Lecture 1: Gauge Theory for Nonexperts

[@ozachar]

So refreshing! As a condensed matter physicist in my past, it is rare that I see a mathematician makes things intuitively easier to understand. Here, right from the start I was hooked, and it was clear this is going to be a different kind of exposition.

[@markcarey67]

Great stuff Tim. As Emerson said to Whitman: "I great you at the beginning of a great career" - you are going to be a really good science communicator and the kind we need. A modern Penrose who explains but doesn't dumb down for or condescend to the audience.

[@andrewmorton7482]

Great analogy to use currencies, but I should point out that the currency in the UK is the pound (yes I know - picky picky)

[@dubhd4r4]

Ohh SNAP Tim! Finally a Guage Theory primer for PhDs in Complexity Science like myself! You go boy!

[@notlessgrossman163]

The best lecture I have seen heard on KZbin ever. It is razor sharp focused and motivated

[@joelcurtis562]

The intuition I like to use for gauge connection is that it generalizes unit conversion. Suppose I have a stick whose length can change for whatever reason. I measure the stick, then mail it to my friend and ask her to measure it. I want to know if the stick's length changed on the way from me to her. I can just see if her measurement is the same as mine, right? No. Why not? Because there are two reasons we might have gotten different numbers. 1, maybe the stick actually changed length. 2, maybe she's just using different units, say inches, whereas I used centimeters. In that case we'd get different numbers, even if the stick stayed the same length. Or maybe the stick changed length, but we get the same numbers! The only way to know if the stick really changed length is by "translating" to the same units for both measurements. The way to do that is to build into our equation a term that does this unit conversion automatically. That's what a connection is. Maldacena's forex analogy is quite good, but it makes it a bit harder to drive home the basic idea that a real object is not the same as the numbers we use to describe it. This is because most people are not used to thinking about money so abstractly, i.e. that the number of currency units you have is independent of how much purchasing power you have.

[@eismscience]

Very didactic and very clear video, Tim. You've done more for gauge theory and gauge symmetry in 30 minutes than Eric Weinstein has done in several years. Great talent and great work.

[@connorbrown5267]

Hi, I’m a graduate student studying theoretical physics, really enjoy the analogy for local gauge symmetries. It works so well in real life since if you wanted to convert some currency, at a shop you usually have to pay more than the base conversion, it literally changes spatially! Very handy analogy, and great video, look forward to the rest of the series!

[@soultrick7474]

Big thanks for your time and all of your great and free content. Humble and kind person, never lose these values :))

[@rwmcgwier]

Very nice. Clear exposition and good analogies for the concepts. UK never adopted the Euro. It continues to use the pound.

[@joelcurtis562]

Wish this video had been around years ago. I could have saved myself tons of time wrapping my head around this stuff! Well done.

[@cooperszone]

Excellent refresher! Thank you for sharing!

[@hatmatrix4376]

Tim, thanks for the lecture on this topic. I am a financial economist (with PhD-level training in Math) but couldn't understand the papers on gauge theory (I only had HS physics). BTW, you have a good understanding of international economics/finance (which I teach occasionally).

[@TimothyNguyen]

Correction: UK uses pounds not euros (silly me, I went to London back in 2014!). Noted this when I first made the remark at 2:16 and in the video comments. Notes: This is an expository video that does not draw upon any particular individual's work but is rather a distillation of a field of ideas into a digestible and short video. In particular, citations are reserved for scholarly work that directly draw upon a source - they are not suitable for a medium of general education that is an amalgam of a diffuse set of ideas. (For context: twitter.com/IAmTimNguyen/status/1423320147108909058 )

[@BlakeStacey]

Also, I've read Malaney's thesis. It's devoted to consumer price indices and mentions currency exchange twice, both times in passing, and it treats path dependence in currency exchange as a thing the reader is already supposed to understand, so it can be an analogy or motivation for something else. For example: "Far from being exotic, these risks are well known to all those who must decide how much currency to change when visiting nations with volatile exchange rates. What the differential geometry emphasizes is that path dependence is preferable and that the path dependence of the Divisia is no more counter-intuitive than the path dependence underlying the theory of investment." The other literature cited by Maldacena, like the 1999 paper by Young (and citations therein), develops the idea much more. And as for the general theme of bringing gauge theory into economics or finance, that is at least as old as a 1995 preprint by Kholodnyi ("Beliefs-Preferences Gauge Symmetry Group and Replication of Contingent Claims in a General Market Environment").

[@GabrielHarber]

I’ve been looking for a video explaining how gauge theory works ever since I started hearing Eric Weinstein talk about it. Great work!

[@viiziion0]

Hello! Physicist who is currently working in the machine learning industry here (data scientist) - loved this video. Just finished listening as I had a late night coding session. All the while I was listening, I thought of your treatments on the topic as sounding like someone who might be a high-energy theorist. Low and behold, I was right. I found your blog and I just have to say, your Kernel Ridge-Regression paper is fascinating. Passing this paper off to my team tomorrow to hopefully spark some good conversation. You earned a new sub this evening.

[@larryboulware6483]

Thank you very much. You did not make a difficult topic easy but understandable. I am going all the way with you

[@realdeal139]

Pretty cool stuff. Love your work Tim.

[@ThePhysicsConnection]

Thanks Tim! looking forward to learning more about this!

[@eismscience]

Great work, Tim! I haven't seen this, but very much looking forward. I will be back...

[@harrycohen2594]

The standard currency in the UK is still the pound sterling not the Euro. They never adopted the Euro…and they are no longer in the EU. FYI

[@davidsykes5635]

🇬🇧🏴󠁧󠁢󠁷󠁬󠁳󠁿🙂

[@ziryabjamal]

Funny and informative. I just saw the tweet after Eric's presentation of all the math UChicago didn't know and it is all starting to make sense 🙂

[@alexwilson8034]

Keep it up man we’re here for your truth

[@JohnCorley13]

thanks this is so awesome!!!

[@adamh6565]

Thanks Tim, I *seriously* appreciate this video as Gauge Theory is something which I've wanted to understand for quite some time. This made things a lot more clear! Sorry that you have to deal with the narcissist baby Mr. Weinstein on Twitter, lashing out on you for simply trying to explain concepts in a coherent way instead of Eric's usual use of esoteric terminology and rambling monologues. I like most of what Eric does but a lot of times he reminds me of people who simply try to impress others by talking fast while using terminology very few people have stumbled across. He surely is somewhat of an "anti-Feynman" in his pedagogic style.

[@johnjames5988]

Awesome, thank you 🙏

[@Khashayarissi-ob4yj]

With luck and more power to you. hoping for more videos.

[@tarekhalabi2131]

Thank you.

[@matthewocadiz7333]

this was very helpful

[@morgengabe1]

17:28 Could it also be the case that parallelization generalizes "local" invariants? As in "it's parallel, so even if we know it exists we've no idea how it's changing"? Thanks for this! Been yearning for a good place to start with this sort of stuff!

[@PravdaSeed]

💙 Thanks 💙

[@JoeHynes284]

i was trying to think of it as a gauge, i think, is the measure of the distance between train tracks. So no matter where one track goes, in any direction, the distance (gauge) to the other track is fixed so one can determine the orientation of the other track. this may be a terrible analogy, its what my feeble mind came up with. Thanks for your efforts sir!!

[@oldtom541]

The UK currency is the Pound Sterling (£). The U.K. is no longer in the EU, but never adopted the Euro (€) when it was in the EU.

[@dandupaysdegex]

They use pounds in the UK.

[@jostpuur]

Is this supposed to be a generalization of what we encounter with the vector potential of electromagnetic field? Looks different.

[@TimothyNguyen]

Yes. Its gauge theory from a geometer’s perspective but its the same structure underlying the associated physics.

[@RealLifeTop10s]

This is great!

[@timc7035]

Great video! This is very interesting and well presented. Eric saw this and says "Look forward to hearing from me" after some insults on twitter. I wonder what he thinks he can do here. You cite Maldacena who mentions Pia Malaney.

[@MatrixViolinist]

UK does not use Euro :) Good video

[@BertSperling1]

Great video 👍💯

[@bieberstein64]

Euro in UK?

[@Sharkfan]

eric is mad

[@Randulpheleven]

Can you please explain what he is furious about, I read his tweet and I don't follow?

[@timc7035]

@@Randulpheleven Eric thinks that Tim is purposely using a currency example without citing his wife Pia Malaney to inflame the situation even though he cites Maldacena who mentions her. It sounds like he is threatening legal action which is laughable over something like this. Does Eric have any idea how many ideas KZbinrs use without citing?

[@benjaminandersson2572]

What sort of recording software are you using?

[@TimothyNguyen]

Screenflow for recording. Jamboard for writing.

[@imrematajz1624]

This is a joke, where the banker, the mathematician and the physics professor meet at the kinder garden: here it goes...

[@evariia]

I'm not an expert, but I really like quantum mechanics.

[@bobanderson665]

Thanks for all your work on this video. I don't see a part 2 on-line yet but that is probably not a bad thing as some of the terminology around the 20 minute interval will send me off to do some research on covariant derivatives etc Then possibly I will need a few re-watches to make sure I am clear on the math. Your writing could do with being a little larger on the screen as some of the symbols are difficult to read and the audio needs to be 6-10 dB louder - its on the limit of clarity with my audio turned all the way up. Oh your comment about the UK Euro hurt me so much! Now the UK is not even part of Europe let alone sharing the European currency, so sad! That stupid Prime Minister David Cameron has ruined the UK for decades to come with his botched 2016 EU referendum. All he achieved was a very public kicking of his old Conservative party.

[@TimothyNguyen]

Thanks for the feedback! I've already filmed the second video and it's currently being edited. Let me know if the audio/video is still suboptimal. Are you viewing on a desktop? I imagine my video isn't legible on the phone, and it may be a bit small for a ipad, since the ipad screen shown is a shrunk down version of an ipad pro.

[@elliott8175]

The audio seemed fine to me? I used headphones and kept it at 30% of max dB and it seemed fine. I don't exactly have super hearing either.

[@bobanderson665]

@@TimothyNguyen Good to hear part 2 is coming! I use a laptop. I routed the audio to some Bluetooth Speakers to get maximum audio gain but it is a hassle to set up so having stronger audio would be simpler for me.

[@imrematajz1624]

I blame you for BREXIT!😂

[@lw4423]

nice suit...

[@khatharrmalkavian3306]

If you want to make money just go around the circle backwards.

[@bondmode]

you are great and content is great as well, but you need to invest 10$ on a pop filter for your microphone

[@TimothyNguyen]

Thank you. Still trying to figure this all out being new to the game - will use the pop filter next time!

[@TheDabbleJew]

@Bondmode, first I heard of a pop filter, cool. Can you potentially timestamp where this popping sound is occurring? OR, is it anciente and just throughout? TY!!

[@eismscience]

I didn't notice any popping. Very clear to me.

[@bondmode]

@@eismscience the popping refers to all the sounds coming from your mouth that are not voice and can be quite disturbing for some, it's mainly due to saliva moving around plus a very sensitive microphone. that's why every pro has always one between them and the mic. an example @Kenneth E. Barnett is @00:02:14 before the words "and in the UK". the popping is most evident when he leans closer towards the mic

[@JustNow42]

Gave up a little after halfway. Does he really get to the point?

[@davidhand9721]

W = n(x)v(x), dW/dx = 0. This has to be the most overcomplicated, convoluted way to say describe that idea I have ever listened to. W is wealth, n is number of bills, v is local value of bill. I would have understood much better if you just wrote out those two equations and didn't draw up a contrived "real world" example.

[@lowersaxon]

The UK has the Euro? Go to Great Britain and tell there what you think their currency is! Good luck and - good health.

[@abubakarisa7675]

Life is fascinating. Someone with vast knowledge of one of the most complex concepts, thinks UK uses euros.

[@TimothyNguyen]

I had a space cadet moment as a pure mathematician. What can I say :-)

[@abubakarisaadamu5872]

@@TimothyNguyen hahaha. Thanks for the informative videos by the way.

[@RaymondRChammas]

Damn, I

[@davidhand9721]

Tf is a fiber? You just start using the word, no introduction, no definition. From what you're saying I'm guessing it's a single scalar value? Please don't do that.

[@stopkillingmemes7259]

Fairly common term in math... it's like getting mad he didn't define what a function was

[@mutlucankartal9524]

good stuff, but I got really bored in 7 minutes. I felt like im in a macroeconomics class, which is not for me.

[@KipIngram]

You really shouldn't say "Ben Franklin *dollars* - it's all dollars and the Ben Franklin bill is worth a hundred of them. Maybe you could have said "bills."