My Dominant Hemisphere

The Official Weblog of 'The Basilic Insula'

Archive for the ‘Nature’ Category

Meeting Ghosts In The Chase For Reality

leave a comment »

Sunrise

Sunrise (via faxpilot @ Flickr CC BY-NC-ND license)

Watching the morning sun beaming through the clouds during today’s morning jog, I was struck by an epiphany. What ultimately transpired was a streak of thoughts, that left me in a overwhelming sense of awe and humility for its profound implications.

Perhaps the rejuvenating air, the moist earth from the previous night’s rains and the scent of the fresh Golden Flamboyant trees lining my path made the sun’s splendor much more obvious to see. Like in a photograph coming to life, when objects elsewhere in the scene enhance the main subject’s impact.

As I gazed in its direction wondering about the sunspots that neither I nor anyone else around me could see (but that I knew were really there, from reading the work of astronomers), I began thinking about my own positional coordinates. So this was the East, I found. But how did I know that? Well as you might have guessed, from the age old phrase: “the sun rises in the East and sets in the West”. Known in Urdu as “سورج مشرق میں نکلتا ہے اور مغرب میں ڈوبتا ہے ” or in Hindi, “सूरज पूरव में निकलता है और पश्चिम में डूबता है” and indeed to be found in many other languages, we observe that man has come to form an interesting model to wrap his mind around this majestic phenomenon. Indeed, many religious scriptures and books of wisdom, from ancient history to the very present, find use of this phrase in their deep moral teachings.

But we’ve come to think that we know this model is not really “correct”, is it? We’ve come to develop this thinking with the benefit of hindsight (a relative term, given Einstein’s famous theory, by the way. One man’s hindsight could actually be another man’s foresight!). We’ve ventured beyond our usual abode and looked at our planet from a different vantage point – that of Space. From the Moon and satellites. The sun doesn’t actually rise or set. That experience occurs because of our peculiar vantage point – of relatively slow or immobile creatures grounded here on Earth. One could say that it is an interesting illusion. Indeed, you could sit on a plane and with the appropriate speed, chase that sliver of sunlight as the Sol (as it’s lovingly called by scientists) appears or disappears in the horizon, never letting it vanish from view and do so essentially indefinitely.

Notes In The Margin About Language

Coming back, for a moment, to this amusing English phrase that helped me gauge my position, I thought about how language itself can shape one’s thinking. A subject matter upon which I’ve reflected before. There really comes a point when our models of the world and the universe get locked within the phraseology of a language that can actually reach the limits of its power of expression fairly unexpectedly. Speak in English and your view is different from somebody who can speak in Math. Even within Math, the coming about of algebra expanded the language’s power of expression incredibly from its meager beginnings. New models get incorporated into the lexicon of a language and because we tend to feed off of such phrases to make sense of ourselves and our universe, there is the potential for an inertia to develop, whereby it becomes easy to stay put with our abstractions of reality and not move on to radically new ones – models that are beyond the power of expression of a language and that haven’t yet been captured in its lexicon. In a way we find that models influence languages and languages themselves influence models and ultimately there is this interesting potential for a peculiar steady state to be reached – which may or may not be such a good thing.

So when it comes to this phenomenon, we’ve moved from one model to another. We began with “primitive” maxims. Perhaps during a time when people used to think of the Earth as flat and stars as pin-point objects too. And then progressed to geocentrism and then heliocentrism, both of which were basically formulated by careful and detailed observations of the sky using telescopes, long before the luxury of satellites and space travel came into being. And now that we see the Earth from this improved vantage point – of Space – our model for understanding reality has been refined. And actually, really shifted in profound ways.

So what does this all mean? It looks like reality is one thing, that exists out there. And we as humans make sense of reality through abstractions or models. How accurate we are with our abstractions really depends on how much information we’ve been able to gather. New information (through ever more detailed experiments or observations and indeed as Godel and Poincare showed, sometimes by mere pontification), drives us to alter our existing models. Sometimes in radically different ways (a classic example is our model of matter: one minute particle, one minute wave). There is this continuous flux about how we make sense of the cosmos, and it will likely go on this way until the day mankind has been fully informed – which may never really happen if pondered upon objectively. There have been moments in the past where man has thought that this precipice had been finally reached, that he was at last fully informed, only to realize with utter embarrassment that this was not the case. Can man ever know, by himself, that he has finally reached such a point? Especially, given that this is like a student judging his performance at an exam without the benefit of an independent evaluator? The truth is that we may never know. Whether we think we will ever reach such a precipice really does depend on a leap of faith. And scientists and explorers who would like to make progress, depend on this faith – that either such a precipice will one day be reached or at least that their next observation or experiment will increase them in information on the path to such a glorious point. When at last, a gestalt vision of all of reality can be attained. It’s hard to stay motivated otherwise, you see. And you thought you heard that faith had nothing to do with science or vice versa!

It is indeed quite remarkable the extent to which we get stuck in this or that model and keep fooling ourselves about reality. No sooner do we realize that we’ve been had and move on from our old abstraction to a new one and one what we think is much better, are we struck with another blow. This actually reminds me of a favorite quote by a stalwart of modern Medicine:

And not only are the reactions themselves variable, but we, the doctors, are so fallible, ever beset with the common and fatal facility of reaching conclusions from superficial observations, and constantly misled by the ease with which our minds fall into the rut of one or two experiences.

William Osler in Counsels and Ideals

The World According To Anaximander

The World According To Anaximander (c. 610-546 BCE)

The phenomenon is really quite pervasive. The early cartographers who divided the world into various regions thought funny stuff by today’s standards. But you’ve got to understand that that’s how our forefathers modeled reality! And whether you like it or not someday many generations after our time, we will be looked upon with similar eyes.

Watching two interesting Royal Society lectures by Paul Nurse (The Great Ideas of Biology) and Eric Lander (Beyond The Human Genome Project: Medicine In The 21st Century) the other day, this thought kept coming back to me. Speaking about the advent of Genomic Medicine, Eric Lander (who trained as a mathematician, by the way) talked about the discovery of the EGFR gene and the realization that its mutations strongly increase the risk for a type of lung cancer called Adenocarcinoma. He mentioned how clinical trials of the drug Iressa – a drug whose mechanism of action scientists weren’t sure of yet but was nevertheless proposed as a viable option for lung adenocarcinomas – failed to show statistically significant differences from standard therapy. Well, that was because the trial’s subjects were members of the broad population of all lung adenocarcinoma cases. Many doctors realizing the lack of conclusive evidence of a greater benefit, felt no reason to choose Iressa over standard therapy and drastically shift their practice. Which is what Evidence-Based-Medical practice would have led them to do, really. But soon after the discovery of the EGFR gene, scientists decided to do a subgroup analysis using patients with EGFR mutations, and it was rapidly learned that Iressa did have a statistically significant effect in decreasing tumor progression and improving survival in this particular subgroup. A significant section of patients could now have hope for cure! And doctors suddenly began to prescribe Iressa as the therapy of choice for them.

As I was thinking about what Lander had said, I remembered that Probability Theory as a science, which forms the bedrock of such things as clinical trials and indeed many other scientific studies, had not even developed until the Middle Ages. At least, so far as we know. And modern probability theory really began much later, in the early 1900s.

Front page of "Doctrine of Chance – a method for calculating the probabilities of events in plays" by Abraham de Moivre, London, 1718

Abraham de Moivre's "Doctrine of Chances" published in 1718, was the first textbook on Probability Theory

You begin to realize what a quantum leap this was in our history. We now think of patterns and randomness very differently from ancient times. Which is pretty significant, given that for some reason our minds are drawn to looking for patterns even where there might not be any. Over the years, we’ve developed the understanding that clusters (patterns) of events or cases could occur in a random system just as in a non-random one. Indeed, such clusters (patterns) would be a fundamental defining characteristic of a random process. Absence of clusters would indicate that a process wasn’t truly random. Whether such clusters (patterns) would fit with a random process as opposed to a non-random one would depend on whether or not we find an even greater pattern of how these clusters are distributed. A cluster of cases (such as an epidemic of cholera) would be considered non-random if by hypothesis testing we found that the probability of such a cluster coming about by random chance was so small as to be negligible. And even when thinking about randomness, we’ve learned to ask ourselves if a random process could be pseudo-random as opposed to truly random – which can sometimes be a difficult thing to establish. So unlike our forefathers, we don’t immediately jump to conclusions about what look to our eyes as patterns. It’s all quite marvelous to think about, really. What’s even more fascinating, is that Probability Theory is in a state of flux and continues to evolve to this day, as mathematicians gather new information. So what does this mean for the validity of our models that depend on Probability Theory? If a model could be thought of as a chain, it is obvious that such a model would be as strong as the links with which it is made! So we find that statisticians keep finding errors in how old epidemiologic studies were conducted and interpreted. And the science of Epidemiology itself improves as Probability Theory is continuously polished. This goes to show the fact that the validity of our abstractions keeps shifting as the foundations upon which they are based themselves continue to transform. A truly intriguing idea when one thinks about it.

Some other examples of the shifting of abstractions with the gathering of new information come to mind.

Image from Andreas Vesalius's De humani corporis fabrica (1543), page 190.

An image from Vesalius's "De Humani Corporis Fabrica" (1543)

Like early cartographers, anatomists never really understood human anatomy very well back in the days of cutting open animals and extrapolating their findings to humans. There were these weird ideas that diseases were caused by a disturbance in the four humors. And then Vesalius came along and by stressing on the importance of dissecting cadavers, revolutionized how anatomy came to be understood and taught. But even then, our models for the human body were until recently plagued by ideas such as the concept that the seat of the soul lay in the pineal gland and some of the other stuff now popularly characterized as folk-medicine. In our models for disease causation, we’ve progressed over the years from looking at pure environmental factors to pure DNA factors and now to a multifactorial model that stresses on the idea that many diseases are caused by a mix of the two.

The Monty Hall paradox, about which I’ve written before is another good example. You’re presented with new information midway in the game and you use this new information to re-adjust the old model of reality that you had in your mind. The use of decision trees in genetic counseling, is yet another example. Given new information about a patient’s relatives and their genotype, your model for what is real and its accuracy improves. You become better at diagnosis with each bit of new information.

The phenomenon can often be found in how people understand Scripture too. Mathematician, Gary Miller has an interesting article that describes how some scholars examining the word Iram have gradually transformed their thinking based on new information gathered by archeological excavations.

So we see how abstractions play a fundamental role in our perceptions of reality.

One other peculiar thing to note is that sometimes, as we try to re-shape our abstractions to better congrue with any new information we get, there is the tendency to stick with the old as much as possible. A nick here or a nudge there is acceptable but at its heart we are usually loath to discard our old model entirely. There is a potential danger in this. Because it could be that we inherit flaws from our old model without even realizing it, thus constraining the new one in ways yet to be understood. Especially when we are unaware of what these flaws could be. A good example of abstractions feeding off of each other are the space-time fabric of relativity theory and the jitteriness of quantum mechanics. In our quest for a new model – a unified theory or abstraction – we are trying to mash these two abstractions together in curious ways, such that a serene space-time fabric exists when zoomed out, but when zoomed in we should expect to see it behave erratically with jitters all over the place. Our manner of dealing with such inertia when it comes to building new abstractions is basically to see if these mash-ups agree with experiments or observations much better than our old models. Which is an interesting way to go about doing things and could be something to think about.

Making Sense Of Reality Through The Looking Glass

Making Sense Of Reality Through The Looking Glass (via Jose @ Flickr, CC BY-SA-NC license)

Listening to Paul Nurse’s lecture I also learned how Mendel chose Pea plants for his studies on inheritance rather than other complicated vegetation because of the simplicity and clarity with which one could distinguish their phenotypes, making the experiment much easier to carry out. Depending on how one crossed them, one could trace the inheritance of traits – of color of fruit, height of plant, etc. very quickly and very accurately. It actually reminded me of something I learned a long time ago about the various kinds of data in statistics. That these data could be categorized into various types based on the amount of information they contain. The highest amount of information is seen in Ratio data. The lowest is seen in Nominal data. The implication of this is that the more your experiment or scientific study uses Ratio data rather than Nominal data, the more accurate will your inferences about reality be. The more information you throw out, the weaker will your model be. So we see that there is quite an important caveat when we build abstractions based on keeping it simple and stripping away intricacy. When we are stuck with having to use an ape thumb with a fine instrument. It’s primitive, but it often gets us ahead in understanding reality much faster. The cost we pay though, is that our abstraction congrues better with a simpler and more artificial version of the reality that we seek to understand. And reality usually is quite complex. So when we limit ourselves to examining a bunch of variables in say for example the clinical trial of a drug, and find that it has a treatment benefit, we can be a lot more certain that this would be the case in the real world too provided that we prescribe the drug to as similar a patient pool as in our experiment. Which rarely happens as you might have guessed! And that’s why you find so many cases of treatment failure and unpredictable disease outcomes. How the validity of an abstraction is influenced by the KISS principle is something to think about. Epidemiologists get sleepless nights when pondering over it sometimes. And a lot of time is spent in trying to eliminate selection bias (i.e. when errors of inference creep in because the pool of patients in the study doesn’t match to an acceptable degree, the kinds of patients doctors would interact with out in the real world). The goal is to make an abstraction agree with as much of reality as possible, but in doing so not to make it so far removed from the KISS principle that carrying out the experiment would be impractical or impossible. It’s such a delicate and fuzzy balance!

So again and again we find that abstractions define our experiences. Some people get so immersed and attached with their models of reality that they make them their lifeblood, refusing to move on. And some people actually wonder if life as we know it, is itself an abstraction :-D! I was struck by this when I came upon the idea of the Holographic principle in physics – that in reality we and our universe are bound by an enveloping surface and that our real existence is on this plane. That what we see, touch or smell in our common experience is simply a projection of what is actually happening on that surface. That these everyday experiences are essentially holograms :-D! Talk about getting wild, eh :-D?!

The thought that I ultimately came with at the end of my jog was that of maintaining humility in knowledge. For those of us in science, we find that it is very common for arrogance to creep in. When the fact is that there is so much about reality that we don’t know anything about and that our abstractions may never agree with it to full accuracy, ever! When pondered upon deeply this is a very profound and humbling thing to realize.

Even the arrogance in Newton melted away for a moment when he proclaimed:

If I have seen a little further it is by standing on the shoulders of Giants.

Isaac Newton in a letter to rival Robert Hooke

Here’s to Isaac Newton for that spark of humility, even if it was rather fleeting :-). I’m guessing there must have been times when he might have had stray thoughts of cursing at himself for having said that :-)! Oh well, that’s how they all are …


Copyright Firas MR. All Rights Reserved.

“A mote of dust, suspended in a sunbeam.”


Search Blog For Tags: , , , , , ,

Written by Firas MR

November 16, 2010 at 12:18 am

Revitalizing Science Education

with one comment

[Video]
Richard Feynman: “… But you’ve gotta stop and think about it. About the complexity to really get the pleasure. And it’s all really there … the inconceivable nature of nature! …”

And when I read Feynman’s description of a rose — in which he explained how he could experience the fragrance and beauty of the flower as fully as anyone, but how his knowledge of physics enriched the experience enormously because he could also take in the wonder and magnificence of the underlying molecular, atomic, and subatomic processes — I was hooked for good. I wanted what Feynman described: to assess life and to experience the universe on all possible levels, not just those that happened to be accessible to our frail human senses. The search for the deepest understanding of the cosmos became my lifeblood […] Progress can be slow. Promising ideas, more often than not, lead nowhere. That’s the nature of scientific research. Yet, even during periods of minimal progress, I’ve found that the effort spent puzzling and calculating has only made me feel a closer connection to the cosmos. I’ve found that you can come to know the universe not only by resolving its mysteries, but also by immersing yourself within them. Answers are great. Answers confirmed by experiment are greater still. But even answers that are ultimately proven wrong represent the result of a deep engagement with the cosmos — an engagement that sheds intense illumination on the questions, and hence on the universe itself. Even when the rock associated with a particular scientific exploration happens to roll back to square one, we nevertheless learn something and our experience of the cosmos is enriched.

Brian Greene, in The Fabric of The Cosmos

When people think of “science education”, they usually tend to think about it in the context of high school or college. When in reality it should be thought of as encompassing education life-long, for if analyzed deeply, we all realize that we never cease to educate ourselves no matter what our trade. Because we understand that what life demands of us is the capacity to function efficiently in a complex society. As we gain or lose knowledge, our capacities keep fluctuating and we always desire and often strive for them to be right at the very top along that graph.

When it comes to shaping attitudes towards science, which is what I’m concerned about in this post, I’ve noticed that this begins quite strongly during high school, but as students get to college and then university, it gradually begins to fade away, even in some of the more scientific career paths. By then I guess, some of these things are assumed (at times you could say, wrongfully). We aren’t reminded of it as frequently and it melts into the background as we begin coping with the vagaries of grad life. By the time we are out of university, for a lot of us, the home projects, high-school science fests, etc. that we did in the past as a means to understand scientific attitude, ultimately become a fuzzy, distant dream.

I’ve observed this phenomenon as a student in my own life. As med students, we are seldom reminded by professors of what it is that constitutes scientific endeavor or ethic. Can you recall when was the last time you had didactic discussions on the topic?

I came to realize this vacuum early on in med school. And a lot of times this status quo doesn’t do well for us. Take Evidence-Based-Medicine (EBM) for example. One of the reasons, why people make errors in interpreting and applying EBM in my humble opinion, is precisely because of the naivete that such a vacuum allows to fester. What ultimately happens is that students remain weak in EBM principles, go on to become professors, can not teach EBM to the extent that they ought to and a vicious cycle ensues whereby the full impact of man’s progress in Medicine will not be fulfilled. And the same applies to how individuals, departments and institutions implement auditing, quality-assurance, etc. as well.

A random post that I recently came across in the blogosphere touched upon the interesting idea that when you really think about it, most practicing physicians are ultimately technicians whose job it is to fix and maintain patients (like how a mechanic oils and fixes cars). The writer starts out with a provocative beginning,

Is There A Doctor In The House?


[…]

Medical doctors often like to characterize themselves as scientists, and many others in the public are happy to join them in this.

I submit, however, that such a characterization is an error.

[…]

and divides science professionals into,

[…]

SCIENTIST: One whose inquiries are directed toward the discovery of new facts.

ENGINEER: One whose inquiries are directed toward the new applications of established facts.

TECHNICIAN: One whose inquiries are directed toward the maintenance of established facts.

[…]

and then segues into why even if that’s the case, being a technician in the end has profound value.

Regardless of where you find yourselves in that spectrum within this paradigm, I think it’s obvious that gaining skills in one area helps you perform better in others. So as technicians, I’m sure that practicing physicians will find that their appraisal and implementation of EBM will improve if they delve into how discoverers work and learn about the pitfalls of their trade. The same could be said of learning about how inventors translate this knowledge from the bench to the bedside as new therapies, etc. are developed and the caveats involved in the process.

Yet it is precisely in these aspects that I find that medical education requires urgent reform. Somehow, as if by magic, we are expected to do the work of a technician and to get a grip on EBM practices without a solid foundation for how discoverers and inventors work.

I think it’s about time that we re-kindled the spirit of understanding scientific attitude at our higher educational institutions and in our lives (for those of us who are already out of university).

From self-study and introspection, here are a couple of points and questions that I’ve made a note of so far, as I strive to re-invigorate the scientific spirit within me, in my own way. As you reflect on them, I hope that they are useful to you in working to become a better science professional as well:

  1. Understand the three types of science professionals and their roles. Ask where in the spectrum you lie. What can you learn about the work professionals in the other categories do to improve how you yourself function?
  2. Learning about how discoverers work, helps us in getting an idea about the pitfalls of science. Ultimately, questions are far more profound than the answers we keep coming up with. Do we actually know the answer to a question? Or is it more correct to say that we think we know the answer? What we think we know, changes all the time. And this is perfectly acceptable, as long as you’re engaged as a discoverer.
  3. What are the caveats of using language such as the phrase “laws of nature”? Are they “laws”, really? Or abstractions of even deeper rules and/or non-rules that we cannot yet touch?
  4. Doesn’t the language we use influence how we think?
  5. Will we ever know if we have finally moved beyond abstractions to deeper rules and/or non-rules? Abstractions keep shifting, sometimes in diametrically opposite directions (eg: from Newton’s concepts of absolute space-time to Einstein’s concepts of relative space-time, the quirky and nutty ideas of quantum mechanics such as the dual nature of matter and the uncertainty principle, concepts of disease causation progressing from the four humours to microbes and DNA and ultimately a multifactorial model for etiopathogenesis). Is it a bad idea to pursue abstractions in your career? Just look at String Theorists; they have been doing this for a long time!
  6. Develop humility in approach and knowledge. Despite all the grand claims we make about our scientific “progress”, we’re just a tiny speck amongst the billions and billions of specks in the universe and limited by our senses and the biology of which we are made. The centuries old debate among philosophers of whether man can ever claim to one day have found the “ultimate truth” still rages on. However, recently we think we know from Kurt Godel’s work that there are truths out there in nature that man can never arrive at by scientific proof. In other words, truths that we may never ever know of! Our understanding of the universe and its things keeps shifting continuously, evolving as we ourselves as a species improve (or regress, depending on your point of view). Understanding that all of this is how science works is paramount. And there’s nothing wrong with that. It’s just the way it is! 🙂
  7. Understand the overwhelming bureaucracy in science these days. But don’t get side-tracked! It’s far too big of a boatload to handle on one’s own! There are dangers that lead people to leave science altogether because of this ton of bureaucracy.
  8. Science for career’s sake is how many people get into it. Getting a paper out can be a good career move. But it’s far more fun and interesting to do science for science’s own sake, and the satisfaction you get by roaming free, untamed, and out there to do your own thing will be ever more lasting.
  9. Understand the peer-review process in science and its benefits and short-comings.
  10. Realize the extremely high failure rate in terms of the results you obtain. Over 90% by most anecdotal accounts – be that in terms of experimental results or publications. But it’s important to inculcate curiosity and to keep the propensity to question alive. To discover. And to have fun in the process. In short, the right attitude; despite knowing that you’re probably never going to earn a Fields medal or Nobel prize! Scientists like Carl Friederich Gauss were known to dislike publishing innumerable papers, favoring quality over quantity. Quite contrary to the trends that Citation Metrics seem to have a hand in driving these days. It might be perfectly reasonable to not get published sometimes. Look at the lawyer-mathematician, Pierre de Fermat of Fermat’s Last Theorem fame. He kept notes and wrote letters but rarely if ever published in journals. And he never did publish the proof of Fermat’s Last Theorem, claiming that it was too large to fit in the margins of a copy of a book he was reading as the thought occurred to him. He procrastinated until he passed away, when it became one of the most profound math mysteries ever to be tackled, only to be solved about 358 years later by Andrew Wiles. But the important thing to realize is that Fermat loved what he did, and did not judge himself by how many gazillion papers he could or could not have had to his name.
  11. Getting published does have a sensible purpose though. The general principle is that the more peer-review the better. But what form this peer-review takes does not necessarily have to be in the form of hundreds of thousands of journal papers. There’s freedom in how you go about getting it, if you get creative. And yes, sometimes, peer-review fails to serve its purpose. Due to egos and politics. The famous mathematician, Evariste Galois was so fed-up by it that he chose to publish a lot of his work privately. And the rest, as they say, is history.
  12. Making rigorous strides depends crucially on a solid grounding in Math, Probability and Logic. What are the pitfalls of hypothesis testing? What is randomness and what does it mean? When do we know that something is truly random as opposed to pseudo-random? If we conclude that something is truly random, how can we ever be sure of it? What can we learn from how randomness is interpreted in inflationary cosmology in the manner that there’s “jitter” over quantum distances but that it begins to fade over larger ones (cf. Inhomogeneities in Space)? Are there caveats involved when you create models or conceptions about things based on one or the other definitions of randomness? How important is mathematics to biology and vice versa? There’s value in gaining these skills for biologists. Check out this great paper1 and my own posts here and here. Also see the following lecture that stresses on the importance of teaching probability concepts for today’s world and its problems:


    [Video]

  13. Developing collaborative skills helps. Lateral reading, attending seminars and discussions at various departments can help spark new ideas and perspectives. In Surely You’re Joking Mr. Feynman!, the famous scientist mentions how he always loved to dabble in other fields, attending random conferences, even once working on ribosomes! It was the pleasure of finding things out that mattered! 🙂
  14. Reading habits are particularly important in this respect. Diversify what you read. Focus on the science rather than the dreary politics of science. It’s a lot more fun! Learn the value of learning-by-self and taking interest in new things.
  15. Like it or not, it’s true that unchecked capitalism can ruin balanced lives, often rewarding workaholic self-destructive behavior. Learning to diversify interests helps take off the pressure and keeps you grounded in reality and connected to the majestic nature of the stuff that’s out there to explore.
  16. The rush that comes from all of this exploration has the potential to lead to unethical behavior. It’s important to not lose sight of the sanctity of life and the sanctity of our surroundings. Remember all the gory examples that  WW2 gave rise to (from the Nazi doctors to all of those scientists whose work ultimately gave way to the loss of life that we’ve come to remember in the euphemism, “Hiroshima and Nagasaki”). Here’s where diversifying interests also helps. Think how a nuclear scientist’s perspectives could change about his work if he spent time taking a little interest in wildlife and the environment. Also, check this.
  17. As you diversify, try seeing science in everything – eg: When you think about photography think not just about the art, but about the nature of the stuff you’re shooting, the wonders of the human eye and the consequences of the arrangement of rods and cones and the consequences of the eyeball being round, its tonal range compared to spectral cameras, the math of perspective, and the math of symmetry, etc.
  18. Just like setting photography assignments helps to ignite the creative spark in you, set projects and goals in every avenue that you diversify into. There’s no hurry. Take it one step at a time. And enjoy the process of discovery!
  19. How we study the scientific process/method should be integral to the way people should think about education. A good analogy although a sad one is, conservation and how biology is taught at schools. Very few teachers and schools will go out of their way to emphasize and interweave solutions for sustainable living and conserving wildlife within the matter that they talk about even though they will more than easily get into the nitty-gritty of the taxonomy, the morphology, etc. You’ll find paragraphs and paragraphs of verbiage on the latter but not the former. This isn’t the model to replicate IMHO! There has to be a balance. We should be constantly reminded about what constitutes proper scientific ethic in our education, and it should not get to the point that it begins to fade away into the background.
  20. The current corporate-driven, public-interest research model is a mixed bag. Science shouldn’t in essence be something for the privileged or be monopolized in the hands of a few. Good ideas have the potential to get dropped if they don’t make business sense. Understand public and private funding models and their respective benefits and shortcomings. In the end realize that there are so many scientific questions out there to explore, that there’s enough to fill everybody’s plate! It’s not going to be the end of the world, if your ideas or projects don’t receive the kind of funding you desire. It’s ultimately pretty arbitrary 🙂 ! Find creative solutions to modify your project or set more achievable goals. The other danger in monetizing scientific progress is the potential to inculcate the attitude of science for money. Doing science for the joy of it is much more satisfying than the doing it for material gain IMHO. But different people have different preferences. It’s striking a balance that counts.
  21. The business model of science leads us into this whole concept of patent wars and Intellectual Property issues. IMHO there’s much value in having a free-culture attitude to knowledge, such as the open-access and open-source movements. Imagine what the world would be like if Gandhi (see top-right) patented the Satyagrah, requiring random licensing fees or other forms of bondage! 🙂
  22. It’s important to pursue science projects and conduct fairs and workshops even at the university level (just as much as it is emphasized in high school; I would say to an even greater degree actually). Just to keep the process of discovery and scientific spirit vibrant and alive, if for no other reason. Also, the more these activities reflect the inter-relationship between the three categories of science professionals and their work, the better. Institutions should recognize the need to encourage these activities for curricular credit, even if that means cutting down on other academic burdens. IMHO, on balance, the small sacrifice is worth it.
  23. Peer-review mechanisms currently reward originality. But at the same time, I think it’s important to reward repeatability/reproducibility. And to reward statistically insignificant findings. This not only helps remove bias in published research, but also helps keep the science community motivated in the face of a high failure rate in experiments, etc.
  24. Students should learn the art of benchmarking progress on a smaller scale, i.e. in the experiments, projects, etc. that they do. In the grand scheme of things however, we should realize that we may never be able to see humongous shifts in how we are doing in our lifetimes! 🙂

    Srinivasa Ramanujan

    Srinivasa Ramanujan

  25. A lot of stuff that happens at Ivy League universities can be classified as voodoo and marketing. So it’s important to not fret if you can’t get into your dream university. The ability to learn lies within and if appropriately tapped and channelized can be used to accomplish great stuff regardless of where you end up studying. People who graduate from Ivy League institutes form a wide spectrum, with a surprising number who could easily be regarded as brain-dead. IMHO what can be achieved is a lot more dependent on the person rather than the institution he or she goes to. If there’s a will, there’s a way! 🙂 Remember some of science’s most famous stalwarts like Michael Faraday and Srinivasa Ramanujan were largely self-taught!
  26. Understand the value of computing in science. Not only has this aspect been neglected at institutes (especially in Biology and Medicine), but it’s soon getting indispensable because of the volume of data that one has to sift and process these days. I’ve recently written about bioinformatics and computer programming here and here.
  27. It’s important to develop a level of honesty and integrity that can withstand the onward thrust of cargo-cult science.
  28. Learn to choose wisely who your mentors are. Factor in student-friendliness, the time they can spend with you, and what motivates them to pursue science.
  29. I usually find myself repelled by demagoguery. But if you must, choose wisely who your scientific heroes are. Are they friendly to other beings and the environment? You’d be surprised as to how many evil scientists there can be out there! 🙂

I’m sure there are many many points that I have missed and questions that I’ve left untouched. I’ll stop here though and add new stuff as and when it occurs to me later. Send me your comments, corrections and feedback and I’ll put them up here!

I have academic commitments headed my way and will be cutting down on my blogular activity for a while. But don’t worry, not for long! 🙂

I’d like to end now, by quoting one of my favorite photographers, George Steinmetz:

[Video]
George Steinmetz: “… I find that there is always more to explore, to question and, ultimately, to understand …”

Footnotes:

  1. Bialek, W., & Botstein, D. (2004). Introductory Science and Mathematics Education for 21st-Century Biologists. Science, 303(5659), 788-790. doi:10.1126/science.1095480


Copyright Firas MR. All Rights Reserved.

“A mote of dust, suspended in a sunbeam.”


Search Blog For Tags: , , , ,

Written by Firas MR

November 6, 2010 at 5:21 am

Let’s Face It, We Are Numskulls At Math!

with one comment

Noted mathematician, Timothy Gowers, talks about the importance of math

I’ve often written about Mathematics before Footnotes. As much as math helps us better understand our world (Modern Medicine’s recent strides have a lot to do with applied math for example), it also tells us how severely limited man’s common thinking is.

Humans and yes some animals too, are born with or soon develop an innate ability for understanding numbers. Yet, just like animals, our proficiency with numbers seems to stop short of the stuff that goes beyond our immediate activities of daily living (ADL) and survival. Because we are a higher form of being (or allegedly so, depending on your point of view), our ADLs are a lot more sophisticated than say those of, canaries or hamsters. And consequently you can expect to see a little more refined arithmetic being used by us. But fundamentally, we share this important trait – of being able to work with numbers from an early stage. A man who has a family with kids knows almost by instinct that if he has two kids to look after, that would mean breakfast, lunch and dinner times 2 in terms of putting food on the table. He would have to buy two sets of clothes for his kids. A kid soon learns that he has two parents. And so on. It’s almost natural. And when someone can’t figure out their way doing simple counting or arithmetic, we know that something might be wrong. In Medicine, we have a term for this. It’s called acalculia and often indicates the presence of a neuropsychiatric disorder.

It’s easy for ‘normal’ people to do 2 + 2 in their heads. Two oranges AND two oranges make a TOTAL of four oranges. This basic stuff helps us get by day-to-day. But how many people can wrap their heads around 1 divided by 0? If you went to school, yea sure your teachers must have hammered the answer into you: infinity. But how do you visualize it? Yes, I know it’s possible. But it takes unusual work. I think you can see my point, even with this simple example. We haven’t even begun to speak about probability, wave functions, symmetries, infinite kinds of infinities, multiple-space-dimensions, time’s arrow, quantum mechanics, the Higgs field or any of that stuff yet!

As a species, it is so obvious that we aren’t at all good at math. It’s almost as if we construct our views of the universe through this tunneled vision that helps us in our day-to-day tasks, but fails otherwise.

We tend to think of using math as an ability when really it should be thought of as a sensory organ. Something that is as vital to understanding our surroundings as our eyes, ears, noses, tongues and skins. And despite lacking this sense, we tend to go about living as though we somehow understand everything. That we are aware of what it is to be aware of. This can often lead to trouble down the road. I’ve talked about numerous PhDs having failed at the Monty Hall Paradox before. But a recent talk I watched, touched upon something with serious consequences that meant people being wrongfully convicted because of a stunted interpretation of DNA, fingerprint evidence, etc. by none other than “expert” witnesses. In other words, serious life and death issues. So much for our expertise as a species, eh?!

How the human mind struggles with math!

We recently also learned that the hullabaloo over H1N1 pandemic influenza had a lot do with our naive understanding of math, the pitfalls of corporate-driven public-interest research notwithstanding.

Anyhow, one of my main feelings is that honing one’s math not only helps us survive better, but it can also teach us about our place in the universe. Because we can then begin to fully use it as a sensory organ in its own right. Which is why a lot of pure scientists have argued that doing math for math’s own sake can not only be great fun (if done the right way, of course :-P) but should also be considered necessary. Due to the fact that such research has the potential to reveal entirely new vistas that can enchant us and surprise us at the same time (take Cantor’s work on infinity for example). For in the end, discovery, really, is far more enthralling than invention.

UPDATE 1: Check out the Khan Academy for a virtually A-Z education on math — and all of it for free! This is especially a great resource for those of us who can’t even recall principles of addition, subtraction, etc. let alone calculus or any of the more advanced stuff.

Copyright © Firas MR. All rights reserved.


# Footnotes:

  1. ذرا غور فرمائیے اپنے انسان ہونے کی حیثیت پر
  2. Decision Tree Questions In Genetics And The USMLE
  3. The Story Of Sine
  4. On The Impact Of Thinking Visually
  5. A Brief Tour Of The Field Of Bioinformatics
  6. Know Thy Numbers!

, , , , ,

Wilson!

with 6 comments

Remember Wilson the volleyball, from the movie ‘Castaway‘? In a dash of newfound creativity and imagination, I shot a couple of photographs today of a coconut that shared an uncanny resemblance to Wilson! Seemed like the perfect opportunity for some prop-photography :-D.

Wilson reads for the USMLE

Wilson reads for the USMLE.

Somehow he seems quite absorbed with the book ;-), don’t you think? Ah, nothing beats the joy of laying back, relaxing and reading a nice book.

Wilson in the Orient.

Wilson in the Orient.

On his travels to the Orient, he received a fancy hand-held fan as a gift from a monk. In fact, that is exactly where he discovered his inner intellectual :-P.

Wilson is a bike rider and loves his moped.

Wilson is a bike rider ...

… and loves his moped. How else would an intelligent coconut choose to conquer the streets?

Copyright © Firas MR. All rights reserved.

Share

Written by Firas MR

August 21, 2009 at 3:25 pm

On The Impact Of Thinking Visually

with 5 comments

Romanesco broccoli - One of many examples of fractals in nature. (Wikipedia)

Romanesco broccoli - One of many examples of fractals in nature. (Wikipedia)

What do Mandelbrot and Einstein have in common?

They were/are both math aficionados. But more importantly, they both laid down the foundations for thinking about abstract natural phenomena in a geometrical way. The impact was reverberating.

Before Einstein came along, people had no real sense of gravity at all. Yea sure, there was Newton’s universal law of gravitation. But no one really could make any sense whatsoever of how exactly gravity might operate. Was it a wave? If so, at what speed could it act? Was there something particulate about it? Gravity was so mystical. And as always, so have been the concepts of time and space. Einstein’s greatest achievement in my view is that not only was he able to lay out the underpinnings of such phenomena in the form of a couple of abstract equations, but perhaps more importantly, that he devised a method to think about them visually. In developing his theories of special and general relativity, Einstein proposed the idea of the space-time fabric. It has a 3-D structure, yet represents four dimensions – 3 in space and 1 in time. Gravity would result from distortions in this fabric. The speed with which gravity could influence an object would depend on how fast these distortions could travel. And this central notion of ‘distortions in a fabric’ would also influence our understanding of the more difficult to grasp concepts of time and space. Time and space could mean different things to different observers depending on how this fabric was warped or sliced.

Mandelbrot achieved the same thing with his theory of fractals. How can complex natural structures and phenomena be represented mathematically? How to mathematically model a plant, the form of a human or a mountain range? In spite of how incredibly difficult it all sounds, these complex shapes could all be simplified into repeating units of tiny yet geometrically simple components – fractals. Mandelbrot went on to write his epic, “The Fractal Geometry Of Nature” and there was no turning back. Suddenly so many of nature’s workings could now be analyzed mathematically. An immensely significant step for mankind indeed. What I find absolutely fascinating about fractals, is the discovery that many intangible natural phenomena also contain a fractal component. Dr. Ary Goldberger and his team of researchers at Harvard Medical School have been working on applying fractal theory to medicine and biology. For those of you who might not be familiar with Dr. Goldberger, the name might ring a bell if you’ve read his books on electrocardiography. For Dr. Goldberger, interest in electrocardiography runs in the family, his father having invented the augmented limb leads back in the day. Among some of the things I learned about his work on electrocardiography, is that his team has shown that there is a fractal nature to ECG waveforms! This isn’t something like representing the heart itself in fractal form. It’s the activities of the heart that we are talking about here. Something really quite abstract. By looking at these fractal patterns, one could potentially detect pathology at a much earlier stage. Fractal patterns and their aberrations could help detect diseases in ways that no one had ever imagined! If you want to dig what’s cool, check out what’s been going on in the world of fractals in medicine – from human vasculature, to the brain and beyond. A quick PubMed query would lead you to a lot of riveting literature on the topic. Don’t forget to also take a look at the excellent documentary on fractal theory from PBS NOVA, “Hunting The Hidden Dimensions“.

Copyright © Firas MR. All rights reserved.

Readability grades for this post:

Flesch reading ease score: 61.1
Automated readability index: 8.6
Flesch-Kincaid grade level: 8.2
Coleman-Liau index: 10.8
Gunning fog index: 11.6
SMOG index: 11

Written by Firas MR

August 18, 2009 at 11:48 pm