Nothing

This is a first part of the post. I have decided that for the comfort of the reader, it better be divided into several parts.

Something which has been never completely understood by man, which is probably never meant to be understood, an elusive search to understand nothing leads us to a maze of endless questions and gets one caught in the ever expanding and entangled web of understanding the meaning of nothing. Nothing in its various guises has never failed to capture the imagination of man. Philosophers have struggled to grasp it, while mystics dreamed they could imagine it, scientists strove to create it, astronomers searched in vain to locate it, logicians could never fathom it, and mathematicians succeeded. Writers and jesters were more than happy to create much ado about nothing. From the zeros of the mathematician to the vacuum of the scientists, to the void of the philosophers, to the erudite wanderings of Shakespeare, over centuries and with passage of time, nothing has seen kings come and go, civilizations vanquished, resurrected just to be vanquished again, to be reduced to nothing. Man may have evolved from a primordial state to a highly developed one, but he still struggles to answer the question that surpasses all human intelligence and has been bothering people from all walks of life, albeit intermittently, but nonetheless it is an inseparable part of life. God's greatest creation has clearly failed to understand this void. It holds a special place amongst the elite, the educated academicians, a subject of never ending speculation and discussion for them; with each of them well aware that we are miles away from understanding what this innocuous looking word really means. The point about nothing is that we do not need to use it in the operations of daily life. No one goes out to buy nothing. It is in a way the most civilized of all the cardinals, and its use is only forced on us by the needs of cultivated modes of thought. And I being Homo sapien have also failed to understand it, which shall be clearly reflected in my writings. Here, I will try to bring out a few facets of Nothing and Zero as seen by us.

Mathematics

Simply put, in mathematics nothing can be equated to zero. Probably and by far the most important number in our world of mathematics, its origin has been attributed to Indians.In fact, G B Halstead once remarked

“The importance of the creation of the zero mark can never be exaggerated. This giving to airy nothing, not merely a local habitation and a name, a picture, a symbol, but helpful power, is the characteristic of the Hindu race from whence it sprang. It is like coining the Nirvana into dynamos. No single mathematical creation has been more potent for the general on-go of intelligence and power."

The oldest known text to use zero is the Jain text from India entitled the Lokavibhaaga, dated 458 AD. It was first introduced to the world centuries later by Al-Khwarizmi, a Persian mathematician, astronomer and geographer. The very name Algebra has been derived from his famous book Al-Jabr wa-al-Muqabilah. 'Algorithm' or 'algorizm' is named after him. Zero is such a profound and powerful idea which appears to be so simple that we appear to ignore its true merit. Zero has single handedly shown mathematics the way to connect to reality and be a part of the real world. Be it geometry, where understanding the concept of point as having dimension as zero, or the concept of almost impossible in probability, or something as basic as the Mobius function in number theory and combinatorics, which applies to all numbers except zero to being the First Perrin number to simply being anything that is not seen and cannot be quantified, Zero has lent mathematics more credibility and acceptance amongst the people and has established its hold over human thought. But what does zero mean to a mathematician? It probably means his success to prove the Riemann Hypothesis, his ability to find mathematical tools to solve the Navier Stokes Equation, his understanding of the empty set or the infinite applications of zero in his works- all of which amounts to nothing. Our poor understanding of the connection between mathematics, reality and nothing, probably compelled one of the greatest minds of the 20th century, Dr Albert Einstein, to say "what we are sure about in reality is not reflected in mathematics and what we're sure about in mathematics is not reflected in reality". In fact, in hieroglyphics, zero means the "courageous one".

Zeno's Paradoxes

I will not get into explaining the paradoxes. Just read them and enjoy.

Achilles and the tortoise

"You can never catch up."

“	In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead	”
—Aristotle

In the paradox of Achilles and the Tortoise, we imagine the Greek hero Achilles in a footrace with the plodding reptile. Because he is such a fast runner, Achilles graciously allows the tortoise a head start of a hundred feet. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run a hundred feet, bringing him to the tortoise's starting point; during this time, the tortoise has "run" a (much shorter) distance, say one foot. It will then take Achilles some further period of time to run that distance, in which said period the tortoise will advance farther; and then another period of time to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, Zeno says, swift Achilles can never overtake the tortoise. Thus, while common sense and common experience would hold that one runner can catch another, according to the above argument, he cannot; this is the paradox.

The Dichotomy paradox

"You cannot even start."

“	That which is in locomotion must arrive at the half-way stage before it arrives at the goal.	”
—Aristotle

Suppose Homer wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on.

This description requires one to complete an infinite number of tasks, which Zeno maintains is an impossibility.

This sequence also presents a second problem in that it contains no first distance to run, for any possible first distance could be divided in half, and hence would not be first after all. Hence, the trip cannot even begin. The paradoxical conclusion then would be that travel over any finite distance can neither be completed nor begun, and so all motion must be an illusion, which in simpler words is nothing

Probably with calculus coming into play, the paradoxes seem to be resolved but they only address the geometry of the situation, and not its dynamics. It has been argued that the core of Zeno's paradoxes is the idea that one cannot finish the act of sequentially going through an infinite sequence, and while calculus shows that the sum of an infinite number of terms can be finite, calculus does not explain how one is able to finish going through an infinite number of points, if one has to go through these points one by one. Zeno's paradox points out that in order for Achilles to catch up with the Tortoise, Achilles must first perform an infinite number of acts, which seems to be impossible in and of itself, independent of how much time such an act would require.

It raises an even more intriguing question- Are time and space infinitely divisible?

Enough of Bheja-Fry for you guys, though gyaan freaks like this blogger, can also look into Paradox of place and paradox of the grain millet.

Vaccum

Historically, there has been much dispute over whether such a thing as a vacuum can exist. Ancient Greek philosophers did not like to admit the existence of a vacuum, asking themselves "how can 'nothing' be something? "Plato found the idea of a vacuum inconceivable. He believed that all physical things were instantiations of an abstract Platonic ideal, and he could not conceive of an "ideal" form of a vacuum. Similarly, Aristotle considered the creation of a vacuum impossible — nothing could not be something. Later Greek philosophers thought that a vacuum could exist outside the cosmos, but not within it. Christians believed that the idea of vacuum is immoral or even heretical; the absence of anything implied the absence of God, and since God was the ultimate power, it would be against god to create nothing. A common notion in earlier times was that Nature abhorred a vacuum and a true vacuum doesn’t exist. Even the finest thinkers of the century like Plato, were convinced that a vacuum cannot be created. But the inquisitive young minds of those times thought otherwise and the famous Magdeberg’s Spheres, Michelson Morely and Torricelli experiments (Kindly strain your memory and recall your school days) proved beyond a doubt that there exsists a vacuum and ether is fictional. Even Newton was later convinced that for his theory of interplanetary motions to hold true, a vacuum needs to exist. Yet even today, our concepts and fundamentals of the VAccum are still very shaky.

This rounds off the first part. The second part should be coming soon once the battle with UNIX and PL/SQL is over.

This is a first part of the post. I have decided that for the comfort of the reader, it better be divided into several parts.