I do an exercise where I'll visualize geometries. Starting with a point, then a line, then a triangle, a square, a tetrahedron, and so on. At each stage once you really have control over it (you're able to translate/scale/rotate your visualization) add another point to the object.
Ask HN: Resources on how to improve abstract thinking skills?
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Re: Ask HN: Resources on how to improve abstract thinking skills?
#32Accumulate more concrete knowledge. Our brains develop abstractions when we identify patterns in disparate phenomena. Can't identify those patterns if you don't study the concrete phenomena themselves.
As you learn more you'll build up a toolbox of abstractions that will make thinking and learning easier.
Re: Ask HN: Resources on how to improve abstract thinking skills?
#33So I'm laughing at all the examples that have made the rounds on HN innumerable times. How about this. "Possible Worlds: An Introduction to Logic and Its Philosophy" https://www.amazon.com/Possible-Worlds-Introduction-Philosop... Analytic philosophy has produced a methodical approach to thinking about things that we don't seem to teach as methods. Instead it trickles down into pop-science takes on thinking which tell…
I also like this guide: https://www.av8n.com/physics/thinking.htm "Learning, Remembering, and Thinking". I recommend checking out his other work for a model of working through problems coming from physicists.
One more thing. Oftentimes the key step to thinking is figuring out what you're questions are, and questions are always determined by what uncertainties you have in a domain, as specifically relevant as you can make them.
I'm gonna quote Venkat Rao (of Breaking Smart and Ribbonfarm fame) from an article he deleted years ago:
> Real questions, useful questions, questions with promising attacks, are always motivated by the specific situation at hand. They are often about situational anomalies and unusual patterns in data that you cannot explain based on your current mental model of the situation… Real questions frame things in a way that creates a restless tension, by highlighting the potentially important stuff that you don’t know. You cannot frame a painting without knowing its dimensions. You cannot frame a problem without knowing something about it. Frames must contain situational information. There are two types of questions. Formulaic questions and insight questions. …. Formulaic questions can be asked without knowing much. If they can be answered at all, they can be answered via a formulaic process. …. Insight questions can only be asked after you develop situation awareness. They are necessarily local and unique to the situation.
The world is /extremely/ information rich to the point of absurdity, and what fails is not the richness of our input data but rather our awareness of how we ought to use it. George Polya tried to teach his students how to problem solve in mathematics by means of getting people to ask questions. By verbalizing his thought process he hoped to convey these principles, as well as giving them a standard template to prompt their cycle of questions. But to adhere to a strict plan like that is to defeat the point. The real point is to maintain a conversation with yourself, giving yourself and refining your own questions until insight develops, and keeping yourself talking.
Ultimately I like to take an information-theoretic approach as the basis of my philosophy here. /Some/ information is /always/ going to be contained in /any/ comparison that I can make between two phenomena in the world. Most of this "information" would be considered noise relative to most reference frames. But it is always possible to extract /something/ from a situation by creating these tensions between yourself and your uncertainties in the world.
You can muddle around questioning things for awhile, but gradually things come up. The key is to let your uncertainty start off however it is and keep pruning away at it until your solution is sculpted from the clay. It can and will happen.
If you've ever tried doing Fermi Estimates (like those prescribed in https://www.amazon.com/Street-Fighting-Mathematics-Educated-... , https://www.amazon.com/Art-Insight-Science-Engineering-Compl... , https://web.archive.org/web/20160309161649/http://www.its.ca... , https://www.amazon.com/How-Measure-Anything-Intangibles-Busi...), then you'll be able to perceive the mindset that has significant transfer to many problems that have even just approximate answers.
Re: Ask HN: Resources on how to improve abstract thinking skills?
#34My personal recommendation just based on personal experience would be to study philosophy. It doesn't much matter which philosophies, but a variety that differ fairly substantially would probably be best. When you read a very different viewpoint you can occasionally almost feel your brain shift sideways when you 'get' how the other viewpoint is seeing things. That leads to questions about the exact points where your viewpoint and their actually diverge, and considering a wider scenario where both exist or develop is inherently a move in the abstract direction.
Re: Ask HN: Resources on how to improve abstract thinking skills?
#35I started studying economics in my free time because abstracting how humans behave with math fascinates me and you start to understand what a complex system really is.
Markets are very complicated and unpredictable in the short term, but you can understand the atomic unit of the market just fine; a transaction. It’s the same with all complex systems; try to work from the bottom and up, always begin with what you can wrap your head around.
After a while, you see that the methodology of building abstract models that are good enough is very similiar in most fields. You discover that it’s never easy and you should always be careful trying to recycle a model by mapping it to an entirely new system.
Re: Ask HN: Resources on how to improve abstract thinking skills?
#36I'm just being a snarky smartass, but you could probably improve your abstract thinking skills by trying to find the answer to this question yourself. :-)
Yeah there's no one fix other than struggling to contextualize the skills being built here.
Re: Ask HN: Resources on how to improve abstract thinking skills?
#37Study higher level math! Category theory is a brainfuck that exercises that skill well. This book https://mitpress.mit.edu/books/category-theory-sciences doesn't have any real mathy prereqs but is fun. Added benefit from studying math is that its a foundation for a whole bunch of other cool stuff.
This is another good one:
http://www.cambridge.org/gb/academic/subjects/mathematics/lo...
Re: Ask HN: Resources on how to improve abstract thinking skills?
#38Why do you want to improve your abstract thinking skills? I would be surprised if there is anyway to improve these skills, g(aka IQ) is notoriously hard to improve. But I imagine you want better abstract thinking skills for a specific reason, and it'll probably be much more effective to skip directly to the reason you want to improve these skills.
It is not, and by thinking so you are limiting yourself.
Re: Ask HN: Resources on how to improve abstract thinking skills?
#39Suspension of judgment was the very first step I discovered, I clearly remember, from when I was quite little. Perhaps I started out especially daft, but I kept making discoveries ever since. Something which served me well a long time was a mental game of following logic to extreme conclusions and then asking myself "what if this is true, and my premise was wrong?" One of the most powerful methods I use now when appr…
I prefer your style of thinking over the "brute force" method in the top comment. If thinking was an olympic sport, I feel it is more akin to gymnastics than power-lifting. I believe that if you are rational, disciplined, and take your time you can have more accurate beliefs and make better decisions than someone with greater raw intellectual power.
I also agree that premature conclusion is the most common error of thinking. We must be mindful of irrational fear causing a false sense of urgency. Thinking compulsively without forming a conclusion can be a problem too, but it's probably a better problem to have.
Re: Ask HN: Resources on how to improve abstract thinking skills?
#40Eno and Schmidt’s Oblique Strategies is a classic. It’s based on the idea that creativity is based on constraints, so artificially adding new boundaries to a problem helps the mind find new solutions. https://en.wikipedia.org/wiki/Oblique_Strategies Read up on “lateral thinking,” it’s sort of the gospel of graphic design. https://en.wikipedia.org/wiki/Lateral_thinking
Interesting - there are two different takes on this question in this thread. This comment is about generating new ideas and thinking creatively, whereas itamarst answered in the sense of organizing thoughts in order to solve problems and communicate them.
one of the things I love about asking random questions (I care about) on HN is that answers never get constrained in the ways I had devised or expected :)