Monthly Archives: November 2002

Women of Mathematics : Sophie Germain

 

Marie Curie worked hard for 10 years. She sacrificed her life for Science. In the end she was rewarded with a Nobel Prize.

  Have we not heard such tales of Scientists sacrificing pleasures of life and working real hard to contribute to Science. Such tales are written by historians and parents who want to “inspire” thier kids. These are all false stories. A Scientist loves science. They appreciate the beauty of the laws of nature. They want to spend their lives surrounded by this beauty. Science makes them happy.They do not sacrifice the pleasures of life. Science is their pleasure of life. So the true story would be ” Marie Curie enjoyed herself for 10 years finding why radioactivity happens. Everyday
was a new adventure. In the end she also got a lil medal called the Nobel Prize.”

       Today in VERITAS we will remember the story of Sophie Germain. You might think that it is a story of struggle and sacrifice. Try and read it from the correct angle: it is a story of love.

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       Sophie Germain was born in 1776 in Paris.  When she was 13, Sophie read the story of Archimedes. She was surprised to read that Archimedes was so engrossed in doing mathematics that he ignored the soldier who threatened to kill him(and killed him). She thought that this subject must be really interesting. She started studying mathematics on her own and she loved it.

       Now in those days women were not supposed to study Science and Mathematics. Her parents discouraged her. They even went to the extent of taking away her clothes at night and depriving her of heat and light so that she would only sleep and not get up to do mathematics. She
could not study in the daytime because they would not let her. But she loved the subject and eventually her parents realized the futility of keeping her away from it. They let he do whatever she wanted.

       Women were not allowed to study in universities so she studied on her own. She borrowed lecture notes from Lagrange’s students to study. She assumed the male name of M. LeBlanc and even submitted a paper to Lagrange. Lagrange was impressed by the work and wanted to meet
his student. He was surprized when he realized that his student was actually a female and that she had been studying on her own. He advised
her on her work and encouraged her to do more.

       Sophie became interested in number thery and started corresponding with Gauss. She did not reveal her real name and corresponded as LeBlanc. They discussed mathematics for three years(1804 to 1807 ) before Sophie revealed her true identity. Gauss was thrilled to find that his
“pen-friend” was a very talented woman. She even saved Gauss’ life. In 1806 when Napoleon invaded Germany she contacted a french commander, who was a friend of her family and told him that Gauss should not be harmed. She remembered Arichmedes and did not want Gauss to have the same fate.

Sophie proved that if x,y and z are integers then if x^5+y^5=z^5 then x,y or z must be divisible by 5. Sophie’s proof was a major step in proving Fermat’s last theorem.

In 1808 the physicist Chladini conducted experiments on vibrating plates which exibited some strange figures called  Chaldini figures. The
Institut de France set a prize for anyone who could mathematically explain these figures.

       Sophie Germain started thinking about this problem. In 1811 her’s was the only entry trying to explain the figures. But her analysis was wrong( since she was not formally educated and did not have access to modern journals she had holes in her knowledge). She did more research. In 1813 she came up with a better explanation of the figures. This work was rejected too. In 1815 however her third work on the subject got her the prize.

       Most Scientists and Mathematicians however chose to ignore her and her work.  Sophie was not discouraged by this and kept working on mathematics till her death in 1831. Her death certificate did not list her as a Scientist or a Mathematician, but a property holder.

      Sophie did not have any formal education.  Despite that she made great contributions to number theory, theory of elasticity, theory of vibrations etc.

       Most of us lay too much stress on degrees acquired in colleges and universities. Are these degrees really important? Isnt having a “fire within” more important. Isnt love the supreme conquerer?

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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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Veritas by Kanwarpreet Grewal is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.

Mysteries of the Brain : Part – 5

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The last VERITAS was on the mysteries of the brain and I would have liked to wait for sometime before sending something on the same subject. But what I saw on TV last week was so interesting that I could not wait.

People say that blind people develop other senses to help them overcome their handicap. Is this really true? Are our brains changable? or are their functions fixed at birth ?
A very interesting experiment was conducted by Dr Alvaro Leone to see if brain functions can change to suite the individual. A patient was blindfolded for a period of 100 hours and made to learn braille for several hours a day. So the patient could not see anything for a period of hundred hours and had to just learn to “read” braille.As you all know Braille script is made of dotted patterns and a blind person can feel the shape of the patterns and thus read the “text”.
Now we must understand that the brain area for touch (and therefore responsible for “reading” braille) and visual recognition are different. The visual cortex is responsible for interpreting what we see. The brain area for touch is the parietal lobe. The visual cortex is located near the back of the brain. The touch area is in the middle part of the brain.
       In the first 2-3 days of “blindness” the patient’s ability to “read” braille was very limited. She learned very slowly. But in the last 1-2 days her progress became really fast. The scientists used electrodes to see which parts of the brain were active at this time. They were surprised to find that the visual cortex was equally active alongwith the parietal lobe when the patient was reading braille.
It is as if the visual cortex realized that the person can no longer see and that it has nothing to do. The visual cortex changed its role and started helping the area responsible for the sense of touch.
So in blind people the visual cortex tries to help cope with the handicap by helping the other parts of the brain responsible for the other senses. That is how blind people develop other senses more than people. A handicap in one sense would develop the other senses more. The physical handicap does not waste the brain part responsible for it. The brain part changes its role to further develop the other senses.

        The wonderful thing is that it just took about 5 days for the brain to change! Think about this….

  At the end of the 100 hours the blindfold was removed and the patient could see again. After a few hours the patient’s visual cortex returned to its real role: visual recognition. The patient’s ability to read braille again decreased. The visual cortex no longer helped the sense of touch.
Isnt this wonderful! We see that our brain is a very efficient organ. It tries to adapt to help the individual as much as it can. Most of us realize that excercising the body is important. But excercising the mind is important too. If you just use your mind on one activity then you should know that the areas responsible for other activities would adapt and change. You should restart doing some maths again or soon you would be
mathematically challenged! Enjoy your brains… there is a whole kingdom in there:
                     My mind to me a kingdom is,
                     Such present joys therein I find,
                     That it excels all other bliss
                     That earth affords or grows by kind:
                     Though much I want which most would have,
                     Yet still my mind forbids to crave.
( The TV program that inspired this VERITAS was “Changing your mind” which appeared as a part of the National Geographic series Scifiles.
The poem that appears at the end of this VERITAS is a part of the poem “My Mind to Me a Kingdom Is” by Sir Edward Dyer)

Kanwar

|======================================================|
  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;                             
|======================================================|