Tag: QFT

An Effective Recipe for Mathematical Modelling

By: Danny Geisz | July 20, 2020

Project: Orchid

Sup readers. Prepare yourselves for another disjointed post. I’m basically using my blog as a repo for and log of my thought processes.

K, so basically a big thing that I’ve learned about myself is that even though I really enjoy learning about pretty much anything technical (math, physics, CS, etc) it’s immensely hard for me to stay motivated to continue working on a project unless I can very easily discern why the project benefits humanity. That’s part of the reason why I’m really enjoying my current project.

Oh wait. I forgot that I haven’t written a single blog post about my current project yet. RIP. I’ll do that soon. Basically, I’m trying to build a social media platform that psychologically incentivizes healthy, non-violent conversations about traditionally controversial and polarizing topics. I’m bringing this up simply because I perceive the goal of this project as being of upmost importance for the future health of the purportedly self-healing super graph that is humanity.

Anyway, back to Orchid. The reason I bring all this up is because in past months, I haven’t really been able to come up with a compelling reason why building Orchid would be beneficial to humanity, which has meant that it’s somewhat difficult to remain motivated to work on it, which in turn means I haven’t prioritized working on it, which means I haven’t worked on it all that much.

Orchid, however, has been dancing around the back of my head for the past couple of months simply because I think it would be super cool if it worked. If nothing else, it would give me a way to work on learning things like QFT without the overwhelming frustration of working with ginormous equations with pencil and paper. While I personally don’t see learning QFT as a particularly meaningful pursuit at this juncture of my life, the equations that govern quantum fields are super, super juicy, and it’s fun to play around with them.

Anyway, in trying to come up with ways that Orchid could benefit the humanity graph, I’ve had a couple ideas. This first one kinda showed its head in my last post, but I’ll flesh it out a bit more here. Basically, if Orchid works as I intend, it will essentially create a method for storing mathematical entities of all varieties in well-defined computer data structures. Neat. Additionally, the rules governing mathematical manipulations of these particular mathematical entities will also be stored in similarly well-defined computer data structures. The reason why this is compelling is because computers would then have the ability to work with and manipulate these structures on their own, without human interference. Obviously, the algorithmic approach the computers would take in manipulating the mathematical structures would be defined by humans, but it would essentially allow computers to perform the same sorts of computations humans do all by themselves.

Why is this potentially cool? Because up until this point, most mathematical software is essentially super-powered calculators. Mathematica, for example, has been built over the last 30 years, and during that time, human beings have translated all varieties of mathematical processes into code. There’s a reason it takes up like 20 GB. It’s gigantic. But if you want to numerically solve erf, like I did back in high school, well then boy is Mathematica for you. How is orchid different? Instead of having a bunch of hard-coded algorithms for solving and manipulating previously defined mathematical expressions, Orchid allows you to define entirely new mathematical entities and the rules that govern them. This, furthermore, allows users to have a central location for creating a manipulating all varieties of mathematical entities.

Not only that, but the computer itself would have a way of creating and manipulating exotic mathematical structures. This means that computers would be able to do what previously could only be done with pencil and paper, or on a blackboard. Instead of slaving away doing a bunch of predefined calculations, computers could actually be “doing the math” in the same way that humans have for the last several centuries.

I imagine it might not be immediately clear why computers doing pencil and paper mathematics would be beneficial to humanity. Let me explain as clearly as I can. Mathematics has provided humanity with perhaps the most robust and effective method for quantitatively understanding the world around us. And when humans better understand the world, they can make better predications about the state of the world. As I’ve discussed in previous posts, whenever a structure exhibits stable characteristics and behaviors, that structure can be effectively utilized in the creation of another, larger stable structure. In this context, that means that whenever humans are able to understand the stable characteristics and behaviors of a system, they are frequently able to use that system in a manner that increases humanity’s overall fitness.

Theoretical physics, as a field of study, is perhaps the best and most well-established example of what I’m describing. The phone in your pocket, the missile defense system that keeps you safe, and the lightbulb that illuminates your house are each examples of the staggering amount of technologies that fundamentally would not exist without developments in theoretical physics.

And what is theoretical physics? It is the practice of modelling physical systems in terms of well-defined mathematical structures, and then making predictions about the systems themselves using well-defined mathematical manipulations on those structures. In case you are wondering, experimental physics is the practice of designing and carrying out experiments to gather data on physical systems. Analyzing these data sets is what allows theoretical physicists to determine the degree to which their models accurately describe reality. So, if you’ve ever wondered what those nerds up in national labs, universities, or particle accelerators are doing, it’s that.

Physics is all fine and good, but I’ve found that much of what goes on in modern day physics doesn’t actually seem to affect many people. Some of it certainly does, but a good deal of it is documented in papers that 99.99% of humanity can’t understand and don’t really do people any good.

However, there are plenty of other real-world systems that could be analyzed using the aforementioned methodology. Data scientists are basically the people attempt to understand large data sets using machine learning or other statistical methods. From what I understand of current practices in data sciences, there really isn’t a large amount of coming up with novel mathematical models for understanding data sets in a manner similar to theoretical physics. There certainly is some, but nothing compared to physics.

And there’s a very good reason for this: coming up with appropriate mathematical models for different systems requires a huge amount creativity and intellectual capacity. In other words, it’s really, really hard. Ever wonder why everyone thinks Einstein was so smart? It’s because he came up with extremely precise mathematical frameworks for describing relativistic systems. He did a bunch of other stuff too, but he’s celebrated mainly for his ability to create compelling mathematical models for physical systems. And let me tell you, General Relativity is no small pill to swallow. There are a ton of moving parts and different mathematical structures at play, but my gosh, the resulting theory is objectively gorgeous.

Anyway, I could fawn on about GR all day long, but that’s not why we’re here. The reason Orchid is compelling is because it would drastically simplify the process of coming up with mathematical models to describe different systems. Not only that, with the right set of algorithms, the computer could by itself create mathematical models to describe data sets.

That last sentence probably didn’t have the desired effect on you, so let me rephrase. Orchid could potentially allow a computer to do the same thing Einstein did that made him famous as one of the smartest people in history.

IMHO, that’s pretty dank. But even if that last bit doesn’t happen, Orchid would still provide humanity with a framework for easily constructing and manipulating mathematical entities, which could in turn be used to understand the world around it with a degree of precision previously unattainable.

Well, maybe that’s being overly optimistic. We’ll see.

Anyway, when I started this post, I wasn’t going to talk about Orchid, I was going to give the recipe for consistently and efficiently modelling a system mathematically. Here goes.

  1. Determine which parts of the system in question that you would like to understand.
  2. Create a set of mathematical structures that quantitatively describe the interesting characteristics of the system in question.
  3. Clearly lay out the method that can be used to extract observable quantities from the structures in part 2.
  4. Describe all factors that effect the system in question as transformations on the mathematical structures from part 2.
  5. Use the defined mathematical entities to make predictions about the system in question. Queso (K, so) I think this is, if nothing else, a reasonable starting point for understanding a system in terms of mathematical structures. It also gives me the spiritual reassurance that Orchid is actually a tool that could be used to improve and optimize the humanity graph.

Just hit page 7, which is about 5 pages longer than I thought this post was going to be, so I’m going to wrap this sucker up. I guess as one last thing, if this stuff interests you, shoot me an email. After leaving Berkeley, I haven’t talked to a lot of people interested in this stuff.

May your socks always come bedecked with cool designs. Peace.

The Birth of an Orchid

By: Danny Geisz | January 23, 2020

Project: Orchid

Good morning, schmeagy deags. I bring tell of great tidings. I have finally started birthing an Orchid. To formalize the previous statement, my mind has begun the painful, several-year-long process of giving birth to Orchid. What is Orchid? Certainly not a human child. I don’t have the biological hardware for that. Will it be as good as a human child? I suppose that will be for the world to decide.

You’ll notice I never answered the first question. To put it in the most boring way humanly possible, Orchid will be a piece of mathematical software. Bleh. To put it in a far more intriguing way, Orchid will be a tool that allows human beings to mercilessly take advantage of the parts of computer that are better than humans to construct magnificent pieces of logical structure with extreme simplicity.

If you’re at all involved in STEM, you probably have some level of familiarity with Mathematica, Maple, or Matlab. For the uninitiated, these are all programs that have been developed over the course of several decades and are essentially superpowered calculators. I do not mean for Orchid to attempt to overthrow these three giants of this particular industry. That would be ultimate folly for several reasons:

  1. Mathematica, Maple, and Matlab are all extremely good at what they do. It would be a staggering waste of time for me to try to build something even slightly like these pieces of software.
  2. These pieces of software are actively being developed by large groups of people. Regardless of any claims made about my arrogance or egotism, I assure you all that I would never hope to accomplish in any short amount of time what a group of several hundred people have accomplished over the last several decades.

Goodness, that was only two reason. Last I checked, “two” doesn’t fall within the set of numbers described by “several.” Well I think they are both good enough. Those of you familiar with the Big Three mathematical programs know the staggering breadth of mathematical material that they support. What then could I possibly wish to accomplish with Orchid? What will Orchid be able to do that these pieces of software cannot?

I will answer by giving you the story that motivated Orchid in the first place. Last semester, I wanted a break from my regular schoolwork, so I bopped on over to the law library and violently threw open Steven Weinberg’s Foundations of Quantum Field Theory. That book is, in a word, dense. With my other courses last semester, I took me about four months to get through the first (real) chapter of the book. I was finally at the point where I could start working through the problems at the end of the chapter. To many of you readers not actively involved in physics, you may be wondering why on Earth I was purposely subjecting myself to the third level of hell. To many of you readers actively involved in physics, you may be wondering why on Earth I was purposely subjecting myself to the third level of hell. To those of you readers who actually enjoy theoretical physics, you will know exactly why I was purposely subjecting myself to the third level of hell, and understand I was doing this for the same reason a drug addict will go to any lengths to get another sweet, sweet hit of whatever particular substance has been giving them problems.

Because I was in Weinberg’s book, the problems were hard. Like really, really hard. However, I wasn’t annoyed by the length of the problems, I was annoyed at how I was doing the problem. I was naturally doing everything with pencil and paper, and I found that I was constantly rewriting extremely long equations with an incredible number of moving parts. I think everyone except the true weirdos can agree that the act of constantly rewriting extremely long equations is incredibly tedious, but it is also extremely prone to errors. Eventually, blessed readers, I had had enough. You better believe I wanted to find the Lie Algebra of the Galilean group, but at a certain point, a girl has got to put her foot down. I, being the metaphorical girl, fled the Law Library feeling particularly defeated.

As a budding computer scientist, however, I had another reason to be frustrated. Literally one of the biggest purposes of computers is to do simple monotonous tasks that probably could be done by humans. Why couldn’t I just use a computer to find the Lie Algebra of the Galilean group for me?
With this question glistening upon my tongue, I started a deep dive into the documentation of all the major pieces of math software with which I’m familiar. These pieces of software are incredibly good and fast at doing standard computations in a wide variety of fields in mathematics. Their issue is that they don’t allow you to define your own logical structures with their own rules. The particular piece of mathematics that I needed to do cannot easily be done using the Big Three.

I then began researching the incredibly huge variety of other pieces of mathematical software. The closest thing I found to a software that could solve my problems are two programs called Coq and Lean. Let me tell you, the language and interface for both of these pieces of software are absolutely disgusting. Coq in particular has that “90s software” feel that makes everyone want to amputate one of their feet.

From the beginning of this venture, I felt I would likely need to develop my own piece of software to accomplish my needs, and as I continued to research, the requirements and features of what I now call Orchid came to me as though from a half-remembered dream. In essence, I have two main requirements for Orchid:

  1. It does math like we normally do with pencil and paper.
  2. It looks good. We’re talking LaTex, but LaTex that is mathematically interactive.

As a final note, some of you overly masculine readers may ask why I am choosing to call the system Orchid. I could give you some hooplala about Orchids being beautiful yet unique, or them having cool adaptations that mirror logical structures. That ain’t true. I wanted to name it something cool that in my mind evokes a similar emotion in my being as when I think about the Euler-Lagrange equation. “Orchid” therefore, fit the bill remarkably well.

Micromanaging will be the Death of Me

By: Danny Geisz | January 5, 2020

Project: XFA Genesis

Shalom, brethren. I have spent this week of winter recess in Arizona with my family, which means I have had time to obsessively build the XFA site. I understand that many of you readers may not be programmers, but let me tell you, if you’re looking for a hot, passionate night of shameful pleasure, learn Python and then build a web app with the Django framework. I can barely contain my feelings toward Django. It is juicy, juicy sauce. If you are in fact a programmer, and have previously used Django in your endeavors, I’m sure you share my sentiment.

My compulsive programming this week has also been a time of self-learning for me. I know all you readers care deeply about even the most minute details of my work life, so I won’t hold anything back. Actually scratch that, I am going to hold some stuff back. Otherwise, many of you might be concerned I’m an egotistical sociopath, which isn’t good for business. Anyways, I have specifically been paying attention to my micromanaging tendencies. When building a web app you generally have to keep track of several moving parts (models, views, CSS styling, whatnot), and I very much tend to spend far too much time perfecting small details when much larger pieces aren’t in place. For example, you know how sometimes you go to a news or blog site that only displays part of an article, and then the text fades out with a “Read More,” button at the bottom? For some reason, I had a spontaneous love affair with incorporating that effect on the XFA site, and I honestly think I spent an hour (“…A full hour!” –Crazy Craig) getting everything right. Now, this wouldn’t have necessarily been the end of the world, except for the fact that the entire site looks like garbage right now because I haven’t started styling the site yet. The engaged reader might be tempted to ask the question, “Why oh why, Danny, did you spend so much time perfecting the text fade away effect when you haven’t even started styling yet?” Well, my wonderfully engaged reader, I don’t really have a good answer for you, aside from the fact that I derive an irrationally large amount of utility from having perfect control over small details. Some might say I’m a perfectionist. Others would be wrong.

I think because I’ve spent the last five years mostly doing physics (not hard stuff like QFT or GR or String Theory. I’m not Wolfram sigh) I’ve generally been rewarded for being cripplingly OCD about the minute details of derivations. However, recently I have been attempting to tackle more complex theories (the hard stuff like QFT and GR), and I have been running into issues because I tend to spend way too much time trying to understand the incredibly minute details of every equation instead of trying to grasp the central tenets of the theories. It's also hard because the minute details of the mathematical theory usually give me the most pleasure (the details are a bit fuzzy, but at one point I believe I was accused of having romantic feelings for eigenvalues. I can’t say that’s too far off the mark. Honestly, eigenvalues are the Django of basic linear algebra). The issues I’ve been having with these theories specifically have genuinely caused me to wonder if my brain is already slowing down, but I think it’s far more likely that my perfectionist tendencies are finally catching up to me.

So then, the ~groundbreaking~ (really pretty obvious) conclusion I’ve come to is that I have to be much more militaristic with myself when it comes to my organizational approach to learning new subjects or working on my projects. As a practical example, I will have to force myself to implement the architecture of the XFA site before I go about trying to style the thrice-fracked thing. This organizational approach is pretty obviously the best way to go, but my time of self-reflection has really showed me how shamefully unorganized I’ve been with my past projects.

As an example of this shameful, shameful behavior, for the past two semesters, I’ve been doing a research apprenticeship for the ATLAS group at Berkeley (For the uninitiated, the ATLAS detector is a detector in the Large Hadron Collider in Geneva, Switzerland, which just so happens to be the largest particle collider in the world). I won’t go into the specifics of my projects with ATLAS, but this last semester I was primarily working with the incredibly elaborate data readout system used by ATLAS.

It’s honestly a bit painful to think back to my project this semester, because I really did a poor job learning the necessary material to do the project I was working on. The fundamental issue was that in order to understand anything about anything, you had to first develop a basic understanding of the system as a whole. This was an issue for wee physicist Danny because I’m used to reading out of a physics textbook, understanding equations line-by-line, and then watching the main ideas unfold before me like the glorious phoenixes they are. When confronted with a subject that wasn’t possible to learn line-by-line, I hopelessly floundered about like the weird fish in Harry Styles music video for Adore You.

The moral of the story is that if you’re a perfectionist, you’re annoying and I don’t like you. JK, we’re all friends here. The moral is that in the future, I’ve learned that I need to make a much more concerted effort to outline whatever it is I’m working toward, and only dive into the details when I can see how they support the bigger picture. Unless I’m just looking to trip out on some delicious math. Then I’ll just shamefully and giddily open Weinberg’s QFT book to the section about the topology of the Lorentz Group. Until next time, my friends.

Forging the Blog – Entry 1

By: Danny Geisz | January 2, 2020

Project: XFA Genesis

Like so many others, today was a remarkably interesting day. As the title might suggest, I began work creating the site for XFA today. I am currently refamiliarizing myself with Django, which is a python framework for building web applications. I naturally will need to have perfect control over the XFA site in order to convey the precise information and emotion I wish to convey, and thus I feel as though I necessarily must build the site myself, instead of turning to some easy way out, like WordPress. I simply cannot convey my excitement about enacting my vision for the XFA site, and it is a gift from life itself that I have the ability to birth this site from my mind in the form of succinct blocks of code.

Now then, I feel as though I ought to expound upon my first statement pertaining to the interesting character of this very day. After a brief stint journaling, I began reading Srendniki’s book on Quantum Field Theory. Up until now I have been attempting to learn the subject by means of Weinberg’s text, but let me tell you, that book is dense. A good friend of mine suggested I use Srendniki’s text instead of Weinberg for an introduction to the subject, so I decided to give it a whirl today. I read through the first section which motivated the use of Quantum Fields to deal with the problem of unifying special relativity and quantum mechanics, and the math was quite interesting. I am currently on Winter Recess and am spending time in Arizona with my family, and at about 12 I went to play 18 holes of golf with my father, brother, and Grandmother.

It was a truly gorgeous day. Arizona can sometimes be reconkulously hot, especially when playing golf in the desert, but this winter day was wonderfully temperate, and the sky was an incredibly compelling shade of eggshell blue. Anyway, I was able to enjoy the day and the golf for about 9 holes, when I was suddenly overtaken by the compulsion to work on quantum field theory problems. Gone was my enjoyment of the day, my family, and ridiculous sport of golf. This compulsion is very interesting to me. It happens fairly frequently to me, and it honestly seems quite silly. It robs me of the joy of living and fills me with a profound sense of anxiety.

I’m going to abruptly cut off this entry simply because it’s nearly midnight, and I’m quite tired.

Stars; in your multitudes; scarce to be counted; filling the darkness.