Story of spin

Both Harshini and Shruthi were quite excited about GR’s lectures last Sunday -- which, I was told, revolved mainly around “spin”. I told them I will post an historical account of spin and here it is.

This goes back to 1920’s during which Quantum physics was being intensely explored. Specifying a complete list of quantum numbers associated with electrons in atoms had occupied much of interest. A decisive contribution was made by Wolfgang Pauli (he was 25 year old at that time). Like many theoreticians of the day, Pauli was concerned with understanding the spectral lines emitted by atoms. Bohr’s original model worked only for the relatively simple spectral patterns emitted by hydrogen; but heavier, more complex elements were much harder to understand. For example, Cesium, Sr, and Ba (alkaline earth materials) produce spectral lines that are seen to split into two – they were called doublets. In December 1924, Pauli suggested that a complete set of quantum numbers of an orbiting electron would include its energy, angular momentum (l), and its orientation in space (m); in addition, to explain the alkali doublets, he suggested that there had to be a fourth quantum number, which he referred to – rather unhelpfully – as “Zweideutigkeit” (two-valuedness). During the summer of 1925, Samuel Goudsmit, a young Dutch physicist, was trying to explain Pauli’s ideas to another young countryman, George Uhlenbeck. During such afternoon talks, it occurred to Uhlenbeck that Pauli’s “Zweideutigkeit” was not really another new quantum number, but simply another property of an electron. He suggested that perhaps an electron spins about its axis like a toy top – but unlike a toy top, the spin of the electron would be quantized, and so, it could only “spin” at certain specific values. Looking at Pauli’s formulae, Uhlenbeck and Goudsmit realized that if electrons had a second angular momentum, this would perfectly account for “two-valuedness”. of the alkaline earth metals. The amount of “spin” turned out to be ½ hbar. Both men took their idea to Paul Ehrenfest, Uhlenbeck’s teacher, who made them write up a short paper on spin and then told them to take it to H. Lorentz, the grand old man of Dutch physics.
In 1925, Lorentz was 72, retired, but he still taught a class at Lieden every Monday morning at 11.00 AM. After one such class, Uhlenbeck and Goudsmit showed Lorentz their paper, which was only a few paragraphs long. Lorentz said that it was interesting and he would think about it further. Thinking, for Lorentz, was apparently an active occupation. Two weeks later, Lorentz gave a stalk of papers with long calculations to Uhlenbeck: Lorentz had calculated the speed of the spinning electron with ½ hbar angular momentum to be 10 times that of light!! Uhlenbeck and Goudsmit were most unhappy – they went back to Ehrenfest and said “You better not publish that paper, because Lorentz has shown that it is not correct”. But Ehrenfest had already submitted the paper and the paper was expected to be published within a few days! Later, Bohr, dismissed Lorentz’s objections saying that the faster-than-the-speed-of-light problem disappears when the full quantum theory is applied to a structureless point electron – apparently, Lorentz’s calculations were valid for a classical extended particle with spin ½ hbar. As it turned out, Bohr was correct. The eigenvalues, eigenkets of angular momentum and the matrix representation of angular momentum operators was first obtained in a 1926 paper by Max Born, W Heisenberg and P. Jordan (Zeitschrift fur physic, 35 (1926) 557). It was shown, basing the analysis wholly upon the commutation properties of the angular momentum operators, that there are two types of angular momentum, one with eigenvalues that are only integral multiples of hbar and the other, which can assume half odd integral multiples of hbar values also.

Wise man

Book reviews aren't usually quite as long, and are rarely so touching. This is the tribute of one great man to another, honest admiration, with no hint of envy or self-service. It is full of insight. This is an article published by Freeman Dyson about Feynman in the New York Review of Books

"Great scientists come in two varieties, which Isaiah Berlin, quoting the seventh-century-BC poet Archilochus, called foxes and hedgehogs. Foxes know many tricks, hedgehogs only one. Foxes are interested in everything, and move easily from one problem to another. Hedgehogs are interested only in a few problems which they consider fundamental, and stick with the same problems for years or decades. Most of the great discoveries are made by hedgehogs, most of the little discoveries by foxes. Science needs both hedgehogs and foxes for its healthy growth, hedgehogs to dig deep into the nature of things, foxes to explore the complicated details of our marvelous universe. Albert Einstein was a hedgehog; Richard Feynman was a fox.

Many readers of The New York Review of Books are more likely to have encountered Feynman as a story-teller, for example in his book Surely You’re Joking, Mr. Feynman! than as a scientist. Not many are likely to have read his great textbook The Feynman Lectures on Physics, which was a best seller among physicists but was not intended for the general public. Now we have a collection of his letters, selected and edited by his daughter, Michelle. The letters do not tell us much about his science. For readers who are not scientists, it is important to understand that foxes may be as creative as hedgehogs. Feynman happened to be young at a time when there were great opportunities for foxes. The hedgehogs, Einstein and his followers at the beginning of the twentieth century, had dug deep and found new foundations for physics. When Feynman came onto the scene in the middle of the century, the foundations were firm and the universe was wide open for foxes to explore.

One of the few letters in the collection that discusses Feynman’s science was written to his former student Koichi Mano. It describes the fox’s way of working:

'I have worked on innumerable problems that you would call humble, but which I enjoyed and felt very good about because I sometimes could partially succeed…. The development of shock waves in explosions. The design of a neutron counter…. General theory of how to fold paper to make a certain kind of child’s toy (called flexagons). The energy levels in the light nuclei. The theory of turbulence (I have spent several years on it without success). Plus all the “grander” problems of quantum theory.

No problem is too small or too trivial if we can really do something about it.'"

A Good Weekend

Last few of my weekends have been spent having to attend environmental science classes all through the day. They have come up with a scheme where we are made to complete these compulsory foundation courses by attending them on weekends. This weekend we didn't have any for class for some reason.

I therefore ended up going to BU yesterday and spent some time with friends, playing tt, some problem solving etc. It was a nice break from the usual weekends. I had planned to go to brainstars around 5 in the evening, and then get home at 7 to watch a nice football match. Harshini and Shruthi climbed the bus to go home and then I got on my bike and on my way out I bumped into Karthik. And then all my plans later that evening went down the drain. But it was worth it I must say.

We went to the canteen back in BU and had a good conversation. We spoke about many things ranging from the "scientific outlook" to the nature of mathematics and then inevitably discussed physics. It was nice talking to him about some of the subtle things in physics. We spoke about things like inertia and many other things that we simply take for granted.
The funniest part was when we would talk about seemingly different things and then realize that we were arguing about the same thing. We agreed on quite a lot of things and the best part was when I heard him say that he is " not the only Bakra" after all.
Hope to have more of such reality checks every once in a while.

And now its a nice sunday morning and I made a random choice to read something just until I'm done drinking coffee.

" The tremendous transformation of the scientific view of Nature could only be compared with the change of outlook brought about by Copernicus. It originated, like all really important intellectual revolutions, in places where to all appearance deep tranquillity reigned. The most far-reaching revolution of the twentieth century was born in idyllic circumstances. It came from a picturesque park in Copenhagen, from a quite street in Berne, from the seashore of the island of Heligoland, from the meadows and tree-shaded river at Cambridge, from the Hofgarten in Munich, from the quiet neighbourhood of the Pantheon in Paris, from the peaceful Zurichberg and from the ancient fortifications, along which tall trees now rustle, of the town of Gottingen"
-Brighter than a thousand Suns.

Looking forward to GR's class today, hope its a good one.
Have a nice day!

Ramblings

I was just on the phone talking to Harshini, and she was telling me about the discussion they had in BU today. I asked her, " What do you think about quantum mechanics?", and she said " What do you mean?". I told her that somehow deep down inside I felt Quantum Mechanics was wrong. I really don't know much about Quantum Mechanics to actually say that but then it was just a kind of an intuitive feeling. Anyway, she replied saying, " You Einsteinians!".
Well, I may be a little biased but then I have my reasons. When I first started out reading popular articles as a kid who was fascinated by science, it was quantum mechanics and string theory that seemed more appealing ( the things about teleportation, extra dimensions etc). To be fair, relativity had its own attractions. I started working on special relativity first I guess because of its mathematical simplicity. It's just amazing being able to show that time slows when things move just using high school algebra. But, I have NO idea about how or what drove me to even consider working something as sophisticated as the general theory of relativity. Not to say that I know much about it, I really don't. Considering that I was very weak ( still am ) at mathematics and school physics, it surprises me to no end that I actually had the guts to work out a few things in gtr. I think it was its beauty that blinded me and I just couldn't see any of my weaknesses or any other problems in front of it. I don't know what Einstein's Field equations mean, but still when I look at them I get goosebumps all over me.

How could a man, sitting in a patent office, having never even looked through a binocular predict that the planet mercury's orbit will undergo a shift and give precise calculations showing it? How could he predict that GRAVITY could bend the path of LIGHT? That Gravity could slow down TIME? And the technology was far from even being able to confirm these predictions. And all he knew was that Newton's laws worked pretty well and that the speed of light is same for all inertial observers. To be fair, he also knew that Galileo showed that objects of different masses fall with the same acceleration. Who would have thought that a few facts like these could lead to a theory that predicted black holes, to be only confirmed a few years ago.  Unparalleled elegance, I would say.

I find it really hard to find that I don't have many around me to discuss this with wonderful thing with. Sometimes it seems that happiness is only real when shared. I was the happiest while talking about it during the lecture sessions in BU. Well, I don't think that's going to happen for a while. Entrance exams coming up. Prof. Vishweshwara, Joseph Samuel, Lee Smolin, Carlo Rovelli, Abhay Ashtekar are a few people I know who have done it all in relativity. What I would give to just exchange a few words with them. I was crazy about Chandrashekar sir the moment I heard he had seen Lee Smolin.

Lee Smolin and Carlo rovelli are currently working on Quantum Gravity. Rovelli formulated a new approach known as Relational Quantum Mechanics. Abhay Ashtekar formulated general relativity by creating self-dual variables so that you could have a hamiltonian (a.k.a Ashtekar Variables). And Lee smolin, well, you will be hearing a lot about him from me, and a I will be quoting a lot from his books. And here is the first,
from his book, The Trouble With Physics,

" This is the story of a quest to understand nature at its deepest level. Its protagonists are the scientists who are labouring to extend our knowledge of the basic laws of physics. The period of time I will address - roughly since 1975 - is the span of my own professional career as a theoretical physicist. It may also be the strangest and most frustrating period in the history of physics since Kepler and Galileo began the practise of our craft four hundred years ago.
The story I will tell could be read by some as a tragedy. To put it bluntly - and to give away the punch line - we have failed. We inherited a science, physics, that had been progressing so fast for long that it was often taken as the model for how other kinds of science should be done. For more than two centuries, until the present period, our understanding of the laws of nature expanded rapidly. But today, despite our best efforts, what we know for certain about these laws is no more than what we knew back in the 1970's.
How unusual is it for three decades to pass without major progress in fundamental physics? Even if we look back more than two hundred years, to a time when science was the concern mostly of wealthy amateurs, it is unprecedented. Since at least the late eighteenth century, significant progress has been made on crucial questions every quarter century".   - Lee Smolin (The Trouble With Physics)

Well, in a less elaborate way, all this can be said by quoting G Ramchandra's one sentence "Yen agillapa." We laughed it off then but I think its time for us to do something. Is it the Education system? Is it the research Institutes? Do we even Care?
How long is it just going to be about clearing entrance exams and worrying about how many papers are being submitted per month?
Ofcourse, there are a lot of us who are very optimistic about the system and that it is changing. But I guess hope is a luxury we cannot afford right now. It seems the time has come to use our strengths and collective differences in a harmonious way. To what end? I don't know. But it's the journey that matters, not the destination.

Bongos

Here is a really nice video of Feynman playing the bongos. For some reason I really enjoy watching this:)
Click here to watch

Wonderful:) ... as a follow up to ur post i would like to show an extract from Mlodinow's, "Feynman's Rainbow"...

" When I got to him, Feynman was gazing at a rainbow. He had an intense look on his face, as if he were concentrating. As if he had never seen one before. Or maybe as if it might be his last.
I approached him cautiously.
"Professor Feynman. Hi," I said.
"Look, a rainbow," he said without looking at me.
I joined him in staring at the rainbow. It appeared pretty impressive, if you stopped to look at it. It wasn't something I normally did-in those days.
"I wonder what the ancients thought of rainbows", I mused. There were many myths based on the stars, but I thought rainbows must have seemed equally mysterious.
"All I know," Feynman said, " is that according to one legend angels put gold at its ends and only a nude man can reach it.
"Do you know who first explained the true origin of the rainbows?" I asked.
"It was Descartes," he said. After a moment he looked me in the eye.
" And what do you think was the salient feature of the rainbows that inspired descartes' mathematical analysis?" he asked.
" Well, the rainbow is actually a section of a cone that appears as an arc of the colors of the spectrum when drops of water are illuminated by sunlight behind the observer."
"And?"
"I suppose his inspiration was the realization that the problem could be analysed by considering a single drop, and the geometry of the situation."
"You're overlooking a key feature of the phenomenon," he said.
" Okay, I give up. What would you say inspired his theory?"
"I would say his inspiration was that he thought rainbows were beautiful."
I looked at him sheepishly. He looked at me. " How's your work coming?" he asked.
I shrugged. " It's not really coming."
"Let me ask you something. Think back to when you were a kid. For you, that isn't going too far back. When you were a kid, did you love science? Was it your passion?"
I nodded. " As long as I can remember. "
"Me, too", he said. " Remember, it's supposed to be fun." And he walked on. "


Along with science being fun, I think there is a certain appreciation for beauty inherent in human beings. We cannot define beauty. What we find beautiful is usually something natural. ( Personally, I find Einstein's relativity beautiful, even if eventually it turned out to be wrong).
Curiosity may drive us to do science. The fact that it is fun is another motivation. Whatever it is, these things feed on us. Curiosity transforms itself into a strong driving force that pushes us through the greatest extents. We don't know where our search will lead us, but the journey sure is fun. In the end, I think it is the journey that matters, not the destination. And that I think is one of the most beautiful things about life and physics.

What remains to be answered about present day science is whether this is what still drives every physicist? Or have the motivations changed a bit?

The pursuit of science: its motivations

We have been talking about how Feynman influenced our learning of science and towards our scientific imagination – with the help of a mathematical abstract view, Julius Sumner Miller’s exciting science demonstrations … I felt I should continue this stream of thoughts by adding some observations on the pursuit of science. (These are my compilations from the wonderful book “Truth and Beauty” by Professor S. Chandrashekhar, Penguin Books Ltd (1991) – don’t miss to read this book if you happen to come across). I am aware that I am not offering here any concrete thinking on the “pursuit of science” -- but surely it helps to put things in their places, and it invites deeper thinking on this issue.

“The pursuit of science: its motivations” is a difficult topic because of the variety and the range of the motives of the individual scientists; they are as varied as the tastes, the temperaments, and the attitudes of the scientists themselves. Besides, their motivations are subject to substantial changes during the life-times of the scientists. Indeed it is difficult to discern a common denominator! We may consider some examples to get some better ideas on this. Let us think of Albert Michelson: His main preoccupation throughout his life was to measure the velocity of light with increasing precision. His interest came about almost by accident, when the commander of the United states Naval Academy asked him – he was then an instructor at the Academy – to prepare some lecture demonstrations of the velocity of light. That was in 1878 and it had led to Michelson’s first determination of the velocity of light in 1880. On 7th May 1931, i.e., fifty years later and two days before he died he dictated the opening sentences of a paper, posthumously published, which gave the results of his last measurement! Michelson’s efforts resulted in an improvement in our knowledge of the velocity of light from one part in 3,000 to 1 part in 30,000 – i.e., by a factor of 10. But by 1973, the accuracy had been improved to 1 part in 100000000000 -- a measurement that made obsolete, beforehand, all earlier measurements! Were Michelson’s efforts over fifty years in vain? Leaving that question aside, one must record that, during his long career, Michelson made great discoveries derived from his delight in “light waves and their uses”. Thus, his development of interferometry, leading to the first direct determination of the diameter of a star, is breathtaking. And who does not know the Michelson-Morley experiment, which -- through Einstein’s formulation of the special and the general theory of relativity -- changes irrevocably our formulation of the nature of space and time? It is a curious fact that Michelson himself was never happy with the outcome of his experiment!! Indeed, it is recorded that when Einstein visited Michelson in April 1931, Mrs. Michelson felt it necessary to warn Einstein in a whisper when he arrived: “Please don’t get him started on the subject of the ether”!
When Michelson was asked towards the end of his life, why he had devoted such a large fraction of the time to the measurement of the velocity of light, he is said to have replied “It was so much of fun”! There is no denying that “fun” does play a role in the pursuit of science. What are the other factors? Difficult to say! I leave it open to your own jurisdiction now.

Prof Julius Sumner Miller

It's been my pleasure of late that I'm getting opened to a very necessary scientific outlook, i.e, in the form of "seeing" physics in action everywhere. In this context I ran into several of the blogs of scientists{ students and Profs included} who have poured out their cynicism about the sorry state of science in India and teaching in particular, read and saw more about Feynman. Nevertheless, what I noticed in all, is their enthusiasm to do something "off the track" like us. Something not for the sake of it but for the love towards it.

To this end, I would like to draw your attention to this one of a kind Professor by name Prof Julius Sumner Miller. I don't know how many of you already know him but i ran into him only this day and thought that you ought to know him for his infectious love towards Physics. He has featured in cadbury Dairy Milk chocolate ads {which by the way, I -- guess that even you--would not have seen it}. I accidentally happen to watch his demonstration of Bernoulli's principle and went Eureka!! {not the Archimedes way!!!} So, I would request you all to watch his demonstration of Bernoulli's principle part 1 and 2 -- and a lot more--for the fun of it-- and to know how things work. You can find one of his cadbury ad here.

Scientific imagination

I have a free afternoon session today – no lab work to take care of and no students came with some bothering questions! So, I decided to post what Harshini’s Fine Man says about scientific imagination – which had fired my imagination for sure!

“Let us try to imagine electric and magnetic fields; you may say, “Professor, All this business of electric and magnetic fields is pretty abstract! What is actually happening? Why can’t you explain it? Please give us an approximate description of the electromagnetic waves, even though it may be slightly inaccurate, so that I too can “see” them!” I am sorry – I can’t do that for you. I don’t know how. I have no picture of this electromagnetic field that is in any sense accurate. The only sensible question is, “what is the most appropriate way to look at their effects?” Some people prefer to represent them as field lines and feel that writing vector E and vector B is too abstract! The field lines, however, are only a crude way of describing a field. Field lines cannot efficiently describe superposition of electromagnetic waves. From the mathematical stand point, on the other hand, superposition is easy – we simply add two vectors to get another vector. The field lines have some advantage in giving a vivid picture, but they also have some disadvantages. So, the best way is to use the abstract field idea. That it is abstract is UNFORTUNATE but NECESSARY!

Our science makes terrific demands on the imagination. It appears that scientific imagination requires mathematical view and then its experimental verification. Now, what is a mathematical view?
For example, from a mathematical view, there IS an electric field vector and magnetic field vector at every point in space. This concept is abstract – true, but in some sense the fields are real, because after we are all finished fiddling around with mathematical equations, we can still make the instruments detect electromagnetic signals.

The whole question of imagination is often misunderstood by people in other disciplines. They try to test our imagination in the following way. If someone asks me: “Here is a picture of some people in a situation. What do you imagine will happen next?” I would say “I can’t imagine (because I don’t have enough facts”. So, people think that I have a weak imagination. They overlook the fact that whatever we are allowed to imagine in science must be consistent with EVERYTHING else we know.

The electric and magnetic fields we talk about are not just some happy thoughts which we are free to make as we wish, but ideas which must be consistent with all the laws of Physics we know. We can’t allow ourselves to seriously imagine things, which are obviously in contradiction to the known laws of nature. One has to have the imagination to think of something that has never been seen before, never been heard before. But creating something new, has to be consistent with everything, which has been seen before, is extremely difficult and requires scientific imagination.”

So, tell me if this caught your imagination (poetic – if not scientific) too!

Duality and Reality

After Harshini's post, this is probably going to seem very pale. I've never written anything of this nature before. Please do comment, honest criticism will be well accepted and I will be more than happy to fill in the gaps. I am supposed to be giving a talk tomorrow on "Symmetry in nature and mathematics"in college and that has made me think again about something that I started thinking when I first began working on the General theory of relativity. This post is a result of those rambling thoughts.
It was in the book by Simon Singh, " Fermat's last theorem", where I first read Pythagoras' famous statement - " Everything is a number". This is indeed true. Theoretical physicists and experimental physicists are both trying to get meaningful numbers out of nature. Numbers are one of the most important things that define our reality. Theoretical Physicists have a way of getting to these numbers. Its called duality. Duals are paths to real numbers.
The first time I encountered duality was when I started out on general relativity and had to study tensor calculus [or according to G. Ramachandra, I was just raising and lowering indices ;-) ] There are vectors that are a part of dual vector spaces, the contravariant and covariant vectors. For those who are more into QM , its the Bras and the Kets. They do not make any physical sense individually. You need both to describe a physical quantity. They are the yin and yang of everything. For a long time I wondered why this was true. Why does a description of reality require two different things? Why not three or four? Can I not know the "one" thing knowing which I can know everything else? While working on Quantum Information, I was introduced to a new concept known as distinguishability.

Imagine a universe where you could not distinguish between any two things or events. Imagine not being able to differentiate between the correct answer and the wrong answer. The universe simply could not exist without any distinguishability. And now, while preparing for tomorrow's thought, it seems to me that duality is a consequence of symmetry. Can there be a perfectly asymmetric object?
I have come to realize so far that as long as a mathematical structure defines reality, there is an inherent duality. I may be wrong, but I haven't seen anything that doesn't satisfy my argument. For example, if you want to get rid of the notion of distance between two points, you need to get rid of the metric, which means ur getting rid of the dual vectors and the inner product between them. And the space thus becomes a simple topological space in which there in only a notion of connectedness but no distance.

I am yet to find a reason for this duality in nature to exist. Is it actually there? Or is the duality in our heads? Are our brains wired to think that way? At this point I silence a horrible thought occurring to my head about the struggle towards Quantum Gravity. I have in this post spoken about duality from a theoretical point of view. I will let you answer the question about the duality in experimental physics :) .

More on this and self-duality yet to come.


P.S: It may have no relevance with what I have said, but for some reason I am inclined to end by quoting Niels Bohr - " The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth."

A Fine Man Indeed

A funny thing happened in Sharath Sir's class this week. I think I'm one of two people sitting in that class who found it funny. It went like this- He was showing us these slides he'd made as an introduction to Atomic Physics. He chose to quote Feynman, who, in his Lectures said, famously, 'everything is made of atoms'. Sharath Sir repeated that, and then said, quite seriously, "I hope you all know who Feynman is. If you don't...get out of my class and don't come back..". I think the threat was quite real. But nevertheless, funny. You can't talk physics without bumping into Feynman.

My first encounter was a happy accident. I was in a book store, sometime in 8th standard when I came across 'Surely, you're joking Mr. Feynman'. And then my dad came around and told me I had to read it. This, from a doctor who hasn't "studied" physics since he was in Class 12. And yes, after reading it, I almost decided to hang around book stores, grab random people, and ask them to read it too! But I wasn't that insane(yet!).

What is it about Richard P. Feynman that brings out such reactions in us? To use a cliche, like him or hate him(Oh yes, there are those too), you just cannot ignore him. I thought about this for a long time. It is finally becoming clear to me. Feynman, to me, represented what I wasn't, but wished I could be. A free thinker, a free learner, and a free liver(as in life, not the organ, just clarifying).

Much has been said about his 'zest for life', his 'unique style of teaching physics', etc etc that I don't think I'll be able to say anything that hasn't been said before. Feynman for me, personally, embodies the complete man(not Raymond, whoever that is). Aristotle(see footnote) said "The whole is greater than the sum of the parts", and Feynman, you see, is greater than the infinitely many tales about him. He was one of the most outstanding physicists of the 20th century. Leonard Mlodinow says, in Feynman's Rainbow, "..there indeed was no problem in the world of physics into which he couldn't provide the greatest insight..". But he was equally well-known later, for his fun-loving nature, his various eccentricities and the like, having completely smashed away the notion of a scientist being a boring creature that can be found in labs, working on experiments with fuming liquids, or buried neck-deep in huge books, and the only thing more boring than the work was the person doing it. Feynman made science relevant. He made it fun! I actually have much more to say on this matter but will take mercy on the hapless readers(if any), and edge nearer towards an ending. But not just yet.

Feynman probably wasn't born that way, but everything that went on inside his head, and outside, made him who he turned out to be. He didn't have any grand plans for himself, and he certainly never had any grand plans for humanity. He touched millions of lives without even knowing it, by simply having the courage to be himself. Everything else that followed was a consequence of that. And that is the biggest lesson I learned from him. I try everyday to be a little more like Feynman. I try everyday to be a little more like me.

Harshini




P.S. This is the aforementioned footnote. I googled the quote to see who had said it first and found that it was Aristotle. Alongside that, I saw this, and found it interesting: Kurt Koffka: "It has been said: The whole is more than the sum of its parts. It is more correct to say that the whole is something else than the sum of its parts, because summing up is a meaningless procedure, whereas the whole-part relationship is meaningful." (Kurt Koffka, 1935: New York: Harcourt-Brace. p 176). Incidentally, Aristotle meant the same thing too. Whoever interpreted it otherwise, goofed up.

Intro

I'm sure the name of the blog will tell you lots about it. The people who will be invited to co-author the blog are like minded friends. Please feel free to share any insights, experiences, views and ideas with regard to learning in general, physics in particular. Since we share common concerns about our education system, this can be considered a platform for individual expression and action oriented discussion.


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