Monthly Archives: February 2001

The Twin Paradox

Before we start today’s VERITAS there is a thought I wish to share with you . I read this somewhere( I dont remember where) : When we read philosophy , religion , poetry , literature etc we usually read the author’s orignal works . For example if you want to read Socrates’ philosophy you would have to read SOcrates or Plato(his pupil ) . If you wish to read Kant’s philosophy or Vivekananda’s thoughts you would have to read their orignal/translated works . Now on the other hand when you read Science you rarely read the orignal works … None of us have read Newton ‘s Principia Mathematica to understand his laws . None of us have read Darwin ‘s book to understand his evolution theory . The reason is that when Science comes to us it comes as the KNowledge of the present times .

The Orignal works are applied , changed and modified and then the theory is taught to us . Science is Knowledge . Philosoply(or similar subjects ) are more of viewpoints of people which cannot be modified and rarely improved .

      Now for Todays VERITAS : Einstein’s special theory of relativity changed our understanding of space and time and made some exciting predictions of how things behave when they move close to the speed of light . To take an example : time moves slower in a body moving close to the speed of light . The faster the body moves the slower time flows in its reference frame . People were so excited about these implications of the ralativity theory that they thought of various paradoxes . Now in Physics there is no paradox . There might be two different ways of looking at a problem and these different ways may yield different results . But if these two viewpoints yield different results then one of them has to be wrong . Physics has no room for paradoxes .

      The most famous “paradox”  was the twin paradox . Imagine two twins who decide to part ways . One of them ( say A ) sits in a rocket and blasts off into space . The other twin( say B ) stays on earth ( being more interested in seeking earthly pleasures ) . The rocket carrying A reaches fantastic speeds ( close to speed of light ) .

50 earth years later A decides to visit earth . The age of the twin B has advanced by 50 years . But to B’s surprise A is only 7 years older .

Wow ! The reason is simple …. A moved close to the speed of light so time was slower in his reference frame and so he aged slower .

      The “paradox” is this . If we take B’s point of view then A was moving at close to the speed of light so he should be younger . ANd the explanation we have given above is valid .But if you take A’s viewpoint then B was moving close to the speed of light ( the reference frames are relative . There is no absolute motion ) . So B says that A should be younger and A says that B should be younger . Who is correct ? who is younger ? This looks like a perfectly symmetric argument and it looks like a paradox .

      How do we resolve the paradox ? The solution is this : One of the viewpoints is wrong. What we have to understand is that Einstein’s special theory of relativity is valid only for bodies moving at constant velocities . Accelerated frames of reference are not the correct ones . So if B and A keep moving forever(and dont ever meet ) then both the viewpoints are correct . But the symmetry is broken when B decides to meet A . At that time he has to come back to earth . He has to change his direction of motion ( from away from earth to towards earth ) .

And this is accelaration . So his frame of reference is not valid .

The twin B has to be younger than A . The acceleration , the comparison breaks the symmetry of the 2 arguments and makes the earth frame of reference valid . There is no paradox.   

Mathematical Quotes

Hi Friends ,

 

      Today I found a very interesting site which has quotations on mathematics or by mathematicians . Here are some of them for you to enjoy :

Anonymous

If thou art able, O stranger, to find out all these things and gather them together in your mind, giving all the relations, thou shalt depart crowned with glory and knowing that thou hast been adjudged perfect in this species of wisdom.

 

 Bell, Eric Temple (1883-1960)

Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions.

 

Byron

When Newton saw an apple fall, he found …

A mode of proving that the earth turnd round In a most natural whirl, called gravitation; And thus is the sole mortal who could grapple Since Adam, with a fall or with an apple.

 

Carlyle, Thomas (1795 – 1881)

It is a mathematical fact that the casting of this pebble from my hand alters the centre of gravity of the universe.

 

Churchman, C. W.

The measure of our intellectual capacity is the capacity to feel less and less satisfied with our answers to better and better problems.

 

Caballero, James

I advise my students to listen carefully the moment they decide to take no more mathematics courses. They might be able to hear the sound of closing doors.

 

Eddington, Sir Arthur (1882-1944)

Proof is the idol before whom the pure mathematician tortures himself.

 

Edwards, Jonathon

When I am violently beset with temptations, or cannot rid myself of evil thoughts, [I resolve] to do some Arithmetic, or Geometry, or some other study, which necessarily engages all my thoughts, and unavoidably keeps them from wandering.

 

Whitehead, Alfred North (1861 – 1947)

Familiar things happen, and mankind does not bother about them. It requires a very unusual mind to undertake the analysis of the obvious.

 

Augarten, Stan

Computers are composed of nothing more than logic gates stretched out to the horizon in a vast numerical irrigation system.

 

Pascal, Blaise (1623-1662)

The sole cause of man’s unhappiness is that he does not know how to stay quietly in his room.

A Strange Animal

 

    Yesterday while watching Discovery Channel I learnt about a very strange creature . DO you know that there is only one mammal that is poisonous and it is the   Platypus .

      And this is not the only thing that is strange about it . The Platypus is found only in eastern Australia . They lives on the edges of rivers and lakes . Platypus are excellent swimmers and can stay underwater for 3 to 5 minutes . Platypus must continuously swim downwards with its forefeet to remain submerged . They only way it can rest underwater  is by resting under submerged rocks . The Platypus closes its eyes and ears once underwater . Then how does it catch its prey ( snails , shrimps etc ) ? It does so using its very sensitive duck like snout and by electric navigation . It does not eat its food underwater . It stores it in the folds in its cheeks and eats it once it comes back to the surface .

      A platypus is about 60 centimetres in length and weighs about 2 kgs . The male platypus has two sharp , hollow , horny spurs(projections) on its hind legs . These are connected to poison glands . They have enough poison to kill a man . Platypus “stings” are extremely painful . Females dont have poison glands or spurs so the main function of spurs in the male platypus is during fights over female platypus .

      Another funny thing about the platypus is that it is a mammal but it lays eggs ! The only other mammal that lays eggs is the Echidna ( a small animal found in Australia ) . Such mammals are called monoterms .

      The platypus females dont have any teats . They ooze the milk from the fur and the platypus young lick off it .

      Platypus have a beak which resembles duck beaks . So it almost looks like a cross between the birds and the mammals .

 The platypus’s red blood cells carry larger amounts of hemoglobin than any other mammal . This allows the platypus to go without air for longer periods. The heart rate of a platypus can drop from 140 – 230 beats a minute to almost 0 beats per minute .

 

            I found a nice little poem on written by Ogden Nash (who also happens to be my favourite poet ) .

PS : anomalous means having an anomaly ( defect ) , platitude means dullness .

 

                  The Platypus     by Ogden Nash

                  =============

  I like the duck billed platypus

  Because it is anomalous

  I like the way it raises it family

  Partly birdly , partly mammaly

  I like its independent attitude

  Let no one call it duck billed platitude .

 

 

Enjoy,

Kanwar