Exploring Mental Blocks in Mathematics: A Personal Perspective

[expos4ever]

Since this is a "general lounge" area, I will assume this rather personal story is not out of line. I am 64 years old (relevance of my age should become clear shortly) and graduated from an Ivy League University in 1980 with a degree in Electrical Engineering. I also scored over 700 on my math SAT (yes, I remember the score even though this more than 45 years ago). So you would think that I would not struggle with math. But I confess that I really do. I have been recently watching the series "Quantum Sense" which is almost exclusively about mathematics. From the comments below each video, everyone seems to rave about the clarity of the presentation and how it appeals to intuition. For me, it is an absolute grind to follow the arguments. Each video is only about 12 minutes long, but I am exhausted at the end. To be fair to me, this is new material - while I have some basic linear algebra in my background, almost all the concepts are new to me. Also, I am not ashamed to posit that a 64-year-old brain has less inherent plasticity to grasp new and challenging concepts. After all, even though we may not wish to admit it, I believe it is very likely that our brains are simply machines that get less functional as they wear out.

Let me draw a contrast. When it comes to language, things seem to come very easily to me. I do not need to struggle to find the right word and I easily, almost effortlessly, can create clear, concise prose (in fact, I make my living via the written word even though I am trained as an engineer). No doubt, you may be parsing this message looking for examples of mistakes in my writing. Fair enough. The point is that I have a strong intuitive sense that for whatever reason, innate mental wiring or the effects of life experience, the mathematical faculty of my brain does not work well. If this is true, I feel no, or very little, sense of culpability for this. After all, brains are just machines and perhaps my particular brain is not innately that well-suited to grasping mathematical concepts. Or perhaps my brain is wearing out. However, I must say that even while at university, I struggled substantially with the mathematics.

An alternate explanation, one that is less charitable to me, is that I'm allowing myself to be intimidated by the math and/or am giving up too easily. I do not believe this is the case but, to be fair, this is a possibility.

What is the point of all this? Well, I am quite sure that almost all who participate in this forum, because it is a forum about physics, are likely among the mathematically gifted. But I wonder if there are other people here like me - people who struggle with the math and wonder why this is especially if they, hopefully correctly, see themselves as quite intellectually gifted in other areas. I am simply curious about other opinions - how should we make sense of areas of seeming mental weakness? Can these be overcome with sheer effort? Are there "hacks", to use a modern expression? Or is the harsh truth that perhaps nothing can be done - no matter how much effort we put in, and how many novel approaches we try, perhaps the brain is simply not up to the task?

 

[jedishrfu]

I can appreciate your dilemma. I was once a physics major (1974) and took graduate level physics courses (1980) but veered to the darkside and recently retired as a software engineer. I am somewhat competent (a strong word) in Calculus ie I know enough to use integral tables and extend it to vector analysis but that's where my math fades.

I've always wanted to complete my physics studies but have had to realize that I have limited time and a poor memory for new things outside of programming.

I would suggest starting with SusskindsTheoretical Minimum books that are designed to teach people like us who still have a curiosity and want to understand Quantum concepts and see the math that supports the theory.

He has four books out:
- Classical Mechanics
- Quantum Mechanics
- Special Relativity
- General Relativity

One could start with the Classical Mechanics to get a feel for how Susskind approaches his subject or just jump into the Quantum Mechanics. As you read the book try to reproduce the line of thought he presents over and over in your mind. Its a lot like mud and for it to stick you need to throw a lot of it at the wall and it will become clear in your mind.

For concepts that are confusing, you could post a question here at PF and we will attempt to answer or provide resources for investigating it more. Basically you have to become single minded, take good notes, and go over the subject repeatedly. Its like you're trying to always be ready to explain it to a stranger like a student, grandchild, your petor a gameshow host.

Believe in yourself and you will begin to master it. It just takes longer when you're older and you have to accept that you've either forgotten some of your math or never really learned it when you first encountered it. Just don't despair.

I've heard brilliant.org has courses on various physics subjects. Also there are some good science channels on youtube most notably Veritaseum that covers Quantum topics from time to time. However they may not get into as much detail as Susskind and Susskind is light on his math compared to a standard Quantum Mechanics textbook.

When I first learned QM, it was taught in a historical sense starting with the Bohr atom and then progressing to the square well problem, the double slit experiment and progressing to the wave particle duality of DeBroglie and later to Schrodinger's equation and its solutions. The first book we used was Modern Physics by Tipler which used the historical sequence and had a lot of sidebars on the actual history.

Later courses got into Matrix Mechanics and Dirac, and then we spent a lot of time with computing cross-sections (yuck) needed for actual QM papers and understanding QM experiments and that's when I started to get lost. Now I appreciate this teaching strategy and understand why they went that route but I plan to avoid it (haha).

Lets not forget that Feynman once said "I think I can safely say that no one understands Quantum Mechanics."

And more quotes on QM and related sciences to brighten your day:

https://www.goodreads.com/quotes/tag/quantum-physics

Good luck in your endeavor and take care don't despair and enjoy your senior years without fear.

 

[Rive]

I am simply curious about other opinions - how should we make sense of areas of seeming mental weakness? Can these be overcome with sheer effort?

In my book, the question is rather about the optimal distribution of available resources (what's my capability of attention in this case).

I believe that by enough effort I would be able to grasp some deeper math, but if I'm able to push myself further (and that includes both the joy of knowledge and my career) with similar effort spent on my strong points, then ... Duh. Just do the math

 

[DrClaude]

I have been recently watching the series "Quantum Sense" which is almost exclusively about mathematics. From the comments below each video, everyone seems to rave about the clarity of the presentation and how it appeals to intuition.

I haven't watched much of those videos (actually, only the bits you have posted), and do not like them very much. Too much verbal description instead of equations.

I second the suggestion to look at Susskind. He also has a series of video lectures. The ones on QM can be found at https://www.youtube.com/playlist?list=PL84C10A9CB1D13841

 

[gleem]

I can commiserate with you. I am considerably older and like you am trying to fill in gaps in subjects that I had no exposure to in school. In my delving into tensor analysis to understand general relativity I didn't have the best references to start. For some reason perhaps arrogance I assume since I was fairly good in math that it would be quick and easy. I was impatient to get to the end quickly. Some things were familiar and thinking that I understood them I tried to take them in big gulps. I had to be more humble and accept that learning new things now was different. You don't have a lesson plan made up in advance. You don't have that special learning environment which was/is important for me. you have to find good references that work for you.

For concepts that are confusing, you could post a question here at PF and we will attempt to answer or provide resources for investigating it more. Basically you have to become single minded, take good notes, and go over the subject repeatedly. Its like you're trying to always be ready to explain it to a stranger like a student, grandchild, your petor a gameshow host

This is a good goal, make it your own as if you were expecting to teach it. In school when you ran across something that was challenging you had an instructor to ask for assistance. In PF you have a lot of guys (some professors (or former ones) available to assist. (they live and breathe this stuff).

Believe in yourself and you will begin to master it. It just takes longer when you're older and you have to accept that you've either forgotten some of your math or never really learned it when you first encountered it. Just don't despair.

Confidence in yourself is very important. If you did it before you can do it again. It may take a little longer but everything does when you get older but then again you have a lot more time. I have a lot of my old texts and if it were not for the margin notes and underlines I would have never thought that I took those courses, well almost never. Unless you use something on a regular basis you can't pull stuff up at will. Even tools not having been used or maintained for 40 years are bound to be rusty.

Disclaimer: I am not gifted.

 

[gmax137]

When I first learned QM, it was taught in a historical sense starting with the Bohr atom and then progressing to the square well problem, the double slit experiment and progressing to the wave particle duality of DeBroglie and later to Schrodinger's equation and its solutions. The first book we used was Modern Physics by Tipler which used the historical sequence and had a lot of sidebars on the actual history.

This is how I was taught, in the mid 1970s. I take it the historical approach is currently somewhat denigrated. I understand: 100 years on, the subject should be taught without crippling intuition by building false mental models (eg, tiny solar systems where somehow the accelerating electrons don't radiate). On the other hand, I loved Tipler's "Modern Physics." That's the book/class that convinced me to major in physics.