What type of "thinker" are you?

Nikitin

Hey. I'm studying Chemical Engineering (1st year), and I noticed that I'm much better at stuff like programming (but I rarely find the perfect algorithm when solving practice-problems.. this annoys me), calculus and logical thinking than geometry (I'm bad at geometry despite wanting to learn) or philosophy (extremely boring and makes little sense).

So I've had a moment of introspection, and I started to wonder what kind of "thinker" I am, if such a thing exist, and what kind of "thinking" is needed in different fields. Does one generally need to think intuitively for chemistry, and analytically for physics? Is Geometry more about spatial thinking, while calculus' about slugging through problems using logic?

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If TL,DR: What are your strengths, and which type of thinking do you think match with various scientific fields?

jtbell

Don't let it bother you. I've been programming for forty years, and I've never written a program that I couldn't do better if I could start over from scratch.

micromass

I would say that all sciences require intuition. Using intuition in mathematics seems much more important to me than thinking logically. I can never solve a math question if I don't see it intuitively first. I would say that logic is certainly the language with which we convey mathematics, but I don't think it is necessarily the language with which we discover new math or solve new questions.

In my own experience, all of mathematics requires visual thinking. This is pretty weird to most people: how can abstract algebra, solving equations or solving integrals require visual thinking? It's hard to explain if you don't experience the same thing, but I do try to see every kind of mathematics visually. If I cannot visualize something, then I don't understand it.

Of course, intuition should never be blind. Intuition should be guided by results that you know to be true. This can be very hard on your intuition sometimes: how can you possibly have intuition for strange results such as length contraction in SR? You just need to give it some time, your intuition is very flexible and will adjust itself after a while. I think that is the entire point of a science education: to develop a new and better intuition for things.

So, to summarize: I would classify myself as an intuitive and visual person. Certainly not as a logical person.

Jimmy Snyder

All programs can be rewritten with one less line of code and all programs have bugs. Therefore any program can be replaced by an equivalent program with one line and it's wrong.

BobG

Way back when I took a class on programming in Basic, I tried that philosophy. The objective was to write a program that sorted 100,000 names alphabetically. My program was:

10 Print "Hello"

My professor only saw one error in the program. He said I should have used "Goodbye".

And then he kicked me out of the class.

zoobyshoe

Geometry is the only math I remotely understand because it's visual. In my mind it's the "easy" math because it's the most visually literal as opposed to unreferenced abstractions you encounter in algebra and beyond. I have no idea how to approach algebra visually. If I could I'm sure it would be much easier for me.

lisab

So true! I glanced at the math GRE many years ago and saw this problem:

Which has greater area, a circle with diameter A or a square with sides measuring A?

I could "see"...


...and so immediately had the answer. I'm sure what the question was really asking.

wuliheron

I'm a contextual thinker which is something Asians tend to excel at, but I'm American. The mixture of eastern and western thought makes my perspective unique in some respects. Geometry is the obvious to me because it is all about context as far as I'm concerned. Is the earth flat, round, a dimensionless point, or nonexistent? To me it's a meaningless question without context. From the ground the earth looks flat, from orbit round, far way a dimensionless point, and from the dark side of the moon it appears nonexistent.

Which is "real" is another meaningless question to me without context. It's safe enough to assume the moon is still there when no one is looking, but I couldn't care less about what people think constitutes "ultimate" reality or whatever. Either something is useful or it's a waste of my time and, of course, what is useful depends on the context.

AnTiFreeze3

I would like to think that I'm naturally analytical. I get most of my kicks and giggles from reading something and not only understanding it, but analyzing it more so as to create my own ideas and whatnot.

What I've noticed recently, however, is that I can change the way I approach something merely by submersing myself in an environment with people who think the way that I would like to think. PF is a great place for logically approaching something, which I love not because I'm a logical person, but because I love the idea of a logical world where most everything makes sense (sadly this couldn't be further from the world that we actually live in).

Different people are different, obviously, which makes the world interesting. I might see a problem one way, whereas another person may approach it in an entirely different manner, not because one way is intrinsically better than the other, but because that particular way works better for that particular person.

However, some domains do require certain thinking to excel, but like I said earlier, the way in which you approach something can be altered if you really want to have it done. That adaptability makes me enjoy life that much more; I'm not constrained to doing only what I do best, but I can acquire the required skills to do something that interests me more.

I don't see any reason to doubt that there are different kinds of "thinkers" in the world. Now, whether it depends upon the way that we're brought up, or just the formatting of our brains, genetics, DNA, etc. is beyond me. I wouldn't be surprised if it was just an interplay between the two.

Galteeth

Linear and abstract. I have an excellent memory for stories, events, etc. I can often remember events (in terms of order, changes etc.) in other people's lives better then they can. Anything I can turn into a story, I can understand (and then this happened, then this happened.) I am also good at seeing layers of nuance and comping up with multiple interpretations of events (literary analysis.) Unlike some here, i am extremely BAD at visualization. I wound understand a math concept better by hearing a story of how someone came to discover it then by a diagram or visual representation, which often initially intimidates me.

symbolipoint

An equation or a numeric expression IS visual. It is not visual in the same way as a graph or a diagram, but still it is visual. We can read and understand it, depending on its complexity and our familiarity with number properties. We can often see mentally the first one or two steps in transforming it into an equivalent version, as when we solve for a variable.

symbolipoint

Visual thinker who has a hard time visualizing. I need to see real pictures, graphs, and diagrams. I or someone else must draw them.

Nikitin

Hmm, weird. I rarely think visually when solving math problems.

Hmm. My first thought was plugging the data into the area-formulas and see what I would get, even though it is indeed easier just to "see" it if you try to combine such a square and circle.

Zarqon

From a personal point of view I agree, because I do the same thing myself (working in quantum physics), I also rely on intuitive/visual thinking for feeling that I've actually understood something.

However, I'm not so sure this is true for everyone, I've met several people who pretty much always expressed themselves "theoretically". For example, at an earlier working place I shared a room with someone who roughly new the system we worked on as much as me. But we had repeated incidents where we would discuss a problem that both knew the explanation for but neither realised the other also did, because we just used so different words to explain the same thing we went around each other. He used a much more theoretical vocabulary and I got the feeling he really understood things from a theoretical point, rather than intuitive. He's also not the only person I've run into that gave me that impression.

From what I can tell, the theoretical way of thinking has some advantages when it comes to figuring out non-intuitive results (there are some in quantum physics :P ) whereas the intuitive way of thinking seems at least to have a strong edge in teaching and explaining to others.

ImaLooser

Yes, there are different types of thinking. It's not simple. I do math visually, but am no good at graphics design and that sort of thing. In math grad school I was great at linear algebra, which is basically geometric, but rotten at everything else.

As far as I'm concerned calculus is geometric.

When I was young I was unable to think logically, but my intuition and clever trickery was so good I didn'trealize it. I learned later.

On the other hand my dominant sense is sound, not eyes. So I dunno how to make sense of all this.

I was no good at the higher levels of mathematics. It helps to be able to do math with no need to refer to the real world at all. I wasn't able to do that.

Dembadon

I rely on intuition (heavily), pattern-recognition (serves intuition), and other visual cues. I tend to create visual "structures" in my mind; like templates of information or generic pictures that can be applied to a wide range of problems. If you've ever seen the phrase, "This is of the form...", or something similar, then you've experienced the very thing I ask myself whenever I see something new. I'm always looking to generalize, because it's exponentially more useful than storing information only relevant for certain problems.

I'm not working in a scientific field yet, nor do I know enough about any one field to be able to answer your last question.

Dembadon

Geometric problems can get pretty beastly! There are a few problems on the putnam exams that give even the brightest undergraduates trouble. Even the GRE can have some tricky questions if one hasn't internalized some of the concepts in geometry. My wife is studying for the GRE right now, and I'm helping her with the mathematics section. I haven't taken a course in geometry for about 10 years, so there are a few things I've simply forgotten, but Google has never let me down. Usually, what most of the problems on the practice test boil down to: first, understand what is being asked of you (most important part!), then use relevant geometric axioms/rules to make logical inferences about the unknowns. Intuition can definitely help you see what should be true about the object, and you can use it to develop a strategy for solving the problem.

Interestingly enough, this is a very similar process to what I do when attempting to prove something. Figure out what is actually being stated (one cannot move forward without knowing this), then allow my intuition to help me develop a strategy for how I'm going to go about proving it. Finally, I start making my argument while constantly checking if I'm actually getting "where I need to be." It's an awkward process to apply to abstract objects at first, but like anything, practice is essential for progress.

This process has been extremely beneficial in almost every single course I've taken, even humanities courses. While there isn't always a problem to "solve," the ability to make connections between two seemingly unrelated objects is a useful skill to have and can make for some interesting constructions that are worthy of further discussion.