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ltmaybe your brain not your genitals that decides what sex you really are

OUR brains could be hard-wired to be male orfl-male long before we begin to growtestes or ovaries in the womb. This discovery might explain why some people feel trapped in a body that's the wrong sex, and could also lead to tests that reveal the true "brain sex" ur babies born with ambiguous genitalia. Till now, the orthodoxy among developmental biologists has been that embryos develop ovaries and become female unless a gene called SRYon the Y chromosome is switched on. If this gene is active, it makes testes develop instead. This switch is seen as the key event in determining whether a baby is a girl or a boy. Onty after the gonads form and flood the body with the appropriate hormones, the theory goes, is the sex of our minds and bodies determined. But in a study of mice, a team at the University of California, Los Angeles, has now found that males and females show differences in the expression of no fewer than 50 genes well before SRYswitches on. "It's the flmt discovery cvf genes differentially expressed in the brain," says Erlc Vilain, who led the UCLA team. "They may have an impact on the hard- wired development of the brain in terms of sexual differentiation independent of gonadal induction." irilain is presenting details of seven of the 50 genes to the annual meeting of the American Society af Human Genetics in Baltimore this week. Three of these genes are dominant in females and four are dominant in males. The next step for Vilain and his team will be to show that the genes in question really do influence brain sexuality - and notjust in mice. This is likely to be a much tougher preposition than merely showing there are differences in expression. But if the findings are confirmed, they could one day yield blood tests that allow doctors to establish the brain sex of babies born with genitalia that share features of both sexes. At present doctors and parents have to guess which gender to assign fbr surgical "correction". Robin Lovell Badge of the National institute fbr Medical Research in London, who discovered the SRYgene, is already looking at mice with a Y chromosome lacking the SRYgene, to see if their brains and behaviour are in ariy way male despite their lack of testes. "The growing feeling is that there will be direct effects on the brain, anatomy and behaviour due to X ory-linked genes," says Lovell Badge. "It's early days yet, but we're pretty sure there are effects on some aspects of aggression and reproductive behaviour independent crf gonadal sex." Andy Coghlan *

Bunker busters set to go nuclear
Fifty years after the first hydrogen bomb was detonated, nuclear weapons are about to get a terrifying new role


THE US government is set to fund research into a new type of nuclear weapon that's designed to penetrate and obliterate deeply buried targets such as underground weapons bunkers. Coming 5o years after the world's first hydrogen bomb was detonated in the Pacific, the news has alarmed scientists opposed to nuclear proliferation. They say the thousands of tonnes of radioactive debris produced by a bunker-busting nuclear weapon would not be contained within the rock, concrete and soil above the target, but would contaminate a wide area around it. Funding Of $15 million has been proposed for research into the so-called Robust Nuclear Earth Penetrator (RNEP), as part of the government's draft Defense Authorisation Bill for 2003. But the bill has not yet been passed by the Senate Committee on Armed Services, which as New Scien tis t went to press was controlled by the Democrats. While a decision has been delayed until after this week's Congressional elections, a source close to the committee says the RNEP will get the green light. Research into the nuclear bunker-buster follows the Bush administration's leaked Nuclear Posture Review, which in part set out the circumstances under which nuclear weapons might be used. It says the RNEP could be used in pre-emptive strikes against rogue states using deeply buried facilities to store weapons of mass destruction, for example. The RNEP would be used on targets that may be immune to conventional weapons. Its backers claim it would create little contamination above ground, but critics say that it would produce huge amounts of nuclear fallout. The RNEP may also remove the distinction between a nuclear deterrent and conventional weapons, increasing the risk of a nuclear exchange.

US law prevents development of new "mini-nukes" that have an explosive yield of less than 5 kilotons. But the RNEP falls outside this ban because it is not a new weapon. Rather, it will be a modification of an existing nuclear bomb, probably a highly modified B61, sources say, a weapon whose explosive yield can be set from anything between 0.3 and 34o kilotons. The bomb uses fission at low yields but is a fusion (hydrogen) bomb at high yields. The Hiroshima fission bomb had a yield Of 12 kilotons. Underground explosions are 10 tO 15 times as effective against buried facilities as airbursts. A conventional bunker-buster is dropped from high altitude and hits the ground at enormous speed. It penetrates earth, rock and concrete before exploding. A nuclear version has the advantage of a far more powerful shock wave, increasing the depth of its destructive effect. T'he US already has around fifty'penetrating'nuclear weapons in its stockpile, but these can only reach a depth of six metres in earth. David Wright, a nuclear-weapons expert at the Union of Concemed Scientists in Washington DC, says this would not be nearly enough to contain the radioactivity. "Even for a 0.3-kiloton explosion, you would need a burial depth of about 70 metres in dry soil and about 40 metres in dry, hard rock to contain the blast," Wright says. An explosion at the maximum depth achievable so far would throw thousands of tonnes of highly radioactive debris into the air. Moreover, Wright's calculations show that a warhead of this size at the depths currently possible would only destroy a hardened target buried less than 10 to 20 metres deep in rock. Some Iraqi facilities are said to be under 6o metres of rock, requiring a warhead of hundreds of kilotons, which would cause unacceptable devastation above ground. But a study by the Federation of American Scientists concludes that greater penetration with the RNEP is unlikely, as there is a threshold at which increasing impact velocities simply cause the warhead to deform and melt. Attempting to make the RNEP and its warhead robust enough to withstand impact will require extensive R&D. Weapons designers at three Department of Energy labs - Lawrence Livermore in Califomia, and Los Alamos and Sandia in New Mexico - will have to come up with the new ground-penetration technology. Sandia has already patented a new penetrator (see Graphic). While the Comprehensive Test Ban Treaty bars any test with a live warhead, this would not prevent the RNEPs use untested.

From bugs to birds to giant reptiles, werre finally growing a Tree of Life

ONE ar science's great outstanding projects Is about to begin - mapping what Charles Darwin called the "great Tree of Life". When complete, the tree will finally reveal how all IMng creature are related to one another. The fimt projects, funded by the US National Science Foundation, were announced last week and will unrdvel the secrets of plants, spiders, birds and dinosaurs among others. But the whole pmgramme Is expected to take more than a decade. "The fundamental question of biology is the connection among species on the Earth," says Shannon Hackett of the Field Museum of Natural History in Chicago. Making those connections will help researchers conserve species, restore ecosyslems and control invading spedes. Medical researchers can use evolutionary data to trace the origin and spread crf diseases, and to develop new medicines. Assembling the complete tree is no mean feat. Generations cvf biologists have sketched broad evolutionary patterns bet6veen groups crf plants and animals and we have described around 1.7 million lmng species. But most are little studied, and millions of other I!Wng species have yet to be catalogued. The Tree of Life project will take advantage of the latest techniques in molecular genetics and computer technology in a bid to reolve long-standing debates over the interpretations of morphologic data. Genedc tests can distinguish between species that look nearly identical, and DNA comparisons can tell you how long since the species diverged.

"The fundamental question of biology is the connection among species on the Earth"

The extent af genetic divergence can reveal long-lost relationships between highly evolved species, such as the links betneen whales and their nearest land-dwelling relations. The fimt grants will pay fbr the mapping of seven key parts of the Tree (yf Life. At the base of the tree, the [email protected] fbr Genomic Research in Rockville, Maryland, will fully sequence several diverse types cyf lltde-studied bacteria in a bid to find out how they are related and trace the development cvf photosynthesis. A team led by Chadle O'Kelly of the Bigelow Laboratory fbr Ocean Silences in Maine will analpe DNA ftm 50 VM of green algae and plants, and then use traditional morphology to identify fundamental dmsions among non-flowering plants. ether groups will collect and analyse genetic and morphological data on over 1000 species of nematodes and 500 genera of spiders. Hackett's group will collect DNA sequence data ftm some 500 bird species, hoping to learn how modern birds diversified, and how their behaviours and other traits evolved. A separate project will build a database including digital photographs and l features of every signlflcant specimen of the predatory dinosaurs called theropods, thought to have given dse to birds. This will allow researchers to compare specimens at a more detailed level than before - previous studies only looked at the differences between theropod genera, says dinosaur project head Mark Norell of the American Museum of Natural History. The scientists involved will have to come up with new ways of storing and searching data in order to handle the vast expanse of information. But Norell hopes to make the Tree of Life database so intumm that researchers can compare specimens at their desks, [email protected] of flying to museums around the wodd. Jeff Hecht *

Why copy protection on CDs is worthless

THE technology built into some CDs to stop people copying them is futile. So says a computer scientist who has put today's antipiracy systems under the microscope. He believes the continual software and hardware upgrades issued by the makers of computer CD drives and audio CD players render copy protection systems pointless in the long run. John Halderman, a computer scientist from Princeton University in New Jersey, plans to show delegates at a digital copyright conference in Washington DC next week that the idea of CD copy-prevention is "fundamentally misguided". Princeton University scientists last year debunked the technology the music industry planned to use to inaudibly watermark sound. Halderman is now doing a similar job on copy prevention systems. Halderman looked at three widely available copy-protected CDs. He found that the three different copy protection formats they used all had one thing in common: they all index the contents of music discs using a system meant only for recording CDs on a computer's CD drive. A conventional music CD has an electronic table of contents at the beginning of each disc. But a PC-recorded CD has several tables, with a new one written every time a new recording session adds something to the disc. Each of these tables points back to the previous one. Personal computer CD drives read the last, most recent table first and work back through the series of indices - but audio CD players read only the first table. A CD containing a copy- prevention system indexes the music correctly in the first table but then adds dummy tables containing deliberate errors. So CD players that read only the first table will play the music normally. But PC CD drives - which people use for copying - look at the last table, see garbage, get confused and play or record nothing. Unfortunately, some audio CD players and in-car players use PC CD drives, and will not legitimately play a protected CD you've paid for. Nor can people play music CDs on their PCs. But all these measures can be sidestepped, says Halderman, thanks to the computer industry's habit of continual upgrading and bug fixing. Makers of CD players and CD-ROM drives only need to make "relatively simple modifications" to their software and supposedly protected CDs can be played with ease. So playback and recording equipment is becoming resistant to copy- prevention techniques. "Software upgrades can be delivered easily using the Internet," says Halderman, "and this will permanently undermine the usefulness of audio CD copy prevention." To ban upgrades, he argues, would lead to "buggy software and poor hardware." The record industry could lose a fortune if people stop buying CDs and make their own copies. Halderman reckons he has a solution for them. "Reduce the cost of new CDs; if discs cost only a few dollars each, buying them might be preferable to spending the time and effort to make copies or find them online:' Barry Fox

Cloned stem cells may give you a new lease of life


CLONEDstemcellsmaybe 11 younger", "fitter" and much better at replacing tissue damaged by disease or age than those from other sources. If confirmed, the finding will provide a major boost for therapeutic cloning. The idea of therapeutic cloning is to take adult cells from a person's body, create cloned embryos and extract embryonic stem cells that can turn into a wide range of tissues, all a perfect match for the patient. But recent research suggests that stem cells in adults are just as versatile as embryonic ones, which might make cloning unnecessary. NowNewScientisthas uncovered a patent application that claims cloned stem cells have a big advantage over other stem cells. A team at Advanced Cell Technology (ACT) in Massachusetts, working with Malcolm Moore of the Memorial Sloan-Kettering Cancer Center in New York, cloned skin cells from two cows and injected blood- forming stem cells (which also give rise to immune cells) from the cloned fetuses back into the cows. One cow had its immune systems suppressed with drugs. The cloned cells seemed to have an amazing ability to take over from adult ones, replacing up to 50 per cent of the cows'blood stem cells after just one infusion, even in the cow whose immune system was untouched. The team thinks the stem cells could be "younger" and more competitive as a result of cloning. "We can confirm that we have had success," says Robert Lanza of ACT, who declined to comment on details and wanted it made clear that the company did not seek to make the research public prior to journal publication. ACT has been criticised for this before. The obvious implication is that you could replace the immune system of people with leukaemia or autoimmune diseases such as arthritis. "It would be great if we could do this in humans," says stem cell specialist Diane Krause of Yale University. She says it's risky to use blood stem cells from a cancer patients' own bone marrow to restore their immune system, as some might be cancerous. And when patients are given bone marrow cells from donors, these can tum on their new host. The cloned cells could also be modified before being implanted, Lanza says. For example, cells from an HIV patient could be altered to resist the virus. Perhaps most significantly, people who get "younger" cells derived by therapeutic cloning might end up with stem cells that have significantly improved repair capabilities. Blood stem cells are known to help repair other organs, though this ability wanes with age. "We could introduce cells with regenerative ability," says Lanza. The cloned cells may be more vigorous because nuclear transfer - the key step in cloning - restores the "fuses", or telomeres, on chromosomes, which burn down as cells divide (see New Scientist, 6 May 2000, P 4). Of course, a greater ability t6 divide and regenerate also means a greater risk of the stem cells becoming cancerous. And there is some evidence that cloning can disrupt normal gene expression - some cloned animals are stillborn or have abnormalities. Another major issue is the fact that the blood stem cells injected into the cows came from loo-day- old fetuses, since that's when the cells can be found in the liver and can be easily harvested.

"People who get'younger cells derived by therapeubc cloning might end up with stem cells that have significantly improved repair capabilites"

There's no question of allowing human cloned embryos to grow to that stage to harvest stem cells, but Lanza says ACT and others are trying to derive blood stem cells directly from embryonic ones. Other experts are reserving judgement until the work is published. "It makes me sceptical because I can't understand from a patent application what they are doing," says another stem cell researcher, Dan Kauftnan of the University of Minnesota.

Ecstasy has a dramatic effect on Parkinson s symptoms


A FEW weeks ago ecstasy was condemned for causing Parkinson's. Now, in a complete turnaround, it's being hailed as the key to better treatments for the disease. Animal studies have confirmed anecdotal reports that ecstasy can dramatically curb the uncontrollable arm and leg movements that plague so many people with Parkinson's. But the finding may be of little immediate help to sufferers. The researchers aren't calling for patients to be given legal supplies of ecstasy (MDMA). Instead, they want to look for related drugs with the same beneficial effects. And patients are being warned against trying MDMA for themselves. "It's impure, illegal and dangerous," says Robert Meadowcroft, policy director of Britain's Parkinson's Disease Society. Others are calling for further animal studies to establish the effective dose, followed by human trials. "People who are suffering should have the right to decide carefully for themselves whether or not to take MDMA," says American drugs policy campaigner Rick Doblin. His organisation, MAPS, recently won approval from the Food and Drug Administration for a human trial of ecstasy for treating post- traumatic stress disorder. The latest study was prompted by the experiences of a former stuntman, Tim Lawrence. He made headlines when he claimed in a BBC TV documentary that "E" enabled him to regain control of his body for hours at a time. Parkinson's experts at the University of Manchester decided to test Lawrence's claims. Concerns about the dangers of MDMA ruled out human trials, says team member Jonathan Brotchie, who now runs Manchester-based biotech company Motac. So the researchers tumed to marmosets with a form of the disease. Parkinson's is caused by a loss of the dopamine-producing cells in the brain. Symptoms include rigidity and a shuffling gait. Since the late 196os doctors have treated it with L-dopa, a chemical precursor to dopamine that can 11 unfreeze" patients. The downside is that patients develop uncontrollable movements after taking L-dopa for a while. Their condition tends to oscillates between flailing limbs while on the drug and immobility off it. To mimic Parkinson's, they gave six marmosets a chemical that kills dopamine neurons.

"People who are suffering should have the right to decide carefullyfor themselves whether or notto take MDMA!'

Then, over the next few months, the monkeys had daily doses of L-dopa until they developed the usual side effect of uncontrolled movements. At this point the animals were given MDMA. The effects were dramatic. Normally, monkeys on L-do0a move their arms and legs around in a repetitive and uncontrolled way virtually all the time. But in the six hours after a dose of MDMA, these movements happened no more than 15 per . cent of the time. MDNM somehow reduces the debilitating side effects of L-dopa without blocking its beneficial effects. "The magnitude and quality of the effect took us by surprise," says Brotchie, whose team's findings were unveiled this week at the conference of the Society for Neuroscience in Florida. "It was always possible that Tim's response to ecstasy was unusual.' The researchers suspect the finding reflects MDMA's ability to stimulate the release of the neurotransmitter serotonin in the brain. That might make up for a lack of serotonin caused by taking L-dopa for prolonged periods, says Brotchie. However, there are fears that MDMA can damage serotonin-producing cells. And last month the joumal Science published a paper claiming that MDMA can actually cause the type of damage to dopamine cells that can lead to Parkinson's. But the evidence was far from conclusive (New Scientist, 5 October, p 26).

Eightfold Way Octonians and the laws of Nature

1,2,4,8 What comes next? Nothing. i If we're talking numbers, the obvious next term is 16. But if we're talking a particular kind of algebra, there is no next term. And it tums out that this is highly significant. The ultimate number- the humble 8 - lies at the heart of a mathematical system known as the octonions, and this system appears to be the key that will allow physicists to fit quantum theory and gravity together. Strange as it may seem, the number 8 may provide us with a "theory of everything". The tale of the octonions begins in the mid- 16th century. Until that time, mathematicians had thought that numbers were God-given, a done deal. No one could contemplate inVenting a new number. But around 1550 the Italian algebraists Girolamo Cardano and Raphael Bombelli did just that, by writing down the square root of -1. It took about 400 years to sort out what the thing meant, but onlY 300 to convince mathematicians that it was too useful to be ignored. By the 18oos, Cardano and Bombelli's concoction had crystallised into a new kind of number, i, whose square is -1. The square of a "real number" - the usual kind that we all know - is always positive. So whatever i may be, it's not a real number, and mathematicians call it an "imaginary" number to make this clear. A combination of real and imaginary numbers, like 4 + 5i, is said to be "complex". We live in a curious Universe in which, as physicist [email protected] Wigner memorably announced, mathematics is "unreasonably effective". Complex numbers may seem weird, but they turn out to be a marvellous tool for understanding physics. Problems of heat, light, sound, vibration, elasticity, gravity, magnetism, electricity and fluid flow all succumbed to this complex weaponry - but only for physics in two dimensions. Our own Universe, however, has three dimensions of space - if not more. So, since the two-dimensional system of complex numbers was so effective for two-dimensional physics, might there be an analogous three- dimensional number system that could be used for physics in the real world? The answer is a resounding no. The Irish mathematician William Rowan Hamilton spent years trying to find a three-dimensional number systi!M - burwith no success. Then, on 16 October 1843 he had a flash of insight: don't look in three dimensions, look in four. And it worked. Hamilton named his new numbers quaternions". Two months later, having heard about quaternions from Hamilton, John Graves - a British mathematician and an old college friend of Hamilton's - announced he had found an eight-dimensional number system. He called it the "octaves". But before Graves could publish, the British lawyer- mathematican Arthur Cayley made the same discovery, and published it as an addendum to an otherwise awful paper on elliptic functions. He called the system "octonions". The discovery of the octonions was ever after credited to the wrong person (they are often known as Cayley numbers, even today), but it didn't really matter because nobody took any notice of them anyway. The octonions appeared to be nothing more than Victorian mathematical whimsy. Graves was not to be put off though, and spent a long while convinced that his method of going from 4 to 8 could be repeated, leading to algebras with dimensions of 16,32, 64 and so on for any power Of 2. He called his 16-dimensional algebra the sedenions, but he couldn't find a way to make it - or any of the others - work, and began to doubt whether it could exist. His doubt was well-founded. We now know that those four algebras, of dimensions 1, 2,4 and 8, are the only ones that behave remotely like ordinary real numbers. The reason is that, with increasing numbers of dimensions, these systems obey fewer and fewer algebraic laws - the amount of algebraic structure keeps decreasing. Put rather too simply, by the time we reach Graves's sedenions, there's pretty much no algebraic structure left. Real, complex, quaternion, octonion; 1, 2,4, and 8 dimensions: even by mathematical standards this is an odd set of tools. These four number systems have several features in common, the most striking being that they are "division algebras". There are many number systems in which notions of addition, subtraction and multiplication hold good: when these notions are applied to the integers (... -2,-l, 0,1,2,3,...), for example, they transform two integers into another integer. But the same can't be said for division: divide some integers by others, for example, and the result is often not an integer. But in these four number systems, you can always divide and yet remain within the same system. And that's not the only mathematical operation that sets them apart. Numbers in these systems are the only ones to have a "norm", effectively the number's distance from the origin (see Graphic, page 32). With the complex numbers, the norm of x + iyiSX2+y2. Because of the existence of a norm, and their divisibility, these number systems are known as "normed division algebras" ' This is all very pretty, to mathematicians at least. But surely the only really important cases are the real and complex numbers. Well, not quite: the quaternions have shown up in some useful if esoteric researches - fields such as abstract algebra and topology. But it's certainly true that the octonions remained in the shadows for a long time. In 1925 Wigner, working with the mathematician John von Neumann, tried to make the octonions the basis of quantum mechanics.

"The octonions started out as mathematical curiosities, and were almost entirely ignored for l5O years, but their time has now come"

But he failed, and the octonions slipped back into obscurity. Until now, that is. Rather surprisingly, the octonions have revealed themselves as the most important system of all. That's because they are crucial to string theory, the best candidate for a physical theory of everything. After 150 years, physics is finally telling us the purpose of the octonions: they are essential to space and time. String theory is an attempt to marry the large-scale geometry of Einstein's general relativity to the small-scale uncertainties inherent in quantum theory. Both these theories are brilliantly successful in their own domain. But they can't be fitted together: put into the same framework, they effectively contradict each other. So the search has been on for a unified theory that modifies them well enough to fit them together consistently but doesn't destroy their existing successes. The current front runner in this search is known as string theory. Very roughly, the traditional idea that a fundamental particle is a featureless point is rejected, and particles are modelled instead as tiny loops of energy - the aforementioned strings. The loops can vibrate in ways that give them integer quantum numbers, such as spin, charge and charm. But all this only works if the loop is a many- dimensional surface that protrudes beyond the familiar four-dimensional space-time, and one of the burning questions is just how many dimensions there are. At the moment, finding the answer seems to depend on finding the number of dimensions where the theories work most elegantly. And though physicists have not pinned it down precisely, they have noticed that something rather pleasing occurs when they work with 3,4, 6 and lo dimensions. Interestingly, each of these numbers iS 2 greater than that of a normed division algebra: subtraCt 2 from 3,4,6 and lo, and you get 1, 2,4 and 8. And that's no coincidence: these algebras are a vital part of the theory. Consider, for example, the relationship between two mathematical objects: vectors and spinors. A vector is essentially a way to describe the size and orientation of something. Velocity, for example, is a vector because it describes a body's speed and the direction in which it is moving. The spinor is a more esoteric mathematical gadget invented by Paul Dirac to describe electron spin. It tums out that the relationship between vectors and spinors holds precisely (and only) in space-times Of 3,4, 6, and io dimensions. This happens because, in 3,4,6, and lo-dimensional string theory, every spinor can be represented using two numbers in the associated normed division algebra. This doesn't happen for any other number of dimensions, and it has lots of nice consequences for physics. So we have four cafididate string theories here: real, complex, quaternionic, and octonionic. The one that is thought to have the best chance of corresponding to reality is the lo-dimensional one, because it neatly avoids a mass of mathematical obstacles while allowing the physics to work properly. And, in this system, the relationships between the properties of matter are specified by the octonions: if this particular theory really does correspond to reality, then our Universe is built from pairs of octonions. if lo dimensions turns out to be not quite enough, however, it seems that the octonions will still be found to play a vital role in the theory of everything. The other very fashionable candidate string theory, "M- theory", involves 11-dimensional space-time.

Although that means the vector-spinor relationship won't hold, something almost as good does. In M-theory, the extra dimensions don't need to be curled up tightly, so the restriction to six extra dimensions can be relaxed to allow a seventh, but again it doesn't work without the octonions. In order to reduce the perceptible part of space-time from ii dimensions to the familiar four (three space and one time), we have to hide seven of them. We do that by rolling them up so tightly that they can't be detected. And how do you do that? You make use of the octonions' symmetry- The idea of symmetry - a property that allows you to move something in a certain way and leave it looking the same - has turned out to be central to physics, especially the quantum world.


All our theories of fundamental particles, and their strange properties such as spin, charge and charm, which come in whole-number chunks, boil down to symmetries. And the use of octonionic symmetry in M-theory even gives a purpose to a mathematical peculiarity, discovered around the same time as the octonions, whose existence has always mystified mathematicians (see "The eightfold way"). So the efficacy of the octonions here is doubly pleasing. While the octonions started out as mathematical curiosities, and were almost entirely ignored for 15o years, their time has come. They are no longer quaint Victorians, but a hefty clue to a possible theory of everything. Daunting though their mathematics is, physicists are beginning to take up this new set of tools and work with it. A paper published this year by John Baez of the University of Califonia, Riverside, has prompted much Web-based discussion between string theorists. it all boils down to one extraordinary realisation: the humble 8 is no longer just a number. it's our key to the Universe.

Ian Stewart is a professor of mathematics based at the University of Warwick Fu rther reading: "The octonions" by John Baez, Bulletin of the America n Mathematical So(iety, vol 39, p 145 (2002)