In recent years, the search for an alternative to conventional semiconductors has resulted in the discovery of a nanotechnology called ‘’spintronics,” which uses a property of electrons called ‘’spin” to produce a novel kind of current that integrated circuits can process as information. Spin refers to how an electron rotates on its axis, similar to the rotation of the Earth. In 2003, Zhang and colleagues at the University of Tokyo showed that producing and manipulating a current of aligned electron spins with an electric field would not involve any losses to heat-a technique they called spintronics.

For about 40 years, the semiconductor industry has been able to continually shrink the electronic components on silicon chips, packing ever more performance into computers. Now, fundamental physical limits to current technology have the industry scouring the research world for an alternative. In a paper published in the Aug. 1 online edition of Physical Review Letters (PRL), Stanford University physicists present ”orbitronics,” an alternative to conventional electronics that could someday allow engineers to skirt a daunting limit while still using cheap, familiar silicon.

”The miniaturization of the present-day chips is limited by power dissipation,” says Shoucheng Zhang, a professor of physics, applied physics and, by courtesy, electrical engineering, who co-authored the PRL study. ”Up to 40 percent of the power in circuits is being lost in heat leakage,” which he says will eventually make miniaturization a forbidding task.

Zhang now co-directs the IBM-Stanford Spintronic Science and Applications Center, along with Stanford electrical engineering Professor James Harris and IBM research fellow Stuart Parkin. The center, established in 2004, is investigating many applications of spintronics, including room-temperature superconductors and quantum computers.

Playing the angles

For all its potential, a drawback of spintronics is that it doesn’t work very well with lighter atoms, such as silicon, which the microelectronics industry prefers. Enter Zhang’s new research. In the PRL paper, he and graduate students B. Andrei Bernevig and Taylor L. Hughes show how, in theory, silicon could be used in a related technology they dubbed orbitronics. By using orbitronics, Zhang says, computer chip makers could get the benefits of spintronics without having to abandon silicon.

Both orbitronics and spintronics involve a physical quantity called ”angular momentum,” a property of any mass that moves around a fixed position, be it a tetherball or an electron.

Like an electric current, which is the flow of negatively charged electrons in a conventional integrated circuit, an orbital current would consist of a flow of electrons with their angular momenta aligned in an orbitronic circuit. ”If you push electrons forward with an electric field, then an orbital current will be generated perpendicular to this electric current,” Zhang says. ”It will not carry charge, but will carry orbital angular momentum perpendicular to the direction in which the electrons are moving.”

Therefore, he explains, with orbitronics, silicon would still be able to provide a useful current with no losses to heat at room temperature. Some alternative technologies require cold temperatures that are difficult and expensive to maintain, he adds.

From theory to application

The authors point out that orbitronics still has a long way to go to become an applied technology in the semiconductor industry. ”This is so new,” Zhang acknowledges. ”When something is first discovered it is hard to say. There are many difficulties in the practical world.”

Harris agrees, noting that spintronics will likely still take decades to become a mature commercial technology. ”It’s not going to happen immediately, even if we are incredibly successful,” he says.

But if orbitronics turns out to indeed be an economically feasible technology to manufacture, it will be a boon to the industry to stick with silicon, Zhang says. ”There is a huge, huge investment in processing silicon,” he says. ”We don’t want to switch overnight to a new material.”

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The ‘infinite series’ - one of the basic components of calculus which was discovered by Newton and is one of the founding principles of modern mathematics was discovered in about 1350 AD by a little known school of scholars in southwest India hundreds of years before Newton — according to new research.

According to Dr. George Gheverghese Joseph of The University of Manchester that the ‘Kerala School’ discovered first the mathematical formula but is currently and wrongly attributed in books to Sir Isaac Newton and Gottfried Leibniz at the end of the seventeenth century.

The team from the Universities of Manchester and Exeter reveal the Kerala School also discovered what amounted to the Pi series and used it to calculate Pi correct to 9, 10 and later 17 decimal places.

And there is strong circumstantial evidence that the Indians passed on their discoveries to mathematically knowledgeable Jesuit missionaries who visited India during the fifteenth century.

That knowledge, they argue, may have eventually been passed on to Newton himself.

Dr Joseph made the revelations while trawling through obscure Indian papers for a yet to be published third edition of his best selling book ‘The Crest of the Peacock: the Non-European Roots of Mathematics’ by Princeton University Press.

He said: “The beginnings of modern maths is usually seen as a European achievement but the discoveries in medieval India between the fourteenth and sixteenth centuries have been ignored or forgotten.

“The brilliance of Newton’s work at the end of the seventeenth century stands undiminished — especially when it came to the algorithms of calculus.

“But other names from the Kerala School, notably Madhava and Nilakantha, should stand shoulder to shoulder with him as they discovered the other great component of calculus- infinite series.

“There were many reasons why the contribution of the Kerala school has not been acknowledged - a prime reason is neglect of scientific ideas emanating from the Non-European world - a legacy of European colonialism and beyond.

“But there is also little knowledge of the medieval form of the local language of Kerala, Malayalam, in which some of most seminal texts, such as the Yuktibhasa, from much of the documentation of this remarkable mathematics is written.

He added: “For some unfathomable reasons, the standard of evidence required to claim transmission of knowledge from East to West is greater than the standard of evidence required to knowledge from West to East.

“Certainly it’s hard to imagine that the West would abandon a 500-year-old tradition of importing knowledge and books from India and the Islamic world.

“But we’ve found evidence which goes far beyond that: for example, there was plenty of opportunity to collect the information as European Jesuits were present in the area at that time.

“They were learned with a strong background in maths and were well versed in the local languages.

“And there was strong motivation: Pope Gregory XIII set up a committee to look into modernising the Julian calendar.

“On the committee was the German Jesuit astronomer/mathematician Clavius who repeatedly requested information on how people constructed calendars in other parts of the world. The Kerala School was undoubtedly a leading light in this area.

“Similarly there was a rising need for better navigational methods including keeping accurate time on voyages of exploration and large prizes were offered to mathematicians who specialised in astronomy.

“Again, there were many such requests for information across the world from leading Jesuit researchers in Europe. Kerala mathematicians were hugely skilled in this area.”

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The earliest hominoids according to paleoanthropological studies began to use more of its thinking or mental other than its physical capabilities by the advent of the homo sapiens or thinking ape at the end of the Paleolithic period, some 2 million to 10,000 years ago or the Upper Paleolithic when man started to use tools in its daily activities.

At the advent of the Mesolithic Period, humans already have refined its tool making capability and enhanced its hunting capabilities resulting to the decline of animals near his domains requiring him to plan for his next hunting endeavor and this might have further sharpened his thoughts and his development of expressing his concept about quantity by recognizing how to count which is very important in his daily survival and this led him to the discovery of using numbers even before the discovery of writing.

During this period of illiteracy, the concept of quantity and counting was made evident by the use of numbers through the use of some physical representations through objects and some refined tools such as the quipo used by the Incas as tallies using knotted strings to record numbers.

The discovery of writing came as a breakthrough and this gave man the ultimate process to enhance his ability to manipulate or process any physical and abstract entities by the use of numbers and this started the early advancements in the history of mathematics.

By 1800 BC, the Babylonians already had solid knowledge of almost all aspects of elementary arithmetic which is the earliest branch of mathematics as shown in the clay tablet Plimpton 322 which seems to be a list of Pythagorean triples although historians can only guess at the methods used in generating the results because there were no workings to show how the list was originally produced. In the same way the Egyptian Rhind Mathematical Papyrus dated from 1650 BC which was evidently a copy of a much earlier text from 1850 BC shows evidence of addition, subtraction, multiplication and division utilized within a unit fraction system.

Within this period up to the 7th century AD, basic arithmetical operations were very complicated affairs because of the seemingly unsophisticated method of operation and numerical representation that were being used until the introduction of a new numerical and arithmetical system called the “Method of the Indians” which became the arithmetic that we used today.

Hindu-arabic arithmetic system as being called today because the Arabs popularized its use and led the way to its introduction to the Europeans by Fibonacci in 1202 is a much simpler method than all the other arithmetical system is then widely used because it uses zero and place-value notation.

From the early realization of the concept of quantity and counting and onwards, the use and manipulation of numbers to represent physical and abstract entities lead to one of the most important branches of knowledge of humanity that resulted to vast monumental achievements of societies from early civilizations until today as evident in the mysterious constructed monuments of olden times up to the present technological marvels of our time.