What I meant to say (and I agree with you that I didn't really say it), is that the point of an SOP is to show that you will have "success as a future independent researcher" and so projecting any "characteristics of potential success as an future independent researcher" is a good thing.
Is it good to show that I have the traits that will lead to success in research? Duh--that's the point.
Okay, sorry if my question wasn't clear enough. I actually tried to establish a distinction (this question was actually on my mind after PMs I had with another poster).
And that's the distinction between "future independent researcher" and "future obedient uncreative lab grunt".
I'll give a quote someone gave me some time ago:
So find a department that is heavy in scientific computing, and try to convince the admissions committee that you have the basic knowledge to work as a serf there.
And another quote someone gave me from a PM:
I'm not sure that showing them I'm competent (in terms of working on something they're not interested in) is useful. What they want is people to work on their work. And it's not that they don't have curiosity, it's that they're very busy and don't have any spare time. To advance, they have to work on stuff that will get them tenure, etc.
Now, of course, it's possible that a future independent researcher is fully compatible with a future obedient lab serf. Some people can be both. *But*, there are some concrete examples that *show* that one has high potential for becoming a future independent researcher - even though these are the same examples that wouldn't help one with being a lab serf (in fact, these examples might even predict that one may be impatient with staying as a lab serf) - these examples are often things like independent work (this question actually applies more for some posters than it does for me) - which one might put in arxiv or something, and maintaining an independent physics blog (that one could give a URL to in a personal statement). The question is - should people with those examples mention them?
Also, there's another difference between "future researcher" and future grad student. A future grad student has to pass his coursework too - but in terms of research, there really is no difference in outcomes between getting a 3.8 rather than a 3.5 (in fact, focusing too much on coursework isn't a good thing). But still, maybe a grad school might care about whether a potential applicant would get a 3.8 rather than a 3.5.
Many people have highlighted *concrete* examples of past success with "indicators of successful scientists". So I have a question: What if I highlighted that I self-studied enough science to succeed in grad-level coursework? (I would mention independent books that I've self-studied - books like Lodish's "Molecular Cell Biology" and "Atmospheric Science" (Wallace and Hobbs) - and I would say that self-studying these books in a short amount of time has enabled me to get decent grades [these grades are in the transcript that they'll read] in several graduate level courses even though I didn't have the background that other students had). I know that research examples are always best, but the research I did was pretty much research that any other undergrad could have done. Of course, I'll still highlight it (to show that I can *stick* with something). But it's not something that is going to distinguish me from other people in the way that self-studying entire subjects from scratch would do. Obviously, I have to convince them that I will stick with astrophysics, but that can come in a separate paragraph. Many people who apply to grad school in field X have really done their best work in field Y - they just have to convince professors that they'll stick to field X once they're in grad school.
For example, this is an example that a professor would find useful (in a LOR, of course, but the personal statement also does many of the same things):
If you do a research project (e.g. REU) at a non-academic institution (e.g. govt. lab)
make sure the person writing your recommendation letters can make a useful
comparison of your performance with those of other students. General statements such
as “I was amazed how quickly Amanda learned how to analyze the data” are nice but
useless for admission committees. We are looking for “I was impressed that within a
month Amanda taught herself IDL, learned how to extract and calibrate data from the
BLAH database and re-plot them in the new co-ordinate system she developed with my
assistance. I have worked with 10 students over the past 3 summers and the only student
of her caliber is now finishing a PhD at Top Notch U.”
And apparently, at least one professor is quite impressed when a potential student can self-teach herself material quickly.
Also, I'm sorry for being too insecure. I was actually a complete wreck 2 years ago (before I was able to get meds), and I'm still recovering from it (of course, I know that I will have to improve more, and show that I have improved more).