epicurus

90

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.

00

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.

10

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?

00

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...

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.