Too Stupid for My Own Interests

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I kind of feel that way as well. I really like music but I entirely fail at reading music for one, and cannot play anything but luckily there is plenty to listen to at least. Then I like hearing about various scientific theories and what not, but I've never done well in science classes except for certain portions which did not involve a lot of math...which I also suck at but I am not very interested in it either.

Hi Evam,

I just got back from a trip without good Internet access -- thank you for the reply. I've canceled the dissertation with my advisor, but I appreciate your kind thoughts.

This is a multilayered subject, basically involving several decades of push-and-pull between proponents of Modern Buddhism (basically new-agers from about a hundred years ago, the Theosophists) and those who tried to keep the old, failing traditions going. The monks didn't actually fight the Japanese, but a communist propagandist, the monk Juzan (rather famous since then) claimed they did. What actually happened was more complex and involved the GMD-CPC alliance using the Hengshan monastic complex as a training base soon after the Japanese invaded Changsha, the capitol of Hunan Province, right before the tide turned against the Japanese invasion. The sources are in Chinese and all highly biased and politically charged, so it's tricky to parse.

Anyway, thanks again for your kind thoughts.

I can understand the need to learn by being shown and explained. I too like to know the "why" of something is happening and not just take someones word for it.

I can also relate to the programming issue. Do you feel that there is a "perfect" way to program? I did. I still rears its ugly head at times. I have to do the things "the way they are meant to be done". Which in programming is tough, because there isn't a single way.

I would say I am an advanced level programmer. But you will not see my code. a) much of it doesn't belong to me, and if it does it's either not finished, or I'm keeping it to myself for a reason b) I am very nervous of showing others my code

And that's coming from someone who has been programming in some way or another for the past 15 years. I know a lot of languages, but not from the top of my head. I can't go anywhere without my man pages, Dash, and some PDFs. I use them a lot. And I've learnt to understand that this is how the experts work too. We're human, very few off us can retain so much information. We only really remember what we use a lot, or repeat a lot, once we stop using it, or we stop learning it, it sinks to the back of our mind. That's natural for any human (except the abnormally gifted). So we all need books and manuals.

Although, programming logic should be second nature. You should know how to solve problems programatically. You should know the fundamentals of your given language. And you should want to learn more about it. BUT, all of that comes with experience, and it comes with making mistakes.

The experts make mistakes. The proof is in the undiscovered Heartbleed vulnerability. Apparent experts write the original code but the left it buggy. What about the constant Microsoft security updates? That's because Microsoft leave bugs in their code. Same for Apple, and the same for the gigantic Google. All companies are the global leaders in the IT industry, yet all have been highly susceptible to serious security flaws.

I stopped looking at other programmers as experts. Some are just more experienced, but even they will make mistakes, and sometimes pretty serious ones.

The code was beyond buggy. The design itself was buggy.

The trick is that most people who write code are not experts on security and typically do things that are insecure.

My interests are too specific and specialized while lacking any broad knowledge base on the subjects needed to ever have any employment on the topics.

I can cook and design my own dishes from scratch but lack any mulitasking skills and am slow and disorganized so these skills are worthless when it comes to a job.

I am pretty good at troubleshooting computers except when it comes to issues regarding networks which again makes this skill set useless.

I have a great interest in tech gadgets but lack understanding of certain science and technologies behind some of them.

Most of my skills have no real world value because of the gaps in my skill sets and are only useful to myself.

this is mostly about the math, but I assume replacing "writing proofs" with "writing code" and making other small adjustments gives a reasonable answer for the cs side of things.

tl;dr version: you're not too stupid, you're doing math wrong. Get an intro to proofs book, read it slowly, reread things as many times as needed for 100% comprehension, and do the problems(no you can't skip the problems). then get math texts for undergrads and do the same. then texts for advanced undergrads and early grads, etc.

longer answer:

This is a common problem most people studying math face. There are many books and even full college courses designed with the sole purpose of helping students learn to handle proofs. If you haven't taken such a course or worked through such a book then you should do that before doing more math.
DO NOT skip this, these books/courses exist because this is important. If you don't have a firm grasp on how to read and write proofs you will not be able to learn advanced math until you learn how to handle proofs.

on another note:

This is a problem. You don't learn math just by reading. You learn by doing. If you're not writing proofs you're not learning math.

Another (related) problem might be the way you're reading. You don't read math texts the way you read a novel. You're supposed to go over the same part several times, re-read old theorems/definitions/proofs whenever necessary, go slowly to ensure 100% comprehension of one section before even starting the next one, and most importantly, you're supposed to do the problems at the end of chapters (usually this involves writing proofs). If it takes several tries at reading a proof, then doing some exercises and going back and reading the proof a few more times before you completely understand it, that is not because you're stupid, it is because thats what you're supposed to do. In fact, if you understand all the proofs on your first pass through you should probably get a more advanced book since that one is beneath your level.

Lastly, it might be a problem with the "level" of the text. Math texts are generally written at different "levels", corresponding to an expected amount of "mathematical maturity" which loosely corresponds to how much time you've spent reading and writing proofs. If you just finished an intro level text on how to write proofs, its probably too early to try a text aimed at graduate math majors even if it says its an introductory text. This is because graduate texts will implicitly assume you've spent at least 4 years of your life writing proofs. To try and gauge which level texts you should read, think about your ability to handle abstract ideas and proofs. If your just getting started you should only read texts for undergraduates. when texts of that level start to feel easy (as in, you could prove many of the theorems yourself and solve most problems in less than an hour) then you should move on to texts for advanced undergrads or early grad students. And when you can handle those without much issue you can work on more advanced material.

source: myself. I'm a senior (pure)math major taking graduate level courses and doing an REU in algebraic geometry. I'll also be teaching the discussion section for my schools intro to proofs class next semester. Math and proofs are kinda my thing.

With programming, the material is usually not cumulative so the sequence in which the different concepts are taught can be changed. For example, it wouldn't really matter if linked lists were taught first or classes. Some people just need a more structured learning plan than others though, and that's not a bad thing. It's just a way of learning, like some people need well organized text books.

With mathematical proofs, don't be dissuaded because most people in STEM fields struggle with these. I doubt most people remember proofs either. It's sufficient that as you are going over them, the individual steps make sense. As for proving things yourself, those who excel at this tend to be in the minority. There are books dedicated to teaching people how to do proofs if one is so inclined to read them.

Also, it is very important when learning to do proofs to have someone who is very knowledgeable in the subject to check them. It is far too easy to skip points that must be proven and to make mistakes of logic.

It's been said that writing a good computer program is like writing a proof in that the program needs to handle everything correctly. In the case of computers, there is at least a compiler and linker to find and point out errors in the code that interfere with it being compiled. And then you have to run it against a great many cases to check for potential errors. Trying to write proofs on your own as a novice without someone to check them would be kind of like writing a computer program without compiling and linking it and then running tests on it. The odds are very much against doing so successfully for anything at all complicated.

I think there is some misunderstanding about the math and proof issues I posted about. I was not studying math proper; I was studying mathematical logic, which is relatively obscure as a subject by itself, and forms the underpinnings of proof-based mathematics. Not many people have specific knowledge of this, and courses are rare.

https://en.wikipedia.org/wiki/Mathematical_logic

Furthermore, my problems with mathematical logic don't involve writing proofs. There is no reason for me to write mathematical logic proofs. I'm reading the books and working on understanding the proofs in them because I want to understand the logical foundations of math, not, for example, topology or abstract math taken by themselves. The mathematical logic proofs differ from the proofs in these more mainstream sub-disciplines in that they are more fundamental and are more directly based on pure symbolic logic. They are not and cannot be proved with the reasoning used in mainstream math proofs because their whole purpose is to develop that reasoning. For example, one of the theorems in my textbook is:

For every u, for every v, P implies that for every v, for every u, P.

In other words, it is proved that changing the order of universal quantifiers (u and v) has no effect on the meaning of the doubly quantified statement (P). This fact is taken for granted in mainstream math, but, with mathematical logic, it cannot be used to prove other things until it has itself been proven, simple though it is.

An even more basic theorem that is proved in my textbook:

If P is true for every v, then there exists some v for which P is true.

Mathematical logic makes explicit the whole conceptual edifice that underlies this fact. I don't know much about mathematicians (students, professors, or professionals), but I would be surprised if many of them had sufficient low-level knowledge or awareness to prove this easily or to efficiently aid in understanding how it is true.

That doesn't seem to follow to me. It seems like you are arguing that there is no null set. If P is true for every v∈V, how does that handle the case when V=∅?

What's the name of your textbook?

I don't understand what you mean. If there are no v, then what is or is not true for any v is meaningless and the theorem applies to nothing.


First Order Mathematical Logic by Angelo Margaris

Also, it is not stated that P is true for every v. P true for all v is the antecedent of a conditional.

Consider the question of whether ∅⊂A for any set A, including A=∅. Trivially, if x∈∅, then x∈A and, equivalently, there is no x∈∅ such that x∉A.

I thought the circle with the line through it represented the null set, so I don't understand why you are positing its having any elements at all.

I take it that there is some kind of implicit assumption that the set of all v for which P is true is not a null set.