Week 1: The Road to Reality
I love watching educational Youtube channels. It’s a great way to constantly keep myself exposed to science and technology. And this is nothing new: I’ve always been engrossed with STEM. Even at a young age, I was sure that I would become a scientist or an engineer, destined to discover and build marvelous things. I wanted to understand the distant stars, peer into a black hole, and prove that Einstein-Rosen bridges could be traversed.. one day. Around highschool, my dreams of becoming an Astrophysicist were pushed aside by a (more practical) desire to become an engineer at a major tech company. I had a knack for computers and felt I would be able to more easily achieve success for myself there. However, I couldn’t help but feel some cognitive dissonance at times. I gave up one passion for another, sure, but at the same time I had failed to satisfy all aspects of my nature.
In the endless pursuit to stay abreast of this kind of knowledge, I had discovered this incredible Youtube channel created by PBS Digital Studios. My impression at first glance was this channel would be the kind that focuses on widely approachable, boiled down explanations of complex astrophysical topics; however, I was astounded by the thoroughness of the content, accuracy, and the fact that jargon and mathematics were not off-limits for the content. At the same time, they somehow figured out how to capture a less technical audience, as evident by the view count and comments section. What a wonderful project!
A recent live stream, hosted by Matt O’Dowd (pictured above), recommended a book that was on Matt’s bookshelf called “The Road to Reality” by Roger Penrose. He mentioned that the first 16 chapters were focused on covering the mathematics needed to understand the remaining chapters which covered topics like SpaceTime, Minkowski space, QFT, and String Theory. How daunting! Having just recently finished the channel’s excellent videos on Penrose diagrams and how they’re used to describe the behavior of objects traveling near and through event horizons, I knew I wanted to conquer this book.
Why Am I Reading this Book
After the book arrived I started asking myself “Why even is the point of me reading this?”. It seems like a silly question, but it’s important that my motivations be honest if I wanted a chance to finish the book (or even make a noticeable dent). I’ve been known to lose motivation for things that don’t capture my attention (hence why I’m trying to track my reading here).
I think I’ve come to the following conclusion: I want some inner peace.
I often question “Why am I here?”, “What am I doing?”, “What is the nature of reality?”, “What even is ‘real’?”. Having given up my original dreams of working in science over a decade ago, I think my mind has been craving this knowledge. Just thinking about how wonderful it would be to truly understand the way our reality works. Some of the ideas in physics are so fantastical:
- Our existence may be built on infinitesimal 6 dimensional closed, vibrating strings (What are the Strings in String Theory?).
- Spinning black holes may contain a singularity “donut” that, upon traveling through one, could take you to brand-new universe (Mapping the Multiverse).
- The results of many quantum experiments may actually lead to the conclusion that a near-infinite realities may exist and it’s the divergence of these realities that gives rise to the otherwise pure randomness we see when observing quantum phenomenon (Parallel Worlds Probably Exist. Here’s Why).
How amazing.
While I may achieve this “inner-peace” by learning more about philosophy (and maybe getting some therapy), it feels, now self-evident, that I am reading this book to stay truer to myself.
Also: science is rad.
Week 1
In addition to the preface, I’ve read chapters 1 and 2 this past week. The first chapter was more a discussion on the value of an objective, separate reality in which mathematical structures exist in (to not misconstrue pure mathematical ideas not aligning perfectly with our less simple reality). It was very philosophically focused and really brought out some interesting historical ideas around the idea of an objective truth in numbers (with many callbacks to Platonism). In all honesty, one could skip this chapter and probably not lose much detail other than the introduction to Pythagoras and the Pythagoreans.
Chapter 2 is when the mathematics started to really be introduced. The chapter starts off with a simple introduction to the five postulates of Euclidean geometry:
- A straight line segment may be drawn from any given point to any other.
- A straight line may be extended to any finite length.
- A circle may be described with any given point as its center and any distance as its radius.
- All right angles are congruent.
- If a straight line intersects two other straight lines, and so makes the two interior angles on one side of it together less than two right angles, then the other straight lines will meet at a point if extended far enough on the side on which the angles are less than two right angles.
The book then showed light on the fifth postulate as being particularly.. problematic. Many mathematicians felt it could be proven merely as a combination of the original four postulates. In fact, one mathematician, Giovanni Girolamo Saccheri, spent a significant amount of their time working on this problem. Near the end of their tenure on this problem, they concluded that it may not be possible to specifically prove this postulate from the first four.
This was actually an amazing revelation as it suggested the first non-euclidean geometry: hyperbolic geometry. Hyperbolic geometry, unlike euclidean geometry, exists on a surface that is negatively curved; warped into a saddle shape. In fact, hyberbolic geometry has its own parallel postulate which is opposite of the euclidean one. Instead of exactly one parallel line passing through at point P not on line l, the hyperbolic parallel postulate calls for at least 2 distinct parallel lines passing through a similar construction. The chapter also briefly touched on elliptic geometry (positive curvature) but little detail was presented on this topic.
Takeaway
This book is intimidating. It’s clear that even at its massive 1,000+ page size, each page is incredibly chock-full of information; Penrose pulled no punches. I’m starting to treat each page as a guidebook on topics to read up on and push myself to understand. For example, I didn’t readily understand how combining two reflections in Euclidean geometry can result in a rotation about a defined point. After reading up on the topic a bit, I felt that I had a better grasp on some of the important pieces (which is good for me to hear.. as Geometry was one of my weakest math disciplines).
I do have some concerns after taking a second look at the Table of Contents again.. as I’ve said over and over: this book is daunting. I’m just hoping to vaguely understand topics at the higher levels of mathematics and physics when I get to them. This publication will serve as a testament to that outcome, one way or another.
