Posts Tagged ‘Education’
I’ve always been struck by how nerds can act differently in different fields.
An art nerd is very different from a tech nerd. Whereas the former could go on and on about brush strokes, lighting patterns, mixtures of paint, which drawing belongs to which artist, etc. the latter can engage in ad-infinitum discussions about the architecture of the internet, how operating systems work, whose grip on Assembly is better, why their code works better, etc.
And what about math and physics nerds? They tend to show their feathers off by displaying their understanding of chaos theory, why imaginary numbers matter, and how we are all governed by “laws of nature”, etc.
How about physicians and med students? Well, like most biologists, they’ll compete with each other by showing off how much of anatomy, physiology or biochemistry or drug properties they can remember, who’s uptodate on the most recent clinical trial statistics (sort of like a fan of cricket/baseball statistics), and why their technique of proctoscopy is better than somebody else’s, the latest morbidity/mortality rates following a given procedure, etc.
And you could actually go on about nerds in other fields too – historians (who remembers what date or event), political analysts (who understands the Thai royal family better), farmers (who knows the latest in pesticides), etc.
Each type has its own traits, that reflect the predominant mindset (at the highest of intellectual levels) when it comes to approaching their respective subject matter. And nerds, being who they are, can tend to take it all to their heads and think they’ve found that place — of ultimate truth, peace and solace. That they are at last, “masters” of their subjects.
I’ve always found this phenomenon to be rather intriguing. Because in reality, things are rarely that simple – at least when it comes to “mastery”.
In medicine for instance, the nerdiest of most nerds out there will be proud and rather content with the vast statistics, nomenclature, and learn-by-rote information that he has finally been able to contain within his head. Agreed, being able to keep such information at the tip of one’s tongue is an achievement considering the bounds of average human memory. But what about the fact that he has no clue as to what fundamentally drives those statistics, why one drug works for a condition whereas another drug with the same properties (i.e. properties that medical science knows of) fails or has lower success rates, etc.? A physicist nerd would approach this matter as something that lies at the crux of an issue — so much so that he would get sleepless nights without being able to find some model or theory that explains it mathematically, in a way that seems logical. But a medical nerd? He’s very different. His geekiness just refuses to go there, because of the discomforting feeling that he has no idea whatsoever! More stats and names to rote please, thank you!
I think one of the biggest lessons we learn from the really great stalwarts in human history is that, they refused to let such stuff get to their heads. The constant struggle to find and maintain humility in knowledge was central to how they saw themselves.
… I can live with doubt and uncertainty and not knowing. I think it’s much more interesting to live not knowing than to have answers which might be wrong. I have approximate answers and possible beliefs and different degrees of certainty about different things, but I’m not absolutely sure of anything and there are many things I don’t know anything about, such as whether it means anything to ask why we’re here, and what the question might mean. I might think about it a little bit and if I can’t figure it out, then I go on to something else, but I don’t have to know and answer, I don’t feel frightened by not knowing things, by being lost in a mysterious universe without having any purpose, which is the way it really is so far as I can tell. It doesn’t frighten me.
— Richard Feynman speaking with Horizon, BBC (1981)
The scientist has a lot of experience with ignorance and doubt and uncertainty, and this experience is of great importance, I think. When a scientist doesn’t know the answer to a problem, he is ignorant. When he has a hunch as to what the result is, he is uncertain. And when he is pretty darn sure of what the result is going to be, he is in some doubt. We have found it of paramount importance that in order to progress we must recognize the ignorance and leave room for doubt. Scientific knowledge is a body of statements of varying degrees of certainty – some most unsure, some nearly sure, none absolutely certain.
Now, we scientists are used to this, and we take it for granted that it is perfectly consistent to be unsure – that it is possible to live and not know. But I don’t know everybody realizes that this is true. Our freedom to doubt was born of a struggle against authority in the early days of science. It was a very deep and very strong struggle. Permit us to question – to doubt, that’s all – not to be sure. And I think it is important that we do not forget the importance of this struggle and thus perhaps lose what we have gained.
Besides being an important aspect for high-school students to consider when deciding what career path to pursue, I think that these nerd-personality-traits also illustrate the role that interdisciplinary thinking can play in our lives and how it can add tremendous value in the way we think. The more one diversifies, the more his or her thinking expands — for the better, usually.
Just imagine a nerd who’s cool about art, physics, math or medicine, etc. — all put together, in varying degrees. What would his perspective of his subject matter and of himself be like? Would he make the ultimate translational research nerd? It’s not just the knowledge one could potentially piece together, but the mindset that one would begin to gradually develop. After all, we live in an enchanting web of a universe, where everything intersects everything!
Copyright Firas MR. All Rights Reserved.
“A mote of dust, suspended in a sunbeam.”
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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.
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:
- 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?
- 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.
- 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?
- Doesn’t the language we use influence how we think?
- 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!
- 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! 🙂
- 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.
- 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.
- Understand the peer-review process in science and its benefits and short-comings.
- 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.
- 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.
- 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:
- 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! 🙂
- 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.
- 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.
- 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.
- 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.
- 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!
- 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.
- 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.
- 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! 🙂
- 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.
- 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.
- 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! 🙂
- 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!
- 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.
- It’s important to develop a level of honesty and integrity that can withstand the onward thrust of cargo-cult science.
- 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.
- 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:
George Steinmetz: “… I find that there is always more to explore, to question and, ultimately, to understand …”
- 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.”
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.
“You are more than a score”, or so the saying goes. But how much of that comes out as an emotional outburst as opposed to objective and rational thinking? Let’s try to see why the above is totally true, scientifically speaking.
In medicine, we’ve learned a lot about diagnostic tests, right? In fact everything investigative in nature can be considered a diagnostic test. Be it a screening exam for cervical cancer, that blood test for glucose, an X-ray for a broken arm, or your palpating hand feeling for that enlarged liver. Heck, even an entire research study could be considered a diagnostic test. The ‘null hypothesis’ technique often used in analytical research studies is nothing more than a diagnostic test of sorts.
When considering the dynamics of a diagnostic test, a fundamental underlying principle is that we separate what is observed via the test from the actual truth. In the case of tangible phenomena like death, disease and disability, it is quite easy to distinguish the actual truth from what the test predicts. Because of this, you have terms like ‘false positives’, ‘false negatives’ and the like. A pregnancy test for example could be positive, but you could easily compare that prediction to the actual outcome (pregnancy vs. non-pregnancy) and say that this particular test has got such and such false positive rates. More or less, all tests have the following attributes in this regard:-
- Positive Predictive Value
- Negative Predictive Value
We ought to think about examinations such as the USMLE, etc. in this manner as well. Why? Well, because they are investigations too! Think of them as X-rays to diagnose your intelligence or whatever, if that metaphor helps. And as a consequence, notions about false positives, false negatives and all of the other things on that list also apply to them. Being the abstract intangible thing intelligence is, it is impossible to know its true value. And because there’s no way to compare prediction versus truth, it is impossible to say for sure what the false positive or negative rates (or any item on that list) for an exam are. And that’s why, ‘you are more than a score’ ! Statistically speaking, examinations are just so lame !
Do send in your comments!
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