Help me think abstractly

November 2, 2007 6:02 PM

Any tips on improving my abstract reasoning?

I find I have below-average abstraction skills. Specifically, when problem solving I find I am unable to think of things in the abstract, removing all details to hone in on the problem.

Often, when solving problems I am unable to make progress unless I visualise it, and even when I try and abstract away detail I find they cloud my thinking and bias my solutions.

Personally I feel like this is "fuzzy" thinking because I have all these wishy washy answers and then some person will come along, abstract away the cruft, come up with a solution and I'll go "I wish I could think like that!" I really want to be able to do it.

Even more so, I find that presented with a technical solution I seem to have inifinite capacity to remember all the tiny tiny details but tend to loose the big picture about what problem the solution is addressing or how it could be adapted elsewhere.

Does anyone here have any ideas how I could build these skills? Is there anything I can read or anything I can do? Is there a process for this? [This is in the area of compsci btw]

posted by gadha to grab bag (14 answers total)

I have two thoughts on this:

1. Make the abstract concrete. If your strength is visual, then come up with visualizations for abstractions. Don't let anything ever stay abstract. Even a dumb visualization (e.g. a heart for love) is better than none. Turn the abstractions into visual tokens that you can shuffle around. Constantly refine these symbol. That's what I do as a writer and teacher when I'm explaining abstractions. I come up with concrete metaphors for them. I constantly strive to come up with better metaphors.

Pens and paper are your friends. Draw pictures. Draw all the little pieces of the "machine." Get as detailed as you want. When you're done, you'll literally be able to look a the big picture.

2. If you've good with the tiny details, then go over many similar problems with tiny details. Focus on the details, but keep changing the problems. Eventually -- hopefully -- an abstract pattern will emerge.

This happened to me all the time when I was learning specific Design Patterns. I had a hard time grasping the pattern as an abstraction, so I just kept reading concrete implementations of it. After studying ten or twenty examples -- without trying to consciously abstract from them -- my mind started making connections and noticing patterns.
posted by grumblebee at 6:32 PM on November 2, 2007

Maybe that isn't the way you are wired. There are distinct learning styles and yours is probably different than the people you admire for having that ability. Here is a link that might give you some insight: it is more info on learning styles.
posted by 45moore45 at 7:01 PM on November 2, 2007

Okay, don't get the whole linky thing on this site... that is the way I am wired!

Here is the link: http://www.tecweb.org/styles/gardner.html
posted by 45moore45 at 7:01 PM on November 2, 2007

In my opinion, the culture surrounding scientific education is largely responsible for this problem. There is a constant competition to be the first to come up with the answer to a problem. No one notices the second guy to blurt out the (seemingly) correct answer in class, for example. Personally, this attitude has a tendency to creep into situations where I am alone as well.

I sometimes find myself stuck in the same rut that you describe and the problem always seems to be that I don't have all of the pieces of the puzzle loaded into my mental RAM, so to speak. I seem to have developed a behavioral switch in the form of saying, "OK, hold on", aloud. This is useful in a group because it gets everyone to take a step back from the problem, but I have no qualms about saying it to myself. I begin by reiterating the problem at hand or the goal to be achieved.

Next, I generally explain the steps that have been taken to solve the problem up to that point. I find sketching out a quick flowchart helpful. An example of a flowchart step for me would be "performed a PCR to obtain blunt end DNA", NOT "performed a PCR using 0.2 uL pfu turbo polymerase, 80 uL buffer....". Just writing out that step forces me to think about what the end result of that small segment of the overall solution produces. This forces me to question the theoretical basis behind everything. More often than not, I'll see that the result of some small step is not what I wanted, so I know where things went wrong.

If I do happen to reconstruct the entire problem solving process without a realization of the aforementioned type, I at least have everything fresh in my mind. I'll generally force myself to relax and remember that a few minutes of calm analysis can be worth hours of freak-out mode thinking.

I realize that this isn't a quick fix, but this approach really helps me when I remember to take it.
posted by hooves at 7:16 PM on November 2, 2007 [2 favorites]

I had a scheme, which I still use today when someone is explaining something that I’m trying to understand: I keep making up examples. For instance, the mathematicians would come in with a terrific theorem, and they’re all excited. As they are telling me the conditions of the theorem, I construct something which fits all the conditions. You know, you have a set (one ball)—disjoint (two balls). Then the balls turn colors, grow hairs, or whatever, in my head as they put more conditions on. Finally, they state the theorem, which is some dumb thing about the ball which isn’t true for my hairy green ball, so I say, “False!’’ --Richard Feynman
posted by solotoro at 7:16 PM on November 2, 2007 [4 favorites]

Also, I think that skill in abstraction gets better with every problem that is conquered using some form of the method that I described, rather than merely stumbling upon solutions. The individuals that I look up to for their problem solving skills seem to run through similar thought processes, but they are much faster at it because they have been doing it for ~40 years. Everyone starts somewhere.
posted by hooves at 7:22 PM on November 2, 2007

How are you with making mistakes? Do you find them really embarrassing? I think you should practice goofing up in front of other people. I'm thinking about Toastmasters for some reason...maybe based on your other previous questions. Or an improv comedy group. If you get more comfortable/less afraid of messing up, I just have this feeling your abstract thinking skills will improve. Fear impedes creativity.
posted by Eringatang at 7:47 PM on November 2, 2007

Timed reminders.. every 15 minutes or however often makes sense you need a small dialog to pop up and say "Take two steps back. What is the original problem that needs to be solved? What problem am I trying to solve right now? Where does it fit in to the grand scheme of things? Retracing how I got to this problem, can any steps be eliminated or changed to eliminate other steps?"
posted by anaelith at 8:52 PM on November 2, 2007

Polya's "How to Solve It" addresses the general topic in the context of the educator, and illustrates that the process of developing abstraction and problem solving skills is fuzzy, initially uncertain, but improves with exercise. He has suggestions, of course, and his tiny book is geared towards math (as one may expect!), which is nothing if not abstract. You can read it in a day and master it in a few years. It's a math classic.

If you are REALLY young (sub 22 or so), there are brain structures still congealing and you should have faith that you'll get better as you age if it's important to you to do so. Also, your increasing experience will enhance process with content and eventually, many things will begin to look simpler because you have seen them before.

Don't despair. Also, don't presume you will "get" everything. You'll eventually get good with some stuff, and like the rest of us, struggle constantly with being less than a genius at the rest. You've got plenty of company in your fuzzyheadedness!
posted by FauxScot at 4:12 AM on November 3, 2007

It's OK to struggle with this stuff. I've heard Hilbert was extremely slow, often slower on the uptake than his graduate students. Yet he made many revolutionary contributions to Mathematics.
posted by Coventry at 6:24 AM on November 3, 2007

Since there are so many different parts of CompSci, it might help to know which parts or classes you are having trouble with. In general, I second grumblebee's idea that looking at existing implementations or writing your own would probably be helpful. You might look on Sourceforge for open source projects related to the topic you are studying.

Of course, you asked for tips on improving abstract reasoning skills. I find that they best things for me are plenty of sleep and a lack of stress. The game Set is also one of my favorites.
posted by broady at 6:42 AM on November 3, 2007

I'm great at abstracting problems to see the greater forces behind them. I'm horrible at keeping track of details. When I mediate complex disputes, I love working with someone like you. That way, I can deal with the big picture and the other person can keep track of all the pesky little realities that sink a deal when I'm mediating by myself. So maybe the answer is accepting your strengths, capitalizing on them, and pairing up with folks who have complementary strengths.
posted by equipoise at 7:57 AM on November 3, 2007

One thing you could do is take some classes that require a lot of abstract thinking. The two things that come to mind for me are physics and philosophy, but there are probably others.
posted by overhauser at 8:24 AM on November 3, 2007

Try reading the problem backwards. Also, try guessing, then prove the guess wrong, then repeat.
posted by Brian B. at 5:31 PM on November 3, 2007