Geometric Analysis: Day Three

I have much to say today. Where to begin. [13:31:29 6 set 2024.]

I've been wanting to study physics for about a year. That's not exactly true, there were always seedlings and they've been there a while, but I believe the clear statement "I think I want to study physics" finally realised itself somewhat out loud around a year ago.

This is significant. I wanted to study physics because I want to study space. Physics in itself is interesting under other domains and through other disciplines, but I had a motivation, a determined end goal. This motivation still exists. I'd also wanted to study more in Earth's Atmosphere, Ocean Science, and Climate Dynamics, which I know will be aided by a refreshed foundation in physics. I hadn't yet begun, because I thought I'd first review Calculus. It's still listed here as one of my topics under learning, but I've yet to approach. All to say, a destination for space and the universe through physics has been set for some time. And now, incidentally, serendipitously, and quite marvellously the more I look into Geometric Analysis [which I entirely expected to be more related to Real Analysis, study of real numbers, and the like] the more I find I have unwittingly found my way to the universe.

It seems I was always meant to study the universe, one way or another. It was going to happen regardless, no matter how much I tried to delay.

This has my attention now. It had my interest, but it has my attention now. There is no longer excitement. This is something more grand. More calm, more steady, more consuming, and more grand. This is now a kind of unification of my selves, and I'm beyond intrigued. I'm driven.

First, in my commute, I did what I could do as far as review and studying new terms. I focused particularly on "Higgs model". If you don't recall, the title of the seminar was as follows:

Decay of excess for the abelian Higgs model.

'Decay of excess' operates on or refers to 'abelian Higgs model' and 'abelian' is a modifier for 'Higgs model', so 'Higgs model' takes priority.

I found more than is in my notes [shaky commute, unable to write quite as much as I would like] and I was able to understand the significance of all of this, the answer to "why do you want me to care". I care and I'm happy to care. I may not understand all, but I care.

Key terms that now have far more sense to me: particle, field, excitation of field, Higgs field, Higgs [particle] boson, mass.

The following note was also of particular significance to me:

"The fundamental building blocks of our universe, of Nature, are not discrete particles. They are fields, fluid-like substances spread throughout all of space."

This captured me. The note pictured immediately before it thrilled me, but this captured me.

I have a lot of images in my head. When I speak and when I write, I use a variety of analogies that communicate aspects of these images, to the best of my ability. A number of images lately have involved the kind of existence, state of being, and construction this note is describing, and I've been unsatisfied not having a forum and mode to thoroughly explore what it is I see.

There's a chance, I have just happened on one. This is grand.

These are not fields I've previously studied, but as I read these words, my thoughts were along the lines of Yes, exactly. I have found words and ideas I can conceptualise, and largely due to an intrinsic connection and relationship I didn't really know I had. I'm looking forward to studying this further and taking time.

Gosh, we haven't even gotten to the seminar.

There was some initial difficulty gaining access, so I was only able to hear and watch the last 20 minutes of the lecture. I was intrigued. Although I said the mathematical understanding is of no interest to me currently, once I saw it, I wanted to know more. I think there may always be some sort of little trigger there. What the lecturer showed felt more familiar than I expected it to. It opened a window of hope, a kind of the mathematics will aid you, not inhibit you. The use of certain terms that I do know from my own studies in "pure" mathematics actually served as a bridge and helped me understand the significance of what was said without understanding in totality what was said. I may've been worried I'd forgotten too much, but I was okay.

The notes from the lecture are very brief, in black, at the bottom of the second page. These are not things I understood, but things that felt remarkable that I know I will recognise if they appear again in my research. The idea is: today was my first exposure at a higher level. I will continue learning and when I cross these terms again, likely at a comprehensible level, moments from today's lecture will retroactively make sense. I've found little time-jumping moments like this, "aha" moments, moments of recognition, have an incredible impact in my learning experience. I have them most often when I self-study and the emotional spark of that one moment secures my memory, makes me attached, and strengthens reasoning ability. Having already had a few of these moments in this topic and enjoyed them, this is almost an attempt to plant seeds for a few more.

At the end of the seminar, I was able to enquire about resources for beginners, so I will be beginning with those soon. I think I will also return to the YouTube video. It was actually a series, but I'd only started the first. Now that I have focused curiosity, intention, and questions, a talk to establish basics will be helpful. It will also probably lead to those "aha" moments I was describing.

I think an objective may be to simply share what I know or learn of this topic here, and share it with confidence that my understanding is accurate. This may just become a place to discuss a new interest. I will say, I am just beginning, there are a lot of errors in my understanding so for a while any summary I tell will be an attempt and nothing I write on this topic should be accepted as "fact".

[14:42:22 6 set 2024.]

14:48:34

I forgot to mention: when I searched ‘Higgs model’ this morning, the first explanation I found was from the U.S. Department of Energy. Quite immediately, I could contextualise, just based on the fact this topic is of interest to the Department of Energy. I learned specifically of the energy consumption in attempting to create a Higgs boson a few moments later.