# Cantor

A very interesting article on the mathematician Georg Cantor posted for VERITAS by Soumyaroop Roy. See also VERITAS: History of Set Theory, 8 May 2002)

Given the old maxim about an infinite number of monkeys and typewriters, one can assume that said simian digits will type up the following line from Hamlet an infinite number of times.

“I could confine myself to a nutshell and declare myself king of infinity”.

This quote could almost be an epithet for the mathematician Georg Cantor, one of the fathers of modern mathematics. Born in 1845, Cantor obtained his doctorate from Berlin University at the precocious age of 22. His subsequent appointment to the University of Halle in 1867 led him to the evolution of Set Theory and his involvement with the until-then taboo subject of infinity.

Within Set Theory he defined infinity as the size of the never-ending list of counting numbers (1, 2, 3, 4….). Within this he proved that sub-sets of numbers that should be intuitively smaller (such as even numbers, cubes, primes etc) had as many members as the counting numbers and as such were of the same infinite size. By pairing off counting and even numbers together, we see that the number of counting and even numbers must be the same:

1 -> 2

2 -> 4

3 -> 6

4 -> 8

5 -> 10

6 -> 12

He then went on to demonstrate the impossibility of pairing off all the real numbers (those including irrational decimals like Pi) with the counting numbers, concluding that one was larger than the other. The result, confusing though it may seem, is that some infinities are bigger than others!

Cantor’s work represented a threat to the entrenched complacency of the old school mathematicians. Up until then infinity, to quote mathematician Carl Friedrich Gauss, had been treated as a “way of speaking and not as a mathematical value”. This stonewalling inevitably brought Cantor into conflict with his less enlightened peers. His most vocal critic was Leopold Kronecker (ironically one of Cantor’s past professor) who undertook a personal crusade to discredit his lapsed protg. Using his position at the University of Berlin he dedicated himself to rubbishing Cantor’s ideas and ruining him personally.

His coup de grace was blocking Cantor’s lifelong ambition of gaining an appointment at the University of Berlin.

In 1884, consigned to a backwater University and under constant attack from Kronecker, Cantor had his first nervous breakdown. He spent the rest of his life in and out of mental institutions, his serious work at an end.

Cantor’s later years may have been defined by tragedy but his contribution to modern mathematics is colossal. His one-time collaborator David Hilbert once said of him in tribute “No one will drive us from the paradise that Cantor has created.”

# In Defence of Astrology

Before I start this VERITAS lets me say this: I HAVE NO BELIEF IN ASTROLOGY AS AN INSTRUMENT FOR PREDICTING FUTURE. But I am facinated by it because of its complexity. My aim in this VERITAS is to defend vedic astrology from the modern day cheap imitations and from scientists who try to find fault with it without even understanding it.

First let me destroy a modern day fashion : sun signs. Sun Sign “astrology” isnt even astrology! It is nonsense! In vedic astrology your exact time of birth is needed to make a chart in which the signs in which each planet( sun, moon, mercury, venus, mars, jupiter, saturn, rahu and ketu) is placed is calculated. Also the sign that was rising from the east is calculated. This sign becomes the first house( or lagana).

Sun sign “astrology” is only based on the position of the sun. So it is based on just one factor out of the several that exist. If you want to play the game play the big game of vedic astrology.

Now let me destroy a class of modern scientists. These scientists say that since these planets are so far away so thay cannot have any effect on us. Did vedic astrology say that planets have an effect on us???? NO! Vedic astrology says this: Your past life decides your karma in this life. It is not that planets affect you when you are born. The time and date of your birth is fixed according to the deeds of your past life. The planets just signify that time. So in vedic astrology the position of planets only signifies that time of your birth. The planets dont send rays to affect you.  SO scientists should not just argue against things without gaining knowledge about things.

Vedic Astrology is a very complicated and vast subject. It is based on Maharishi Parashar’s teachings. The book that collects these teachings’s is called “Brihat Parashar Hora Shastra”. It is available in a 2 volume set. It is a no nonsense book.

Vedic Astrology is fully integrated with what the vedas teach us. So if you are a devout hindu who believes in rebirth, karma and that the ultimate aim of a soul is moksha then you cannot stay away from vedic astrology. The real aim of vedic astrology is to give you an indication of your past life and how that will affect your present life. The real aim is to be a spiritual guide to attain a higher self.

SO vedic astrology is supposed to tell you what you should do to rise to a higher spiritual plane. So the modern day astrologers who just tell you how much money you  will have are ignoring the real aim of this subject. Also astrology only tells you about your fate. But Krishna said ” Do your work and dont care about your rewards”. That is what vedic astrology  says. Fate is just an indication based on your previous lives. But the free will in this life in entirely in your hands. This the modern day astrologers dont tell you. If you go to an astrologer he will recomment a gem for a badly placed planet. But he could also tell you that you can work hard in such and such area to ward off its effects. Your work is the ultimate thing. But since the modern astrologer does not make money in your work so he recommends a gem stone.

vedic astrology is so integrated with the vedas that it is not possible for anyone who does not have a deep knowledge of hinduism to get a detailed knowledge of astrology. I have read the Brihat Parashar’s english translation but the real work is in sanskrit. So you should know sanskrit as well to make sense of that book.

Now lets look at the time it takes for a horoscope interpretation.

There are > 10 charts made for each individual. Modern astrologers will just look at one chart( rashi chart). The interpretation of a chart is a very complicated business and can take several days for each individual.

Astrologers who tell you everything in 15 – 20 minutes are frauds.

For example a person will go to an astrologer and ask ” do I have raj yoga?”. The astrologer will look for a few minutes and say yes or no.

But do you know how many yogas are there in astrology? Over 300 ( see B.V Raman’s “300 Important Combinations”). To just check which of these are present in you chart is a huge task.

vedic Astrology is a very mathematical subject. There are hundreds of calculations to do for each chart. Our ancient scholars were mathematically very sound. Which planet is in which sign is just the basic thing. The exact degree of each planet, its exact strength, the exact aspect it gets from other planets etc etc all have to be calculated. Modern day computers have simplified this a little.

So what I am sayin here is that though I do not believe in vedic astrology I still have a great appreciation for this marvellous work. Our ancient scholars have put in a huge amount of effort to create this system. If you decide to learn about this subject you should read the real texts and not go to modern day astrologers. You will then share my awe of this subject.

kanwar

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Go, wondrous creature! mount where Science guides:

Go, measure earth, weigh air, and state the tides:

Instruct the planets in what orbs to run,

Correct old time and regulate the Sun;

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# Invisible and Mysterious

IN 1932 Wolfgang Pauli was working on the theory of radioactivity. Scientists had noticed that the energies of particles coming  out of a radioactive decay  did not add up to the energy before the dacay. So there seemed to be a non conservation of energy during radioactive decay. Pauli suggested that there could be another particle which could be taking this energy away. This particle was later named neutrino. According to Pauli’s theory this particle should have no charge, it should have no mass but it should have a lot of energy. But how could a massless , chargeless particle be detected?

Pauli wrote: ” I have done a terrible thing. I have postulated a particle that cannot be detected!”

There are neutrinos everywhere. According to a rough calculation about a 100 trillion neutrinos pass through your body every second. They dont cause any harm because they are electrically neutral. In fact their ability to pass through matter without getting absorbed is their most useful property. That means that a neutrino from a star millions of light years away will reach you on earth if it starts in this direction. It will not get absorbed. Even if there is a light year of solid lead on the way still it will pass right through. Just stop and think about that!

Light does not have this property and is absorbed on the way. So detecting neutrinos would be very useful for astronomy.

But how do we detect neutrinos? They do not interact with charged particles in the usual way. But every once in a while a neutrino will hit an electron in an atom which will be bumped to a lower orbit producing a flash of light. So detecting this flash of light would show the presence of a neutrino. So we have an indirect way to detect a neutrino. But this bumping of neutrino is a very rare phenomenon. The approach that Scientists take is to have a huge number of atoms and then the chances of this happening increase.

But seeing a flash of light is a very common thing and can happen due to a veriety of reasons. So isolating that flash of light which is caused by a neutrino from the rest is a near impossible thing.

The solution is to have a really dark room in which there is no useless light. Scientists usually do neutrino detection underground.

For example there is a neutron detector in the Antarctic about 2 miles below the earth. But this is not enough. There are other particles which can easily penentrate 2 miles. So the detector faces the earth. In other words the detector is 2 miles below the ground and facing the earth ( the 12,800 Kms of mass ). It is an “upside down telescope”. The aim is to detect neutrinoes which can pass through the whole of earth to be detected on the other side.

Recent experiments with these “telescopes” have shown that neutrinos change their form while travelling from the hot insides of the sun to earth. There are three types of neutrinoes.

And they change from one type to another on their 150 million km journey from Sun to the earth. But according to the “Standard theory” of particle Physics the only particles which are capable of changing their form are particles with mass! So if recent studies are true then neutrinos have a very small mass.

90 % of the mass of the universe is unaccounted for. That means that 90 % of the mass that theories of Big Bang predict should be there is just not there. People dont know where it is. This is called dark matter. And this is one of the biggest mysteries in Physics.

But if neutrinoes have mass then the zillions of these tiny particles would add up to a huge mass and that could explain where a lot of this dark matter is.

A sher for the neutrino:

“khoob pardah hai ki chilman se lage baithe hain

saaf chupte bhi nahin, saamne aate bhi nahin”

( chilman =  curtain )

Kanwar

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Go, wondrous creature! mount where Science guides:

Go, measure earth, weigh air, and state the tides:

Instruct the planets in what orbs to run,

Correct old time and regulate the Sun;

|======================================================|