The poetry of equations: The 'Alice approach'

“And what is the use of a book," thought Alice, "without pictures or conversation?”
― Lewis Carroll, Alice's Adventures in Wonderland

In No Small Matter, a book on the 'science on the nanoscale', famous chemist George Whitesides and photographer Felice Frankel achieve to convey the poetry and beauty of science with elegance and erudition. Their unique manner of presentation - saying much, by saying less - is more effective than most other books on science written for the lay audience. There is no surfeit of words, no clamour of explanations, and no riot of reasons.

Felice Frankel’s photos (or visualizations) show  bits - 1s and 0s - using wine glasses with red Shiraz, a prism on Venetian blinds, and a 'faked' quantum apple (to make the point that quantum mechanics confounds our ‘normal’ intuitions) and quantum dots, that are simultaneously beautiful art and beautiful science. George Whitesides’s prose is the 'second voice' in this lovely duet of images and words and strikes a wonderful balance between explaining and making us ponder.  He asks to reconsider what we take for granted - the magic of listening to music, for instance, is the ‘magic of transformation’. Using the LP track of Eleanor Rigby, Whitesides makes us rethink this amazing feat of alchemy. The the voices of the Beatles were recorded (copied) in the variations of grooves in vinyl, transmuted to electrical impulses by the needle, transduced by the vibrating speaker diaphragm into vibrations that are carried in the air, through our outer ear, and then via tiny bones and fluid in our inner ears back into sound, back into the emotion of Eleanor Rigby and all the lonely people. With the well-crafted images and sparse sentences the book has the economy and power of poetry. Saying much, by saying little. 

 Curiosity is an itch, that understanding scratches

From the dawn of time, humans have had that itch and that need to scratch won’t ever go away. That’s what we humans do. Whitesides, for all his accomplishments, shows no trace of arrogance in what we now know; showing, that with greater understanding comes greater humility. For there is still lots we cannot explain. It’s not just arcane quantum or cosmological phenomena. We have the DNA code, but we don’t know how proteins ‘do what they do’ from messages in the code. As he writes, its like constructing the lives of people by looking at a telephone book. We don't understand how water molecules work in the cell.  Even the the everyday, plain and mundane confounds us. We don't understand cracks - how a crack actually ends. We don't understand bubble formation. We don’t understand colliding water jets.

More: Fishbones from water jets

Maybe someday we will get to a more complete explanation, or it may elude us, but the strange beauty of the water jets and the rest will continue to enchant us forever.

What really got me was the piece titled 'Duality': 

We're burdened by a curious conditioning that blinds us to one of the greatest - perhaps the greatest - of art forms. We live for poetry; we live in terror of equations.

We see a poem, and we try it on for size: we read a line or two; we roll it around in our mind; we see how it fits and tastes and sounds. We may not like it, and let it drop, but we enjoy the encounter and look forward to the next. We see an equation, and it is as if we’d glimpsed a tarantula in the baby's crib. We panic.
An equation can be thing of such beauty and subtlety that only a poem can equal it....
It's an idea worth trying on for size. Poetry describes humanity with a human voice; equations describe a  reality beyond the reach of words. 

He quotes De Broglie’s equation:

 λ = h / mv

In a compact and precise way it says, “A moving object is a wave”. That is poetry of the highest order, he says, and I agree. Even haikus seem long in comparison.

There no end to technological reductionism, but Whitesides urges us to write that love letter from Indiana in long hand. Science will only scratch that itch. It’s up to us to use our judgement as well. As we delve deeper there is more need of caution. As he admits, even in the case of equations, not all equations are alike and ann do not lead us to delight in their beauty, “Some are porcupines, some are plumber's helpers, and some are tarantulas.”

At the end of the book, scientist and non-scientist will have gained some understanding of science works. That is secondary. What is more important in my opinion, is that it shows how fascinating all this really is, and how we go about finding and exploring things that we cannot see, or hold, or smell. I call this the ‘Alice approach’ - create wonder. Draw attention to that itch, and the scratching will take care of itself. Drawing people into the beauty that nature is.

My issue with the polemics and arguments offered by science apologists is that they are written to appeal to the already convinced choir, who silently smile and cannot but nod in approval, but they do little to draw the ‘others’ in, and often achieve the opposite effect of turning them away. The God Delusion by Richard Dawkins was wonderfully written, but I cannot think it actually convinced anyone (barring a few fence-sitters) to actually change what they already believed in. It was divisive and that does not help. This is not the ‘Alice approach’.

Jonathan Haidt’s recent book, Why Politics and Religion Divide Good People, talks about ways to end the partisan politics of the Right vs. the Left, but this can be also applied elsewhere. In a twist of the Western adage - 'shoot first, questions later', his work as a moral psychologist has shown that ‘we are emotional first, and rational later' and when reason is brought into play it’s in support of the initial emotion. We make up reasoning post-hoc to bolster what ever was our initial emotional response. Reasoning and reflection can cause us to change our opinions but it is rare (We are less in this mode than we would like to believe). The approach to begin to gain any traction in an opponent’s mind is to use methods that ‘talk to their intuitions, and not to their reason’. Keep the reasons for later.

There is a similar problem in Science v. Faith/Religion debates. It’s not that the reasoning of the science boosters is not sound, but that the tone is wrong and reason alone is inadequate. You need to appeal to the intuitions that believers have. Richard Dawkins in his recent book, The Magic of Reality written for children and ‘curious’ adults, has tried really hard to create that ‘Alice approach’. It contains beautiful expositions of scientific experiments and phenomena with a preamble of folkloric and mythical explanations. It works, but only somewhat as they serve as ‘foil’ and straw-men to be knocked down later. What then remains of wonder when it really an argument, a quarrel in another guise? 

In a less intrusive way and with greater effectiveness, Whitesides/Frankel give us a tour of this Wonderland of the nanoscale and quantum phenomena that any one of any stripe cannot fail to be moved.

Alice would’ve  heartily approved.

Apples vs. chips: an experiment into food behavior

Last week I conducted an informal experiment at work. This the kind of 'scientific' experiment that J. classifies as needless and silly, since the general conclusion is quite obvious. My reasons to do that experiment were:
a) People could surprise you with their behavior,  and b) mainly, because it's fun to do experiments, c) I had a grant (meaning the raw material was paid for)

The main motivation was  to determine if people make good food choices when such choices are available. As a graduate student I often found that when stuck in the lab late in the evening or  night the only 'food' option was  the vending machine mostly full of all kinds of crappy snacks. The kind of snacks that Indra Nooyi, CEO of Pepsi food has decided to re-brand as 'fun for you'. Their other labels are 'good for you' and 'better for you'. Of course, the irony of Pepsi marketing itself as a health-food company and the relativistic nature of their labels is inescapable.  Another disturbing story that I read was that experiments on rats have shown that babies could acquire a taste for junk food in-utero.(In review of Lindstrom's book on advertising in the Economist).

At some point, I wrote to the President and the authorities to make such healthy snacks available. The University did make this available and called it M-healthy. They were not not that healthy, but better than just chips and other crap that's usually in vending machines.

Yet, it begs the question - do people actually want to eat healthy?  When polled people  it is unlikely that anyone would say something other than - "I want to eat healthy, if such choices were available." Though what people say and what they do is quite different. The actual pattern of behaviors exposes their 'revealed preferences'.

The question is that faced with an apple or a potato chip what does one do? More honestly speaking, what would I do?

The Experiment
In the company lunch room where people leave stuff to share/ give-away I placed the following items last Monday morning:
18 apples ( 11 Red Delicious, 4 Fuji, 3 Granny Smiths)
3 bags of chips (regular, multigrain and tortilla chips without any salsa)
2 packets of crackers

Null Hypothesis:
All free food is equal and will be eaten in equal amounts.


Hypothesis
The chips would be all eaten.
Apples would not be as popular.
Crackers would be more popular than apples

Observations:


Wednesday: Two bags of chips were finished. Tortilla chips were not. 13/18 apples were eaten
Thursday: All bags of chips were gone. Packet of crackers gone. 11/18 apples eaten
Monday: One packet of crackers remained. 10/18 apples remained. Interestingly, all the Granny Smith apples were gone.

It must be noted that the experimenter also was part of the experiment and ate 1 apple and some amount of chips to keep the consumption roughly equal.

Possible explanations and factors at play.


1) Chips are tastier and pound for pound offer more calories and are a better 'investment'.
2) Apples have a higher 'adoption barrier', as they have to be washed, either cut, or bit into and it can be messy with juicy apples
3) Red Delicious is not so delicious. If there were more Granny Smiths, then the ratio could have been different leading to different conclusions.
4) People bring their own apples, and not chips and were supplementing their diet with the chips that were laid out.
5) Chips don't go bad, and apples do. So after Day 3, the apples were less appealing.
6) Eating chips requires less commitment, meaning that chips can be eaten in small quantities (one chip to a dozen or more), but you have to commit to eating an entire apple.
7) Corollary to the above: you may not be hungry for an entire apple. In a sense, an apple will actually increase your caloric intake in large quanta.
8) The chips were of better quality than the apples. The experimenter admits that this was not controlled for.

Conclusions:
I leave that you to gentle reader.( I would hate to give it away). I am sure J. would appreciate my silence and absence of analysis).

PS:
What happens next?
I am curious to know what is the half-life of the apples. They still stand at 11.

Is Doing a PhD a waste of time?

This article showed up in the Economist a while ago (December, 2010) but I got to reading it only now. I am currently in what can be described as 'evangelical zeal to read magazines' that have been piling up.

While this article -- The disposable academic: Why doing a PhD is often a waste of time -- might be late in coming, it's still an interesting read in the manner of the perfect 20/20 vision of hindsight.

One thing many PhD students have in common is dissatisfaction. Some describe their work as “slave labour”. Seven-day weeks, ten-hour days, low pay and uncertain prospects are widespread. You know you are a graduate student, goes one quip, when your office is better decorated than your home and you have a favourite flavour of instant noodle....Whining PhD students are nothing new, but there seem to be genuine problems with the system that produces research doctorates (the practical “professional doctorates” in fields such as law, business and medicine have a more obvious value). There is an oversupply of PhDs. Although a doctorate is designed as training for a job in academia, the number of PhD positions is unrelated to the number of job openings. Meanwhile, business leaders complain about shortages of high-level skills, suggesting PhDs are not teaching the right things. The fiercest critics compare research doctorates to Ponzi or pyramid schemes.

It's true that it takes a number of years, and perhaps your best ones. I sometimes felt that I spent all my youth in school. Of course I was much better off than students in anthropology and physics who on average take 7-10 years. As a PhD who is no longer working in academia, and for the record most of my friends who finished one are not working in academia either, I have never regretted for a moment taking/or wasting years finishing the degree. I enjoyed doing it and I had many rich experiences that were totally unconnected with academics, which I would never have enjoyed if I had a regular 9-5 job.

Academics tend to regard asking whether a PhD is worthwhile as analogous to wondering whether there is too much art or culture in the world. They believe that knowledge spills from universities into society, making it more productive and healthier. That may well be true; but doing a PhD may still be a bad choice for an individual.

Now being done, I have not suffered greatly either. I admit that it may not reflect the experience of every PhD as it is in a 'somewhat useful' and currently 'somewhat hot' field of biomedical engineering. It may not make sense for everyone to do one. And as the article points out, everyone does not have the right motivation or reasons for doing one.

Many students say they are pursuing their subject out of love, and that education is an end in itself. Some give little thought to where the qualification might lead. In one study of British PhD graduates, about a third admitted that they were doing their doctorate partly to go on being a student, or put off job hunting. Nearly half of engineering students admitted to this. Scientists can easily get stipends, and therefore drift into doing a PhD. But there are penalties, as well as benefits, to staying at university. Workers with “surplus schooling”—more education than a job requires—are likely to be less satisfied, less productive and more likely to say they are going to leave their jobs

As the article points out there are about 100,000 PhDs minted each year and only about 16,000 new academic positions. People have to find work elsewhere, or may choose to find work elsewhere. The central assumption of the article that the PhD should lead to a academic job is not entirely correct. There are lots of well-paying, and often better-paying jobs in industry, non-profits, think-tanks, government, and startups. The article states that only 57% of the student actually finish a PhD casting some doubt on the enterprise. People quit for various reasons and I think that for many it might be the right decision. As in most things in life, the training and experience can always come handy later. I do agree that it's best to quit early. I am not quite sure if you can treat it as a 'sunk cost' if you quit in the 6th year of your program.

I do agree that there is an oversupply and universities should practice, as the article calls it, more voluntary birth-control. In addition there should be more training for PhDs who will be looking for non-academic jobs and developing soft-skills given that 90% of the people will not pursue jobs in academia.

Many of those who embark on a PhD are the smartest in their class and will have been the best at everything they have done. They will have amassed awards and prizes. As this year’s new crop of graduate students bounce into their research, few will be willing to accept that the system they are entering could be designed for the benefit of others, that even hard work and brilliance may well not be enough to succeed, and that they would be better off doing something else. They might use their research skills to look harder at the lot of the disposable academic. Someone should write a thesis about that.

Towards a Monoculture

I cannot explain why I am attracted to words and sounds: there is this mystery to alien sounds, like listening to strange music. There are words like caïque* which sound and read mysterious and interesting. Naturally, sounds in other languages are even more interesting that words in the dictionary. Even if you don't understand a word there this is mysterious enjoyment of just listening to the phonemes, phrasing, the cadences and rhythms.

My abilities in German have been asymptotically diminishing, but it's fun to be able to catch some snatches of Italian and Spanish and guess the meaning by using the Latin roots. But, do languages have utility? The general attitude is to learn languages that are 'useful'. So, English, Spanish and lately Chinese, are more useful than learning say, Pashto, Tagalog or Swahili. While communication and understanding maybe improved when people speak the same language, it's not entirely a good thing as the world drifts to a monoculture, or monopoly of a few select language. It's well known that when the last speaker of a language dies, he or she takes with him/her a whole way of expression, an entire culture, and often it's the end of a way of life.

Sadly, in India, a land of many languages we are losing reason to learn or master the vernacular. It seems likely that in a generation, chaste Hindi or even Urdu will be lost. I will not dwell individual dialects and accents that color languages. My own mother tongue - Gujarati has variants depending on whether the speaker is Parsi, or Bohri, or from Surat, Kathiawad, or Ahmedabad. Of course, these dialects and other Indian languages will survive in the the hands of few. But, it's quite likely that poetry, plays and books will cease to be written as often as they were. First, there won't be writers with the fluency, and sadly they will be starved of an audience. An artist needs an audience that actually understands the nuances or subtleties to appreciate the skill in creating within the confines of the language.

It's sad but true that many of my friends have not taken any great effort to teach their kids languages other than English thinking that it will 'confuse' them. A common idea is that child development is hindered with learning more than one language and that they won't get admission since they can't speak English properly.

The polymath Jared Diamond presents research to the contrary. In a piece for Science he demonstrates that conventional thinking about language confusing kids is quite wrong. (See: The Benefits of Multilingualism, by Jared Diamond, Science 15 October 2010: 332-333| link to summmary)More importantly there are additional benefits:

Recent studies show that children raised bilingually develop a specific type of cognitive benefit during infancy, and that bilingualism offers some protection against symptoms of Alzheimer’s dementia in old people.

He goes on to write...

More recent studies, comparing subjects matched for those other variables, have found bilinguals and monolinguals to be largely similar in cognition and language processing.

He presents additional material to show that those who speak more than one language are better at handling multiple inputs, ie better multi-taskers. Now who wouldn't want that?

So, if you aren't so interested in sounds, or saving poetry and languages from extinction you may be interested in conferring some benefit to your kids by teaching them more than one tongue.
--------------------
*caïque: A Turkish hand-rowed boat

Pew Science Quiz

Excellent post by Raghu K. on the results of the Pew Science quiz. He wrote a longer article in the Michigan Daily.

Among the scientists polled, 87 percent think evolution is true and 84 percent agree that human activity is the cause of global warming, whereas the corresponding numbers among the public are 32 and 49, respectively.

Surveys like the Pew study are useful in alerting us to differences in opinion between scientists and the public, especially on scientific issues. It’s crucial that these divides be bridged to improve the quality of debate on social issues.

I took the Pew Science Quiz and got all the questions right(wipes brow an breathes sign of relief!)

Outliers - Old Wine in a New Bottle

Malcolm Gladwell has a gift for sticky phraselogy, and why not? he wrote an entire book on it. His first book The Tipping Point made 'stickiness' a new buzzword. If his first book was about how things/ideas manage to cross a threshold after which there is no looking back, his latest book Outliers is about success itself. He looks at the fundamental reasons for success.

If you don't have time to read through the 300 pages of the book, don't be alarmed. It has chiefly four points. To be successful you need:

1) To work hard (>10,000 hours at something).
2) To be at the right place at the right time.
3) To be only above average smart, but not a genius.
4) To leverage or adjust your cultural advantage/ disadvantages.

None of the above are anything but conventional wisdom. Yet, the book is an interesting read only because Gladwell is so incredibly gifted at paraphrasing the obvious and coming up with interesting examples.

The 10,000 hour rule at first seemed a very good quantification of expertise, but then you realise that it's fairly obvious. A PhD takes about 10,000 hours of work (5 years x 50 weeks/year x 40 hrs/week), and about the same amount of time if you combined an undergrad + master's degree.

Once armed with the right stuff, we all know we have to also be located at correct spot in space and time to even have a chance to grab the opportunity when it comes knocking. It's an interesting observation that being born around 1955 was a good thing for Jobs, Gates, and others as it enabled them to jump into the PC revolution. Ultimately, is this really useful? We are simply unaware what skills will be valuable in 20 years that we can prepare. It's mostly just dumb luck to a large extent that some people come out on top.

We all know that to simply be smart is not enough. This reminds me of Richard Feynman, reported to have an IQ of 124 (just above average), who joked that winning a Nobel prize was no big deal, but to do that with an average IQ of 124, now that was genius!

There is no need to waste any more ink on cultural environment and the important role that it plays in eventual success. Sometimes it makes me guilty to think about my own accident of birth. There was at least one kid running around begging for a meal, who if he had half my advantages while growing up, would have done twice as much.

Most of Gladwell's work is good journalism, but he often falls short of good science. The most astounding leap that he makes is to draw the conclusion that rice farming teaches patience that makes Asians better at math since it teaches persistence and attention to detail. There is something to be said about language and how Asian languages are more calculation-friendly in terms of syntax. But, mathematics is not just merely arithmetic. Even if we consider calculation efficiency as an indicator of math skills, it would be interesting to show that American-born Asians who don't speak their mother tongues are somehow worse at math than their Asian counterparts who do. Indian languages are perhaps syntactically worse as we have more unique words for numbers than English, yet we are pretty good calculators. Why? A quick reason is that we have large families and children have to learn to add and count fast. I dislike these 'gee-whiz' sort of explanations.

The math behind galli cricket teams, and other interesting diversions

Group Theory in the Bedroom and Other Mathematical Diversions is Brian Hayes's set of collected essays from the American Scientist.

Full marks for the slightly risque title that will pique anyone's interest, but the book has nothing to with mathematics of partner swapping. The subject of the investigation is to find the golden rule for mattress flipping. Mattresses should be flipped periodically to ensure that all sides of the mattress get equal wear. It's easy enough to see that there are 4 possible configurations: (Side A, Side B) x (Top, Bottom). The goal is to find one rule, or a set or rules, that you can apply each time to perform a set of operations that ensures that you end up cycling through all 4 configurations.

If you only flip (along the long or short axis) you cycle through only two sides - A and B. If you only rotate in a plane then you cycle through - Top and Bottom. Using group theory, Hayes shows why there is no golden rule. You cannot perform the same set of operations again and again because the mattress is a Klein-4 group . A rotate and a flip along the short axis is the same as a flip on the long axis. Any set of two operations are equivalent to one operation. This proves to be the undoing of any rule, as we know that any ONE set of operations is not enough to cycle through all 4 configurations. So, you either need a fixed schedule, or a set of markers to ensure you do an opposite set of operations.

Being a kinda random fellow, I best liked Hayes's analysis of the effects of random flipping. If you randomly performed any one operation on a quarterly-basis then, on average, one side will get 31% of the wear instead of ideal 25%. A rather tolerable discrepancy of 6%. Then he goes on to discuss tire rotation and shows why that is completely different beast since it is a cyclic-4 group and hence there is a golden rule - "quarter turn clockwise (or anti-clockwise)".

What is most interesting about the book is that all these mathematical diversions start as anecdotes and rather innocuously. Consider the problem of partitioning a set of players into two teams: a problem that is encountered and solved on thousands of galli cricket and football 'fields' every day. The usual practice is to select two captains who then toss to decide who picks first. Then they go turn-by-turn to pick the rest of the players. Naturally, the players are chosen in order of ability. In general, this rule results in fairly balanced teams. Hayes calls this the Greedy Algorithm, because at each step the largest number (if you assigned numerical values to the strengths of the players) is chosen in each partition. In reality, of course this partitioning problem is quite a hard one, more technically, it's an NP complete problem and there are number of other algorithms, including the Karmarkar-Karp difference algorithm, but no optimal one. Then Hayes goes on to show why this does not matter on the playing field because on a log scale, abilities don't differ that much between strongest and weakest players and the simple 'greedy' partitions are reasonable without the need for fancy partitioning.

I greatly enjoyed reading the other chapters on namespaces, gear train ratios, and finding the continental divide. If only, mathematics was taught this way in schools.

Help classify galaxies

Participate in Public science and help classify galaxies: Galaxy Zoo 2. An excellent idea to use human intelligence in classification to make sense of astronomical amounts of data.

End of Days

It's 6pm and everybody has gone home. I am sipping my last coffee as a graduate student. I had always looked forward to the day when I would finally be able to say 'I'm done with this crap'. Sometimes, it looked like that day would never come. It always seemed a goal that was too impossible, too far, somewhere in the distance, a year or two away. Now it's finally here, it's not what I had expected to feel.

Today everyone, including my advisor, told me to go home early and get some sleep. Actually, for the first time in my life I genuinely want to stay here. Not because there is work to be done, but I just want to enjoy the last evening here at my desk - alone. I see piles of old papers that are all marked up and with coffee stains, old lab notebooks with failed experiments and incorrect analyses. They make feel that was time well-spent. My finished papers, in comparison, look too clean.

Tomorrow, in about 45 minutes I am supposed to wrap six years of work. They want the cream. I shall present three of my greatest hits, and if that's a hit with the committee, they are going award me a PhD.

My personal experience makes me compare doing a PhD to running a marathon. You have to be slightly mad to think of doing one, and a little more so to finish one. Just as the marathon is not a test of speed, but of stamina, a PhD is not a test of quick intelligence, but of rigor and intellectual determination. For the most part, you hang in there and keep going, and not be afraid of falling down or going down blind alleys.

I recall Chicago. After many miles, I finally rounded the bend on Columbus Drive and saw the finish, less than 400 meters away. Suddenly, all the weariness of those miles disappeared seeing that green banner with large, friendly letters reading, 'FINISH'. It was nice to get that medal around my chest once I crossed. That will always remain. And looking back, what I really enjoyed was running all those miles in the different neighbourhoods. Today, it's that same sort of feeling of seeing the finish line, one that you dreamed about for a few years. Yes, I look forward to crossing the line tomorrow, but tonight I want to sit here and look back.

Lincoln and Darwin

Abraham Lincoln and Charles Darwin were born on the same day, February 12, 1809, two hundred years ago. As the Birthday Paradox illustrates, you need only 23 people in a room to get better than 1/2 chance of any two people sharing a birthday. The coincidence is welcome however, as I admire them both. What I find more interesting is how separate these people live in the consciousness of people and the media. In all my calendars/dairies I find the day marked as 'Lincoln's birthday', but Darwin goes unmentioned. The newspapers are going to devote more space to Lincoln, while Darwin's going to get a footnote somewhere in the Science page. Perhaps, the man of the moment, Barack Obama shares more with the former Illinois Representative than a would-be-curate-turned-naturalist.

In another parallel universe, Darwin's day has not gone unnoticed as Science magazine is running series on Darwin. The National Geographic had a Darwin cover story. Some folks in the city of Ann Arbor have decided to celebrate Darwin's Day. Now that I shall have more time this week, I intend to re-read the Origin of Species and Lincoln's speeches.

I am curious to see if Google's logo tomorrow is going to pay homage to Darwin or Lincoln. Regardless of the final choice, both were truly great men who contributed in immensely in two completely separate spheres. It also occurred to me that people are rarely shot for their scientific beliefs, merely excoriated or excommunicated. Political belief seems to be a more dangerous responsibility.

Impossible Indian chick!

If you guys have a minute to spare while your women are getting ready. Check this out!
From Reuters: Indian Chick does the impossible!

For the first time, there is evidence that a woman can get her hair, makeup and clothes done in under one minute! What makes this even more of an achievement is the fact that it is an Indian woman! In my most sanguine moments, I thought that half hour would be a reasonable demand for someone to get ready, but this is an Olympian achievement.

It would indeed be a shame if this feat only managed to get in the Guinness Book of World Records. That book is meant for people eating nails, twenty hamburgers in 2 minutes, cycling backwards while playing a violin, or for pogo-sticking to Mt. Fuji. All impressive, but ultimately useless human achievements. This, my dear Gayathri, is worth at least a couple of Nobel prizes.

Here are some of the reasons:

Physics: Doing your hair in a French roll in the time it takes me to tie my shoelaces! And getting in a 9-yard sari in less than thirty seconds! The prize should be awarded for proving that the laws of physics as discovered by scientists no less than Newton, Planck, Einstein and Feymann do not need to be violated for a woman to get ready in less than a minute.

Peace: Surely, guys all over the world would appreciate her sharing this technique with their gals. I mean Al Gore got one for a Powerpoint presentation!


Chemistry: One definite woman has been synthesized by biological means that can ready in less than a minute.

Medicine/Biology: Nothing in the XX chromosome is responsible for any delay in getting ready.

Economics: Let's not even start. Gas, time, lights, etc. saved.

Literature: This might be the only tough sell, but heck! fact is stranger than fiction. This should count for something.

On Shoulders of Giants

When I should have been doing something else, I spent last evening reading Keith Devlin's book and the exchange of letter between Blaise Pascal and Pierre De Fermat.
In a series of letters Pascal and Fermat developed the theory of probability, or more accurately a priori or objective probability.

The problem that concerns the letter is the Problem of Points which Fermat solved rather easily using his more elegant and shorter 'method of combinations', and which Pascal solved correctly, but without the intuition, using his more complicated recursive formula.

Two things were striking - people had been gambling for centuries before anyone took the challenge in the early 17th century to find a mathematical method to predict the odds.

Also, what took the greatest minds in Europe a better part of a century to solve, took me only about few minutes to solve the 'Problem of Points'. Upon reading Pascal's source of confusion, I realized how simple it is to apply a method, but how very subtle it is the really understand the problem. We truly stand on the shoulders of giants.

The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern

How Many Neurons Must One Man Have?

Every year, my colleagues and I put up a joke/satirical/thought poster at Annual Society for Neuroscience Meeting under the teaching section. This poster is usually finished last minute. More last minute than our regular posters (There was more controversy this year which I shall get into some other day as it deserves a couple of posts.)

However, coming back to November 2006:
Borrowing a riff from Bob Dylan, our poster posed the question, "How Many Neurons Must One Man Have? (Before you call him a man)". We have about a 100 billion of them, but how do these neurons makes us what we are? How do we remember? Why and how do we forget? As is usually the case, the poster sort of evolves over the week with us, the pranksters/jokers/dunces, feeding off ideas and encouragement from the gallery and adding ideas. While, Tim and Greg were getting parts of the poster printed after the conference began, I started scribbling a back-of-the envelope equation which was pretty close to this -

At some point, it struck me that there is no better place to put a back-of-the-envelope equation than an envelope itself. Everybody simply loved it! Nothing gets scientists/engineers more amused than jargon puns.

After coming back from the meeting, Tim and I decided to do something beyond a few laughs. Which means in scientific currency - a publication. We worked on it in our free time. It was an interesting question and as we scoured the literature, we discovered that the research on the subject was rather thin. We read interesting papers from Bell Labs, papers on pigeon learning, autistic savants (Daniel Tammett), phenomenal mnemonists (A.K.Luria), artificial brains (Jeff Hawkins). At one point, we both realised that we were just enjoying this garage science project so much, that we weren't really making any progress with a publishable manuscript. Our research was all over the place and it took some work to curb our enthusiasm and coalesce collected ideas into one coherent manuscript.

Even then the road was not easy. One unrelenting reviewer took a while to 'get it' and made us go through what seemed like endless and silly revisions. Yet, to his credit, the manuscript was a little less folksy-sounding and perhaps more rigorous than we were planning. Also, since we decided to go for hand-drawn illustrations harking back to a simpler and purer time in magazine publishing, it was somewhat of a chore to redraw the illustrations.

So, finally almost after exactly two years since that scribbling in an Atlanta Holiday Inn, the ideas have been honored to be oozed with ink in IEEE Potentials Magazine. Tim's friend Thad, a commercial artist, gifted a wonderful drawing to use as the opening cover. However, the editor disagreed with us last minute and decided to go ahead with an computer image over the wonderful black-ink sketch. We were a little upset with some of odd-looking coloring.

This is the actual IEEE Potential Article as it appeared.

This how the article would have appeared, had we got our way:
Our Aesthetically Pleasing Article. We leave you, the reader, to decide if you agree with us.
As they say: Ars longa, vita brevis

---------
Previous post on the 2007 Poster:
Published in the Annals of Improbable Research: The Cingulate Cortex does Everything!

Where literature comes in

Sometimes as a scientist, you wonder if literature has anything really important to say that science won't be able to answer given adequate time, resources and techniques. Can everything be reduced to some laws, even they are quantum or probabilistic ones? Experiments in giant fMRI machines are showing which areas of the brain are responsible for what affective qualities in decision making. While we still try to understand these phenomena literature fills that void. That void is literature's essential subject matter.

More from Menand's piece on Lionel Trilling:

In Trilling’s view, the faith that liberals share, whether they are Soviet apologists, Hayekian free marketers, or subscribers to Partisan Review, is that human betterment is possible, that there is a straight road to health and happiness. A liberal is a person who believes that the right economic system, the right political reforms, the right undergraduate curriculum, and the right psychotherapy will do away with unfairness, snobbery, resentment, prejudice, neurosis, and tragedy. The argument of “The Liberal Imagination” is that literature teaches that life is not so simple — for unfairness, snobbery, resentment, prejudice, neurosis, and tragedy happen to be literature’s particular subject matter. In Trilling’s celebrated statement: “To the carrying out of the job of criticizing the liberal imagination, literature has a unique relevance . . . because literature is the human activity that takes the fullest and most precise account of variousness, possibility, complexity, and difficulty.” This is why literary criticism has something to say about politics.

Daily Grind

I think I am ready based on the number of coffee cups.

From Litmuszine -- part-blog, part-magazine and part-litmus test.

Speed dating issues

I would like to think that my dating days aren't over, but just in a perpetually suspended state. However, I was at a speed-matching event yesterday which attempted to have a bunch of people meet everybody else one-on-one in a space of an hour.



First, there were only fifteen ppl and it was apparent that at every round someone would have to sit out. Then another guy showed up and we were sixteen. Since that was an even number no one would have to sit out. The person in charge did the obvious thing - he made two concentric rings of chairs splitting ppl two groups - 'inners' and 'outers'. The 'outers' rotated around the inner ring. After the first rotation, everybody had met half of the people in the group, except the ppl in their own ring. Then he did the next obvious thing, made another two concentric circles of the rings themselves and repeated the process. After the second rotation, everybody had met 3/4th of the ppl. For the next round, these rings needed to be split further into similar rings. As you can see, this process stops when each of the two concentric rings have exactly one person.

Of course, since we had the fourth power of 2, i.e. 16 ppl, this scheme works beautifully. Since, I was part architect of the idea, I wondered if this arrangement would work for other even numbers, leaving the rather odd case of odd numbers aside for now. Very quickly, you can see that this scheme breaks down for 6 people.

Round I            Round II
A D             A-B       D-E
B E             C (sits out)       F (sits out)
C F

After the first rotation, you have Ring I meet everyone in Ring II. Proceeding as before, you end up with 3 ppl (an odd number) in each new sub-ring. Now every subsequent iteration will have one person in each group simply sitting one session out. As you can see from the example, we can form a pair with C and F in Round II, but they have already met each other in Round I. So, every subsequent period, one person will be sitting out and wasting his time. This would require 6 time periods.

Thus, the concentric circles thing is inefficient for all non 2ⁿ even numbers. I tried to come up with a pairing scheme for n=6. Since ⁶C₂ = 15 total pairs, and we have 3 pairs at each stage, we should need at a minimum five rounds. With the schedule below no one sits out and we achieve efficiency.

Table for 6 ppl

Station	1	2	3	4	5
S1	AD	AE	AB	AF	AC
S2	BE	BF	CE	BC	BD
S3	CF	CD	DF	DE	EF

The movement of people is non-intuitive and the schedule is complicated. You would need to hand people a schedule map: A would not move at all. B would move to stations: S2-S2-S1-S2-S2. I was certain that there was a solution to this problem, floating in graph theory or combinatoric literature. And indeed there is! But, this is no simple can of worms as I was to discover.

Famously, in 1850 Reverend Thomas Kirkman sent a query to the readers of a popular math magazine, Lady's and Gentleman's Diary:

Fifteen young ladies in a school walk out 3 abreast for seven days in succession: it is required to arrange them daily, so that no two will walk twice abreast.

1 of 7 possible solutions

The more general case of problem is called the Social Golfer Problem: Determine the maximum number of days 'w' that 'n' golfers can play in groups of 'r' each without meeting each other. This is still an UNSOLVED mathematical problem!!! If you are interested in reading more see: Social Golfer Problem

My original question of dividing 'n' ppl in pairs has been solved at least up to n=200. Round-robin scheduling is a wonderful site for those scheduling matches, or speed-dating style events. There is no simple movement order that can be prescribed. You have to pretty much follow the schedule blindly. Some schedules are unique, in other cases there are over 1000 solution, usually when 2ⁿ numbers are involved.

Yeah! Even speed-dating has issues!

Ignoble Research

While my so-called 'real' publications are limping along, one of my side-projects got published in this month's Annals of Improbable Research. A journal that is self-styled as " the journal of record for inflated research and personalities" . These are the good folks who dish out the Ig Noble Prizes each year

For the past three years, at the Society for Neuroscience conference my labmates and I present a 'joke' poster in the vein of The Onion. The Cingulate Cortex Does Everything started off as a satire on the field of fMRI research in neuroscience. There are tons of papers in journals like Nature and Science that implicate the cingulate cortex in all kinds of behavior. Brain fMRI scans detect oxygenation levels in the blood and determine if blood flow to particular part of the brain increases or decreases with respect to a behavioral event. It seemed rather interesting to us that the use of fMRI correlates so strongly with cingulate cortex sightings. We suspect that since the cingulate cortex is above the saggital sinus, a major drainage vessel for the brain, it seems to light up in fMRI studies as an artifact.


On scanning recent literature on the subject, we saw an explosion in cingulate cortex research and reached our startling conclusion - "Cingularity", i.e. if current trends continue the cingulate cortex will not only take over neuroscience research, but everything!!

Another interesting fact is that the word cingulate is derived from the Latin word cingulum meaning belt. Specifically, a belt protecting your family jewels.

Dawkins's Mirror Question

A really good book is one that makes you want to put it down for a while so that you can think.

This is taken from Richard Dawkins's latest book The Oxford Book of Modern Science Writing. See the review in Science (Mail me if you need access).

For years as a college tutor at Oxford, I would try the intelligence and reasoning powers of entrance candidates by asking them at interview to muse aloud on the conundrum of why mirror images appear left-right reversed but not upside down. It is a provocative puzzle, which is hard to situate among academic disciplines. Is it a question in psychology, in physics, in philosophy, in geometry, or just commonsense? I wasn't necessarily expecting my candidates to "know the right answer." I wanted to hear them think aloud, wanted to see if the question piqued their interest and their curiosity. If it did, they would probably be fun to teach.

The book is maybe good bedtime reading, but not the paragraph above. I read the paragraph and I couldn't sleep till had some sort of satisfactory answer. It's rather intriguing and wanted to discuss this below. My friends in Mathematics have a better idea of this, but I am taking a stab at it here.


STOP HERE IF YOU WANT TO THINK ABOUT THE PROBLEM ...



It is about particular symmetry? That lead me away from thinking about mirrors to drawing mirror images and considering that we reflect images about a particular axis. This is a practical issue when it comes to making stamps, or printing for example.

(Pardon my sloppy drawing. It's much harder to draw accurate mirror images than is popularly believed.)
Upon drawing this simple figure, I realised that mirroring (reflection) is a not really a 2D transform, but is a 3D transform since there is no strictly planar or 2-D operation(rotate, shift) can be performed that convert A to B. Of course if you reverse the X-axis then you automatically reflect. It's like looking at the 2-D figure from the bottom instead of the top.

Thinking about it in another way, if you had simply an outline figure (shown on top), you wouldn't really see any lateral inversion. If viewed from one perspective, there is no lateral inversion. That's because the figure being hollow does not have a correct viewing side.

So, according to me it boils down to a frame of reference. By imposing your frame of reference onto the mirrored image you get the perception of lateral inversion. In that parallel universe of mirror images, the X axis is reversed and hence correctly speaking left is actually right! The absolute values of all the points along X have not changed, only the signs have.

Coming back to the other question of top and bottom inversion, the simple four figure shows that top bottom is achieved by rotation around the Z-axis, or by two repeated mirrorings on the Y and X axis. So, you can ask why rotation only changes top and bottom, but not left and right. They are simply two different transformations.


More generally speaking, there is really left or right, or top and bottom. It's all relative all perceptions are due to the frame of reference. So, if you perform a transformation then you have to choose the appropriate frame of reference or grid to view it correctly. In a more extreme case, even in case of a distortion, the square will be a square in the distorted frame, but appears warped only because you impose your original frame on the 'new' square.

So, I think the problem is one of pure geometry and not of psychology or even physics. Perhaps, humans are predisposed to think of particular frames of references which cause this effect.

Was Proust a neuroscientist?

Recently there as been a spike in number of popular books on the brain and a lot them have made it to the best seller list. Everybody wants know how the body's CPU works. The most ambitious of these projects has been the one by Jonah Lehrer, editor-at-large for SEED magazine, a Rhodes scholar and neuroscience blogger.


His basic premise about neuroscience is: Sub sole nihil novi est. (meaning, There's nothing new under the sun. It's remarkable how intelligent everything sounds when you quote in Latin, or talk in a BBC accent). Lehrer claims that artists and writers were incredibly prescient and had long discovered basic neuroscientific truths. He ascribes each of the following artists with different discoveries in neuroscience: Proust (memory and recollection), Woolf (mental states), Escoffier (taste and smell), George Eliot (neurogenesis), Whitman (unity of body and soul/mind), Gertrude Stein (internal grammar/syntax), and Stravinsky (neural plasticity). All modern science is currently doing is simply rigorously verifying their discoveries by rigorous testing, or re-discovering it.

Jonah Lehrer writes beautifully and the anecdotes of the giants of the arts are interesting to read. There are no new facts and the juicy anecdotes will come as no surprise to anyone familiar with the particular artist (available cheap and free on Wikipedia). For example, the background on Stravinsky's premiere of The Rite of Spring was identical to the one I read in Alex Ross's excellent book on music in the 21st century, The Rest is Noise. I guess it is hard to come up with unique historical quotable quotes.

Where Lehrer's really contributes is in highlighting interesting experiments in neuroscience and explaining them. There is a great deal of misinformation and school textbooks have not been updated for decades. Why was Einstein smart? People believe that we use only 5% or 10% of our brains, and that Einstein used 20%, or some such figure. This is utter nonsense. But, someone has to inform the people and science is not always easy to explain and is not sexy. To complicate matters further, science is always forging ahead, not really waiting for things to be digested. The perverse nature of science overturns conventional wisdom and even central dogmas of science to create the 'latest' science.

Experiments have overturned what many believed to be true for a long time - "We all start with a set of neurons and they all die. No new neurons are created". This has been proven to be false. There is a great deal of life in the brain. Such experiments are fascinating to read and this book performs a great service in taking neuroscience to a broader audience.

The spectacular failure of the book is in putting the its title claim together. It's easy to find correlations if you look hard enough and the ones that Lehrer seems to suggest are rather tenuous and require a tremendous leap of faith. To reverse engineer Monsieur Proust and Ms. Stein as neuroscientists is more poetic license than science. The cover notes that Leher worked in Nobel prize-winning Eric Kandel's lab, but it is disappointing to report that he missed the essential lesson of the scientific method - framing a good hypothesis and then collecting data to confirm or disprove it. It is rather plain, even to a non-neuroscientist reader, that his hypothesis is weak and his conclusions are based on rather weak correlations.

This would all have still been okay, but then Lehrer goes on to commit parricide. Drawing from C.P Snow's Two Cultures theory, scientists like Dawkins, Pinker and Gould formed the 'Third Culture', scientists who bridged the gap between science and the lay audience with their cogent writing. Lehrer faults them, however, for viewing everything from the lens of science and missing the arts and humanities completely. What is needed, is a new'Fourth Culture', one that combines the arts and sciences and brings them both to the lay audience. This book and Saturday by Ian McEwan are examples of such writing, Lehrer goes on to write in his Coda to the book. Anyone who has read Dawkins, Gould or Pinker would suggest to Lehrer that he first work on coming up with a decent thesis for books before trying to create a new genre of writing. Clearly, Mr. Lehrer does not believe in half-measures when it comes to being audacious. He's young, the severe panning won't kill him and hopefully make him stronger.

On the Two Cultures, I think
Salon.com put it beautifully:

Science is material for the arts and art is material for the sciences, yet each must maintain its own integrity. After all, each has its own virtue: The sciences lift us outside of experience, so that we can more clearly survey it. The arts immerse us in experience, so that we can more fully encounter it.

My perception while reading the book was that I was reading two separate books at the same time. One on art, and the other on science. Take any random set of artists and you could come up with essentially an identical book. Maybe this book is a grand joke on everybody; if not, it's ripe for parody.

A few selections:
Genghis Khan was a cell-biologist, or
Napoleon was an investment banker,

There are others, which I will get to once I, like Monsieur Proust, am in bed.

Economics of God

From The Economist:

Religion cries out for a biological explanation. It is a ubiquitous phenomenon—arguably one of the species markers of Homo sapiens—but a puzzling one. It has none of the obvious benefits of that other marker of humanity, language. Nevertheless, it consumes huge amounts of resources. Moreover, unlike language, it is the subject of violent disagreements. Science has, however, made significant progress in understanding the biology of language, from where it is processed in the brain to exactly how it communicates meaning. Time, therefore, to put religion under the microscope as well.

Scientists in Europe have embarked on scientific quest for God. Even if religion or God are scientifically baseless, there can be numerous economic and social benefits. It is said that humans and chimpanzees are the only species that laugh; religion separates us from our cousins on the evolutionary tree. Really, a sticky 'meme' such as religion could not have survived if it did not confer any evolutionary benefits.

(the) long-term co-operative benefits of religion outweigh the short-term costs it imposes in the form of praying many times a day, avoiding certain foods, fasting and so on.

Indeed, research has shown the religion-based groups tend to survive longer as compared to secular groups, which are four times more likely to break up. The fear of the supernatural, or the after-life makes people cooperate. God is the ultimate stick and Heaven the ultimate carrot. We all know that incentives work!

As Dr. Wilson points out "... Secularism is very maladaptive biologically. We're the ones who at best are having only two kids. Religious people are the ones who aren't smoking and drinking, and are living longer and having the health benefits."

It is hard to separate religion from culture and group membership. Even there was a God, or not we want to belong to some group. Atheism can be intellectually and scientifically more honest, but can lead to impoverishment and even alienation in other ways.