Suggestions for Improving Abstract Thought
December 17, 2008 12:15 AM Subscribe
I have just realized that I am appallingly bad at abstract thought. Anytime I need to solve a problem that requires higher-level abstract thinking, I am unable to do so. So, for example, if I see an argument spelled out in symbols, I have to translate those symbols into real-world terms for me to understand them. What can I do to gradually improve my ability to handle abstract thoughts and ideas in my brain.
I have been studying for LSATS and I find myself doing especially badly on a lot of the abstract sections on it. I am a very good student and very bright. However, looking back on my life, my difficulties in mathematics foreshadowed a lot other academic problems in the future. The only way I could do biology (and I was very good at it) was through visualizing everything that occured as though the body was a rube goldberg machine where x causes y and y causes z so on...well now I feel I have an underdeveloped higher abstract learning ability.
What exercises could I set aside for myself that would help me with understanding highly abstract ideas. Has anyone written about this issue before? Is there a self-help book out there helping to improve higher abstract abilities in people.
I have been studying for LSATS and I find myself doing especially badly on a lot of the abstract sections on it. I am a very good student and very bright. However, looking back on my life, my difficulties in mathematics foreshadowed a lot other academic problems in the future. The only way I could do biology (and I was very good at it) was through visualizing everything that occured as though the body was a rube goldberg machine where x causes y and y causes z so on...well now I feel I have an underdeveloped higher abstract learning ability.
What exercises could I set aside for myself that would help me with understanding highly abstract ideas. Has anyone written about this issue before? Is there a self-help book out there helping to improve higher abstract abilities in people.
There are many possible meanings for "abstract thoughts". Some examples of LSAT-type problems you find particularly difficult would help.
Math in general? Variables? Logic problems?
What is a highly abstract idea? The Pythagorean theorem? The meaning of life? The subtle economic implications of lower taxes with changing rates of unemployment?
Having said that, you say it all started with difficulties in mathematics - and I can't think of a more basic form of abstraction than mathematics. So I suggest you study math. Take an extra non-credit class. Read a book. Get a ruler and calculate the volume of your home in cubic centimeters.
I would expect it to be incredibly difficult, but worthwhile.
A brief personal experience: My biggest difficulty is in "outside the box" thinking, one of the possible meanings of "abstract". I can write incredibly complex software or systematically troubleshoot just about anything, but creative solutions to problems don't always come easy.
I've been forcing myself to do creative things (drawing, music) and to do daily exercises in this kind of thinking - for example, cryptic crossword puzzles. I don't know if it's helping the rest of my life, but I'm certainly better at the puzzles than I used to be...
posted by mmoncur at 5:11 AM on December 17, 2008
Math in general? Variables? Logic problems?
What is a highly abstract idea? The Pythagorean theorem? The meaning of life? The subtle economic implications of lower taxes with changing rates of unemployment?
Having said that, you say it all started with difficulties in mathematics - and I can't think of a more basic form of abstraction than mathematics. So I suggest you study math. Take an extra non-credit class. Read a book. Get a ruler and calculate the volume of your home in cubic centimeters.
I would expect it to be incredibly difficult, but worthwhile.
A brief personal experience: My biggest difficulty is in "outside the box" thinking, one of the possible meanings of "abstract". I can write incredibly complex software or systematically troubleshoot just about anything, but creative solutions to problems don't always come easy.
I've been forcing myself to do creative things (drawing, music) and to do daily exercises in this kind of thinking - for example, cryptic crossword puzzles. I don't know if it's helping the rest of my life, but I'm certainly better at the puzzles than I used to be...
posted by mmoncur at 5:11 AM on December 17, 2008
Seconding programming, and Python in particular. While I'm a programmer, so probably a bit biased, Python is quite friendly towards people without programming experience. While I disagree with Free_word_order!'s comment that Python's syntax is "close to normal language", I think its syntax is relatively forgiving. It has a shell where you can type code in line by line and immediately see what it does (the immediate feedback will help tremendously), and it has a relatively large community, so there will probably always be somebody hanging about on irc / forums who will be willing to answer questions. (Note that some people consider it their duty to be mean about answering what they consider to be poorly-worded questions, though — often they're just rude people, but sometimes it's because they want you to read a FAQ that answers exactly your question rather than repeating it an 11,000th time.)
How to Think Like a Computer Scientist is recommended as an intro for non-programmers. There are also other tutorials. (For people with some programming experience, Dive Into Python is probably better still.)
Since you're doing this to learn abstract thinking (rather than to build something specific), the Python Challenge is probably also up your alley. You'll need to have a handle on the basics first, but then it's a series of puzzles solvable using Python and its library.
Doing any puzzles (particularly a wide variety of them) will be good practice for abstract thinking, but the PC will tie in with Python, if you like.
posted by silentbicycle at 5:14 AM on December 17, 2008
How to Think Like a Computer Scientist is recommended as an intro for non-programmers. There are also other tutorials. (For people with some programming experience, Dive Into Python is probably better still.)
Since you're doing this to learn abstract thinking (rather than to build something specific), the Python Challenge is probably also up your alley. You'll need to have a handle on the basics first, but then it's a series of puzzles solvable using Python and its library.
Doing any puzzles (particularly a wide variety of them) will be good practice for abstract thinking, but the PC will tie in with Python, if you like.
posted by silentbicycle at 5:14 AM on December 17, 2008
What's wrong with translating the abstract into the concrete? It's well established that our brains are much better at thinking about things in concrete terms: if you can translate back and forth with no loss of generality then do so!
Feynman always used to talk about translating mathematical problems into geometrical ones that he could picture in his head, before (sometimes) turning the proof picture back into abstract mathematics. If he did things that way, why can't you?
posted by pharm at 5:24 AM on December 17, 2008
Feynman always used to talk about translating mathematical problems into geometrical ones that he could picture in his head, before (sometimes) turning the proof picture back into abstract mathematics. If he did things that way, why can't you?
posted by pharm at 5:24 AM on December 17, 2008
It struck me as kind of funny that you say that you aren't good at abstract thought, and then you say that you create these huge Rube Goldberg machines in your head to understand things. It sounds like you are in some sense fantastic at abstract thought. Perhaps you can translate your ability to create pictures to understand things into the type of thinking that you need to do now.
posted by jefeweiss at 6:48 AM on December 17, 2008 [1 favorite]
posted by jefeweiss at 6:48 AM on December 17, 2008 [1 favorite]
Drawing pictures. I swear that's the only way to solve some of the "abstract" problems on the LSAT. When I looked at a Kaplan book on the topic, they actually spelled out diagrams to draw to help with different kinds of problems. Writing stuff down isn't cheating. Nobody can do those crazy multi-step problems in their head.
posted by abirae at 8:22 AM on December 17, 2008
posted by abirae at 8:22 AM on December 17, 2008
As someone who has done OK on the LSAT Games section despite scoring a D in algebra in 8th grade, I would question your premise and encourage you not to see yourself as abstract-thought-challenged. In fact, the best advice I read in one of the test prep books was that you shouldn't expect answers to leap into your head through logical intuition, nor hold it against yourself that it's not happening.
Instead, you develop an orderly 1-2-3 procedure for breaking down the "abstract" into easier, visual work, you stay focused on going through the steps of the system you've developed, and try not to let it unnerve you.
posted by Kirklander at 8:27 AM on December 17, 2008
Instead, you develop an orderly 1-2-3 procedure for breaking down the "abstract" into easier, visual work, you stay focused on going through the steps of the system you've developed, and try not to let it unnerve you.
posted by Kirklander at 8:27 AM on December 17, 2008
Response by poster: Thanks so much for your guys' help. I think. I will look into finding ways to visualize these analytical problems before attempting to solve them. All the links were also very helpful.
Thanks.
posted by leybman at 4:41 PM on December 19, 2008
Thanks.
posted by leybman at 4:41 PM on December 19, 2008
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I'd suggest recommend python, its syntax is so close to normal language that comparing what your code claims to be doing and what you want it to do is easier.
Programming is also about finding holes in your thinking, all the time, and being more sensitive to them and understanding the inevatibility of making these mistakes.
posted by Free word order! at 2:26 AM on December 17, 2008 [1 favorite]