Kantian idea of constructing concepts.

It stands as fundamental and key one for his conception (understanding) of mathematics. Although Kant's constructing is present, as we explained above, at the level of definitions and axioms, but only in mathematical activity constructing finds its essential meaning. In this case mathematics is conceived by Kant as a complex two-level (two-component) way of cognition. It begins with the creation by using definitions “pure sensible concept”.

Their specificity is that they are formed by “arbitrary synthesis”, i.e., contain some mathematical [mental/mind] action. Further, when we constructing concepts we implement descent to the level of (quasi)sensuality (imagination) and relating of the concept to universally valid contemplation — scheme. Here, as if upon the reverse reading (from left to right) of the Hume’s principle, happens the decoding (or construction) of the concept, i.e., the transition to a deep information level: from rational (declarative) level of the concept on contemplative (procedural pragmatic) level of schemes. This can be represented as an expansion of the original abstract concept to lower-level objects that are in some [space-time] environment and with which (therefore) we can perform certain mathematical operations. Actually exactly here the creative mathematical activity of the corresponding type is performed: geometric constructions, algebraic calculations or logical-mathematical proofs, each of which, in turn, represents a certain set of permissible in this environment local action – operations (like drawing the line, division of numbers, etc.). We can say that in this “descent” through sensory intuition the egress beyond the original concepts and the [synthetic] increment of knowledge occurs, as any [dynamic] action (as opposed to static concepts) is a synthesis of at least two views42. The result of this synthesis by reverse return (rise) on the cerebral (conceptual) level is fixed as a formal result of the construction, calculation or the proved theorem.
Schematically, mathematical acts can be represented as follows:

(Understanding) formalized approach
Concept A -------------------> Concept B
^
|
| "Constructing a
concept to descent" |
|
V "Return rise backwards"
(Imagination) |

Scheme A --------------------> Intuition B
mathematical act

Here, following by I. Lakatos (Lakatos, 1976), we should distinguish the actual mathematical activity as a certain sequence of mathematical actions in contemplative environments (space and time) in the lower part of the scheme and its logical design, which can be represented in the upper block of the scheme as a formal-logical transition (“conclusion”) from the concept (formula) A to the concept (formula) B. And the first can not be completely reduced to the second, as the task of the formal proof is not in the modeling of real mathematical activity (for example, as a process of mathematical constructions in the proof of the theorem on the sum of the angles of triangle), but in ensuring the logical rightness (correctness) of its implementation. Therefore, the structure of the real mathematical process differs from its logical design in some formal meta-language.

It is also clear that the situation in modern mathematics is much more difficult, since the above principle of abstraction can be applied iteratively, generating abstractions of increasingly higher levels. Accordingly, the specifying these abstractions “descents” will also be multi-level ones, and intermediate “descents” will likely be not “descents” to the level of sensuality (imagination), but on a preceding more specific rational level. However, the Kantian thesis about the need to “to make an abstract concept sensible” should be the principal one here, it suggests a final “descent” to the level of sensible intuition, for example, geometric drawing.

In his analysis of mathematical activity, Kant distinguishes two types of constructing: geometric and algebraic. Along with the ostensive (from Lat. Ostentus — showing) constructing, based on the spatial intuition, or the intuition in space, Kant also distinguishes founded by time intuition — symbolic construction, underlying the algebraic operations.

But mathematics does not merely construct magnitudes (quanta), as in geometry, but also mere magnitude (quantitatem), as in algebra, where it entirely abstracts from the constitution of the object that is to be thought in accordance with such a concept of magnitude. In this case it chooses a certain notation for all construction of magnitudes in general (numbers), as well as addition, subtraction, extraction of roots, etc. and, after it has also designated the general concept of quantities in accordance with their different relations, it then exhibits all the procedures through which magnitude is generated and altered in accordance with certain rules in intuition; where one magnitude is to be divided by another, it places their symbols together in accordance with the form of notation for division, and thereby achieves by a symbolic construction equally well what geometry does by an ostensive or geometrical construction (of the objects themselves), which discursive cognition could never achieve by means of mere concepts.

Turning to the analysis of more abstract algebra as a kind of mathematical activity we would like to draw attention to two things. Firstly, the use of “language of X-s and Y-s” or transition compared to the arithmetic meta-language of variables, which allows us to “work” not only with certain values as in arithmetic (e.g., distinguish even and odd numbers), but also with abstract values whose validity is spontaneous, i.e. with variables, is one of the major constituents of algebra. Secondly, the language of algebra allows expressing not only abstract symbols, but also [arithmetic] operations (“actions”), which can be done with these symbols, is no less important factor, although it almost falls out of the scope of the analysis.

Thus the algebraic language is, unlike declarative language that is used, for example, in metaphysics (“philosophy vs. mathematics”), a specific procedural language in which the possible ways to work with mathematical objects is fixed, i.e. how we need to make certain mathematical operations. Moreover, if earlier such procedural language was the prerogative of algebra only, now it applies to all branches of the modern, which has become super-abstract, mathematics: no logical-mathematical language without special characters for expressing operations on mathematical objects is possible. It is important to note that the symbolic constructing is much more transparent than ostensive, since in the latter actions are is not expressly “affect” but only “shown” (Wittgenstein) through their real implementation in geometric constructions, although they may be explicated by describing the methods of constructing, in meta-languages. Such codification of possible mathematical actions makes mathematics more rigorous, although it restricts its heuristic potential, as it becomes impossible to introduce new mathematical structures.

However, the symbolic constructing, as indicated by its title, is an abstract one in another respect too. In essence, by mathematical symbols of [algebraic] operations the latter are only coded, i.e. presented in abbreviated [symbolic] form, what suggests their real existence already beyond formulaic expressions. So, formulaic (symbolic) record of multiplying of two numbers “a × b” supposes the real action of multiplying of a and b, for example, by multiplying in column, which serves a la geometric construction.

http://s3.amazonaws.com/…/39314927/katr_philmath2015_30-06-…

G Space

The article linked in this post is proclaiming and, above all, calculating that spacetime is emerging from quantum entanglement, a concept that Mark Van Raamsdonk tantalized years ahead. But it is just a twisting the holographic Maldacena's most famous idea with the CFT. Thus it is a role model Universe, a possible Universe, but not our Universe. So far, following up this math way of making "physics" I will bet for the concept in the paper published in ArXiv some months ago and pasted at the end of this paragraphs. It is connected with the "G Space", beyond the Hilbert Space, postulated in the UNST or Nature Mechanics.

That paper has explored a starting point for quantum gravity grounded in quantum mechanics, rather than beginning with spacetime. This approach is suggested by indications that the usual locality of local quantum field theory is not a fundamental property of gravitational theory, as I showed in other posts in my page Nature Mechanics some days ago, and by difficulties of approaches that begin with spacetime and then try to quantize the metric.

If the correct framework for quantum gravity is intrinsically quantum-mechanical, an important question is what mathematical structure is needed beyond that of Hilbert space. While for finite or locally finite quantum systems important additional structure is supplied by a tensor factor structure for the Hilbert space, such a structure is problematic even in field theory both due to the type-III property (infinite entanglement), together with the presence of long range gauge fields. Instead, one focuses on the algebraic structure, and a net of subalgebras which correspond to subregions of the spacetime. Moreover, in gauge theory only certain restricted classes of operators define commuting subalgebras.

These observations prompt exploration of a possible fundamental role for the algebra of observables in quantum gravity, and indicate the importance of understanding further refinements of this algebraic structure. Given that a particle is inseparable from its gravi- tational field, and that gravity apparently cannot be screened, one finds an obstacle to even identifying a subalgebra structure associated with regions, a subtlety going beyond that of gauge theory. This is readily seen if one assumes a principle of correspondence, where the quantum structure of gravity approximately matches onto that of quantized general relativity in the long-distance/low-energy limit. Even in this limit, gravitationally-dressed operators generally fail to commute even when describing excitations which na ̈ıvely are created in spacelike-separated regions. Thus, this further confirms and quantifies the limi- tations of local quantum field theory that have been parameterized by locality bounds. One does find that commutators can be small, in the long-distance/low-energy limit, so it appears possible to recover the subalgebras of local quantum field theory approximately in the correspondence limit.

This discussion appears to have important implications for attempts to find a quantum theory of gravity. There is not a clear primary role for entanglement, given the difficulty with defining tensor factorizations, and it is difficult to see how spacetime itself could emerge from entanglement. Moreover, if one takes a quantum information perspective and thinks of particles as roughly corresponding to qubits, and asks the question “how big is a qubit?” it appears that the answer is that the qubit is arbitrarily large in the sense of having infinitely extended weak field, and moreover its strong-field region grows with the energy of the qubit. This is a qualitative difference with behavior of more familiar quantum systems.

If quantum gravity can be formulated in such an intrinsically quantum-mechanical framework, it will be very important to further characterize the structure of its algebra of observables, and possible refinement of that structure. Important guides in this include correspondence with the known long-distance/low-energy behavior of gravity. Indeed, ul- timately one might anticipate that the familiar geometric structure of spacetime emerges from a more basic quantum algebraic structure, defining such a “quantum emergent geometry.”

In conclusion, the phys-math Nature Individuality is at the very deep bottom of the reality.

http://arxiv.org/pdf/1503.08207.pdf

Noval derivation of pi links quantum physics and pure math

"I find it fascinating that a purely mathematical formula from the 17th century characterises a physical system that was discovered 300 years later," said one of the lead researchers, Tamar Friedmann, a mathematician at the University of Rochester in the US. Seriously, wow.

The discovery was made when Carl Hagen, a particle physicist at the University of Rochester, was teaching a class on quantum mechanics and explaining to his students how to use a quantum mechanical technique known as the 'variation principle' to approximate the energy states of a hydrogen atom.

While comparing these values to conventional calculations, he noticed an unusual trend in the ratios. He asked Friedmann to help him work out this trend, and they quickly realised that it was actually a manifestation of the Wallis formula for pi – the first time it had even been derived from physics.

"We weren't looking for the Wallis formula for pi. It just fell into our laps," said Hagen. "It was a complete surprise," added Friedmann. "I jumped up and down when we got the Wallis formula out of equations for the hydrogen atom."

Since 1655 there have been plenty of proofs of Wallis's formula, but all have come from the world of mathematics, and the new results have people freaking out. The results have been published in the Journal of Mathematical Physics.
"In quantum mechanics, a technique called the variational approach can be used to approximate the energy states of quantum systems, like molecules, that can't be solved exactly. Hagen was teaching the technique to his students when he decided to apply it to a real-world object: the hydrogen atom. The hydrogen atom is actually one of the rare quantum mechanical systems whose energy levels can be solved exactly, but by applying the variational approach and then comparing the result to the exact solution, students could calculate the error in the approximation."

"That a formula for π is hidden inside the quantum mechanics of the hydrogen atom is surprising and delightful."

What's the difference between Physics and mathematics exactly?

The indivi-duality of Nature. The phys-maths Nature

In the article below the author question:

what's the difference between phys and maths exactly?

And answered himself (between *---* my observations)

I think there are two linked, but subtly distinct, differences.

*There is no differences when you consider Nature as individuality, so far they are not linked, just they are two faces of the same coin*.

1. Physics is a science and mathematics is not.

This means that physics has an experimental aspect. In physics, it is possible to disprove a hypothesis by experiment: this cannot be done in maths.

*The author is debunking empiric and/or quasi-empiric maths defended by Stewart Mills and Imre Lakatos respectively. Also, he is obviating Mr. Atiyah assertion about human evolution in a very special physical environment with the physical reality across our brain modelizing it "mathematically" beyond our physical "intuitions" that we developed observing that immediate physical environment as Albert Einstein did with his General and Special Relativity theory for example*.

2. Physics is about this world and mathematics is not (necessarily).

The canvas for mathematical ideas is much wider than the canvas of physics.

A small subset of mathematics seems to correspond with observable physical phenomena to a shocking extent. This we call applied mathematics. However, mathematics describes many things which don't correspond to phenomena in this world.

*Sure, maths are wider than phys. In fact maths is a "world of possibles" and phys is our world now, one world in a period of time between many possible worlds. Thus we can't say that maths describe many things which not correspond to phenomena in this world. On contrary we have many examples which maths without any connection with our world, in principle, but later on they were describing extremely accurately physical phenomena, as for example non-euclidean geometry. It is started just like a toy for some XIX century mathematicians and finally it was the bases to describe space-time by Minkowski and fundamental for the General Relativity by Einstein. There are many examples like that (recently Efimov's triad describe a physical phenomena) and it is very probable to find more and more "connections" like tha when we will get deeper in our knowledge about Nature. Perhaps it will happen with string theory too.

Finally, in the wider sense of science, maths is science as well because Nature is a phys-math individuality.*

https://protonsforbreakfast.wordpress.com/…/physics-is-mor…/

கணக்கு பாடம் சுகம் சொன்னான் கேட்டால் தானே இதைப்பார்த்து எண்டாலும் தெரிஞ்சு கொள்ளுங்கோ

Mathematics reveals the nature of the cosmos

"Let us discuss the very nature of the cosmos. What you may find in this discussion is not what you expect. Going into a conversation about the universe as a whole, you would imagine a story full of wondrous events such as stellar collapse, galactic collisions, strange occurrences with particles, and even cataclysmic eruptions of energy. You may be expecting a story stretching the breadth of time as we understand it, starting from the Big Bang and landing you here, your eyes soaking in the photons being emitted from your screen. Of course, the story is grand. But there is an additional side to this amazing assortment of events that oftentimes is overlooked; that is until you truly attempt to understand what is going on. Behind all of those fantastic realizations, there is a mechanism at work that allows for us to discover all that you enjoy learning about. That mechanism is mathematics, and without it the universe would still be shrouded in darkness. In this article, I will attempt to persuade you that math isn't some arbitrary and sometimes pointless mental task that society makes it out to be, and instead show you that it is a language we use to communicate with the stars."

Sacred Geometry: Flower of Life, Introduction

Sacred geometry may be understood as a worldview of pattern recognition, a complex system of hallowed attribution and signification that may subsume religious and cultural values to the fundamental structures and relationships of such complexes as space, time and form. According to this discipline, the basic patterns of existence are perceived as sacred: for by contemplating and communing with them one is thereby contemplating the Mysterium Magnum, the patterning relationships of the Great Design. By studying the nature of these patterns, forms and relationships and their manifold intra- and interconnectivity one may gain insight into the scientific, philosophical, psychological, aesthetic and mystical continuum. That is, the laws and lore of the Universe.

The term sacred geometry is also used for geometry which is employed in the design of sacred architecture and sacred art. The underlying belief is that geometry and mathematical ratios, harmonics and proportionality discoverable from geometry also gird music, light, cosmology, and other observable and sensate features of the Universe. This value system has been held throughout the World from time immemorial to prehistory, a cultural universal endemic to the Human Condition. Sacred geometry is the foundation of the design, architecture, fabrication and construction of sacred structures such as temples, mosques, megaliths, monuments and churches; sacred space such as altars, temenos and tabernacles; places of congregation such as sacred groves, village greens and holy wells and the creation of religious art, iconography and divine proportionality. Sacred geometry, art, iconography and architecture need not be monolithic and enduring, but may be temporary and yielding, such as visualization and non-permanent sand-painting and medicine wheels

The "Flower of Life" can be found in all major religions of the world.
It contains the patterns of creation as they emerged from the "Great Void". Everything is made from the Creator's thought. After the creation of the Seed of Life the same vortex's motion was continued, creating the next structure known as the Egg of Life. This structure forms the basis for music, as the distances between the spheres is identical to the distances between the tones and the half tones in music. It is also identical to the cellular structure of the third embryonic division (The first cell divides into two cells, then to four cells then to eight). Thus this same structure as it is further developed, creates the human body and all of the energy systems including the ones used to create the Merkaba. If we continue creating more and more spheres we will end up with the structure called the Flower of Life.

more:
more:
http://www.phoenixmasonry.org/sacred_geometry_the_flower_of_life.htm

Physical-mathematical Individuality and maths discovery-invention individuality as well.

There is indivi-duality, not only physical-mathematical, but also in consideration of whether mathematics is invention or discovery; it is an indivi-duality invention-discovery. This is the key to next paragraph of the distinguished mathematician Langlands:

*At times, the opposite happens. I awakes and for some moments Finds a world Where actual mathematical Entities seem as as the furniture.

"It's nightmarish," I says. "It must have something to do With madness. If in the middle of the night you wake up and there's some fusion Between the mathematical objects and the real world, then a you're mad.*

And I would add that I see in his theories to the great Grothendieck as a real instigator or inspiring him. Weyl, Langlands, Serre and others follow his theory of motives, which even says Arthur would not be surprised to be elementary particles in the universe:

*Spectacular discoveries in physics Have Been foretold by mathematics. One of history's foremost mathematicians, the German Carl Friedrich Gauss, in the early 1800s Calculated a theorem on the intrinsic curvature of space, echoed in Einstein's theory of relativity Almost a century later.

In the early 1960s, American physicist Murray Gell-Mann used the math principles of group theory to organize composite particles called hadrons and to predict the existence and distribution of sub-atomic quarks. Experiments confirmed several years later Organizing Both the pattern and the quarks. I have Received the Nobel Prize in physics for esta work in 1969.

"Mathematics Allows you to see the invisible," Frenkel says.

The link Currently some exciting Physicists Involves a "duality" found Between the forces of electricity and magnetism. These forces are Said to be symmetrical - They Affect each other in the same way. In quantum physics, esta duality center is to the quest for a theory Known That unites all physical interactions in the universe, from the stars to the smallest particles.

The symmetry Between electricity and magnetism parallels One That exists in Langlands' conjectures, mathematical Involving groups associate With That automorphic forms. String theorist Edward Witten of the Institute for Advanced Studies describe the existence of esta analog as "amazing."

"We of course do not know how the story will Develop from here," I says in an email to the Star. "Maybe the physics will shed light on number theory, number theory maybe will produce insights That will help Physicists. Maybe for a long time and we will not know the two parts of the picture will mostly just Develop Independently of each other. "

Arthur will not be surprised if Eventually Physicists discover math That's elusive key motives exist as particles in the universe. That Sentimental Dismisses Langlands as fantasy. He's convinced the majority of Physicists, DESPITE Witten's giant reputation, see little value in Applying His Work.*

http://projects.thestar.com/math-the-canadian-who-reinvent…/

The Mysterious connection between Maths and Phys (some questions):

Why does mathematics seem so “unreasonably” effective in fundamental physics? (Or does it?)

Is there a “pre-established harmony” between them, because the world is fundamentally mathematical?

Are we pushed to call certain theories or disciplines more fundamental because they are in some sense more mathematical?

Or, are we just lacking the right mathematics to treat other fields with similar power and rigor as physics?

What would it mean for something in the physical world to be NOT describable or model-able in terms of mathematics?

Why does physical reality obey one particular set of mathematical laws and not others (Or does it?)

How deeply does mathematics inform physics?

How deeply does physics inform mathematics?

How does the structure and availability of existing mathematics shape the formulation of physical theories?

Why do we prefer mathematically simple theories to complex ones?

What even defines simplicity?

And is there an objective measure of complexity?

May we be missing interesting physical theories because we are committed to particular mathematical frameworks, or because suitable ones have not yet been developed?

To what extent can or should we extrapolate our mathematical equations of physics beyond the domains where we have tested them?

How much of mathematics has been constructed as if it had been due to physics motivations?

Should frameworks that are internally consistent and display mathematical elegance, but which lie beyond experimental reach, be regarded as physical theories or rather as branches of mathematics or philosophy?

Out of the countably infinitely many true statements that could be derived from a given set of sufficiently rich axioms, how have we arrived at what we know as mathematics?

How much is evolutionary history? Our mental makeup? Utility? Beauty? Something else?

What are the tensions between physics and mathematics?

Are there hidden subtleties or overt controversies in how or why mathematics is used in physics (or other sciences)?

What is randomness, and what is the nature of probability?

What is the fundamental origin of stochasticity, and does that affect how we think of probability?

Is it quantumness? Or indexical uncertainty of various types? Or lack of knowledge?

Is there true randomness, or is it only apparent?

Are there hidden patterns in things that seem random to us now?

Do incompleteness theorems such as Goedel's play a role in physical theory?

What do they allow, forbid, or elucidate?

How should we think of infinity? Is it a useful mathematical concept that does not really apply to physical reality? Or could real physical systems be infinite?

Are there mathematical contradictions or paradoxes that tell us something about physical reality?

Maryam Mirzakhani has become the first woman to receive the ‘Nobel Prize of mathematics’

Maryam Mirzakhani is one of four winners of the prestigious Fields Medals this year, and has become the first woman to receive the ‘Nobel Prize of mathematics’.

Clockwise from top left: Maryam Mirzakhani, Martin Hairer, Artur Avila and Manjul Bhargava.

Image: International Mathematical Union

The Fields Medal, officially known as the International Medal for Outstanding Discoveries in Mathematics, is given out every four years to up to four mathematicians under the age of 40.

Iranian-born Maryam Mirzakhani is the first female winner out of all the 52 previous recipients of the prize. She’s a professor at Stanford University in California, US, and an expert on the behaviour of dynamical systems.

As Dana Mackenzie from New Scientist explains, she “studies the geometry of moduli space, a complex geometric and algebraic entity that might be described as a universe in which every point is itself a universe.”

The other winners this year are Artur Avila, a researcher in a dynamical systems from the National Institute of Pure and Applied Mathematics in Brazil and the National Centre for Scientific Research in France; Manjul Bhargava from Princeton University in the US, who was recognised for new methods in the geometry of numbers; and Martin Hairer of the University of Warwick in England, who studies the effect of random noise on partial differential equations, which includes the effect of turbulence on ocean currents or the flow of air around airplane wings.

It’s a fantastic achievement for all the winners, but given that 70 percent of the PhDs in mathematics still go to men, this is also good news for the field.

“This is a great honour. I will be happy if it encourages young female scientists and mathematicians,” Mirzakhani said in a Stanford University press release. “I am sure there will be many more women winning this kind of award in coming years.”

Ingrid Daubechies, a professor of mathematics at Duke University in North Carolina, US, and president of the International Mathematical Union, which awards the Medal, told Kenneth Chang from the New York Times over email:

“All researchers in mathematics will tell you that there is no difference between the math done by a woman or a man, and of course the decision of the Fields Medal committee is based only on the results of each candidate … That said, I bet the vast majority of the mathematicians in the world will be happy that it will no longer be possible to say that ‘the Fields Medal has always been awarded only to men.’”

Editor's Note: The New York Times, New Scientist

கணிதத்தின் வரலாறு

ஒருவன் இந்த சமூகத்தோடு படிப்பறிவு இல்லாமலும் ஒன்றி வாழ முடியும். ஆனால் அவனுக்கு சிறிதளவாது கணித அறிவு இருக்க வேண்டும். அப்போது தான் அவனால் இந்த சமூகத்தில் வாழ முடியும். பண்டை காலத்தில் வாழ்ந்த புலவர்கள் கூட தங்கள் பாடல்களை ஒரு குறிப்பிட்ட கணித விதிப்படி தான் அமைத்தனர். உதாரணத்திற்கு திருக்குறளையே கூறலாம். இத்தகைய கணிதம் எப்படி தோன்றி வளர்ந்து இன்றைய கணிப்பொறி வரை வளர்ந்தது என்பதை பார்ப்போம்.

ஆதிகாலத்தில் வாழ்ந்த மக்கள் பொருள்களை ஒப்பிட அறிந்த போதை கணிதம் வளர தொடங்கிவிட்டது. ஆதி மக்கள் தங்கள் கால்நடைகளையும், மற்ற பொருட்களையும் கணக்கிடுவதற்கு கற்கள், குச்சிகள் போன்றவற்றை பயன்படுத்தினர். ஆதி மக்கள் தங்களின் உற்பத்தி பொருட்களை பரிமாற்றிக்கொண்டனர். இதனால் பண்டமாற்று முறை நடைமுறைக்கு வந்தது. இதனால் பொருட்களை அளந்து கொடுக்க தொடங்கினர்.

அப்போது தோன்றியது தான் முகத்தல் அளவைகள். இதற்கு அடுத்து சேர், அழாக்கு, படி, முழம் போன்ற அளவைகள் கண்டுபிடிக்கப்பட்டது. இதன் பிறகு மக்களின் வாழ்க்கைத்தரம் படிப்படியாக உயர ஆரம்பித்தது. இதையடுத்து பல அறிஞர் பெரு மக்கள் தோன்றி பல கண்டுபிடிப்புகளை கண்டுபிடித்தனர். ஆரம்ப காலத்தில் எண்ணிக்கையை கணக்கிட அறிந்த மக்கள் பின்னர் கூட்டல், கழித்தல், வகுத்தல், பெருக்கல் போன்றவற்றை பொருள்களையும,¢ கற்களையும், குச்சிகளையும் கொண்டு செய்ய ஆரம்பித்தனர். இந்த காலகட்டத்தில் சீனர்கள் கம்பிகளை கொண்ட ஒரு மணிச்சட்டத்தை உருவாக்கி அதன் மூலம் கூட்டல், கழித்தல், வகுத்தல், பெருக்கல் போன்றவற்றை செய்தனர்.

இவர்கள் உருவாக்கிய சட்டத்தில் கம்பிக்கு 7 மணிகள் வீதம் இருந்தன. இதற்கு அபகஸ் என்று பெயர் வந்தது. இதையே இரு மணிகளை குறைத்து ஜப்பானியர்கள் சோரபான் என்று பெயரிட்டனர். இவ்வாறு கணிதவியலின் அடிப்படை செயலிகள் அறிமுகமாயின. இன்றைய கணிப்பொறி பிறக்க இந்த மணிச்சட்டமே அடிப்படையாக இருந்தது என்று அறியப்பட்டுள்ளது. பின்னர் ஜான் நேப்பியர் என்ற அறிஞர் மேலும் சில மாற்றங்களை செய்து ஒன்பது மணிச்சட்டம் கொண்டு ஒரு கருவியை அமைத்தனர். இதற்கு நேப்பியர் சட்டங்கள் என பெயரிட்டனர். இதன் மூலம் வர்க்க மூலம் வரை கணக்கி முடிந்தது. இவரின் இந்த அறிய கண்டுபிடிப்பு தான் சில மாற்றங்களுடன் இன்று நாம் மடக்கை என்ற பெயரை பயன்படுத்துகிறோம்.

காலத்தை -குறிப்பாக பழங்காலத்தில் மணல் சாடிகளை பயன்படுத்தி மணல் செரிந்த அளவை கொண்டு நேரத்தை கணக்கிட்டனர். பின்னர் மணலுக்கு பதில் நீரை பயன்படுத்தினர். இக்காலகட்டத்தல் வானவியல் பற்றி கலில¦யோ, ஆர்யபட்டர் என பலர் பல ஆராய்ச்சிக¬ளை செய்து பூமி தன்னைத்தானே சுற்றிக்கொள்ள 23 மணி 56 நிமிடம் 4.091 நொடி என்று கூறினார். அவை பின்னர் விஞ்ஞானி பூர்வமாக நிருபிக்கப்பட்டு அதுவே ஒரு நாளைக்கு 24 மணி நேரம் எனக் குறிக்கப்பட்டது.

இதிகாசங்களில் வெறுமே அல்லது வெற்றிடம் என்பதை குறிக்க சூன்யம் என்ற சொல் பயன்படுத்தப்பட்டது. பின்னர் சுன்னம் என்ற சொல் பயன்படுத்தப்பட்டது. இதையே கணித மேதைகள் மதிப்பில்லாதவைகளுக்கு புள்ளியை பயன்படுத்தினர். பின்னர் குழப்பத்தை தவிர்க்க புள்ளியை சுற்றி வட்டமிட்டனர். பின்பு, வட்டம் என்று பயன்படுத்தினர். இந்த சூன்யம் என்ற சொல் வெவ்வேறு மொழிகளில் மாறி பின்னர் பிரஞ்சு மொழி ஜுரோ என்று பெயரிடப்பட்டு அதுவே நிலைத்துவிட்டது. இதை கண்டுபிடித்து உலகிற்கு வழங்கிய பெருமை இந்தியாவையே சேரும். இதை வழங்கியர் ஒரு பெயர் அறியப்படாத இந்தியர் என்று அறியப்பட்டுள்ளது. இந்த 0 தான் இன்று கணிப்பொறியில் தலையாய எண்ணாக உள்ளது.

பிளாட்டோ என்ற தத்துவ மேதை கிமு 387ம் ஆண்டு ஐரோப்பாவில் முதல் பல்கலைக்கழகமாகிய ஏதென்ஸ் அகாடமியில் வடிவங்களை அளக்க சில கருவிகளை உருவாக்கினர். அவர் உருவாக்கியவை தான் அளவு கோள், காம்பஸ் போன்றவை. அவை தான் இன்று நடைமுறையில் உள்ளது. பல கணித மேதைகள் உருவாக்கிய அடிப்படை தகவல்களை கொண்டு கோப் நிக்கஸ் என்ற போலந்து நாட்டு அறிஞர் கோணகணிதம் என்ற பிரிவை வழங்கினர். பின்னர் இவரின் கண்டுபிடிப்புகளை பயன்படுத்தி கலில¦யோ போன்ற வானவியல் அறிஞர்கள் அண்டத்தை பற்றி பல உண்மைகளை கண்டறிந்தனர். இயக்கம், விசை போன்ற உண்மைகளை கண்டறிய இவரின் கோணகணிதம் தான் பயன்பட்டது. 

அதிவேக மனிதக் கணினி, கணிதமேதை சகுந்தலா தேவி

நவம்பர் 4: அதிவேக மனிதக் கணினி, கணிதமேதை சகுந்தலா தேவி பிறந்த தினம் இன்று அப்பாவைப் பார்த்து மேஜிக் ஆர்வம் இவருக்கு தொற்றிக்கொண்டது. ''அப்பா, எனக்கும் ஏதாச்சும் சொல்லித்தா!' என்றாள். அட்டைகளில் மேஜிக் சொல்லித் தந்தார் அப்பா. கொஞ்ச நேரம்தான், எல்லா அட்டைகளையும் மனப்பாடமாக ஒப்பித்தாள் தேவி. அப்போது அவள் வயது 3. 'இனி சர்க்கஸ் வேண்டாம்’ என முடிவுசெய்த அப்பா, மகளைப் பல இடங்களுக்கு அழைத்துச்சென்று அவளின் அதிவேகக் கணக்குப் போடும் ஆற்றலைக் காட்டினார். ''சின்னப் பெண்ணுக்கு இவ்வளவு அறிவா? கூப்பிடு செக் பண்ணிடலாம்'' எனப் பெரிய பெரிய பல்கலைக்கழகங்கள் அழைத்தன. வீட்டின் வறுமையைப் போக்க, ஊர் ஊராகச் சுற்ற ஆரம்பித்து, பின் அதுவே வாழ்க்கை ஆகிப்போனது. அமெரிக்காவின் டல்லாஸ் நகரில் இருந்து அழைப்பு. இப்போது தேவிக்கு வயது 46. மூளை அதே வேகத்தில் வேலை செய்யுமா? 91674867692003915809866092758538016248310668014430862240712651642793465704086709659 3279205767480806790022783016354924852380335745316935111903596577547340075681688305620821016129132845564805780158806771 என்கிற இந்த 201 இலக்க எண்ணின் 23-வது வர்க்கமூலத்தைக் கேட்டார்கள். கணினி 13,000 கட்டளைகளுக்குப் பிறகு, ஒரு நிமிடத்தில் பதிலைச் சொல்லத் தயாரானபோது, 546372891 என 10 நொடிகள் முன்னமே தேவி சொல்லி விட்டார். அரங்கத்தில் இருந்த பார்வையாளர்கள் நீண்ட கரவொலி எழுப்பினர். லண்டன் மாநகரில் 7,686,369,774,870 மற்றும் 2,465,099,745,779 என இரு எண்களைப் பெருக்கச் சொன்னார்கள். 28 நொடிகளில் விடையைச் சொல்லி, கின்னஸ் சாதனையில் இடம் பிடித்தார். அவர்தான் சகுந்தலா தேவி. தான் பள்ளிக்கல்வி பெறாவிட்டாலும் சுட்டிகளுக்காக கணிதத்தை எளிமையாகக் கதை வடிவில் சொல்லும் வகையில் பல நூல்களை எழுதினார். ''கணிதம் என்பது பாடம் சம்பந்தப்பட்ட விஷயம் இல்லை. நீங்கள் சாப்பிடுகிற சாப்பாடு, பிறந்த நாள், விளையாட்டு என எல்லாவற்றிலும் கணிதம் இருக்கிறது. அதை சுட்டிகளுக்கு சொல்லித் தர வேண்டும். கணிதத்தைக் கதை போலச் சொல்லித் தர வேண்டும்'' என்ற சகுந்தலா தேவி, கடந்த ஏப்ரல் 21-ம் தேதி காலமானார். உலகின் அதிவேக மனிதக் கணினியை அன்போடு நினைவுகூர்வோம். -பூ.கொ.சரவணன்

Vedic Mathematics – Introduction

Vedic mathematics is the natural home of mathematics as we know it today. Mathematics as a subject is the one invented by humans, for our own convenience to represent things and to do calculations, unlike other sciences whose basic laws are found in nature. In Mathematics, it is the humans who have devised the computational methods.

And we all know that the roots of modern mathematics go back to ancient India. To quote Albert Einstein

We should be thankful to the Indians who taught us how to count, without which no worthwhile scientific discovery would have been possible.

Those who have studied the Roman Number System readily understand the difficulty in it. Every single number has its own unique symbol in Roman System and after a few numbers the system runs out of symbols! L gets introduced to represent 50, C gets introduced to represent 100, D at 500, M at 1000 and so on. And so, no reasonable mathematics beyond simplest of additions is possible in this system.

Ancient Indians took a completely scientific approach to mathematics. Mathematics was not about symbols, it was more about the actual numbers. So Indians decided about using a given set of symbols to represent any and every number, so that we don’t have to search for new symbols as we climb towards larger numbers.

The result was a place value based system, where a base was taken first, which simply meant the number of symbols used to represent numbers. And the same symbols would be used everywhere, and as we ran out of symbols, we simply push the symbols to left to represent the new number, and reintroduce other symbols on the right side.

I feel that the world’s best innovation was this place value based mathematical system which forced Indians to invent zero too. As a saying goes, the greatest contribution of Indians to world is Nothing! Nothing meaning Zero

Please note that zero was only a byproduct of this place value based system. The most important concept here is the place value system itself, not Zero.

Let me explain how.

First let us consider a base. Say 1 2 3 4 5 6 7 8 9. So these are our nine symbols for base 10.

Now ancient Indians devised a system where any number however big or small could be represented using only the nine symbols mentioned above.

The nine symbols used today are 1,2,3,4,5,6,7,8,9

Why 9, why not 10 symbols? The actual idea was a base 10 system because humans have 10 fingers, so base 10 looks more natural. But one symbol was left out to make room for symbol promotion, a symbol increases its value 10 times when it shifts one place to the left! This amazing place value based system then can be used to represent any large number however big, without having to add any new symbols to the list!

So what next? well, just repeat the cycle by pushing the first number again one place left (called the ten’s place), and then create a new number by repeating the symbols in the original place (called the unit’s place).

Why was zero invented OR why should there be nothing? To understand this, consider 101. If 1 is in hundred’s place and 1 is in unit’s place, how do we represent it symbolically showing there is nothing between the two one’s in the tenth place?

This is when ancient Indians invented Zero. Zero is called Shunya in Sanskrit, meaning nothing. So zero as a place holder was used to represent an empty space, with no value stored there. Zero is not a number, in fact it was invented to say, there is no numeric value here. 100 means there is no value here(0) and here(0) at the end, but only here(1)

So we had 10 after 9, where the symbol 1 in 10 meant the value of 1 is ten times more than its value in 1, and this was visually indicated by having 0 in the unit place. An amazing system this was, where the value of a symbol is decided depending upon where it is placed! so 1 in 212 is different from 1 in 199! You never run out of symbols here, unlike the roman system!

Vedic Mathematics was again a continuation of this basic mathematical principles, where methods were devised by ancient Indians to make mathematics easy. So easy that, what we call to be difficult problems in modern mathematics, can be done mentally without using a pen and paper in the vedic mathematics! Why? Because vedic mathematics was the math devised by the very same people, the ancient Indians, who had created the basics of the mathematics. They clearly knew how to play with the numbers!

Why then did the vedic mathematics did not enter west along with place value and zero? Well, because most of the modern mathematics was popularized in the west by the arab merchants who borrowed the simple ancient Indian math, which was very helpful for their trade, and popularized this system in the west when they went there to trade the Indian spices, diamonds and other goods. Which is why the base 10 symbols (1 to 9) are called Hindu-Arabic numerals, invented by Hindus i.e ancient Indians and popularized in the west by Arab merchants.

Ancient India was the world’s largest exporter of goods! Entire europe panicked, when ottoman turks captured constantinople by blocking the land route to India in 1453, the turks demanded that the european/arab traders pay a heavy tax to pass to India through Constantinople which was the connecting land route from Europe to India!

Panicked by this european countries started a series of naval adventures to find a sea route to India. Note that it was not the Indians who were desperate to find a sea route to Europe, it was the other way round! Just imagine how dependent the rest of the world was on India then! What is America today was discovered and known to the rest of world because of this quest to search a sea route to India! Columbus who had set out to discover a sea route to India, thought he had reached India when he touched the west indies island and the american continent, which is why west indies is called so, and the native americans were called Red Indians by him!! America was discovered, thanks to India!

Which is what I keep stressing to the Indian youth that we need to bring back those golden days to make India a great power!

Coming back to the vedic mathematics, the ancient greeks learnt mathematics from the Indians. The famous historian Albert Burk, says that Pythagoras visited Arakonam, India, and learnt the so called Pythagorean theorem there! The very fact that Pythagoras never gave a proof to his theorem, proves that he did not discover it.

Baudhayana, a mathematician who lived in ancient India, centuries before Pythargos, has written a list of Pythagorean triplets discovered algebraically, has stated the so called Pythagorean theorem, and also has given a geometrical proof of the Pythagorean theorem for an isosceles right angled triangle!

Another great aspect of vedic mathematics is there is no single fixed way of solving a problem. Students can devise their own better ways also! And this gives scope for ample creativity and fun. Students will ENJOY this form of mathematics, because they UNDERSTAND it, unlike the methods taught in the schools and colleges today where for ex, many students who solve differential equations, really have absolutely no idea of what they are solving or what a limit means!

The beauty of vedic mathematics is the way in which the entire system is inter related, where when you know something is a reverse of an existing thing, all you have to do is to reverse the method to calculate that something! For ex, the multiplication method when reversed becomes the division method, because division is the opposite of multiplication!! The method of finding squares when reversed becomes the method of finding square roots!!

In vedic mathematics, maths becomes , not something that is difficult/cryptic to understand, but like reading a novel or like watching a movie, full of fun and entertainment

Dr David Gray says . .the role played by India in the development (of the scientific revolution in Europe) is no mere footnote, easily and inconsequentially swept under the rug of Eurocentric bias. To do so is to distort history, and to deny India one of its greatest contributions to world civilization .

He also says, The Yajurveda Samhitaa, one of the Vedic texts predating Euclid and the Greek mathematicians by at least a millennium, lists names for each of the units of ten up to 10 to the twelfth power (paraardha). Later Buddhist and Jain authors extended this list as high as the fifty-third power, far exceeding their Greek contemporaries, who lacking a system of enumeration were unable to develop abstract mathematical concepts.

The place value system of enumeration is in fact built into the Sanskrit language, where each power of ten is given a distinct name. Not only are the units ten, hundred and thousand (dasha, shatha, sahasra) named as in English, but also ten thousand, hundred thousand, ten million, hundred million (ayuta, laksha, koti, vyarbuda), and so forth up to the fifty-third power, providing distinct names where English makes use of auxillary bases such as thousand, million, etc.

George Ifrah, the professor of mathematics who traveled around the world in search of origin of numbers has said that By giving each power of ten an individual name, the Sanskrit system gave no special importance to any number. Thus the Sanskrit system is obviously superior to that of the Arabs (for whom the thousand was the limit), or the Greeks and Chinese (whose limit was ten thousand) and even to our own system (where the names thousand, million etc. continue to act as auxillary bases). Instead of naming the numbers in groups of three, four or eight orders of units, the Indians, from a very early date, expressed them taking the powers of ten and the names of the first nine units individually. In other words, to express a given number, one only had to place the name indicating the order of units between the name of the order of units immediately immediately below it and the one immediately above it. That is exactly what is required in order to gain a precise idea of the place-value system, the rule being presented in a natural way and thus appearing self-explanatory. To put it plainly, the Sanskrit numeral system contained the very key to the discovery of the place-value system.

Irfah concluded that place-value numeral system developed in India and this system is embedded in the Sanskrit language

Before we start the actual Vedic mathematic lessons, I strongly recommend that you read this article http://www.infinityfoundation.com/ECITmathframeset.html on the Origin of Mathematics by Dr David Gray.

The problem with maths

The University of Sydney

Why aren’t Australian girls studying maths? Only 1.5% of girls go on to study science or maths for their HSC; 4.4% of boys undertake advanced maths with physics and/or chemistry components. Image: Sergey Nivens/Shutterstock The percentage of girls studying no maths for their HSC has more than doubled in the past decade, a report co-authored by University of Sydney researchers shows. Honorary Professor John Mack from the Faculty of Education and Social Work and Barry Walsh examined data of all Year 8 students in NSW to show the proportion who go on to study maths-science subject combinations for their HSC. The data revealed there was a substantial increase in the number of girls studying no maths at all in the HSC, and also showed a substantial drop overall in the number of boy and girl students undertaking at least one maths and one science subject in the HSC. "The decline in maths and science participation coincided with the removal in 2001 of the HSC requirement for undertaking English and at least one course in maths or science," says Dr Rachel Wilson from the Faculty of Education and Social Work, who helped prepare the report. "It is not a requirement in New South Wales, Victoria and Western Australia; although it is compulsory in SA, and to a small extent in Queensland and the Northern Territory. The study calls for policy change to make these subjects mandatory in order to lift participation in high school and to attract more girls to maths and science." The figures show that in 2001, 9.5 percent of girls undertook no mathematics course for their HSC. In 2011, this figure was 21.8 percent - more than double that of 10 years previously. Furthermore, in the same period the total proportion of Year 8 girls who went on to study intermediate or advanced maths dropped from 25 percent to 18 percent. In terms of undertaking science and maths the study also showed that only 1.5 percent of girls and 4.4 percent of boys go on to study advanced maths with both physics and chemistry. In 2001 some 19.7 percent of boys and 16.8 percent of girls studied a math-science combination in the HSC. In 2011 these figures had dropped to 18.6 percent of boys and 13.8 percent of girls. The decline has occurred despite the fact HSC participation increased by 5 percent over the period. This analysis suggests there is an urgent need to address declining female participation and stagnated male participation in intermediate/advanced maths-and-science combinations of study. The proportion of girls studying such combination subjects has dwindled since 2001 and there is now a greater gender disparity in maths/sciences participation than there was in the 1980s. Editor's Note: Original news release can be found here.

DISCOVERY AND USE OF ZERO

Gaayathre shadsankhyaamardhe apaneethe dvayanke avasishtasthrayastheshu roopamapaneeya dvayankaadha: soonyam sthaapyam

In gayatri chandas, one pada has six letters. When this number is made half, it becomes three (i.e the pada can be divided into two). Remove one from three and make it half to get one. Remove one from it, thus gets the zero (Soonya).

PINGALACHARYA IN CHANDA SASTRA 200 B.C.


CALCULATIONS WITH ZERO
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Vikaaramaayaanthi dhanarunakhaani na soonya samyoga viyogathasthu soonyaaddhi suddham swamrunam kshayam swam vadhaadinaa kham khaharam vibhakthaa:

Nothing happens (to the number) when a positive or negative number is added with 0. When +ve and -ve numbers are subtracted from 0, the +ve number becomes negative and -ve number becomes +ve. When multiplied with 0, the values of both +ve and -ve numbers become 0, when divided by 0, it becomes infinity (khahara).

SRIPATI IN SIDDHANTHA SEKHARA 1039 AD

Successive Differences of Powers

List the squares:

0, 1, 4, 9, 16, 25, 36, 49, ...

Then take their successive differences:

1, 3, 5, 7, 9, 11, 13, ...

Then take their successive differences again:

2, 2, 2, 2, 2, 2, ...

So the 2nd successive differences are constant(!) and equal to 2.

OK, now list the cubes, and in a similar way, keep taking successive differences:

0, 1, 8, 27, 64, 125, 216, 343, 512, ...

1, 7, 19, 37, 61, 91, 127, 169, ...

6, 12, 18, 24, 30, 36, 42, ...

6, 6, 6, 6, 6, 6, ...

Gee, the 3rd successive differences are all constant(!) and equal to 6.

What happens when you take the 4th successive differences of 4th powers? Are they constant? What do they equal? (They're all 24.) And the 5th successive differences of 5th powers?

Aren't derivatives similar to differences? What do you think happens when you take the n-th derivative of xn?

Presentation Suggestions:

Have students do these investigations along with you. If you assign the n-th derivative of xn on a previous homework, then you can make the connection between the two right away.

The Math Behind the Fact:

This pattern may seem very surprising. It can be proved by induction. Taking differences is like a discrete version of taking the derivative, where the space between successive points is 1.

This idea has a very practical application: given a sequence generated by an unknown polynomial function, you use the calculation of successive differences to determine the order of the polynomial! Then use the first N terms of the sequence with the first N terms of the polynomial to solve for the generating function.

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கடவுளும், விஞ்ஞானமும் - கணித மேதைகளின் வியப்பும் !!

கணிதத்தையும் கடவுளையும் இணைத்து சுமார் 941 புத்தகங்கள் சமீபத்தில் வெளி வந்துள்ளன.இவற்றில் விஞ்ஞானிகளின் பெரும்பாலான நூல்கள் அனைத்தும் இயற்கையில் காணும் கணித அமைப்பைப் பார்த்து வியக்கின்றன. பல விஞ்ஞானிகள் கடவுளைக் கணிதத்துடன் இணைத்துப் போற்றி மகிழ்கின்றனர்.

அமெரிக்க விஞ்ஞானியின் கணித நிரூபணம்

அமெரிக்க விஞ்ஞானக் கழகத் தலைவர் க்ரெஸி மாரிஸனை, "இறைவன் இருக்கிறானா? இருக்கிறான் என்றால் அறிவியல் பூர்வமான ஆதாரங்கள் வேண்டும். ஆராய்ந்து கூறுங்கள்" என்று கேட்டபோது விஞ்ஞானிகளுடன் இதை ஆராய்ந்த அவர், "இறைவன் இருக்கிறான். இறைவனை அறிவியல் பூர்வமாக நம்புவதற்கான காரணங்கள் ஏழு" என்று பட்டியலிட்டுக் கூறி உலகையே வியப்பில் ஆழ்த்தினார். அவர் கூறிய ஏழு காரணங்களுள் முதல் காரணமே கணிதத்தை அடிப்படையாகக் கொண்டது என்பது சுவையான செய்தி!

அவர் கூறிய முதல் காரணம் இது தான்:-

கணித முறைப்படி பார்த்தால் இப்பிரபஞ்சம் அமைந்ததும் இயங்குவதும் ஒரு பேரறிவுடைய பரம்பொருளின் அறிவால் என்பதை நன்கு நிரூபிக்கலாம்.

ஒரு பையில் ஒன்று, இரண்டு என்று எண் குறிக்கப்பட்ட பத்துப் பொருட்களைப் போட்டுக் குலுக்குங்கள். ஒன்று என்ற எண் குறிக்கப்பட்ட பொருள் முதலாவதாக வருமாறு எடுக்க முயலுங்கள்! கணித நூல் வல்லுநர், இப்படிப் பொருளை வரிசையாக எடுக்கப் பத்தில் ஒரு வாய்ப்புத்தான் கிட்டும் என்று கூறுகின்றனர். ஒன்று, இரண்டு என்ற எண் குறிக்கப்பட்ட பொருள்களை அடுத்தடுத்து எடுக்கும் வாய்ப்பு நூற்றில் ஒன்றுதான். இது போலவே ஒன்று, இரண்டு, மூன்று என வரிசையாகத் தொடர்ந்து எடுக்கும் வாய்ப்பு ஆயிரத்தில் ஒன்று. இப்படியே வரிசையாக ஒன்றிலிருந்து பத்து வரை குறிக்கப்பட்ட பொருள்களை அவற்றின் எண் வரிசைப்படி அடுத்தடுத்து எடுக்கும் வாய்ப்பு ஆயிரம் கோடியில் ஒன்றுதான்!

இந்த தர்க்க முறையைப் பார்க்கும்போது, இவ்வுலக வாழ்விற்கு வேண்டிய பல்வேறு நிபந்தனைகள் சீராக அமைந்து, நிலைத்திருப்பது தற்செயலான நிகழ்ச்சி என்று கூற முடியுமா? பூமி தனது அச்சைச் சுற்றி மணிக்கு ஆயிரம் மைல் வேகத்தில் சுழல்கிறது. மணிக்கு நூறு மைல் வேகம் குறைவாகச் சுழன்றால் என்ன ஆகும்? நமது பகலும், இரவும் இப்போது இருப்பதைவிடப் பத்து மடங்கு அதிக நீளமுள்ளவையாகும்! நீண்ட பகலில் கதிரவனின் வெப்பத்தில் பயிர்கள் பொசுங்கும்; நீண்ட இரவில் மிஞ்சியிருக்கும் செடி கொடிகளும் விறைத்துப் போய் அழிந்து விடும்!

உயிர்களுக்கெல்லாம் ஆதாரமான கதிரவனின் மேல் பரப்பில் 12000 டிகிரி பாரன்ஹீட் வெப்பநிலை உள்ளது. நமது உடல் வெப்ப நிலை சுமார் 98.4 டிகிரி. நமது பூமி கதிரவனிடமிருந்து நம் உயிருக்குத் தேவையான அளவு வெப்பத்தைப் பெறுகின்ற தூரத்தில் உள்ளது. இந்தச் சூரியன் கொடுக்கும் வெப்பம் இன்னும் ஒரு மடங்கு அதிகரித்தால் நாம் வறுபடுவோம்! அரை மடங்கு குறைந்தால் நாம் குளிரில் விறைத்து உறைந்து போய் விடுவோம்! இப்படியே நிலவுக்கும் நமக்கும் இடையேயுள்ள தூரம், பூமியின் மேல் பரப்பு, கடலின் ஆழம், காற்று மண்டலத்தின் பருமன் ஆகியவை எதைக் காட்டுகின்றன? இவையெல்லாம் தற்செயலான நிகழ்ச்சிகளாக இருக்க முடியாது என்பதையே உறுதிப் படுத்துகின்றன.

க்ரெஸி மாரிஸனின் இதர ஆறு காரணங்கள் இறைவன் இருப்பதை விஞ்ஞான பூர்வமாக மேலும் உறுதிப்படுத்துகின்றன!

விஞ்ஞானத்தின் தாய்

கணிதத்தை விஞ்ஞானத்தின் தாய் என்று அறிஞர்கள் சொல்வர். அமெரிக்கன் மேதமேடிகல் சொஸைடி அதிகாரபூர்வமாக 97 கணித கிளைகளை அறிவித்துள்ளது; இந்தக் கிளைகளுக்கு கிளைகள் நூற்றுக்கணக்கில் உள்ளன! இவற்றில் ஆய்வுக் கட்டுரைகள் ஆயிரக்கணக்கில் வெளிவந்து விட்டன. இவற்றில் வெளிப்படும் சமன்பாடுகளோ எண்ணிலடங்கா. ஆனால் இத்தனை சமன்பாடுகளும் கடவுளை நோக்கி நம்மை அழைத்துச் செல்லாவிடில் அது வீண் என்று கூறிய அற்புதக் கணித மேதை ஒரு தமிழர் என்பதை நாம் மறந்து விட முடியாது!

கடவுளை நினைவுபடுத்தும் சமன்பாடுகள்

ஈரோட்டில் பிறந்து நாமகிரி அம்மனை நாளும் வழிபட்டு அம்மனின் அருளாலேயே தனக்கு கணித ஞானம் மேம்பட்டது என்று கூறிய சீனிவாச ராமானுஜன்தான் அவர்! கடவுளையும் கணிதத்தையும் இணைத்து அவர் கூறிய "கடவுளை நினைவுறுத்தாத ஒரு சமன்பாடு எனக்கு அர்த்தமில்லாத ஒன்றுதான்!" ( "An equation for me has no meaning, unless it represents a thought of God.") என்ற பிரசித்தி பெற்ற வாக்கியம் பொருள் பொதிந்த ஒன்று!

Read more: http://www.livingextra.com/2011/06/blog-post_27.html#ixzz1QdS14i3O