What Learning about Feynman’s Path Integrals Was Good for

I have gone to great lengths on this blog in order to explain how and why a degree in physics prepares you for seemingly different careers, or at least does not hurt.

But it would have been so simple. I will now illustrate this – using just two incomprehensible images.

Actually, I have a hidden agenda: The top page on this blog is my review of the book Student Friendly Quantum Field Theory. Of course I am trying now to coast on its success.

But I swear that each of these images made us – the Chief Engineer and me – spontaneously and independently burst out:

This is more complicated than Feynman’s path integrals!!

So if QFT does not prepare you for plumbing and IT security – I don’t know what does.

1) Feynman diagrams spotted in pipework – especially in the way the Chief Engineer depicts it! Our assumption is that this sort of documentation is commented by your typical HVAC contractor with What does he have smoked??

Piping diagram

The Chief Engineer’s Piping Diagrams. Captions in German but not important anyway. One of his ingenious inventions is built from many of these units.

2) Feynman diagrams in certificate paths – in the way authors of Request for Comments envisage the proper usage of related internet protocols. This is the kind of paper any developer sometimes SHOULD read to cross-check implementation versus best practices but I MIGHT give because the RFC is rather PhD-thesis-like.

Certificate path validation, RFC 4158

Certificate path validation, RFC 4158. Details again not important. It is about trust, cast into cryptographic relationships. Again these structures are fractal and you would see more and more trees and branches the deeper you dig.

OK – and now a true Feynman diagram. As with the other ‘examples’ a full-blown diagram would be built from lots of these units:

Susy Zerfall chi0

Feynman diagram of a SUSY process. Details – again – not important, and I would not be able to answer questions anyway (Wikimedia, user Patrick87).

As a disclaimer in case any practicing theoretical physicist feels offended: Of course I don’t intend to say that either of these things is as complicated or requires as much training as Quantum Field Theory.

But probably there is a more serious message to be uncovered here:

Feynman diagrams are often described as depicting the reactions between elementary particles. Yet they are shortcut for very unwieldy integrals in an abstract space.

Drawings of pipework and also the certificate paths seem more tangible. But the latter is replacing cryptographic relationship by little sticks and the former is after all an abstract map of physical items using 2D symbols.

In The Shallows – What the Internet Is Doing to Our Brains Nicholas Carr reminds us of the significance of our abilities to create maps at increasing levels of abstraction:

Mankind’s first maps, scratched in the dirt with a stick or carved into a stone with another stone, were as rudimentary as the scribbles of toddlers. … As more time passed, the realism became scientific in both its precision and its abstraction. The mapmaker began to use sophisticated tools like the direction-finding compass and the angle-measuring theodolite and to rely on mathematical reckonings and formulas. Eventually, in a further intellectual leap, maps came to be used not only to represent vast regions of the earth or heavens in minute detail, but to express ideas—a plan of battle, an analysis of the spread of an epidemic, a forecast of population growth.

Building and interpreting – abstract – maps of all kinds has become a key ‘skill’ – from software enterprise architecture diagrams to all sorts of infographics shared on social media like How Douglas Adams predicted the iPad.

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12 thoughts on “What Learning about Feynman’s Path Integrals Was Good for

    • If people would do mind maps with some rigorous rules in mind – and not as that exercise in “creativity” and making loose connections – then yes … I find that mind maps are too often used to make something totally mundane, simple, and unstructured look more impressive.

  1. Yup–“combine just anything” certainly applies here. My brain just got stretched a bit by this one.
    You reminded me that perhaps Feynman’s greatest intellectual gift was doing exactly what you just said to Dave, namely visually representing something that is quite abstract.
    That leads me to be reminded of my fundamental doubts about the current quagmire that is The Standard Model. It is a curious collection of particles meant to explain things that have been made manifest on various types of detectors. At some level it seems to me that so much of this–the weirder particles (and I use the name particle loosely)–may either be the result of measurement error or, perhaps a compete misinterpretation of the whole thing, in much the same way as was the mechanical spherical system that was once employed to “explain” the earth-centered astronomical model. Sure we do have the observations that match it and, sure, we do have everything working at a great level of precision but somewhere in there is the rel possibility that we have it all messed up right from the get-go 🙂

    • Feynman also said that he always had a tangible example in mind when speaking about generalizations and models – he was really a hands-on guy…

      Reading about the history of quantum physics it seems to me that the Standard Model and the current state of QFT is probably comparable to so-called (pre-Heisenberg / pre-Schrödinger) “older” quantum physics when some “quantum” rules were tacked onto an otherwise classical model but when the theory still lacked more fundamental underpinnings.
      If I understood correctly this is also similar to what people in phenomenology “beyond the standard model” do today when they try to extend current models.

      • Hi Elke, I just stopped by as I hadn’t seen any post alerts from you in a while. I’m guessing that, like me, with the summer upon us you’re choosing to spend more time outdoors and not at the keyboard. I’ve slowed down my social media use as well. I figure there’ll be plenty of time later on when the weather gets cold again 🙂

        • Hi Maurice, thanks for stepping by! I have been indeed been offline and enjoying nature without any computer in reach the past days and most of the time even without cell phone network – I am just wading through notifications now. The weekend before I worked with a customer onsite … then tried to get all the other projects done before vacation – so basically the last thing I did on social media was posting this post!

  2. I am unable to take a literal interpretation, since I don’t have the science background, but I love the creative reinterpretation of accumulated knowledge. I think that learning one process makes other processes more accessible, especially if you’re willing to play around with it and employ a sense of humour.

    • I don’t think you need a science background – in my reply to Dave I mentioned another non-sciencey example I should have probably added. When I started my first business I taught myself accounting from books (I totally overdid it) – and to me building that mental maps of balance sheets, profits and loss… and the rules about allowed transactions etc… felt exactly the same way if I tinker with hacking some device and learn something about networking protocols as I go.
      “Play” is essential – I totally agree … learning about those connections and building those maps has to be playful exploration; otherwise it does not work at all, I guess. There is a famous quote by Richard Feynman about “the pleasure of finding things out” 🙂

      • Ha, ha. I can so relate to “I totally overdid it.” I really do need a big picture understanding of a concept before I can begin to focus on details. I think the mapping provides opportunity to grapple with both. I map out my projects as well. I’ve noticed that how I organize information also has a significant impact on the finished project, as well.

  3. I’m mostly gasping for understanding here Elke. What’s the relation between a Feynman map and a ‘concept’ map with which I’m familiar? Concept maps, in my experience have allowed me to handle concepts, processes, and mechanisms which were too big to ‘hold’ in my head all at one time. Is that that your Feynman maps do? Or are they simply a shorthand for a complex solution which must be visualized? D

    • Your last assumption is correct – but the solution need not be visualized. Feynman diagrams represent something abstract that actually cannot be visualized (the popular “interpretation” in terms of interacting particles has of course some truth but is misleading, too) – it is more of coding step-by-step instructions for complex calculations into a set if pictures that seem familiar so that you can memorize them and walk through the steps in your mind. Feynman was synaesthetic so that probably explains why he came up with an approach for depicting daunting integrals as pictures.

      I also agree with the notion of concepts or maps being something that allows for keeping knowledge ordered and structured in a way you can turn it around in your head – as if you would explore some interconnected network.

      Maybe I would have my made my point clearer by adding even more examples that for me personally all invoke the same way of abstract thinking: No matter if I try to understand any sort of machinery (e.g. reading a patent which I believe is a worst case of how to describe anything technical as the goal is to make your legal claims not to provide good explanations), any IT or software infrastructure depicted as boxes stacked onto each other or flowcharts – or even the way I visualize double-sheet accounting I once tought to myself… I try to figure our the basic rules and built sort on an image or a map in the broadest sense of the term in my head.
      My goal is to avoid having to “look something up” as few times as possible but deduct from general principles and follow the map in my map… against popular wisdom about “You only know where you have to search for”.

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