Mathematics Then and Now

When Werner Heisenberg worried that human beings might never truly 
understand atoms, Bohr was a bit more optimistic. He replied, “I think we  
may yet be able to do so, but in the process we may have to learn what the 
word understanding really means.”

Today, we use computers to help us 
reason beyond the limitations of our own intuition. In fact, experiments with computers are leading
mathematicians to discoveries and insights never dreamed of before
the ubiquity of these devices. Computers and computer graphics allow
mathematicians to discover results long before they can prove them formally,
thus opening entirely new fields of mathematics. 

Even simple computer tools, such as spreadsheets, give modern mathematicians power
that Heisenberg, Einstein, and Newton would have lusted after. As just
one example, in the late 1990s, computer programs designed by David
Bailey and Helaman Ferguson helped to produce new formulas that
related pi to log 5 and two other constants. As Erica Klarreich reports in
the April 24, 2004, edition of Science News, once the computer had
produced the formula, proving that it was correct was extremely easy.
Often, simply knowing the answer is the largest hurdle to overcome when
formulating a proof.

While at school I was reasonably good at mathematics.
Somehow, I never liked numerals though.
I remember asking the history teacher, what does it matter whether Buddha was born in a particular year or two years that way or this.
What matters is what he said or did.

When I joined biology stream, our beloved maths teacher came to that class and asked me to shift to Math class. He said all my cousins, his earlier students, were very good at mathematics and I should follow them.
I never went.

I did not even continue in biology. I shifted to Language. Then back to biology.
After a good number of years and a doctorate I left the stream once again.
I drifted and drifted.
Where am I now?
Nowhere?
Now I want to read and write about Mathematics.
May be to regain the lost fun!!

Shakespeare and Science

By the Favor of the Heavens

Stratford-upon-Avon, Warwickshire, England
November 19, 1572
6:05 p.m.

“Father!”
A middle-aged man turns to greet his son, one of a dozen schoolboys making their way out of the King’s New School and onto Chapel Lane. It’s getting cold; the man pulls his cloak to his chest. He’s thankful to be wearing his new fur cap rather than the felt one he’d had to make do with the previous winter. The boy, as full of energy as ever, doesn’t seem to mind the cold.

“You don’t need to walk me home, Father. I’m almost nine years old.” The boy’s breath is visible in the crisp winter air.

“Eight and a half is not ‘almost nine.’ But you’re right, William, you are a young man now,” the father replies. “It happens that I had some business at the church, and I was just on my way back. Let us make haste now, your mother and the children are waiting. I hope you didn’t give Master Hunt any trouble today?”

“Master Hunt had to leave for Alveston, on account of his mother being sick.”

The father is taken aback; usually he is the first to hear any news of that kind. “Is that so?”
“But another teacher took his place,” the boy continues. “Master Jenkins. We still had to do all of that Latin grammar. But we also talked about the Bible, and the children in the upper form read a poem by Horace, and got to act out a scene from a Roman play.”

“Horace was my favorite. Can you remember a few lines?”

“Let me think.… There is nothing that the hands of the Claudii will not accomplish—”
“Not in English. Horace isn’t meant to be read in English. In Latin, William, please.”
“Oh, Father, school is out. And I don’t like Latin.”

“Whether you like it is hardly the point. You must learn it to be a gentleman—and, for the next few years, to escape the birch. Now continue. In Latin.”

“Um … nil Claudiae non perficient manus, quas et … um … benignus numine Iuppiter—”
“Benigno numine,” his father interrupted, correcting the boy’s grammar. “It means ‘by the favor of the heavens.’ That’s enough for now. You did very well, William.”

The pair turn from Chapel Street onto High Street. It is now growing dark; the long winter’s night stretches ahead. The full moon will provide some relief, but it is only just creeping above the eastern horizon. It has been a cloudy day—a little snow fell earlier—but as the wind blows, the clouds finally begin to part. In the southeast shines mighty Jupiter—the same Jupiter the Romans had put their faith in as they marched into battle; the same Jupiter that Horace had rhapsodized over. As they reach Henley Street, William stops and gazes upward.

“What are you looking at, son?”

“It’s something Master Jenkins told us about. He said there was a new star in the sky. He said he had been in Oxford yesterday, and everyone was talking about it.”

The father lets out a hearty laugh. “Don’t be silly, William. I heard some talk of it also at the guild, but the reverend said it couldn’t be, and of course he is right. It could be a comet perhaps.”

“But Father, Master Jenkins said it was a star. In the constellation of—the queen with the funny shape. The queen shaped like an ‘M.’”

“Cassiopeia,” the father replies. In spite of himself, he turns northward to see what may be there. His son turns to follow his gaze. “The Lord doesn’t just create new stars, the way Mr. Smith hammers out horseshoes. God created the world thousands of years ago, and he doesn’t need to make improvements.”

A pause.

“I think that’s it!” William points to a bright star, eastward from the pole, just visible now that the clouds have passed. It stands just to the left of the unmistakable “M” of Cassiopeia.
The father has to admit there is something there. Whatever it is, it’s even brighter than Jupiter. Brighter even than Venus had been that morning, as far as he could recall.
“Father—what does it mean?”

“I don’t know, son. And I don’t know that it really is what it appears to be. It could just as well be the devil’s work as the Lord’s. And now we really must carry on, or supper will be cold. Not to mention my fingers.”

“I’m coming, Father.” But the boy lingers for one last look as his father heads off down the street. “It’s beautiful,” he says, and then runs to catch up. “I don’t think it’s a comet, Father, because comets have tails.”

“More nonsense from Master Jenkins? Well, cats have tails too, but Mrs. Olden’s cat doesn’t have one, and it’s still a cat.”

The boy pauses, seemingly deep in thought. “Why doesn’t Mrs. Olden’s cat have a tail?”

“They say Mr. Olden’s dog bit it off,” his father replies.

“Well, maybe a dog bit off the new star’s tail,” the boy offers.

“That’s quite an imagination you have, son. And how many dogs are there in the sky, William?”

Another pause—and then a wide smile. “Two, Father! You showed them to me last winter—the big dog and the little dog!”

The father laughs. “You do have quite a wit, don’t you, son? Now say their names in Latin, please.”

“Oh, Father! Canis … Canis Major and Canis Minor.”

“Very good, son. By Jove, I swear you’ll make a fine lawyer one day!

People think as scientifically as their world around.
Children then are more science oriented than the elders.
The above is a dialogue between the bard as child and his father.
Is it not interesting?
Don't squirm when a child asks an uncomfortable question.
Try to think like the child.
Not like your father.
That takes you further!!!

Will my language become extinct?

Many people speaking many languages and belonging to many cultures are asking this question. No language or culture would really disappear. They may at best undergo a big change whereby become hard to identify. Like the Ranga who turned Ringa in Mauritius

The language that remains will sound some thing different for those who know the present form of it. Same is the case with any vernacular world over.

It is the tongue, style, traditions and practices that make a culture. They continue for generations and give an identity to a group. People very proudly claim they belong to a particular culture or a language group. They take pleasure in speaking the language wherever they are. All this depends on the memory and intellect of the people.

We remember the festivals had their own distinct identity in the past. Now, particularly in cities all of them are celebrated in the same fashion and perhaps with the same food. Those who have not witnessed the diversity of the past can even feel the number of festivals redundant. They do not remember and distinguish one from the other.
They refuse to equate the new ethos with that they knew.

We can not even complain against them. After all they are also true. There are many standards for the diversity in a culture. One of them is the religion. Language is perhaps the most important.

We can even say the change in the language is a pointer to the change in the culture.

Some languages are spreading like the plague of the yore. There are many who do not have an idea about this word plague. In the name of science knowledge, business, politics, and the universalisation or is it globalisation, English is spreading dramatically. The other languages are receding equally fast. There are around 6000 languages spoken around the globe at present. It is estimated that half of them would not last till the next decade. This fact is corroborated by the officials of the trust looking after the languages threatened with extinction. Half of the languages are spoken by less than ten thousand people each. Such of them will disappear very easily. A quarter of the present languages are spoken by only a thousand each. They are as good as gone.

We must be aware that none of the Indian languages fall under these categories. People speaking Maori dialect in New Zealand have opened special schools to spread their language.

There are many, complaining about the disappearance or the changes in Telugu or other Indian languages. As long as you also share such a feeling your mother tongue will never disappear.

Self and not Self

What is change?

The true portait of a man is a fusion of what he thinks he is, what others think he is, what he really is and what he tries to be. says, Dore schary. It is tue. we are all a clmination of a jigsaw puzzle pieced together sometimes with gaps. Why sometimes? Most of the times!!

We grow old and change. This is something we never realise. We think that we are seeing the same face everyday in the morning! We never realise that the face is changing bit by bit! We have grown old even comapred to yesterday!You maight have become better in appearance and in other respects. You might have grown some characters unwanted. You may be pleasing on one day and irritating on the next day.

You are doing all these things without the awareness. If you are aware of your mental attitude, the life will be much better. You cannot do much about the physical appearance. May be avoid eating too much and be careful about the health. Even then may be a paunch will come about.

Be aware that we are changing. We think we are not. People tell us we are changing. We try not to change. But what is the reality?

Make your choices wisely. Tread your steps carefully. Be what you want to be and tell the world the same. Don't do something and say something else!!