Comment author: Lumifer 04 May 2015 05:32:20PM 0 points [-]

Definitely less rigorous formalization and more gestalt pattern recognition.

In general, I think of math as dealing with well-defined "things" -- you may not know the shape/properties/characteristics at the moment, but they exist, they are precisely defined, and they are not going anywhere. In contrast to math, statistics deals with fuzzy amorphous "things" that you will likely never know in precise detail, that mutate as more data becomes available, and that usually require interpretation and/or some guessing to fill in the gaps.

Comment author: epicurus 04 May 2015 07:07:48PM 1 point [-]

Cutting edge math is actually mostly about converting fuzzy stuff, at least the parts of math I am interested in(Algebraic Geometry - Grothendieck/Weil for example). Both the mentioned mathematicians worked in a field where people had some stuff that worked but no foundations.

Also, the foundations of math have been changing for quite a long time and continue to do so. I think your reaction to mathematics might be to badly taught mathematics rather than mathematics as practiced. However, I don't see an easy way to fix it.

To teach mathematics well would require a high amount of mastery and we don't have enough people like that around.

Comment author: Lumifer 04 May 2015 02:54:00PM 1 point [-]

When someone says "I am bad at math," I am not sure if they mean "I can't think carefully at all," "math notation scares me," "I can't think abstractly," [something else].

A data point for you: I am not particularly good at math. What this means is that at certain levels going forwards suddenly becomes much more difficult. I can continue, but slowly and only with a lot of effort. It's a slog. By comparison, I'm much better at logic/patterns and going deeper there is just easier. I do NOT mean that I can't think carefully or abstractly or that notation scares me.

Note that I'm using a fairly narrow definition of math here. In particular, I distinguish math and statistics and believe that they require two different propensities. People good at math are rarely good at statistics; people good at statistics are rarely good at math.

Comment author: epicurus 04 May 2015 04:28:25PM 7 points [-]

I am not sure what exactly going deeper at logic/patterns means if not getting into mathematical logic. It is incredibly easy to read mathematics you know and incredibly difficult to read mathematics that you don't due to how dense it is. It might be the case that your impression is due to comparing these two.

I am training to become a mathematician and I do not know of a single person for whom learning mathematics is not slowly and with a lot of effort, I do not think you are particularly exceptional in that but I know very little about your particular scenario.

Comment author: JonahSinick 04 May 2015 03:43:20PM 4 points [-]

I say everything I'm about to say as a person who is more certain than not that you have something valuable to contribute through this sequence, and who eagerly awaits more. All of your posts in this sequence have purportedly been written to motivate your main thesis, but it's not clear to me what that is. I think you should stop motivating and very clearly reveal your Big Secret.

I very much appreciate your interest. I'm sympathetic to the points that you raise. The trouble is that it's hard to even state my main thesis without presenting a lot of background information (!!). It's as though someone wanted to know about monstrous moonshine, and I started explaining what a modular function is, and the person said "ok, rather than giving so much motivation, I'd prefer it if you just told me what monstrous moonshine is." Then I state the theorem, and the person says "wait, what's the modular j-function?"

But it's much easier to speak to an individual's situation than it is to speak to the general question of how people can get better at math. What's your background and what are your goals? I may not be able to respond at length individually, but I'll try to offer quick thoughts at least, and your comments will inform what I write about subsequently.

Comment author: epicurus 04 May 2015 04:20:08PM 0 points [-]

I am a bachelor's in mathematics and estimate my current knowledge to be around a second year graduate student's if my mathematical knowledge is useful. I am interested in getting better at doing math as well as teaching it.

Note: I am not the person you replied to.

In response to Rationalization
Comment author: epicurus 03 March 2015 03:25:03PM 0 points [-]

According to this article, one can predict a decision 7 seconds before it is actually made. Doesn't this, in some sense, mean that a large amount of our thought process(certainly those 7 seconds) are actually rationalizing a decision we have already made?

Is my thinking off or is this one more thing to actively guard against and realize when we are letting our unconscious decide for us?

Comment author: epicurus 02 March 2015 03:10:31PM *  0 points [-]

This is very curious. I never thought of emergent as an explanation but as a property. I roughly understood it to mean that the emergent quality was transferable. That is, intelligence is a product of neurons firing but it need not have been, it could also have been generated from transistors or whatever else.

This is roughly the opposite of your ant example. Something is emergent if it can be explained/predicted with no knowledge of the lower level. A lot of properties of turing machines do not depend on the actual formalism of the turing machine.

Edit: After browsing the other comments, I realize this is something that has been brought up before. My 2 cents for whatever it is worth, I guess...