Ask an average child junior high school or the hig school about their favorite subject..7 out of 10 will say Math or Science and remaining 3 will come up with subjects wherein the teachers are lenient and they can score “better” marks compared to other subjects. Ask the same set of students to name their 2 favorite subjects.. it will either have Math ( and something else) or Science ( and something else).. then again you will find students who neither prefer science & math. Remember we are talking about high school… I guess they have not yet been introduced to commerce and economics..
Very few times ..( about 5 of 50) I have come across a student who says that Math and Science are his/her favorite subjects.. even so as to say.. Math and Science are never spoken in the same sentence. It so seems that a certain amount of fear-factor somehow gets into a student’s intellect.. that.. if he is able to grasp the concepts of science.. then he starts thinking that..”Oh My God.. How am I going to fare in my Math test.. the theorems just don’t make sense to me”… Vice versa… If the child is able to grasp Pythagoras and trigonometry.. then the thought would be “What’s with all those colored liquids and inclines and pulleys. yuck with those insects…. why cant they speak in a common man’s language”
I humbly ( read proudly) say that my favorite subjects were Math and Science. The reason is my teachers helped me see the “Science in Math” and the “Math underlying Science” in a very convincing and non-confusing manner.
THE SCIENCE OF MATHEMATICS
Science works on the basis of certain principle.. so is Math. Pythagoras theorem did not spring out of air. Pythagoras saw the problem before him and approached it scientifically ( all those derivations will run to 100s of pages).. to give us the 15-step QED for the theorem. Similarly Sin2θ + Cos2θ=Tan2θ did not come as a divine revelation, Experiments were performed….results were aggregated …. analyzed…. anomalies were spotted…and after several hours of human efforts…. such one liners were delivered to us…on a platter
How much we used to curse them for finding these formulas… They make us remember all those formulas.. If only they had not arrived at those results.. we would not be forced into such an agony of memmorising these things…. Those were the yester-years.. isn’t it friends… Now we are lot wiser…aren’t we ? ? ?
Do you know that…….Sri.Ramanujanam ( The Math wiz the world has ever seen).. during his early years of study.. finished his 3hr examination in 30 min.. and he hadn’t even filled up 3/4 of a single sheet of paper. All that was seen in his answer paper was Q(number) -(numb) solution to the problem ;Q(number) -(numb) solution to the problem ;Q(number) -(numb) solution to the problem ;
When the examiner enquired as to why he has not shown his derivations…Sri.Ramanujam said ” Why should i derive the answers on paper.. when they are already there in my mind.. its absolute waste of time.. Had I not derived them in my head.. how do you think i wrote those answers in my paper”… but as the examination system would have it.. he was awarded just 2 marks each for “the answers”…. what do say… System challenged then…System challenges now… moving on..
THE MATHEMATICS IN SCIENCE
A solution to a problem is derived in Math.. (So is science.) and not guessed..( even to say guessing is math involving probability-permutation and combination)…run run.. but u cant hide. Every principle ( gravity – Newton’s law – Doppler effect) are the results of endless series of experiments
The result of every scientific experiment are nothing nut numbers. It takes a statistical bent of mind to read the numbers and translate them as probable scientific outcomes of the experiment in question and finally wait for the experiment to proceed to check if the numbers tell the right story. Numbers helps these scientists to anticipate the result even before the result start taking shape in the laboratory. Finally a 1000 page lab note takes shape of 100 page drossier with charts and graphs for the experts in the field to determine the nature of the experiment and acknowledge the principle that has been derived.
If you come across a confused soul who cannot handle science and math in the same platform.., just make him understand that both indeed compliment each other..( and are not some kind of monsters comming to get him) then watch the difference in enthusiasm of the child towards these two dreaded subjects
So.. Remember you high-school years… how bad were things then… what was your worst exam-nightmare ?
Deepa: I won’t say nightmare, but used to get tensed when I worked with stat’ only when I forget the formula:))
hmm.. stats it is for you.. bu then…did u have stats in your highschool ? ? ?
Damn.. Not in high school Deepa. I went back to my college days. Of science.. physics is my favorite:))
I always hated chemistry may be becoz of how it was presented and other stuff.
Now u know my nightmare.
oh yeah…keep it comming.. lets see some variety
jDeepa,
A well researched write up to establish the nexus between science and math! Both are nightmares for me though:) It’s true that both are inseperable. Calculations without scientific methods and Scientific derivations without tangible numerical facts are always insufficient. The only difference is, Math is a subset of science. Math is both art and science.
That was a good piece from Ramanuja’s life.
“what was your worst exam-nightmare ?”
Exams have never been nightmare for me, as I had the courage to give blank papers even during board exams. Good old days:)
Shiva…
***Math is a subset of science. ****
Could not agree more.. precisely the point to bear in mind
***as I had the courage to give blank papers even during board exams****
Oh ! My My… daring i belive… but somewhere in the back of my mind there is a nagging thought..”Is it REALLY possible ? ? ?”
May be I should post my CBSE marksheet. Infact, I was awarded full marks in all the practicals, which caused real embarrassment for the school to provide it to the board that I really did practicals well:)
Nothing is impossible Deepa!
Deepa actually maths and science ARE different. I am speaking as a person who has been communicating science for over 20 years, I have taught both but i hate maths. They are two ways to talk about Nature like Hinduism and Islam r two In my final year M.Sc., I wrote my entire maths paper in prose. I mean no equations or expressions. I talked abt the physical significance of everything that was asked, physical solutions of even things like laplace and fourier transforms. fortunately my HOD was enlightened enough to understand my thoughts and appreciate them. I got the highest marks in the university for maths despite not writing a single expression. How many people know the physical meaning of Pythagoras theorem? (incidentally the Pythagoras Theorem was given to the world by india atleast 1000 years before Pythagoras – in the form of Sulba and Apasthambha sutras) What does square on the hypotenuse mean? In this connection, there is a joke. Some people were attending a conference on 13 dimensional spaces. During a recess a physicist told a mathematitian ” My head spins! How do you imagine 13 dimesional space?” The mathematitian said “Simple, I just imagine an n dimensional space and set n=13” In fact biology has proved that different parts of the brain are engaged in mathematical and scientific skills. Einstein never did like maths. He was a brilliant physicist. Ramanujan hardly knew any science. If you have seen Raja Ravi Varma’s paintings or for that matter Michealangelo’s paitings and then seen Picasso’s paintings then you would appreciate the difference between Science and maths. One is real, the other abstract. So it is natural that students who really like science never like maths.
Hi Ram..
Nice to see you back..
..I must admit.. your comment ( in toto) is news to me
incidentally the Pythagoras Theorem was given to the world by india atleast 1000 years before Pythagoras – in the form of Sulba and Apasthambha sutras
never know this till now… must find out more,, will google next week or so..
…I could not have imagined in the wildest dreams …taht final year M.Sc., I wrote my entire maths paper in prose. I mean no equations or expressions. I talked abt the physical significance of everything that was asked
You have shown me entirely new dimetions to Raja RAvivarma’s paintings..Guess i need to look more closely form now on..
..The reason is..i am a die-hard supporter of both science and Math.. and howmuch ever i think.. i cant seem to spot the diffrences..
…wow.. Thats an intresting and informative comment
BTW.. just wanted to know…isnt fourier transforms used in cyptography
yes fourier transforms are used in cryptography. Actually the main principle behind fourier transforms is that any wave, however complicated it may be, say a note from the nadaswaram, a baby’s laugh, waves on the seashore can all be converted into a lot of sine waves of different frequencies superimposed on each other. Sine waves, you possibly know are the simplest of waves. It is like saying that be it Aishwarya Rai or Amitabh Bachhan or Indira Gandhi, they all are basically chemical molecules put together in different proportions in different ways. Put that way it sounds simplistic, but in case of fourier transforms it is true. Say Sreeragam is a beautiful ragam, but if u can tell a computer the different sine waves that go into its swarasthanams, and tell the computers the rules for sreeragams aarohanam and avarohanam. It can compose a song on its own. Now as to what fourier transforms do in cryptography. Any coded/encrypted message that is transmitted has to be in the form of waves. catch these waves do a fourier analysis and u end up with a set of sine waves. This is done using what u call FFT or fast fourier transforms. You do this again and again and u see a pattern emerging. You feed all this into a computer because a man/woman cannot remember these patterns. After some time the computer begins to understand what is what and the code is broken. Like say ur hubby gets very upset and stops talikng to u one day when his office canteen is shut. Another day he attends a function which lasts from 4 am to 4 pm and gets lunch after that. He gets upset and stops talking. Say u guys go to Moscow and u dont get vegetarian food and he gets upset after some time and stops talking. Put together u can guess that ur hubby gets annoyed when he is hungry and stops talking to u. All this is not as simple as I have told but it is sufficient for the purpose of understanding what fourier transforms do in cryptography.
You shd get a lot of material on the web abt the Sulba and Apasthambha sutras. So I am not writing abt them. But some websites give information that is wrong. I dont know your Gotram but if Govind performs sandhyavandanam/abhivadanam ask him whether he says “Apasthambhasutradhyayee” meaning a student of Apastambha sutra. The detailed abhivadanam of an apasthambhasutradhyayee states the pythagoras theorem. mOre later.
Ram..
it was indeed a crash course on ourier transforms .. and explained without any equations ( as you have perhaps done u r Msc paper).. I must admit.. i understood this much better than reading about this in wikipedia or other sites
///apasthambhasutradhyayee states the pythagoras theorem////
darn…I must make time to find out about this…
So much to learn.. so little time