So you want to be a polymath

But not just any old polymath, you want to really break ground, shift some paradigms, really go for it. Well, I wouldn't recommend it, but if you must, here's my advice. I won't tell you what courses to take or to memorize anything or to read a certain book or go to a certain school or anything at all that's that specific; that's your job. I also won't tell you to read a lot growing up, be inquisitive and question everything, and so on because you already do that, presumably. You have the right stuff and you take your vitamins. You're smart, athletic, charming, sensitive. Now you just need knowledge to fill up that head of yours. But as they say, you have to "learn how to learn." Here's a good start:

0. Learn, accept, and embrace the second law of thermodynamics. See the entire universe in terms of entropy. This is possibly the most important concept of all, or it's right there with a few of the other heavies. Potentials being tapped and not refilled except at the cost of tapping another potential, energy states endlessly dropping, no free lunch ever, everything trying to average out into a grey useless, random, informationless landfill. The universe runs on batteries, essentially, draining over time. No perpetual motion machines, no way out of the slow slide from order to disorder. Get used to it, because everything else lives within this idea, even localized process, such as life, which seem to buck the trend and create structure and complexity. Rest assured, a greater amount of complexity is lost elsewhere in a closed system (an assumption) to account for it. No free lunches!

1. Learn to interpret, present, and think in graphs. Just simple x,y plot graphs. But get them down cold. When you ask a scientist something, especially a physicist, the first thing she'll do is grab a napkin and draw a graph (just the +,+ region) and then a plot, and maybe tell you what x and y represent. You have to think that way automatically. Read lots of basic Feynman (his undergrad stuff) for practice.

2. Learn the concepts of calculus (approaching limits, the value of one dependent variable as the other goes to infinity or goes to zero, approximation to an nth degree) - essentially, the idea of finding the area under a curve with non-curved "tools." Just grasp it and make it part of your thinking. "I can approximate as close as needed to for my purposes but never get that last bit accounted for..." Like Achilles racing the Tortoise, the concept of diminishing returns, the half-life of a cesium atom, the forever-tightening definition of pi. Pick your favorite metaphor. Just remember it's a grainy world, and tools are grainy, and nothing in the real world is Euclidean or Platonic. The world seems to be discrete in every way we know how to measure, yet our models of it assume continuity at the lowest levels of time and space. What is real? Analog vs. digital. Think of these things, understand the difference.

3. Learn conceptually about non-linear systems: Fractal mathematics (qv. Cantor, Mandelbrot), chaos, complexity, emergence, autonomous synchronization, 'anti-entropy' (life?), and all the other ways of seeing and interpreting the vast floods of data you will be inundated with. Our brains are good at finding order where there is none, good at yelling that a thing is irrational or even miraculous when it's simply very improbable. Improbable things happen all the time. Don't get caught up too much in any of these still poorly-understood disciplines on your first pass, just understand the currents that moves our matter/energy + time around, pull it apart, and reassemble it again. Build up a great muscle-memory feel for what these currents are as they manifest themselves all around you in the pine cone of a tree, the shape of a shoreline, the architectural layout of many tribal villages in Africa, clouds, the shell of the chambered nautilus. Study a fern for an entire day sometime when the weather's nice - bring a good lunch and hours of Indian ragas on your iPod and stay with that fern till you Get It. I'm serious. Stay as long as you need to. Again, simply develop the habit of looking at the world with new eyes. Be able to talk meaningfully about how reality as we currently model and try to understand it is shaped by these forces, these recurring themes, in reality. Entropy eroding structure while self-organization constructs it again seemingly against the odds; systems so complex that a full analysis is beyond the information/computing ceiling in which we work (our universe). One can ask, is something which spirals into infinite complexity even a 'thing' anymore once it has crossed that boundary where it could never be described even in theory given all the computing power of our universe? Or does it lose its nature entirely like a star or an astronaut crossing an event horizon and falling into a black hole, recycled in a way but not in such a way that entropy does not again increase. Don't try to answer that one yet, but this is how you should be thinking almost all the time, day and night, about everything around you. You need to begin to fit things into your web or hierarchy or whatever umbrella mind-crutch you use to keep it all cobbled together and making sense relationally. Me, I'm an Ouroboros guy.

4. Don't think about chance (or determinism) too much, nor infinity, though you will need to use them often enough, especially in imprecise statistical analyses of an existence that doesn't quite live up to Plato's ideals. Whereas you should learn the concepts of #2 and #3 intimately and develop a good intuitive feel for how they work out in the real world but don't necessarily have to be brilliant at applying them practically just yet, #4 is different. Don't try to understand the concepts of infinity or singularities or time (or life or death while we're at it), just learn to use them as tools for solving practical problems. Otherwise you could go mad, for real. Mathematicians have one of the highest suicide rates of any occupation in the academic world, and perhaps in the world at large. I'm not sure of the statistics but I know they're up there. Here are some cautionary tales supporting that statement. History is littered with the broken minds of men who though they could pull the mathematical sword from the stone. Don't be chivalrous unless your only goal is to be a brilliant martyr. If you intend to do anything which survives, you and your faculties must survive. Don't go jumping into rabbit holes. It's way sunnier out here, trust me.

5. Learn to think in terms of orders of magnitude, rough but meaningful approximations that get you in the right ballpark, rather than worry about the digits coming out precisely. Back of the envelope thinking, in other works. It's ok to think that maybe Jupiter is 3 times as far away from the Sun as is the Earth (it's actually 5), but to think it was 30 times farther away would demonstrate a lack of understanding on your part that is more fundamental. Likewise, when talking about large distances, after a certain number of light-years it all seems to mean the same thing - really, really far. But you can't think that way. It's been said that if an atom were blown up to the size of a football stadium, the nucleus would be the size of a marble. And the closest nucleus away (if the atoms were part of a solid) would be in the stadium right next door. That's how much empty space "solids" contain. Liquids and gasses are even more rarefied. Also, human beings seem to be just about in the middle of the size spectrum - take all those atoms that make you up and that's about the same number of you - your body - that it would take to fill up the sun were it hollow. But of course or sun isn't the biggest star there is (have a look). And even the largest star known is many orders of magnitude smaller than any galaxy, and the distance between galaxies on average is something proportionately like a pea in Los Angeles would be from a pea in Manhattan. But even galaxies form superclusters, which tend to make a filamentary web shape with lots of holes of basically nothing within them (some postulate dark matter, whatever it may be, causes the visible galaxies to form that way). And what is the distance between superclusters? So you see what I mean. The "gigantic" Sun is not not even close to the same level of gigantic as are some stars, and so on. If you were a galaxy, the stars which made up your body would be not much bigger than the size of quarks, the smallest things known. And yet there are trillion of galaxies. It's all very mind-blowing, but get used to it and get your ballpark figures straight. A trillion isn't anything like a million, anymore than a million is like one. The cosmos is so vast and empty, and the microworld so minuscule and empty, that there is really nothing in the universe at all, when you add it all up. The matter that's there would be rounded off to zero in most calculations. It's simply not significant compared to the amount of nothingness that exists. In fact, intergalactic space contains a million times fewer particles that does the best vacuum yet created in an Earth lab. And even the solar system, which looked as though it were brimming over with interesting things on the poster tacked to the wall in your elementary school, is so rarefied that if you suddenly appeared at a completely random place within it, you'd likely be in an area millions of times more sterile than a Class 5 Clean Room, the kind the government uses to handle weapons-grade anthrax. And contrary to the common picture many people have that the asteroid belt between Mars and Jupiter is a wild and woolly place teeming with rubble, the fact is if you collected all that matter and made it into a ball, it would be smaller than the moon. And if you were standing on almost any of the asteroids in that belt, you'd be able to see the Sun (of course), Jupiter as a very bright object, Mars and the Earth and Saturn as somewhat fainter objects, and, get this, you almost certainly couldn't with your naked eye even see another asteroid anywhere near you. Even if they glowed of their own accord and weren't as dim as they are, the distance between the average rock in that belt would prohibit you from forming any conclusion other than that you were alone in that orbit. So, getting back to the point, scale, in terms of size, temperature, age, and other attributes is extremely importantly to grasp, but only in a relative way, such that 99% of the time no one cares if you're off by what you might think is a huge amount, if you're in the correct magnitude (power of ten). Your brain has evolved to deal with precise quantities and distances. You need to forget about all that if you're going to have a shot at even beginning to understanding the universe. Getting correct within a factor of ten is usually close enough when you're talking cosmology or particle physics. So, practice your powers of ten. Express yourself in powers of ten in science, and in the metric system, because it's easier in the long run that way, not to mention that if you want to publish anything and not just be an armchair polymath, you'll be required to do so. Watch the old Charles and Ray Eames film showing a steady camera pull away from a human-scale Earth steadily outward by factors of ten, until the galactic superclusters themselves are shown (animated of course), and if you can, try to pay attention to the scale at which each type of object (a star, a solar system, a galaxy) exist. 10^?. If you can remember those scales, you'll have a big leg up. Now the film plunges down back to earth and this time keeps on going, into the subatomic work, which is sort of a mirror image of the pullout, except that each order of magnitude is expressed as 10^-n where n is increasing by one each time. You'll see that, indeed, we live at roughly the "middle" of the size scale in the universe when considered logarithmically like this. The take home message is to leave your calculator in the drawer for now and try to intuitively grasp all the different scales you've seen. Not just us and then "really big" and "really small," but huge leaps of big and small going in both ways for quite some time.

6. Don't worry about the three spatial dimensions. You know enough about them intuitively. For now, think of the universe consisting of 2 fundamental things: a) matter/energy, and b) time. Next, consider information. Information can be represented by the precise state of matter and energy over time, and so is a derived rather than fundamental property. Be aware that unlike in mathematics, in the physical world not all things are solvable, simply because there is not enough informational room, enough computational power, even in the whole of the universe. If we bring the quantum theory's many-worlds interpretation into play, we can perhaps salvage enough such power and storage in one unique world-line, but only at the expense of many others. Some speculations are not sustainable, like God, or like a holographic universal simulacrum designed to fool us by some higher intelligence. It becomes a problem of recursion and endless regress, for who is to construct the constructors? That is going against Occam's law and making things more complex than they need to be to achieve the same thing. For now just think of information capacity as a fundamental property of all closed systems. How much information can such a system store and how much power can it bring to bear on itself in terms of actual physical processes? This isn't just a thought game after all; at least, we must assume it's not, or why do anything? This is actually where I've been stuck for years, being unconvinced that what I am experiencing is real. The ability of a given region of space to store information is a ceiling which is as unbreachable as the second law, though it may be that space is very complex, with many hidden dimensions, or it may be holographic or fractal, in which case things get weird. But if the room to store data is limited in some way, then you must remember that information can only be compressed so much before it becomes lossy. The most basic system of all is a 2-bit system, on or off, black or white, yea or nay. You can arrange it many clever ways, but not infinitely cleverly; there is a minimum amount of matter/energy + time which much exist per unit of information, and it is quantifiable and infrangible (probably). By the way whenever I say something is absolutely, fundamentally true, like the fact that entropy always increases over time (the second law), you should mentally put a "(probably)" at the end. That is because none of us is God and everything we think we know and have achieved has been done with bodies ostensibly evolved for something completely different, and it would be the sheerest act of hubris to ever assume we had reached the fundamental truth about anything. That's why if you're honest with yourself, and bright enough to think about it correctly, you can be nothing other than an agnostic, which is to say, to "be" nothing. Don't believe anything, just experience it, and try to make sense of it if you want.

7. Learn to express yourself precisely. Use the correct word for what it is you mean to say, and try to observe Occam's razor in your speech and your thoughts, even as you would in your scientific inquiries. In a related vein, take at least one formal logic class (or read the textbook) and learn to reason formally and precisely. Learn to spot logical fallacies; practice every day in every conversation, even though you don't have to speak up every time and let the person know that what they just said is spurious, make a note of it in your head. Rationality and precision allow you to construct watertight proofs, which allows you to design good experiments to test theories, and most importantly to do the proper analysis when the results are in. Always be one hundred percent honest. The facts don't lie. To paraphrase Feynman, no matter how beautiful or elegant a theory is, if the facts contradict it, or any part of it no matter how small (in a repeatably demonstrable way), then it's wrong. Hold yourself to the same rigorous standards you hold the world to, or authors or scientists to. Ethics and morality is more important than truth in the real world where we all live and have to get along with one another, so be impeccably ethical in addition to being precise and curious. Polymaths should not use their growing understanding of the interwoven nature of reality as a club with which to bludgeon others; that is despicable. Learn about Zen Buddhism and Taoism and Confucianism. Ignore anything supernatural in them - that stuff was invariably tacked on later. Concentrate on the philosophies. Be a gentleman or gentlewoman. Do good things because you can, and it will make your life qualitatively better, not because there's some reason you have to. Look for balance in your life as you hoover up facts and assemble them into your ever-growing model of understanding. Be humane, love animals and get out into nature as often as possible. Have hobbies like photography or rock collecting or birdwatching, whatever you find fascinating. It's ok to indulge in these things because they too give you knowledge, in a hands-on way much different from what you get while reading or listening. First-hand experience is vital. Learn about the way the ecosystem works by feeling yourself to be a part of it, not isolated in a room somewhere staring at a screen or a page or a person learning about it vicariously. Get your hands dirty. Go on a fossil dig. Go see foreign cultures. Broaden your mind, just be aware that you can't narrow it again once you do. Thomas Jefferson once said, "traveling makes you wiser but less happy." I think that's basically true. The world can be pretty sobering, if not outright depressing in many cases. This is like looking into math too much: If you have a history of depression or a fragile makeup, maybe it's best not to be too ambitious. Of course, only you can determine that.

8. Listen to people you get warm fuzzies about (intellectually) with breathless attention. Absorb all you can that is already known and expounded by the current leaders in every subfield in which you have interest provided that you have a hunch those people know what they're talking about. (I will provide a great resource for you to do this in an upcming post.) Human beings are social creatures, so be as social as you can be in the right circles. Don't reinvent the wheel. Climb up on the shoulders of all the giants who have come before you and left their mark, and you will see further. But don't take everyone at face value either. Many longstanding commonsense ideas are wrong. Challenge these ideas, no matter the pedigree of the person who proposed them, if you feel this to be the case. Einstein had the nerve to challenge Newton, after all, and Einstein was right to do so. And Bohr and Heisenberg challenged Einstein, and they were right to do so. No one is a god, no matter how brilliant they are. You must stick to your guns and your reason. Reduce a conundrum to its most elementary constituents and find the solution using adequate and well-designed experiments and impeccable reasoning, and go where that takes you. Cheerfully admit you're wrong when you are, but don't be afraid to conclude everyone else is wrong either, if that is truly what you find (and keep finding through repeated experiments). Maybe you just discovered some new truth! Old "truths" are being overturned all the time, it's not a big deal. That's how science moves forward. Just remember that extraordinary claims require extraordinary evidence. Expect hostility from the old guard, the mainstream. If you're getting lots of resistance, it probably means you're onto something.

9. Read about the history of science, and read the groundbreaking works in the original, once you are able to. The power of an idea tends to dilute the further removed from the idea the author is at, kinda like the gospels. The best of all would be to have "The Gospel of Jesus," right? But we don't have that. Next best would be to have eyewitness accounts in their original from his apostles, but we don't have those either. The best we get in Biblical study is maybe third or fourth generation accounts written 30 to 100 years after the alleged crucifixion, and to compound matters, these accounts were translated and transcribed so many times prior to the invention of the printing press that they're about as accurate as the last person in a game of "telephone" (in America) or "Chinese whispers" (in Britain). In other words, not very accurate at all. So while popular accounts are fun and by all means, you should read the better ones, eventually you'll have to get to the source itself, if it still exists (and in the modern sciences, they all still exist, which is fortunate), and tough it out. Read Galileo in English translation if you don't speak Italian and Newton's Principia in translation if you don't read Latin. Or even better, learn Latin and Greek. Read all of Darwin for sure; he wrote in English so you've no excuse not to. Read Einstein, Gödel, Cantor, Mendel, Watson, Pascal, Maxwell, Kant, Wigner, Euclid, and so on. And don't neglect your right brain: Go to art galleries, read about art, have opinions about art and argue them with others. Participate in athletics. Read as much history as you can, about anything. Pay attentions to how the same patterns repeat themselves in so many unrelated aspects of life. Read fantasy and (especially) sci-fi. A lot of great ideas which bore practical fruit started life as science fiction, whether from Jules Verne, HG Wells, Arthur C. Clarke, Isaac Asimov, or others. Read sociology and psychology. Learn about anatomy and physiology. Read the most current ideas about consciousness and neuroscience. Read Spinoza and Luria and Damasio. Read Hofstadter and Penrose and Hawkins and Dennet. Read the Greeks! All of them! Read Herodotus, Tacitus, Pliny the Elder, Josephus, and all the other ancient historians, but read them skeptically and remember whose pay they were in. Read about warfare and politics and philosophy (don't get bogged down though), and ancient civilizations, especially Egypt. Study Egypt very carefully: It's where nearly every aspect of our culture and what wisdom we have came from. Before Egypt humans were just smart animals. Something special happened there. Do your own writing too. Make a blog and pour your ideas onto it or create whatever it is you find interesting. Learn a programming or scripting language - why not? It will demystify the Web a bit and one more piece of the puzzle will slide down and lock in. Explain things to others to be sure you understand them yourself. Allow others to ask you questions and see if you can answer them to their satisfaction. Meditate. Sleep and eat well. Stay positive if you can, or you won't want to do any of this. Hang out with children, they see the world with fresh eyes and say surprising things that may lead you in new directions. Volunteer, both to help your community and your soul. Get into gardening or tai-chi or walk or swim every morning. The body is the temple in which the mind lives. Don't destroy the temple.

Good luck. This is just the briefest overview and is probably overwhelming. But if it's compelling as well - if you think you've just found some place on the web that is talking about exactly what you've been wrestling with on your own - then stick around awhile. I'll return to this subject. I'll break down each portion in more detail and recommend certain books and lectures and resources. You realize that the further you want to go, the more alone you will be, and soon there will be no one to guide you. Loneliness is the price of genius. But if you want it that badly, I can offer some help and point the way to certain things. I would like to write a lengthy book assimilating virtually ALL that I know into one cohesive, explicable whole. I've been a data collector for decades seemingly for that purpose. So stick around and watch what happens, or contribute if you feel that compulsion. I know I'm not alone in trying to make sense of it all.