated with a picture of a laptop, on whose screen was displayed a stylised image of a brain. Underneath was printed what seemed to me an attractively mysterious message: Carboncopies: Realistic Routes to Substrate Independent Minds. Randal A Koene, founder.

I took out my laptop and went to the website of Carboncopies, which I learned was a nonprofit organisation with a goal of advancing the reverse engineering of neural tissue and complete brains, Whole Brain Emulation and development of neuroprostheses that reproduce functions of mind, creating what we call Substrate Independent Minds. This latter term, I read, was the objective to be able to sustain person-specific functions of mind and experience in many different operational substrates besides the biological brain. And this, I further learned, was a process analogous to that by which platform independent code can be compiled and run on many different computing platforms.

It seemed that I had met, without realising it, a person who was actively working toward the kind of brain-uploading scenario that Kurzweil had outlined in The Singularity Is Near. And this was a person I needed to get to know.

Randal
Randal Koene: It wasnt like I was walking into labs, telling people I wanted to upload human minds to computers.

Koene was an affable and precisely eloquent man and his conversation was unusually engaging for someone so forbiddingly intelligent and who worked in so rarefied a field as computational neuroscience; so, in his company, I often found myself momentarily forgetting about the nearly unthinkable implications of the work he was doing, the profound metaphysical weirdness of the things he was explaining to me. Hed be talking about some tangential topic his happily cordial relationship with his ex-wife, say, or the cultural differences between European and American scientific communities and Id remember with a slow, uncanny suffusion of unease that his work, were it to yield the kind of results he is aiming for, would amount to the most significant event since the evolution of Homo sapiens. The odds seemed pretty long from where I was standing, but then again, I reminded myself, the history of science was in many ways an almanac of highly unlikely victories.

One evening in early spring, Koene drove down to San Francisco from the North Bay, where he lived and worked in a rented ranch house surrounded by rabbits, to meet me for dinner in a small Argentinian restaurant on Columbus Avenue. The faint trace of an accent turned out to be Dutch. Koene was born in Groningen and had spent most of his early childhood in Haarlem. His father was a particle physicist and there were frequent moves, including a two-year stint in Winnipeg, as he followed his work from one experimental nuclear facility to the next.

Now a boyish 43, he had lived in California only for the past five years, but had come to think of it as home, or the closest thing to home hed encountered in the course of a nomadic life. And much of this had to do with the culture of techno-progressivism that had spread outward from its concentrated origins in Silicon Valley and come to encompass the entire Bay Area, with its historically high turnover of radical ideas. It had been a while now, he said, since hed described his work to someone, only for them to react as though he were making a misjudged joke or simply to walk off mid-conversation.

In his early teens, Koene began to conceive of the major problem with the human brain in computational terms: it was not, like a computer, readable and rewritable. You couldnt get in there and enhance it, make it run more efficiently, like you could with lines of code. You couldnt just speed up a neuron like you could with a computer processor.

Around this time, he read Arthur C Clarkes The City and the Stars, a novel set a billion years from now, in which the enclosed city of Diaspar is ruled by a superintelligent Central Computer, which creates bodies for the citys posthuman citizens and stores their minds in its memory banks at the end of their lives, for purposes of reincarnation. Koene saw nothing in this idea of reducing human beings to data that seemed to him implausible and felt nothing in himself that prevented him from working to bring it about. His parents encouraged him in this peculiar interest and the scientific prospect of preserving human minds in hardware became a regular topic of dinnertime conversation.

Computational neuroscience, which drew its practitioners not from biology but from the fields of mathematics and physics, seemed to offer the most promising approach to the problem of mapping and uploading the mind. It wasnt until he began using the internet in the mid-1990s, though, that he discovered a loose community of people with an interest in the same area.

As a PhD student in computational neuroscience at Montreals McGill University, Koene was initially cautious about revealing the underlying motivation for his studies, for fear of being taken for a fantasist or an eccentric.

I didnt hide it, as such, he said, but it wasnt like I was walking into labs, telling people I wanted to upload human minds to computers either. Id work with people on some related area, like the encoding of memory, with a view to figuring out how that might fit into an overall road map for whole brain emulation.

Having worked for a while at Halcyon Molecular, a Silicon Valley gene-sequencing and nanotechnology startup funded by Peter Thiel, he decided to stay in the Bay Area and start his own nonprofit company aimed at advancing the cause to which hed long been dedicated: carboncopies

Koenes decision was rooted in the very reason he began pursuing that work in the first place: an anxious awareness of the small and diminishing store of days that remained to him. If hed gone the university route, hed have had to devote most of his time, at least until securing tenure, to projects that were at best tangentially relevant to his central enterprise. The path he had chosen was a difficult one for a scientist and he lived and worked from one small infusion of private funding to the next.

But Silicon Valleys culture of radical techno-optimism had been its own sustaining force for him, and a source of financial backing for a project that took its place within the wildly aspirational ethic of that cultural context. There were people there or thereabouts, wealthy and influential, for whom a future in which human minds might be uploaded to computers was one to be actively sought, a problem to be solved, disruptively innovated, by the application of money.

Transcendence
Brainchild of the movies: in Transcendence (2014), scientist Will Caster, played by Johnny Depp, uploads his mind to a computer program with dangerous results.

One such person was Dmitry Itskov, a 36-year-old Russian tech multimillionaire and founder of the 2045 Initiative, an organisationwhose stated aim was to create technologies enabling the transfer of an individuals personality to a more advanced nonbiological carrier, and extending life, including to the point of immortality. One of Itskovs projects was the creation of avatars artificial humanoid bodies that would be controlled through brain-computer interface, technologies that would be complementary with uploaded minds. He had funded Koenes work with Carboncopies and in 2013 they organised a conference in New York called Global Futures 2045, aimed, according to its promotional blurb, at the discussion of a new evolutionary strategy for humanity.

When we spoke, Koene was working with another tech entrepreneur named Bryan Johnson, who had sold his automated payment company to PayPal a couple of years back for $800m and who now controlled a venture capital concern called the OS Fund, which, I learned from its website, invests in entrepreneurs working towards quantum leap discoveries that promise to rewrite the operating systems of life. This language struck me as strange and unsettling in a way that revealed something crucial about the attitude toward human experience that was spreading outward from its Bay Area centre a cluster of software metaphors that had metastasised into a way of thinking about what it meant to be a human being.

And it was the sameessential metaphor that lay at the heart of Koenes project: the mind as a piece of software, an application running on the platform of flesh. When he used the term emulation, he was using it explicitly to evoke the sense in which a PCs operating system could be emulated on a Mac, as what he called platform independent code.

The relevant science for whole brain emulation is, as youd expect, hideously complicated, and its interpretation deeply ambiguous, but if I can risk a gross oversimplification here, I will say that it is possible to conceive of the idea as something like this: first, you scan the pertinent information in a persons brain the neurons, the endlessly ramifying connections between them, the information-processing activity of which consciousness is seen as a byproduct through whatever technology, or combination of technologies, becomes feasible first (nanobots, electron microscopy, etc). That scan then becomes a blueprint for the reconstruction of the subject brains neural networks, which is then converted into a computational model. Finally, you emulate all of this on a third-party non-flesh-based substrate: some kind of supercomputer or a humanoid machine designed to reproduce and extend the experience of embodiment something, perhaps, like Natasha Vita-Mores Primo Posthuman.

The whole point of substrate independence, as Koene pointed out to me whenever I asked him what it would be like to exist outside of a human body, and I asked him many times, in various ways was that it would be like no one thing, because there would be no one substrate, no one medium of being. This was the concept transhumanists referred to as morphological freedom the liberty to take any bodily form technology permits.

You can be anything you like, as an article about uploading in Extropy magazine put it in the mid-90s. You can be big or small; you can be lighter than air and fly; you can teleport and walk through walls. You can be a lion or an antelope, a frog or a fly, a tree, a pool, the coat of paint on a ceiling.

What really interested me about this idea was not how strange and far-fetched it seemed (though it ticked those boxes resolutely enough), but rather how fundamentally identifiable it was, how universal. When talking to Koene, I was mostly trying to get to grips with the feasibility of the project and with what it was he envisioned as a desirable outcome. But then we would part company I would hang up the call, or I would take my leave and start walking toward the nearest station and I would find myself feeling strangely affected by the whole project, strangely moved.

Because there was something, in the end, paradoxically and definitively human in this desire for liberation from human form. I found myself thinking often of WB Yeatss Sailing to Byzantium, in which the ageing poet writes of his burning to be free of the weakening body, the sickening heart to abandon the dying animal for the manmade and immortal form of a mechanical bird. Once out of nature, he writes, I shall never take/ My bodily form from any natural thing/ But such a form as Grecian goldsmiths make.

One evening, we were sitting outside a combination bar/laundromat/standup comedy venue in Folsom Street a place with the fortuitous name of BrainWash when I confessed that the idea of having my mind uploaded to some technological substrate was deeply unappealing to me, horrifying even. The effects of technology on my life, even now, were something about which I was profoundly ambivalent; for all I had gained in convenience and connectedness, I was increasingly aware of the extent to which my movements in the world were mediated and circumscribed by corporations whose only real interest was in reducing the lives of human beings to data, as a means to further reducing us to profit.

The content we consumed, the people with whom we had romantic encounters, the news we read about the outside world: all these movements were coming increasingly under the influence of unseen algorithms, the creations of these corporations, whose complicity with government, moreover, had come to seem like the great submerged narrative of our time. Given the world we were living in, where the fragile liberal ideal of the autonomous self was already receding like a half-remembered dream into the doubtful haze of history, wouldnt a radical fusion of ourselves with technology amount, in the end, to a final capitulation of the very idea of personhood?

Koene nodded again and took a sip of his beer.

Hearing you say that, he said, makes it clear that theres a major hurdle there for people. Im more comfortable than you are with the idea, but thats because Ive been exposed to it for so long that Ive just got used to it.

Dmitry
Russian billionaire Dmitry Itskov wants to create technologies enabling the transfer of an individuals personality to a more advanced nonbiological carrier. Photograph: Mary Altaffer/AP

In the weeks and months after I returned from San Francisco, I thought obsessively about the idea of whole brain emulation. One morning, I was at home in Dublin, suffering from both a head cold and a hangover. I lay there, idly considering hauling myself out of bed to join my wife and my son, who were in his bedroom next door enjoying a raucous game of Buckaroo. I realised that these conditions (head cold, hangover) had imposed upon me a regime of mild bodily estrangement. As often happens when Im feeling under the weather, I had a sense of myself as an irreducibly biological thing, an assemblage of flesh and blood and gristle. I felt myself to be an organism with blocked nasal passages, a bacteria-ravaged throat, a sorrowful ache deep within its skull, its cephalon. I was aware of my substrate, in short, because my substrate felt like shit.

And I was gripped by a sudden curiosity as to what, precisely, that substrate consisted of, as to what I myself happened, technically speaking, to be. I reached across for the phone on my nightstand and entered into Google the words What is the human… The first three autocomplete suggestions offered What is The Human Centipede about, and then: What is the human body made of, and then: What is the human condition.

It was the second question I wanted answered at this particular time, as perhaps a back door into the third. It turned out that I was 65% oxygen, which is to say that I was mostly air, mostly nothing. After that, I was composed of diminishing quantities of carbon and hydrogen, of calcium and sulphur and chlorine, and so on down the elemental table. I was also mildly surprised to learn that, like the iPhone I was extracting this information from, I also contained trace elements of copper and iron and silicon.

What a piece of work is a man, I thought, what a quintessence of dust.

Some minutes later, my wife entered the bedroom on her hands and knees, our son on her back, gripping the collar of her shirt tight in his little fists. She was making clip-clop noises as she crawled forward, he was laughing giddily and shouting: Dont buck! Dont buck!

With a loud neighing sound, she arched her back and sent him tumbling gently into a row of shoes by the wall and he screamed in delighted outrage, before climbing up again. None of this, I felt, could be rendered in code. None of this, I felt, could be run on any other substrate. Their beauty was bodily, in the most profound sense, in the saddest and most wonderful sense.

I never loved my wife and our little boy more, I realised, than when I thought of them as mammals. I dragged myself, my animal body, out of bed to join them.

To Be a Machine by Mark OConnell is published by Granta (12.99). To order a copy for 11.04 go to bookshop.theguardian.com or call 0330 333 6846. Free UK p&p over 10, online orders only. Phone orders min p&p of 1.99

Read more: https://www.theguardian.com/science/2017/mar/25/animal-life-is-over-machine-life-has-begun-road-to-immortality

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‘Granny style’ is best way to take a basketball free throw, study shows

Mathematical analysis reveals that for players with good control, using an unorthodox underarm technique gives better odds of scoring

It might invite ridicule, but it gets results. A scientific analysis has concluded that using a granny style underarm technique is the optimal way to take a free throw in basketball.

Adopting the unorthodox strategy could result in marginal gains for professional players, the research suggests. And, as sporting doctrine goes, marginal gains can lead to remarkable results.

Madhusudhan Venkadesan, who led the work at Yale University, said: Our mathematical analysis shows that if the thrower is capable of controlling the release angle and speed well, the underarm throw is slightly better for a basketball free throw.

However, it remains to be seen whether science will prove more persuasive than professional advocates of the underarm style.

The retired NBA player Rick Barry, a pioneer of the underarm free throw, was one of the most effective shooters of all time and when he retired in 1980 his 90% free throw record ranked first in NBA history. But he struggled to convince his teammates due to the inescapable fact that shooting underarm makes you look like a sissy, Barry said.

Venkadesan acknowledges that it is a difficult case to make.

One suspects there are social and cultural reasons you dont see that practised too often, he said. So what if some call it the granny throw? What matters is that the ball goes through the hoop! Rick Barrys record does support the underarm throw.

The study, published in the journal Royal Society Open Science, considered the chances of the ball being on target, depending on the style, speed and accuracy of a throw.

It found that if the player is capable of controlling the release angle and speed well, the underarm throw has slightly better odds of going in. But for amateurs who have only crude control, the release of the ball overarm is safer, sparing casual players the dilemma of choosing style or results.

An important factor in comparing the two strategies was how the ball approaches its target. When the ball approaches the net from directly above, as in a typical underarm throw, the cross-section of the target is large from the balls vantage point. This is good, as it means that if a throw is close to being exactly on target it has a very high chance of going in.

However, in trying to achieve this straight down entry, the amateur risks lobbing the ball extremely high due to their mediocre control. In this scenario, a small error in the timing of the release can cause the ball to grossly overshoot or undershoot the hoop.

So the overarm shot, where the ball sees a smaller cross-section of the hoop, but is less likely to go wildly off course, is a more conservative strategy.

This competition between the entry angle and speed underlies both the speed-accuracy trade-off and the relative accuracy of one style versus another, said Venkadesan.

For the professional player, the analysis predicts, this trade-off is finely balanced and probably within the margins of error of the model, which did not consider the backboard.

Barry, no doubt, would view the findings as confirmation of what he has argued all along. From the physics standpoint, its a much better way to shoot, he told the author Malcolm Gladwell in a recent interview. You have a little bit more margin for error than when you shoot overhand.

Read more: https://www.theguardian.com/science/2017/apr/26/granny-style-is-best-way-to-take-a-basketball-free-throw-study-shows

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Can you solve it? The incredible sponge puzzle

This brainteaser will wring out your brain

Hi guzzlers.

For todays puzzle, let me introduce you to the Menger sponge, a fascinating object first described by the Austrian mathematician Karl Menger in 1926. Well get to the problem as soon as I explain what the object is.

The Menger sponge is a cube with smaller cubes extracted from it, and is constructed as follows: Step A: Take a cube. Step B: Divide it into 27 smaller subcubes, so it looks just like a Rubiks cube.

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Step C: Remove the middle subcube in each side as well as the subcube at the centre of the cube, so if you looked through any hole you would see right through it. Step D: Repeat steps A to C for each of the remaining subcubes, that is, imagine that each subcube is made from 27 even smaller cubes and remove the middle one in each side and the central one.

We could carry on repeating steps A to C ad infinitum, on smaller and smaller subcubes, but here lets do it just once more:

Menger
Menger sponge. Illustration: Edmund Harriss/Visions of Numberland

Menger sponges are so loved within the maths community that building origami models of them out of business cards is a thing.

Menger
Menger sponge made as part of Matt Parker and Laura Taalmans MegaMenger project. Photograph: MegaMenger

There are lots* of reasons why Menger sponges are cool and one of them is illustrated by todays puzzle.

How
How to slice a cube in two.

On the left here is how you slice a cube in half such that the cross section is a hexagon.

When you slice a Menger sponge in two like this, what does the hexagonal slice look like?

This question is probably the most difficult one I have ever set in this column, as it requires phenomenal levels of spatial intuition. But I urge you to give it a go, even if just a basic sketch. Send me some images, or post them to me on social media. You may draw something along the right lines…

Please forgive me, though, for posing this toughie. The answer is jaw-droppingly amazing. In fact, I was told about the Menger slice by a respected geometer who told me it gave him probably his biggest wow moment in maths. Come back at 5pm BST and see for yourself.

NO SPOILERS PLEASE! Please talk about Karl Menger and origami instead.

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Photograph: Bloomsbury

Both the Menger sponge and the Menger slice are included in my latest book, Visions of Numberland: A Colouring Journey Through the Mysteries of Maths. The book is a gallery of the most spectacular images that Edmund Harriss, my co-author, and I could find in maths. You can colour them in, or just contemplate them in black and white.

I set a puzzle here every two weeks on a Monday. Send me your email if you want me to alert you each time I post a new one.

Im always on the look-out for great puzzles. If you would like to suggest one, email me.

* Here are a couple. 1) Each time you follow the iteration described in steps A to C you decrease the volume of the sponge, but increase its surface area. After an infinite number of iterations, you will have removed an infinite number of cubes. The sponge will then have zero volume and infinite surface area. 2) After an infinite number of iterations, the object is a fractal, that is, it contains parts that are identical to the whole thing.


Read more: https://www.theguardian.com/science/2017/apr/10/can-you-solve-it-the-incredible-sponge-puzzle

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