Avoiding mistakes? What are thought processes and mental checks to use?

Hey pa5tabear.

One thing that I can recommend regardless of the problem or approach used is to check whether something "looks right".

What I mean by this is that you look at the answer and see if it makes sense based on the rules of thumbs and contextual information.

I can't really elaborate on the general case but I'll give a few specific examples.

Some of the more obvious ones are things like calculating probabilities that are > 1 or negative or a value that is just wildly wrong relative to the other probabilities.

Another one is calculating a mean where you have the PDF and intuitively, you know the mean should be positive but it ends up negative.

Other things include doing the same thing with even the simplest operators: You integrate xy over the unit square and if you get a large number you know something is screwed up somewhere.

On top of this you have tangible reference points and this just comes from experience. Say you do a calculation to analyze some process and you look at the answer and you think "WTF?".

If I had to reduce it down, it would be that at every step, you mentally think about the rough kind of state-space that the answer should be and for the general solution, draw on non-mathematical means to think about whether the answer makes sense in the context of a set of related things like the physical interpretation of the result and other related characteristics.

 

On a test or in real life?

In real life you avoid making mistakes by having several people check the calculation, and by having as much done automatically as possible. This is extremely effective. So effective that you can't use them on tests in school. :-) :-(

There are some thing that I do in physics problems

1) make sure that the dimensions are correct
2) have some idea of what the number is that I'm supposed to get
3) check for conserved quantities
4) quick math things. For example, if you do a polynomial equation, set X=1,0,-1, and see if it works at each step