# How to be analytically creative?

March 9, 2011 2:37 PM Subscribe

I have a poetic, creative, intuitive brain. I feel out of my element talking to programmers, mathematicians, and physicists, yet I find their ideas aesthetically intriguing and I want to understand them.

I want to really grok reading Douglas Hofstadter, Richard Feynman, Stephen Hawking, etc. I want to understand quantum physics in more depth, rather than be limited to the way it's presented in popular media as aligned with New Age spirituality (which I find very suspect). I want to develop my ability to think in a quantitatively creative way.

So, where do I begin? Are there specific exercises, like logic puzzles, that I can do to strengthen these skills? Are there basic books I can read to help take me to the next level and beyond? Or classes?

I went up to trig in high school and took a college course in logic, and I still remember a fair amount of this stuff. Unfortunately, it was presented to me in a rote, boring way, and I didn't realize there were dazzling leaps of creativity in the quantitative and scientific fields until I was well out of school, so I focused on developing my interpersonal and artistic skills, which simply interested me more.

When I read about cool theories and inventions, or see things like jokes written as equations and things like that, I feel like there's this whole intellectually tantalizing world out there that I can only see glimpses of. I'm not one to believe that artistic people have brains that "just don't work that way" anymore. How do I get mine to do so?

I want to really grok reading Douglas Hofstadter, Richard Feynman, Stephen Hawking, etc. I want to understand quantum physics in more depth, rather than be limited to the way it's presented in popular media as aligned with New Age spirituality (which I find very suspect). I want to develop my ability to think in a quantitatively creative way.

So, where do I begin? Are there specific exercises, like logic puzzles, that I can do to strengthen these skills? Are there basic books I can read to help take me to the next level and beyond? Or classes?

I went up to trig in high school and took a college course in logic, and I still remember a fair amount of this stuff. Unfortunately, it was presented to me in a rote, boring way, and I didn't realize there were dazzling leaps of creativity in the quantitative and scientific fields until I was well out of school, so I focused on developing my interpersonal and artistic skills, which simply interested me more.

When I read about cool theories and inventions, or see things like jokes written as equations and things like that, I feel like there's this whole intellectually tantalizing world out there that I can only see glimpses of. I'm not one to believe that artistic people have brains that "just don't work that way" anymore. How do I get mine to do so?

Eminent dutch theoretical physicist Gerard 't Hooft (surname literally means

Khan Academy is a great resource for basic (undergraduate level) math.

The thing about these disciplines is that, unlike most of the humanities, you

So get humble. Accept that you'll have to spend some time (re-)learning things taught to middle-school students, e.g., realizing you forgot the 7+ rows of your multiplication tables when you're taking a linear algebra exam.

Progress will be accrued in inches of attempted problems. There is no other way. You can't just skim the book, because even if you are the rare person who groks that way, the next level of math will require you to be totally facile with the levels previous, which can only come about by doing the problems until you don't need to think to do them.

Finally, realize that while traditionally college students are funneled through a basic algebra, trig, calculus, curriculum, there are equally interesting (if not always as practical) branches of math like discrete and topology.

You might enjoy

posted by phrontist at 2:56 PM on March 9, 2011 [6 favorites]

*the head*) has this guide on becoming a theoretical physicist. The first few steps are largely what you're looking for, I think.Khan Academy is a great resource for basic (undergraduate level) math.

The thing about these disciplines is that, unlike most of the humanities, you

*have*to learn topics in sequence, for the most part. If you're interested in continental philosophy you can read a bit a Nietzsche and get a shallow understanding of his approach and the sorts of topics that concerned him. It's not like that with STEM fields - if you're weak on prerequisites, you just won't be able to progress.So get humble. Accept that you'll have to spend some time (re-)learning things taught to middle-school students, e.g., realizing you forgot the 7+ rows of your multiplication tables when you're taking a linear algebra exam.

Progress will be accrued in inches of attempted problems. There is no other way. You can't just skim the book, because even if you are the rare person who groks that way, the next level of math will require you to be totally facile with the levels previous, which can only come about by doing the problems until you don't need to think to do them.

Finally, realize that while traditionally college students are funneled through a basic algebra, trig, calculus, curriculum, there are equally interesting (if not always as practical) branches of math like discrete and topology.

You might enjoy

*The Two Cultures*, by C.P. Snow.posted by phrontist at 2:56 PM on March 9, 2011 [6 favorites]

I'm an artist and I totally did this. There's tons of books out there for lay people. Often I would be able to understand the first couple chapters and the last chapter. I'd read the hard stuff in the middle as far I could until I had to give up, or go research terms to get up to speed. I got basic physics text books and pored over them, trying to get a handle on particle theory. I wanted to understand the uncertainty principle, the double-slit experiment, entanglement, what is a neutrino...and I managed to get pretty far without any math at all.

Richard Feynman's Six Easy Pieces might be a good place to start.

Also, ladybird is right - talk to physicists. And keep your eye open for art/science conferences & symposia. These are increasingly common and are a great way to cross disciplines.

posted by aunt_winnifred at 3:18 PM on March 9, 2011 [2 favorites]

Richard Feynman's Six Easy Pieces might be a good place to start.

Also, ladybird is right - talk to physicists. And keep your eye open for art/science conferences & symposia. These are increasingly common and are a great way to cross disciplines.

posted by aunt_winnifred at 3:18 PM on March 9, 2011 [2 favorites]

one more thing - I once spent the entire day listening to one of Richard Feynman's lectures on audio and 'drawing along.' I tried to make a diagram of every concept. If I'd had the accompanying textbook, I would have had his diagrams to look at, but I didn't, so I tried to make my own. When I got lost I'd just stop, rewind, listen again. I learned SO MUCH from that exercise and my drawings turned out surprisingly similar to the 'real' diagrams. It's amazing what you can understand if you just take the time to work it out slowly. I think doing something like this is way better than all that 'improve your brain' gimmicky stuff that's on the market. If you want to learn something, just sit yourself down and learn it.

posted by aunt_winnifred at 3:25 PM on March 9, 2011 [3 favorites]

posted by aunt_winnifred at 3:25 PM on March 9, 2011 [3 favorites]

A lot of scientists are pretty artistic and creative, physicists and mathematicians have to be. I think you have a lot more in common with them than you think.

posted by fshgrl at 3:31 PM on March 9, 2011 [4 favorites]

posted by fshgrl at 3:31 PM on March 9, 2011 [4 favorites]

I suggest reading some Neal Stephenson books, such as Anathem.

posted by Cool Papa Bell at 4:10 PM on March 9, 2011 [2 favorites]

posted by Cool Papa Bell at 4:10 PM on March 9, 2011 [2 favorites]

If your question is "how can I learn physics starting from the high school level?" the answer is to start with finishing your high school math (especially calculus) and work your way up. But it's going to take you a long, long time. You would probably have to get to the grad school level in order to fully understand all the topics physicists write about in popular science books. That 't Hooft guide is probably like 15 years' worth of education altogether.

If your question is more like "how can I acquire some appreciation of mathematical sciences?" I would NOT suggest trying to learn all of physics or math. Instead, you could get a taste by picking a few topics that don't depend on a huge number of prerequisites. For example, special relativity is an important theory in physics and (unlike general relativity) you can understand the basics of it with only high-school algebra. (Check out a calculus-free high-school physics book like Giancoli, though calculus itself is beautiful and worth learning.) And as phrontist says, there are some topics in math that don't depend on the standard sequence of math courses. Graph theory, one of the many topics in discrete math, has virtually no prerequisites and has many useful applications. Chartrand's Introductory Graph Theory is a fun and informal introduction.

Finally, I don't think there's really such a thing as a "poetic, creative, intuitive brain" or a "scientific brain". Some people may have more innate talent than others in certain areas, but the ability to understand science, poetry, or anything else is skill that anyone with the inclination can learn (though the inclination is often lacking...maybe I will never really learn to interpret poetry).

posted by Chicken Boolean at 4:14 PM on March 9, 2011 [4 favorites]

If your question is more like "how can I acquire some appreciation of mathematical sciences?" I would NOT suggest trying to learn all of physics or math. Instead, you could get a taste by picking a few topics that don't depend on a huge number of prerequisites. For example, special relativity is an important theory in physics and (unlike general relativity) you can understand the basics of it with only high-school algebra. (Check out a calculus-free high-school physics book like Giancoli, though calculus itself is beautiful and worth learning.) And as phrontist says, there are some topics in math that don't depend on the standard sequence of math courses. Graph theory, one of the many topics in discrete math, has virtually no prerequisites and has many useful applications. Chartrand's Introductory Graph Theory is a fun and informal introduction.

Finally, I don't think there's really such a thing as a "poetic, creative, intuitive brain" or a "scientific brain". Some people may have more innate talent than others in certain areas, but the ability to understand science, poetry, or anything else is skill that anyone with the inclination can learn (though the inclination is often lacking...maybe I will never really learn to interpret poetry).

posted by Chicken Boolean at 4:14 PM on March 9, 2011 [4 favorites]

Perhaps you might try as a first step reading a recent series in the New York Times by mathematician Steve Strogatz? Sort of an amuse bouche for the mathematical palate --- he explains some if the quite profound concepts behind elementary math in a way that to me, helps to open up that way of seeing the world to a more habitually literary mind like my own. It might give you a taste for a particular sub-field which particularly intrigues you. For myself, in find when I'm curious about a whole vast area of knowledge, it's far less intimidating to pick up some smaller aspect of it to educate myself on first. You then usually find that when you move onto something else it'll edge up on parts of what you already know, and you build up a sense of the bigger picture by accretion.

posted by Diablevert at 5:01 PM on March 9, 2011 [2 favorites]

posted by Diablevert at 5:01 PM on March 9, 2011 [2 favorites]

Read this: It finds the great universal bindings that encompass mathematics, art, and music, allowing a person who is adept at one to more easily access the other two.

posted by auiricle at 6:53 PM on March 9, 2011

posted by auiricle at 6:53 PM on March 9, 2011

Chicken Boolean makes an excellent point regarding your goal. Starting from highschool math and learning physics *as a physicist would* is a long process, and it requires thousands of hours building skills which aren't in themselves all that interesting before you get to the really fun bits. That's not to say it's a bad thing to do. But, it's hard enough to do if you make it your life's work. Trying it as a hobby is likely to prove discouraging.

If you've any interest in astronomy, starting with a college astro class can be a great way to get a first taste of science as-it's-done. The great thing about astro is that you can explore some of the neat results immediately, with pretty basic math requirements and few prerequisites. A well taught class can fill an important (but largely neglected) niche between lower division physics-for-majors courses, which are *all* method and few results, and gee-whiz descriptive physics books, which are all results and no methods.

If you want to read a book on your own, Frank Shu's

Also, the idea of starting with Special Relativity could be promising, though you may have trouble finding a course that isn't pitched at senior students. When looking for books, Taylor and Wheeler's

posted by eotvos at 6:54 PM on March 9, 2011 [2 favorites]

If you've any interest in astronomy, starting with a college astro class can be a great way to get a first taste of science as-it's-done. The great thing about astro is that you can explore some of the neat results immediately, with pretty basic math requirements and few prerequisites. A well taught class can fill an important (but largely neglected) niche between lower division physics-for-majors courses, which are *all* method and few results, and gee-whiz descriptive physics books, which are all results and no methods.

If you want to read a book on your own, Frank Shu's

*The Physical Universe*is a great one to start with. If you work through it, you'll wind up with a reasonable sense of what it's like to do quantitative science, and also a survey of some pretty nifty phenomena. Just don't skip the problems - they're the most valuable part!Also, the idea of starting with Special Relativity could be promising, though you may have trouble finding a course that isn't pitched at senior students. When looking for books, Taylor and Wheeler's

*Spacetime Physics*is a classic and is very good. (I don't remember quite what math and physics background the authors assume - you may find some parts of it unfamiliar. But, that isn't necessarily a bad thing.)posted by eotvos at 6:54 PM on March 9, 2011 [2 favorites]

Some teachers teach reasoning from first principles rather than rote memorization of all the useful consequences of memorization, and you may find this is more your style. Check out on line free courses (OpenCoursewear). Also look for "survey" talks had articles that cover the basics broadly and accurately, but not deeply. Finally, see if you can get involved in a project - propose to the local cyclotron to be an artist in residence or lab assistant.

posted by zippy at 7:20 PM on March 9, 2011

posted by zippy at 7:20 PM on March 9, 2011

I actually went back to school with the express intention of learning enough math and physics to understand quantum mechanics, but after a year and a half, looking ahead at at least another year and a half, I bailed. It's not so much that it's hard, it's that there's so damn much material. Idle curiosity isn't a sufficient motivation to devote that much of your life to it.

That said, there's a lot of good physics books aimed at the lay reader. These are my favorites:

Start with Feynman's QED - The Strange Theory of Light and Matter. This was originally a set of four lectures on Quantum Electrodynamics (sounds intimidating, but very accessible) explaining how a quantum theory of light works and yet gives the same results as the classical theory in the right circumstances.

If you don't have a good grip on the idea of "curved space," read Flatland next.

Next up, Brian Greene's The Elgant Universe and The Fabric of the Cosmos which are excellent survey books that take you all the way from classical mechanics through relativity and quantum mechanics to string theory.

Lisa Randall's Warped Passages is an alternate take on multi-dimensional universes ("brane" theory).

Lee Smolin's Three Roads to Quantum Gravity critiques and presents alternatives to string theory and was my first exposure to the idea of the "holographic universe."

I think you can jump into Godel, Escher Bach without any preparation. Just be ready to spend some time with it. I also recommend Donald Knuth's (yes, that Knuth) Surreal Numbers, possibly my favorite math book of all time. It's the story of a couple who get stranded on desert island and discover some stone tablets with strange markings. Because they're bored they try to figure out what they mean and end up recreating the notion of "surreal numbers" (numbers defined in terms of sets). Fascinating and fun.

More practically, John Allen Paulos' Innumeracy should be required reading for everyone.

Finally, for math and logic puzzles - Martin Gardner.

posted by zanni at 8:00 PM on March 9, 2011 [4 favorites]

That said, there's a lot of good physics books aimed at the lay reader. These are my favorites:

Start with Feynman's QED - The Strange Theory of Light and Matter. This was originally a set of four lectures on Quantum Electrodynamics (sounds intimidating, but very accessible) explaining how a quantum theory of light works and yet gives the same results as the classical theory in the right circumstances.

If you don't have a good grip on the idea of "curved space," read Flatland next.

Next up, Brian Greene's The Elgant Universe and The Fabric of the Cosmos which are excellent survey books that take you all the way from classical mechanics through relativity and quantum mechanics to string theory.

Lisa Randall's Warped Passages is an alternate take on multi-dimensional universes ("brane" theory).

Lee Smolin's Three Roads to Quantum Gravity critiques and presents alternatives to string theory and was my first exposure to the idea of the "holographic universe."

I think you can jump into Godel, Escher Bach without any preparation. Just be ready to spend some time with it. I also recommend Donald Knuth's (yes, that Knuth) Surreal Numbers, possibly my favorite math book of all time. It's the story of a couple who get stranded on desert island and discover some stone tablets with strange markings. Because they're bored they try to figure out what they mean and end up recreating the notion of "surreal numbers" (numbers defined in terms of sets). Fascinating and fun.

More practically, John Allen Paulos' Innumeracy should be required reading for everyone.

Finally, for math and logic puzzles - Martin Gardner.

posted by zanni at 8:00 PM on March 9, 2011 [4 favorites]

I haven't read it personally, but a friend of mine who just finished his Ph.D. in math has strongly recommended the book What Is Mathematics? It's supposed to be a rigorous introduction to "higher" math, but it only assumes a high school math background, and it covers not just calculus but a variety of interesting problems. Here's a review.

posted by en forme de poire at 10:23 PM on March 9, 2011

posted by en forme de poire at 10:23 PM on March 9, 2011

I definitely recommend starting with some books for the layperson, and then hunting down individual terms + concepts as needed to have a clue what's going on. You won't have the same robustness of knowledge that someone who's done the coursework would, but that's because you won't have spent as much time on it... seems like a good trade off to me. And just as importantly, having that sort of internalized concept of what quantum mechanics is, of wave-particle duality and tunneling and how they affect the world, ends up making the real math and coursework a lot easier if you do go down that path to study it in depth.

posted by Lady Li at 10:58 PM on March 9, 2011

posted by Lady Li at 10:58 PM on March 9, 2011

You mentioned programmers, so I have two cents for you. It's important to understand that programming is an element of software engineering, and like other engineering disciplines it is very hierarchical. There are layers of complexity, where each layer is a domain of knowledge. For example, consider iPhone apps: an iPhone is an embedded computer full of microprocessors and ports, composed of hundreds of thousands, running into millions, of transistors and other little components - all the domain of electrical engineering. All of these components are locked away inside a pretty little black box and exposed to the iPhone OS (iOS), a complex and powerful operating system (OS). The OS is itself a pretty black box exposed to people who write apps, who couldn't care less about the internals of the OS, let alone the circuitry of the actual iPhone.I feel out of my element talking toprogrammers, mathematicians, and physicists, yet I find their ideas aesthetically intriguing and I want to understand them.

(The best exposition I have ever read about the hierarchical, layered nature of computers is "Why Minds Are Not Like Computers" in The New Atlantis).

Hence, whenever approaching a discussion with a programmer / software engineer, ask them what layer they're talking about, and "what boxes are talking to what boxes". Here's a topical example: today a popular topic on Hacker News is Why Everyone Is Talking About Node.Js. I understand everything in the article and have an intuitive feel for all the tradeoffs and evaluations discussed in a article based on my university degree and real-world experience. But the number of topics and concepts in the article is extraordinarily formidable, and this isn't even a technical article!

The point being, whereas with mathematics and physics there

*may*be some impetus to start from the bottom up and get a thorough understanding of the basics before moving on, with software engineering you simply must start from the top down. Forget about transistors, microprocessors, operating system internals, line coding, processor instruction sets, blah blah blah. Start at the very top! What is a web server? How do web servers talk to my web browser? How does my web browser load a web page? What is a web page? What is the Internet?! Then work down. If you go from the bottom up you'll lose your sanity and learn very little in the process.

However, all that being said, I won't lie to you - there's a special magic in becoming knowledgeable and adept at a hierarchical, layer/domain oriented field. I have a distinct memory of being in my second year at university and having a discussion with a classmate about a particular type of power amplifier; standing up against a blank wall and, without drawing, simply pointing at blank pieces of wall saying "Here is your pull up resister with high impedance, here's your current amplifier, ...". And working out all the subsequent conclusions. All the time knowing that you could break into a deeper discussion of the finer details. It's a wild ride, but it comes with a steep ticket price.

Although you'll need other background material to full understand it, I recommend O'Reilly's Beautiful Code. Lots of layers, lots of boxes, but the real clincher is that these are real challenges and how some great software engineers and computer scientists approached them.

posted by asymptotic at 6:19 AM on March 10, 2011 [2 favorites]

*The Elements of Computing Systems: Building a Modern Computer from First Principles*is pretty cool.

posted by phrontist at 9:19 AM on March 10, 2011 [1 favorite]

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posted by ladybird at 2:43 PM on March 9, 2011 [1 favorite]