Seeking book recommendations/resources for learning math and physics to understand hyperdimensional reality

[DiscoveringTruth]

I’ve had a deep interest in learning math and physics at a graduate level or higher for a long time (I have an undergrad degree in chemical engineering but couldn’t pursue a masters in math or physics) in the hope of someday being able to understand hyperdimensional reality, especially the line of research pursued here by Ark and others in the QFG. It has to do with my perennial fascination with the idea of an exotic-yet-elusive fundamental UFT having been discovered yet being kept secret somewhere on this planet that can marry spirituality with science and rigorously answer questions about all the crazy phenomenon here on Earth that Cs talk about in terms of hyperdimensions or densities and their denizens.

I’ve read in multiple C’s session transcripts about using algebra, geometry and calculus to model hyperdimensional interactions and uncovering fundamental physics. When I read some of the transcripts where Ark talks about higher level maths and physics concepts, I don’t grok them much because of my lack of training in these areas. So in my spare time I’ve been revisiting undergrad math and physics books such as the ones that are recommended for competing in International Math/Physics Olympiads since I feel using this approach I will be better able to learn how to think like a mathematician or a theoretical physicist (for which my previous education was woefully inadequate). I’m fully aware this is a lifelong learning endeavour and not one that can be taken up lightly. But I still want to get after it and do the best I can in this life.

I was wondering if the math/physics researchers on the forum could provide book recommendations or resources and tips on how to actually learn these subjects at a deep level and what it takes to get new insights in these fields. Any thoughts or suggestions are appreciated!

 

[DiscoveringTruth]

For reference, here are some of the books and resources I've been using

1. Maths -

Art of problem solving book recommendations

Learn maths from start to finish by The Math Sorcerer

2. Physics -

Kevin Zhou handouts for Physics Olympiads

Book recommendations by Susan Rigetti for learning physics up to Graduate level

MIT OCW courses

 

[Natus Videre]

Hello @DiscoveringTruth,

For the past few years, I have also been trying to wrap my head around hyperdimensional reality from a mathematical perspective. My engineering background helped me form a mental picture of the many areas of mathematics, but it fell short of giving me the adequate skills to make a deep dive. It felt like I was trying to illuminate a 500-meter-deep cave with a small flashlight...

Engineering is an application-driven discipline—experimentation outweighs theory. In this regard, I think engineers are "wired" differently from mathematicians/physicists. If an application is not immediately tangible, engineers can lose interest rather quickly.
And I think this is also exacerbated by the "calculation culture" that permeates the engineering curriculum. There is too much emphasis on getting a "result" at any cost, It's easy to miss the big picture.

From what I understand, one needs to build an intuition around mathematical concepts in order to make any progress. A higher level of rigor (which is possibly foreign to engineers) is required to formulate arguments and outline mathematical facts. Proving statements by using a foundation of facts (theorems, lemmas, etc) becomes a core activity. A lot more time is spend in "theory" mode, which can cause discomfort as engineers ask themselves "ok, but what do it do with this?" Pushing through this urge to "apply" knowledge immediately is what I found to be most challenging. Experimentation by trial and error has its limits—frequently, a great dose of "theory" is needed to unlock new areas of application. The lines between "theory" and "practice" become blurred as one can't make progress without keeping them "in sync" with each other.

Since mathematics is so vast, the puzzle has to be assembled from many sides and it's easy to get lost in one area of study. I would focus on having a strong foundation in Algebra. When I jumped straight to Clifford algebra, I hit a brick wall when concepts from Abstract Algebra emerged in various proofs. It felt like I always had to go back to square one in order to fill my knowledge gaps. When the foundation is missing, it's very difficult or even impossible to make significant progress. Also, it's important to pick material which is challenging enough to "make you sweat," yet not totally out of reach with your current knowledge. After assessing my knowledge, I bought two books Basic Algebra and Advanced Algebra (by Anthony W. Knapp):

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.

In the thread Need Help Understanding Gravity, Ark mentions the importance of learning from high caliber authors:

For instance by modifying its geometry. So, you need to start by learning about space and time geometry. Therefore read about geometries: Euclidean, non-Euclidean, Minkowski, Riemannian. Without that you will be in the dark. It takes a while to get some grip of these concepts. Good popular books of good authors (Hilbert, Coxeter, Einstein, Infeld, Born, Wheeler etc.) can help to get the correct ideas. Do not read book by smaller caliber authors. They will give you a false idea that something is easy - which is not.

Continuous effort and significant mental capital is required, but ultimately the journey is very rewarding.

 

[DiscoveringTruth]

Thank you @Natus Videre for mentioning algebra books and referencing Ark's recommendation to learn from high caliber authors! This is solid advice and one that didn't strike me as obvious earlier.

I am looking to build a strong foundation in mathematical thinking first before I take on more advanced courses since mathematics builds up like a chain of ever more abstract and advanced ideas. Like you mentioned, pure mathematics also involves proving theorems and finding new mathematical properties where engineering has a different bent focused on computation and using those properties to build a more practical, real world focused product or process. It is the former way of thinking that I need to develop for which books on Math Olympiad training/problem solving seem to be helpful, at least in the initial stage. As an engineer I definitely lean more towards application than theory myself. I do hope that some day in the future there will be new technology based on groundbreaking research in the foundations of physics (unless natural or man made cataclysms intervene) and phenomenon that currently seems magical will become common place.