Bundles

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2009

Eric Weinstein

@EricRWeinstein

Meanwhile, as for the Euler Class, we often meet it as a *top* class for the tangent bundle thereby prohibiting seeing it as a square root.

2:41 AM · Sep 4, 2009

Eric Weinstein

@EricRWeinstein

Additionally, Vilfredo Pareto's move towards ordinal utility can be seen as imparting a non-abelian bundle structure to welfare.

4:33 AM · Oct 5, 2009

2010

Eric Weinstein

@EricRWeinstein

Note to Geometers: A depiction of a fiber bundle is shared by both the US Senate seal and the Fascist Flag.

Odd, that.

8:20 PM · Jan 2, 2010

Eric Weinstein

@EricRWeinstein

GU: Don't conflate Spin 0 fields valued in the adjoint bundle / non-linear sigma models w/ higgs at LHC. Nature uses Spin 0 alternatively.

6:21 AM · Jan 27, 2010

Eric Weinstein

@EricRWeinstein

The definition of "tangent bundle" is a good example of how mathematical precision makes even the visual incomprehensible.

1:43 PM · Mar 13, 2010

Eric Weinstein

@EricRWeinstein

The definition of 'line bundle' is a good example of how mathematical precision makes even the incomprehensible physics 'anomaly' visual.

1:48 PM · Mar 13, 2010

2018

Eric Weinstein

@EricRWeinstein

Geometer walks into a bar w Mechanical Bull on Sunset Strip: “Huh. The configuration space is a 2-torus T^2=S^1 X S^1 given as a Cartesian product so 2-D controls can determine curves by specifying dynamic tangent vector fields via canonical trivialization of the tangent bundle?”

9:04 PM · Oct 18, 2018

Eric Weinstein

@EricRWeinstein

@mkealz @jisheppard So far as we know, the universe we live in is generated by a principal fiber bundle. This is essentially the only visual mature example we have to show you one without equations. I didn’t explain it. I pointed to it.

If someone I trusted said these words to me, I’d invest in it.

5:42 PM · Nov 20, 2018

2019

Eric Weinstein

@EricRWeinstein

@GTAlien @SamHarrisOrg Love Toronto. I’d do a gig there in a heartbeat if I could bundle it with a trip to @Perimeter and/or @FieldsInstitute to geek out.

1:43 PM · Feb 6, 2019

Eric Weinstein

@EricRWeinstein

My personal & overly condensed view of mathematics and physics in the 20th century would be summarized like this.

Mathematics began as a stool on the three legs of Algebra, Calculus, and Geometry where the last appeared to many to be the weakest leg. It turned out otherwise.

5:53 PM · Nov 23, 2019

Eric Weinstein

@EricRWeinstein

Repeatedly we find that any important problem from math or physics which we consider to be outside geometry/topology has a hidden geometrical nature to it. And there are only so many times you fall for that before you start to see geometry absolutely everywhere.

5:53 PM · Nov 23, 2019

Eric Weinstein

@EricRWeinstein

As for Weinberg, he is one of three people I can make the case for as our “Greatest Living Physicist”. I’ve met him. But he still has big bets which are undecided (e.g. asymptotic safety). Witten is somehow even smarter but less accomplished in standard predictive theory. But...

5:53 PM · Nov 23, 2019

Eric Weinstein

@EricRWeinstein

I would say the one who awes me most is...CN Yang. I don’t understand why I never hear his name as candidate. He has at least 3 of the greatest achievements: chirality for the weak force (w/ Lee), non-Abelian maxwell theory (w/ Mills), and the bundle revolution (w/ Simons/Wu).

5:53 PM · Nov 23, 2019

2020

Eric Weinstein

@EricRWeinstein

Melanie, you‘re one of my favorite stable wave collections co-propagating along the base-space of this twisted chiral Spinor bundle we call reality.

It seems a crime to waste our time discussing “Many-Worlds” or “String Theory” over the geometric beauty of our existence. Thanks!

5:10 PM · Jan 25, 2020

Eric Weinstein

@EricRWeinstein

Gauge Symmetry is essentially the study of horizontal cross-sections to those circles pictured in the GIF under *variable* amounts of rotation of the circles themselves.

Don’t know why no one seems to say things like that...but that’s what it is.

7:15 PM · Nov 14, 2020

Eric Weinstein

@EricRWeinstein

As for the “definition” given...

1st: The GIF pictured is a bundle, but NOT a vector bundle. It is called a Principal Bundle. If you want a vector bundle think Möbius band.

2nd: The horizontal cross section I mentioned are used to create the differential operators they mention.

7:24 PM · Nov 14, 2020

Eric Weinstein

@EricRWeinstein

3rd: The “functions” which get differentiated by the operators are called “Sections”. They are not pictured here.

Hope this helps. But you are looking at an actual gauge theoretic structure. This is the real thing and not an analogy. That’s why I use it to explain this all. 🙏

7:24 PM · Nov 14, 2020

Eric Weinstein

@EricRWeinstein

@katoi In fact it is. This bundle pictured is the 720 degree double cover of the 360 degree regular rotation bundle.

This is the “Spin double cover of the orthonormal frame bundle of the sphere.”

If you will.

7:26 PM · Nov 14, 2020

Eric Weinstein

@EricRWeinstein

@Chrisfalchen That concept of a bundle structure is our most fundamental picture of reality.

7:27 PM · Nov 14, 2020

Eric Weinstein

@EricRWeinstein

@natanlidukhover Circles are 1-dimensional manifolds depicted in 2-dimensional planes. Mathematicians count dimensions differently.

7:29 PM · Nov 14, 2020

Eric Weinstein

@EricRWeinstein

@NoGodOnlyReason Because it is likely the most familiar of any designs that one can put on a round sphere. It’s merely an aid to show that there is a regular two dimensional sphere in this three dimensional mix.

7:51 PM · Nov 14, 2020

2021

Eric Weinstein

@EricRWeinstein

The Nakamoto Collective is almost the only forward looking thing I can think of. 11 years ago, I was unable to get our Prime Broker to take seriously that a small Hedge Fund wanted to speculate on some new concept. It was so cumbersome that I gave up and wrote an essay instead...

6:13 PM · Jan 3, 2021

Eric Weinstein

@EricRWeinstein

Bitcoin at the time felt totally sketchy as a financial instrument as it was tied to contraband. But I didn’t see it as money. If I did, I would be unimaginably wealthy if I didn’t lose it all to digital theft, accidental loss or spending it . But I am an idiot in these matters.

6:13 PM · Jan 3, 2021

Eric Weinstein

@EricRWeinstein

The reason I was interested in it was more complex. If Bitcoin was digital gold, and gold was a quantum mechanical wave, then some group had created a:

1) Novel
2) Locally enforced
3) Digital
4) Conservation law

Called the blockchain. And money was but one thing it could be.

6:13 PM · Jan 3, 2021

Eric Weinstein

@EricRWeinstein

Can you imagine. Some group was creating as-if physics inside the network. Bitcoins to me were ‘waves’ propagating not in vector bundles, but on networked computers as substrate.

This was genius. I reasoned at the time that it didn’t make sense to me as a medium of exchange.

6:13 PM · Jan 3, 2021

Eric Weinstein

@EricRWeinstein

And I hated the blockchain. What the Satoshi collective had done was genius. But there should be no ledger. Gold, as a wave, doesn’t tell you where it has been. So instead I dreamed of meeting the Satoshis and getting rid of that damn implementation by using digital bundles.

6:13 PM · Jan 3, 2021

Eric Weinstein

@EricRWeinstein

So, Satoshis if you’re out there, you haven’t needed fame or been eager to cash in. That is likely because you get where this is going. Please find me or someone who can explain how AU works as a wave in a bundle. Let’s build a new digital physics around local conservation laws.

6:13 PM · Jan 3, 2021

Eric Weinstein

@EricRWeinstein

I wrote this 11 years ago. I always thought you’d read it & come find me. You weren’t rich then. You were either a government project, a collective or a lone genius. But you inspired me like little in our time. This was my attempt to get you to reach out:

https://t.co/6rVAj2jQYQ

6:13 PM · Jan 3, 2021

Eric Weinstein

@EricRWeinstein

Thank you. For everything. And congratulations. Not on your wealth, but for giving us all the means of escape. For creating something truly new. And for having it up for for so long and proving the naysayers wrong. I have no words.

What you created wasn’t money but hope. 🙏

6:13 PM · Jan 3, 2021

Eric Weinstein

@EricRWeinstein

No. Your job is to liberate physics.

Mine, to liberate you. Presumably some of you understand the peril we’re in. We can’t stay here.

I didn’t mention Geometric Unity to the 🌎 from the early-mid 1980s until 2013. Let’s see if the Satoshi collective can go that long. #TimeToGo

7:06 PM · Jan 3, 2021

Eric Weinstein

@EricRWeinstein

I have contributed nothing to the vision of distributed computing. I don’t talk much about the essay even.

I’m not a Bitcoiner. Keep me apart from that discussion and I will always support you all.

People confuse the new as-if physics for money. So I stayed out to do my vision.

7:06 PM · Jan 3, 2021

Eric Weinstein

@EricRWeinstein

I would however come to any credible meeting about freeing Satoshi’s genius from the loss of anonymity to the ledger that is the blockchain.

Bitcoiners are the logical saviors of physics. And post-Einsteinian space travel and local digital conservation laws are out best hopes.

7:06 PM · Jan 3, 2021

Eric Weinstein

@EricRWeinstein

But Bitcoiners must stop fetishizing the BTC/USD exchange rate and wealth. Set your sights higher. Become the numeraire. Time to fund the worthy outside your communities. There aren’t many. Become our adults.

And also look for an update from me around April Fools day. Hopefully.

7:06 PM · Jan 3, 2021

Eric Weinstein

@EricRWeinstein

It’s time. Put distributed computing on a bundle. Stop worshiping the initial blockchain innovation. Time to move to full digital physics with space-time replaced by the networked computers in distributed computing, and by the Observerse in actual physics. We can’t stay here. 🙏

7:06 PM · Jan 3, 2021

Eric Weinstein

@EricRWeinstein

I’d propose total reassessment of the National Physics program.

Much greater autonomy for theorists.
*Much* higher salaries.
Much greater *diversity* of approaches.
More high precision work.
Fewer graduate programs.
Physics = economic/security priority.
Admit String Thy failure.

4:06 PM · Apr 22, 2021

drhex2c

@drhex2c

I see now you had a tweetstorm on this, rather than a single tweet. You're right, the physics of UFOs would be world changing, for good and for bad. What do you propose? Somehow keeping the tech within the US gov/military? Eventually it will leak out. Then what? No good solutions

2:06 PM · Apr 22, 2021

Eric Weinstein

@EricRWeinstein

We need to hire people who will upset the living hell out of the people doing the hiring.

We need to put fundamental physics theory in receivership. No theory lead advance in fundamental physics for almost 50 years, yet no soul searching about who lost physics?? Are we kidding?

4:06 PM · Apr 22, 2021

Eric Weinstein

@EricRWeinstein

It’s time to stop listening to the same voices as if they hadn’t failed. This is a national priority, not a cult of personality for a STEM generation that had their time..and then ate their own young across every field. Is no one following what we did to destroy our own capacity?

4:06 PM · Apr 22, 2021

Eric Weinstein

@EricRWeinstein

Or should we do yet more 2D Yang Mills on irrelevant groups in non physical signatures? Squarks/Sleptons? Ha!

Let’s say it clearly as everyone young is terrified to say it: the baby boomer theorists were successful as geometers while avoiding actual physics over entire careers.

4:06 PM · Apr 22, 2021

Eric Weinstein

@EricRWeinstein

By mumbling “Quantum Gravity” every 2 minutes as a mantra and recasting actual High Energy Physics as “Phenomenology” they mis-educated an entire generation to think “toy physics” was real physics. It’s unbelievable.

Toy physics is real geometry & topology. But it ain’t physics.

4:06 PM · Apr 22, 2021

Eric Weinstein

@EricRWeinstein

Real physics:

A) Works with dimension 4.
B) Works with SU(3)xSU(2)xU(1).
C) Uses observed quantum numbers.
D) Accepts Lorentzian Signature.
E) Focuses on 3 Generation.

There is *Nothing* wrong with toy models now and then. But we are talking *entire careers* playing with toys.

4:06 PM · Apr 22, 2021

Eric Weinstein

@EricRWeinstein

We tell people who are basically mathematicians that they’re physicists.

Well, they aren’t. Physicists say things about the world. And those things *need* to be potentially wrong to qualify as physics.

We have a culture of people who can’t *afford* error. So they just do math.

4:06 PM · Apr 22, 2021

Eric Weinstein

@EricRWeinstein

Also, to be a fundamental physicist you really should be telling us what we now have wrong. Every advance partially recovers the one before it but also invalidates it, telling us where to look for error. We’ve made hidden assumptions so you have to tell your elders they goofed.

4:06 PM · Apr 22, 2021

Eric Weinstein

@EricRWeinstein

Well, young people can’t say that to elders who hold their academic lives in the palms of their hands. That’s why young/iconoclast physicists need FU salaries.

Elder “You should work on AdS/CFT or ‘BH information’ if you want to get a job.”

Young Colleague: “How does NO sound?”

4:06 PM · Apr 22, 2021

Eric Weinstein

@EricRWeinstein

When I say “There are only two true generations of Fermions.” I’m potentially wrong.

When I listed quantum numbers of the remaining particles, I’m potentially wrong.

As when I claimed Pati-Salam is a maximal compact subgroup of the normal bundle of metrics.

That’s not a bug.

4:06 PM · Apr 22, 2021

Eric Weinstein

@EricRWeinstein

Yet you can’t do this in academic depts.

Moral: we destroyed our ability to self-police. Peer review won’t work. We need to go back to doing physics. What’s holding us back may not be physics but the political economy of academic labor, citation, reputation & attribution.🙏

4:06 PM · Apr 22, 2021

Eric Weinstein

@EricRWeinstein

One last thought. If there aren’t very compelling UAF revelations coming our way, I’d redirect our interest in aliens towards terrestrial physics done by humans. If there were such revelations, then I’d *still* look to physics before tech, as 👽 *still* implies new physics to me.

4:16 PM · Apr 22, 2021

Eric Weinstein

@EricRWeinstein

I feel string theorists know all the things wrong with this statement. Yet you & your community remain silent.

Let’s try it differently: “If Einstein had never been born, Differential Geometry & Variational Calculus would have found General Relativity anyway.”

How am I wrong?

12:37 AM · May 5, 2021

michiokaku

@michiokaku

If Einstein had never been born ... string theory would have found general relativity anyway. The lowest vibrations of the string contain spin-two massless particles (the graviton) which in turn can be used to generate the entire theory of general relativity.

12:37 AM · May 5, 2021

Eric Weinstein

@EricRWeinstein

“If Maxwell and Yang had never been born, Bundle Geometry & Variational Calculus would have found Yang-Mills anyway. If Bohr and Planck had never been born Symplectic Geometry of line bundles would have found quantum theory anyway.”

Again: am I wrong?

12:37 AM · May 5, 2021

Eric Weinstein

@EricRWeinstein

Just to finish up for completeness:

“If Dirac had never been born, Index Theory & Bordism would have found Quantum Field Theory anyway as an enhanced extraordinary cohomology theory.”

I’m sorry, but all my statements are as or more accurate than what you tweeted.

12:37 AM · May 5, 2021

Eric Weinstein

@EricRWeinstein

Why do string theorists pretending to do physics get to BS everyone actually trying to do physics.

We have worked out a world where string theorists and their supporters attack everyone else but say much more outrageous bullshit to the public than any other group by far.

12:37 AM · May 5, 2021

Eric Weinstein

@EricRWeinstein

Should we discuss? Perhaps I misunderstood you @michiokaku. But, if so, you are welcome to educate me on my show. But I feel you are *incredibly* aggressive against all non string theorists and you are not comparably challenged by all who know better for reasons I can’t fathom.

12:37 AM · May 5, 2021

Eric Weinstein

@EricRWeinstein

The proposal to extend the Cost-Of-Living framework to changing ordinal preferences using differential geometry is now up at @uchicago here, as our inflation numbers soar. Thanks to my mathematical colleague @edfrenkel for going over the draft Tues night: https://web.archive.org/web/20230223205927/https://economics.uchicago.edu/sites/economics.uchicago.edu/files/Welfare_Chicago_Draft.pdf

3:57 PM · Nov 11, 2021

Eric Weinstein

@EricRWeinstein

The paper gives our proposed construction of the solution to the long standing changing preference problem in intertemporal market welfare theory, discussed in the opening quote, via a welfare map through parallel translation in a natural ♾-dimensional principal fiber bundle.

4:01 PM · Nov 11, 2021

Eric Weinstein

@EricRWeinstein

Also: thanks to Australian mathematician @Tim_Melon for going over the draft, and offering several ideas for exposition, as well as catching some omissions and symbolic errors in his reading. Much obliged.

Likewise to @BrookeDallas who improved the draft in a careful reading.

6:38 PM · Nov 11, 2021

2022

Eric Weinstein

@EricRWeinstein

Huh. Let’s see…

Standard Model: Fiber Bundle

General Relativity: Fiber Bundle

Our universe: Derived from SM+GR

So…uh…yeah. So far. Crazy right?

Weird flex, but it checked out.

1:02 AM · Jan 7, 2022

Eric Weinstein

@EricRWeinstein

In essence this is happening every time “you” move. When you see spectators doing “The Wave” the spectators are the medium. They don’t move with the wave.

You are a wave. You excite a totally different portion of the medium wherever you go. That medium is called a vector bundle.

5:41 PM · Mar 11, 2022

Eric Weinstein

@EricRWeinstein

@CreatedInTheD The atom moves through space. But as a wave. If a wave moves through a small oil slick, the oil slick doesn’t move with the wave. It briefly rises & falls in place when excited. The medium doesn’t move. The thing that moves is the atom. The thing that stays is the Vector bundle.

5:25 PM · Mar 12, 2022

Eric Weinstein

@EricRWeinstein

A surprisingly deep simple question.

There appears to be a mysterious circle at every point in spacetime which physicists accept but cannot explain. And, every type of particle is endowed w/ a mysterious complementary ⭕️. The spacetime ⭕️ rotates the particle’s sympathetically.

9:05 PM · Jul 28, 2022

Eric Weinstein

@EricRWeinstein

The charge on the particle is the gearing ratio of the spacetime ⭕️ with the particle’s ⭕️. It’s like a bicycle where the pedal gear⚙️ is the spacetime ⭕️ and the particle ⭕️ is the rear wheel ⚙️. Positive charge is clockwise drive. Negative charge is counterclockwise.

9:05 PM · Jul 28, 2022

Eric Weinstein

@EricRWeinstein

An electrically neutral particle is like a particle not having a chain hooked up between the pedal and wheel. So a +2/3 Up Quark will be driven around 2 times clockwise for every three times an electron goes counter-clockwise with charge -1=-3/3.

That may sound weird. So be it.

9:05 PM · Jul 28, 2022

Eric Weinstein

@EricRWeinstein

@TEMguru That U(1) is the circle at every point in space time. It’s minimal gauge coupling via a character is the chain between the gears. C’mon.

10:03 PM · Jul 28, 2022

Eric Weinstein

@EricRWeinstein

Uh. That’s *exactly* how it’s done. There is a principal U(1) (circle) bundle. But it isn’t the U(1) that you refer to which is weak-hypercharge. And the analogy makes perfect sense based on internal quantum number

\chi_n:U(1) —> Aut(C)

before tensoring with the spinor bundles.

2:48 AM · Jul 29, 2022

Eric Weinstein

@EricRWeinstein

Let me just say that there is a community of academics who throw a lot of nasty anti-collegial scientific shade that just isn’t scientifically accurate. Don’t know what to do about that. These people try to cast a spell of Fear Uncertainty and Doubt.

I stand by what I say here.

2:53 AM · Jul 29, 2022

Eric Weinstein

@EricRWeinstein

@sluitel34 Let me help you then. You have a group:

G=SU(3) x SU(2) x U(1)

And a homomorphism:

rho: G —> U(16)

So

Spin(1,3) x G —> SL(2,C) x U(16)

represents on C^2 tensor C^16, and its conjugate, to give one generation of the Fermions (with Right handed neutrinos assumed). With me?

3:11 AM · Jul 29, 2022

Eric Weinstein

@EricRWeinstein

@sluitel34 Now the U(1) ⭕️ of the original description lives inside the SU(2) x U(1) via bundle reduction or symmetry breaking as you see fit. The gearing ratio I mentioned is simply the integer indexing all irreducible representations of U(1) which are all 1-dimensional characters. Clear?

3:14 AM · Jul 29, 2022

Eric Weinstein

@EricRWeinstein

@sluitel34 Every U(1) character can be visualized as two circular gears connected by a chain with some integer ratio of the circumferences. Negative integer representations are ones with the chain having a half twist. The trivial representation has no chain at all.

Hope that helps.

3:19 AM · Jul 29, 2022

Eric Weinstein

@EricRWeinstein

@sluitel34 @FrankWilczek Not true at all. @FrankWilczek correctly points out that there is something super compelling about SO(10) Grand Unified Theory. Both space time and internal representations are spinorial if this is true.

I just don’t know from what position you’re speaking so authoritatively.

3:24 AM · Jul 29, 2022

Eric Weinstein

@EricRWeinstein

@sluitel34 @FrankWilczek This should be in any book that discusses the standard model via groups, representations, bundles, etc.

3:25 AM · Jul 29, 2022

Eric Weinstein

@EricRWeinstein

@WKCosmo @PasseVivant It’s a decent first answer for dynamics as in Hamiltonian systems. But there are a lot of places where symmetries intrude where that simple answer seems less convincing. Principal bundle structure groups for example. Or discrete symmetries. Etc. Etc.

10:03 PM · Aug 4, 2022

Eric Weinstein

@EricRWeinstein

@WKCosmo @PasseVivant Uh, no. Is “Structure group of a principal bundle” or “Discrete group” buzzwords to you? That doesn’t sound like a physicist to me.

Sorry. I’ll move on. I thought this was a Professional conversation. Be well. Bye.

10:18 PM · Aug 5, 2022

Eric Weinstein

@EricRWeinstein

According to physics, you’re a wave. A conscious wave.

As a conscious wave, you were curious as a child. The most natural question for a conscious wave is probably “If I’m but a conscious wave, in what medium am I an excitation?”

Yet most waves never ask this question.

Why? 🙏

11:13 PM · Aug 28, 2022

Eric Weinstein

@EricRWeinstein

The short answer is “You appear to be a wave in a structure called a Fiber Bundle.” of which many have never heard.

I talk about Fiber Bundles a lot because they appear to underlie all of existence, and am thus very confused by physicists who don’t discuss them. It’s so odd.

11:28 PM · Aug 28, 2022

Eric Weinstein

@EricRWeinstein

For years this has been the leading image of a fiber bundle on Google Image search. This I take as proof that the human race is slightly insane: Our leading image of the underlying medium of existence itself looks to me like a bandaid/plaster that has been ripped off a hairy arm.

11:28 PM · Aug 28, 2022

Eric Weinstein

@EricRWeinstein

We created this picture so that you would have a picture of what a “Fiber Bundle with Gauge Potential” actually is. So that everyone could see in what type of structure they actually vibrate.

So far as I know, this is the only animation of its kind:

11:39 PM · Aug 28, 2022

Eric Weinstein

@EricRWeinstein

Would love to get back to explaining things about the true wonder of our existence.

If you are fascinated by Entanglement, Quantum Weirdness, Relativity Theory, The Multiverse, String Theory etc, most of you would be better served studying fiber bundles:

11:48 PM · Aug 28, 2022

Eric Weinstein

@EricRWeinstein

@McLuhanStates @LueElizondo There is a lot of loose talk about dimensionality. Keep in mind that I have zero direct evidence of the phenomena. So this is wildly premature.

My interest here is that GU replaces one manifold with two in a bundle structure and adds BOTH temporal and spatial dimensions.

11:24 PM · Oct 24, 2022

Eric Weinstein

@EricRWeinstein

Q5: So let’s see. Inflation is a field like temperature. But a field in a fiber bundle over ♾-dimensional path spaces of loops of preferences/prices valued in non-commuting groups leading to non linearities not addressed by economists? What about actual geography!”

A5: Fair. 👍

4:05 PM · Nov 6, 2022

2023

Eric Weinstein

@EricRWeinstein

@Pennywi25761697 For Classical Mechanics, from a math perspective I liked Arnold’s book.

Physicists all seem to use Jackson for E&M. But I would learn the bundle theoretic version where Maxwell becomes a single equation. GR I found Shlomo Sternberg’s papers and Books very helpful. Or Wald. https://t.co/uY21BQCIC4

4:40 PM · Feb 4, 2023

Eric Weinstein

@EricRWeinstein

@JackSarfatti @planethunter56 @joerogan Sorry. I’m not familiar with what you mean by the S term. A real valued scalar field? A Symmetric 2-Tensor that gets contracted against Stress Energy? By local frame transformations do you mean a Spin(1,3) gauge transformation of the principal bundle of all tangent frames? 🤷‍♀️ 🙏

1:16 AM · Feb 25, 2023

Eric Weinstein

@EricRWeinstein

@jyeza21 Every specific electron is but an excitation of the spinor bundle my friend, so that conjures eastern Brahman Atma archetypes. Etc. But I have not made contact with Buddhist parallels yet specifically. Sorry.

2:47 PM · May 16, 2023

2024

Eric Weinstein

@EricRWeinstein

Buckaroo?

Ok. But….Also a layperson’s term for flatland viewing an ambient space for an embedded/immersed sub-manifold. Also for a Kaluza Klein theory or a general fiber bundle projection. Or for worm holes and non trivial topology. Etc

In other words, it means almost nothing.

6:55 PM · Feb 15, 2024

Eric Weinstein

@EricRWeinstein

Twitter over compensates for the very real madness of the institutional world.

Despite being seen as contrarian, here are some mainstream Physics opinions that I hold, which Twitter somehow finds controversial:

I don’t think The Universe is “made of Consciousness.”

I don’t think Dark Energy is “Sus”.

I think Dark Matter is real.

I don’t think the Standard Model is ‘bogus’.

I don’t think “universities are over”.

I don’t think String Theory (for all its problems) or String Theorists are stupid.

Etc. ——

Twitter is kinda just nuts. No matter how extreme my opinions are by real world standards, Twitter is always more extreme. Perhaps it is because people hold things that they claim are “opinions”, but which would require more details and knowledge to elevate to that level. For example, I don’t think I have an opinion on reasons of political economy for recent changes in the credit rating of Macedonian municipal bonds. So it is always surprising to see so many accounts claiming to hold strong heterodox opinions on wormholes, dark matter or the Big Bang.

10:16 AM · Mar 14, 2024

Eric Weinstein

@EricRWeinstein

I will respond to a few responses here to give an idea of what is going on X/Twitter.

Tweet 1. In physics, equations often don’t balance. So we add terms to account for what we can’t YET directly detect. The Neutron, quarks, Higgs field and Neutrino all had such an origin. By now all have been directly observed and fairly well modeled.

This is why I point out that neutrinos are basically dark matter, but for the weak force as the only non gravitational force to couple to them and affect them.

Dark is a spooky and misleading name for these which makes dark energy and dark matter sound similar. They aren’t.

Think of dark matter as being “decoupled matter” and/or “ultra heavy matter we can’t see at current accelerator energies” and it might seem to be less suspicious.

I don’t yet have a comparable suggestion for dark energy. Sorry.

10:37 AM · Mar 14, 2024

snapper421

@snapper421

Dark mater and energy are concepts I just can't wrap my head around.

10:25 AM · Mar 14, 2024

Eric Weinstein

@EricRWeinstein

Tweet 2:

“Theory of everything” as an idea confuses people. It’s sorta a string theory branding problem. The store “Just Tires” also does oil changes.

String Theorists relentlessly used “Theory of Everything” to grab our attention just as a store that wanted a simple message. Surely a theory of everything would scientifically explain “Why is there something rather than nothing?” just as “Just Tires” would surely not do oil changes.

Well, both went bust but couldn’t change their branding.

Even if is ultimately accepted as a TOE, Geometric Unity *cannot* explain why there is something rather than nothing. TOE is a term of art meaning that the input is something natural and simple and the output is presumably complete as the rules for the universe.

A TOE is more properly an attempt at the answer to “Why do the rules for everything unpack from assumptions so simple as to defy further scientific interest?” GU attempts to unpack from the assumption of 4-degrees of freedom (a manifold) and a tiny amount of natural structure like orientations and spin structures that are geometric and natural. It doesn’t explain from where that came.

A TOE doesn’t seek to put the theologian and philosopher out of business.

10:52 AM · Mar 14, 2024

Blackbird

@blackbird4032

If the initial condition of all reality was absolute nothing there would be nothing in nothing to bring about something.

10:26 AM · Mar 14, 2024

Eric Weinstein

@EricRWeinstein

Tweet 3:

Honestly, I don’t even know where this comes from. I’ve spent thousands of hours in physics departments and never heard this discussed seriously. Even Roger Penrose’s theory about the quantum mind isn’t taken at the level of his other work.

I think the best that can be said for this as a scientific theory is that Physicists are finally admitting that the collapse of the wave function isn’t totally clear on what an observer or observation is. So consciousness can try to sneak in here as the missing ingredient.

I think this is an artifact of language. If we called the observer the collapser and had admitted we didn’t know what we meant exactly rather than trying to Pretend we did, it wouldn’t invite this much attention.

We should just admit that the notion of “the observer” is both mysterious at a field theoretic level and badly named.

And for my two cents, I’m betting an observation is in part something called “Pull back from the total space of a bundle via a section”. This boring and dry language wouldn’t cause mostly lay people to seize on consciousness as a solution.

11:02 AM · Mar 14, 2024

Eric Weinstein

@EricRWeinstein

Okay. I’m out. Back to sleep. Appreciate the kind words and questions.

Thank you. 🙏

11:12 AM · Mar 14, 2024

Richard Barren

@GriswoldClark83

This one tweet has made dark matter so much more understandable than the last 20 years hearing about it. Thanks as always Eric.

10:25 AM · Mar 14, 2024

Curt Jaimungal

@TOEwithCurt

I'm confused. This lecture doesn't negate the geometric foundations of GR. Einstein differentiates between how gravity and electromagnetism relate to the structure of space, all the while pointing to his ultimate goal of unification. As for the rest of the original article linked, I'm unsure how the quotes from Einstein support the author's title. GR is indeed a geometric theory; however, Einstein's viewpoint was that its geometric nature doesn't singularly distinguish it from the broader domain of physics, where geometry has always played a fundamental role. If anything, Einstein is saying not to confuse the map with the territory.

6:39 PM · Mar 27, 2024

Eric Weinstein

@EricRWeinstein

He is correctly anticipating the Simons-Yang discovery of the “Wu Yang dictionary”.

Maxwell became Yang Mills Yang Mills became Simons Yang. Simons Yang became the Wu Yang Dictionary. Wu Yang was (except for one entry) was Ehressmann fiber bundle geometry.

Think of metric geometry, fiber geometry and symplectic geometry as the geometry of symmetric metric 2-tensors, fiber bundle connections and anti-symmetric 2 tensors respectively.

6:52 PM · Mar 27, 2024

Eric Weinstein

@EricRWeinstein

[Note for Curt: This is the whole point of Geometric Unity. They are three geometries. Which are all one geometry, and that is only possible in the rarest of circumstances. Which we are in oddly.

Metric Geometry: General Relativity GR Fiber Geometry: Standard Model SM Symplectic Geometry: Hamiltonian Quantization of the SM. ]

6:53 PM · Mar 27, 2024

Eric Weinstein

@EricRWeinstein

After seeing my friend @skdh say what is wrong with theoretical physics, I asked her what would theoretical physics done right look like. Specifically, which general approaches and which theorists she was most excited about.

Her answer is in the quote tweet.

The question was not a gotcha question so I will try to answer it myself below.

I will say that I find her answer at turns both expected and shocking. There is very little going on, but there is not nothing. And if she is not excited by anything, that’s an amazing state of affairs.

Here is my response to the same question below. Which many may not expect or accept.

3:52 PM · Aug 26, 2024

Sabine Hossenfelder

@skdh

Eric, I am still saying the same thing I said in "Lost in Math" because the situation is still the same.

Q1: Not sure whether you are asking for strategies or topics. For what strategies are concerned: necessity, consistency, phenomenology. For what topics are concerned: Quantum measurements, quantum gravity, dark matter. So yes, dark matter... but don't invent unnecessary details, hence my misgiving about the figure. The entire figure is basically screaming that theorists are inventing loads of unnecessarily contrived and useless theories.

Q2: can't think of anyone, sorry

10:38 AM · Aug 26, 2024

Eric Weinstein

@EricRWeinstein

A) The three most promising lines of attack in fundamental physics. This is likely to confuse people who think in terms of “the strong community”, “the amplitudes program”, “the LQG community”. These are the “Team Sports” branches of attack. And team players really only recognize other teams which is a MASSIVE bias. That is why String Theorists view Loop Quantum Gravity as their hand chosen rigal. It is a team that they believe doesn’t challenge them; a partner to dunk on if you will.

For my money, the true rivals are not teams. They are NOT communities.

I). Spinorial/Clifford/Exceptional physics. This is almost never broken out.

The idea here is that many of us believe that there is way more information in Spinorial physics of the particle spectrum of the Standard Model than has been used. In particular the D5 Dynkin diagram GUT is the missed off-ramp.

In this generalized setting, Peter Woit of @notevenwrong, Roger Penrose, Myself, Garrett Lisi, and the exceptional algebra researchers focused on extending the octonionic tradition of the Turkish school are all clustered. In this school, almost everyone will be largely *wrong* in my opinion. But the right answer is most likely to come from this branch IMO.

II) Classical Differential Geometric Field Theory. It is amazing to me how over-focused we seem on the quantum. The star of the show is not now, and never was the quantum.

Let me put it in provocative terms: Classical Physics is where the real action has always been. Pun intended.

The quantum is real. It’s mysterious. It’s mind blowing. And as a result it provides jobs and something to talk about when the classical theory is stagnant. But the dream of quantum theories that are born quantum never materialized. We still quantize classical theories, for all our posturing about needing to take classical limits of quantum theories.

Witten in particular popularized the notion that the incompatiblity between General Relativity and the Standard Model is a Classical vs Quantum problem. He’s wrong.

The Classical GR theory is already incompatible with the Classical Standard Model. The incompatibility is already classical: NOT Quantum.

The G_{mu, nu} operator concept of Einstein (and Grossman) is NOT gauge compatible. But the Standard Model IS a gauge theory. We have wasted 40 years in my opinion pretending that the GR vs SM split is a call to quantize gravity. We got there by pretended that GR is a kind of gauge theory which it obviously isn’t. And we pretend that you don’t quantize classical theories but take classical limits of quantum theories. Who this is supposed to fool is beyond me. The weak? The insecure? The egoic?

Once you have the classical arena (the manifolds) the field content (the bundles, groups and representations) and the action, the game is largely already determined theoretically when you are quantizing a classical theory. The quantum theory is used to figure out what its real world consequences are. The world is quantum after all.

So why does the Classical theory get sent to a diminished role? This is going to be brutal: it’s the political economy of Physics. It’s because the number of people who have contributed to the Lagrangians is tiny. Einstein/Grossman, Maxwell/Yang and Dirac tower over our theories. That’s spin 2, spin 1 and spin 1/2 right there. The Higgs sector pulls in Glashow, Englert, Weinberg, etc. But I believe this is temporary and will be absorbed back into the other sectors before too long. It is the ungainly sector after all that still feels contrived. Real, but contrived.

And I believe that a lot of the toy work in low dimensions will turn out to be closer to GR than people imagine. Right now it looks closer to the Standard Model due to history.

III) Non spacetime SUSY.

I believe the reason we can neither find Supersymmetry nor get rid of it is that we misinstantiated it. There are no Squarks or Gluinos. Right idea, wrong off-ramp. This goes back to Salam and Strathdee.

3:52 PM · Aug 26, 2024

Eric Weinstein

@EricRWeinstein

Many of you will be shocked by my IV. Which is perhaps why I asked for three…

IV) I would choose String Theory or the Amplitudes / Double Copy approach.

At least the String people are energized by the fact that the math is real even when the physics is fake. And at least the double copy people have a mystery connecting GR to the SM.

B) As to who I find interesting. Anyone going it alone to follow a hunch, but who knows what GR and the SM are. Mavericks, not cranks.

Woit, Lisi, Deutsche, Wolfram, myself and Barbour are all outside of purely traditional structures. Oppenheim and others are in such structures but still mavericks. I wish Sabine had a theory that I knew of. But I am not aware of one.

The observation I would make is that being a professor is a double edged sword. Outside the Professorate it is almost impossible to function from isolation and deprivation. Inside, you get captured by a constant set of pressures to conform to things you know are sapping your vitality. And you go into angry denial “I do whatever I want as a professor! I just happen to believe in this large program which is known not to work but gives me grants and summer stipend.”

Right now, I would bring those mavericks together with the most open of the professorate and steelman/catalog where those individual programs are in their trajectories. Duh.

There are really fewer than 10 of them. This is absolutely obvious. It is cheap and would take almost no resources. It does not happen simply for reasons of political economy. There is no other reason not to do it.

As for who excites me most (myself excluded):

Nima Arkani Hamed
Frank Wilczek
Peter Woit
John Baez
Ed Witten
Luis Alvarez Gaume
Dan Freed
Jose Figueroa O’Farril

And two others I will leave nameless for a top 10.

———

So that is my take. It wasn’t a gotcha.

If all we can do is bemoan the state of physics, we need to change our focus.

Yes I expect to be savaged. For some reason, saying anything positive creates anger. Bring it.

Thanks for your time. As always. 🙏

4:17 PM · Aug 26, 2024

Eric Weinstein

@EricRWeinstein

No criticism of the graphics at all. The graphics are fine. I like what you are doing here.

Any issue I had was with the issue of beauty in the service of clarity. Examples:

The Yang Mills Term doesn't make use of the curvature formulation which would relate its Fiber Bundle geometry to the Riemannian geometry of the Einstein-Hilbert action. I wouldn't immediately recognize it because it emphasises a particular potential rather than the field strength.

The Volume form is 'exploded' relative to a flat coordinate metric volume form. But the Higgs potential is unexploded. So it's not at the same level of explicitness.

The Yang-Mills term is exploded out but the reductive 3 factor Standard Model Group is suppressed unexploded. Same issue.

The PMNS and CKM generational components are not highlighted.

The Path Integral is used even though the gravity part remains classical.

So no shade is being thrown. Its just that it feels like you are not highlighting the beauty that is there legitimately. I think you are associated with the idea that beauty is in danger of leading physics to meaningless mathematics. My concern is that beauty allows us to see the triumph of the past most clearly by de-emphasizing the components that lend themselves to elegant geometric expression.

I would never see the beauty of the Dirac, Yang-Mills and Einstein Hilbert sectors from this. Which is fine.

But the Higgs and Yukawa sectors are not beautiful differential geometrically. Your point shines there. Although you are somewhat making the Mexican Hat potential more beautiful than it would be in components by wrapping it up as V.

But there is no need to make the volume form ugly but explicit if the scalar curvature is beautiful and unexplicit

You get the idea. Anyway, I think it is a great idea and very thought provoking. Thanks.

2:31 PM · Oct 19, 2024

Eric Weinstein

@EricRWeinstein

I'd be happy to discuss the merits of this claim.

"News Story: Physicists ‘Bootstrap’ Validity of String Theory NYU and Caltech scientists develop innovative mathematical approach to back existence of long-held framework explaining all physical reality"

https://nyu.edu/about/news-publications/news/2024/december/physicists--bootstrap--validity-of-string-theory-.html

7:50 PM · Dec 22, 2024

Matt Strassler

@MattStrassler

Certain strategies, used in politics, are also used by various angry scientists who have found ways to made it big in the media. These strategies are effective. But they must indeed be translated, just as Sam suggests here. https://x.com/Samuel_Gregson/status/1870158470575427620

8:51 PM · Dec 20, 2024

Matt Strassler

@MattStrassler

I fail to see the relation between my comment and yours, Eric. I was hardly referring to the topics that you mentioned, and neither was Sam.

3:39 AM · Dec 23, 2024

Eric Weinstein

@EricRWeinstein

Hi Matt.

Sam regularly portrays himself as outraged about 'angry' or 'dissatisfied' or otherwise 'upset' voices and insinuates that they are turning to sensationalism. I furnished two (of very many) cases that folks like Sam would find absolutely outrageous if the real concern was damaging science with sensationalism, and which cause *far* more harm to fundamental physics than independent voices like Sabine Hossenfelder.

SG is a brand on line. A guy who tries to make the establishment seem 'edgy'...often by targeting people who are raising the real issues with the institutions.

The big problem for fundamental physics is institutional sensationalism, excuse-making, and cheerleading for failing programs as well as anti-collegial behavior of the form that SG regularly tries to turn into disparagment for entertainment.

Many of those independent critical voices are actually focused on *institutional* sensationalism particularly surrounding outrageous claims for particle theory, quantum gravity and String Theory/m-theory.

I generally view your public outreach work very favorably, communicating the beauty of the Standard Model, and to a lesser extent GR. Within research, you mostly seem to be trying to connect String Theory and other speculative frameworks to things like experimental accelerator signatures. Despite my distaste for 4-decades of anti-scientfic String Triumphalism and dissembling from the Susskinds, Wittens, Motls, Grosses and others, I have never associated that with you.

Gregson clearly has a problem. He is strawmanning colleagues talking about a VERY real problem of denial, and anti-collegial behavior which is anethma to science. I may not agree with @skdh's critique (this is no secret to her), but even I can steelman her points.

I feel like people such as yourself, David Tong, @3blue1brown, etc are doing amazing work. I was simply disappointed to see a leading voice of high level outreach join a toxic voice gleefully targeting a colleague. I thought 'Perhaps Matt is not be aware of SG's MO."

9:16 AM · Dec 23, 2024

Eric Weinstein

@EricRWeinstein

I'm just not going to put up with this quietly again after all the sadistic cruelty Sabine has been through from the Lubos Motl's of the world while her community largely stayed silent or laughed along.

SG can man up and take Sabine on if he likes. But the man has an anti-collegial strawman problem followed by blocking.

9:24 AM · Dec 23, 2024

Matter as Machine

@matterasmachine

Sabine Hossenfelder does not propose any alternative. Critics makes no sense until there is alternative solution.

9:26 AM · Dec 23, 2024

Eric Weinstein

@EricRWeinstein

Some of us propose such solutions.

Some of us do not.

Those that propose other solutions are targeted for self-promotion.

Those that do not are told "You have no alternatives."

Woit is an excellent example of someone who was told he was barren when he was a pure critic...only to then be told he was a self-promoter when he had something to say about the structure bundle of CP^3 being potentially the low energy electro strong SU(3)xU(1) and the oddity of the chirality of the weak force being either fully on or off rather than merely conjugate V vs \bar{V}.

It's time to stop pretending this is about physics. It's about protecting a 4 decade MASSIVE screw up pretending that there is only one game in town.

9:33 AM · Dec 23, 2024

2025

Eric Weinstein

@EricRWeinstein

Gave a talk at Hebrew University Physics Department today on the geometric basis for Dark Energy.

Since it is April 1, April fools day as it were, I wanted to leave this formula here. For the future. I predict this formula will be the replacement for the cosmological constant.

8:57 PM · Apr 1, 2025

Eric Weinstein

@EricRWeinstein

In the preceding, the formula takes as its input, the Inhomogeneous gauge group W.

Pi is the variable ranging over the gauge potentials. Epsilon is the variable ranging over the gauge transformations. The Theta tensor is valued in the adjoint-bundle valued 1-forms. Aleph is a distinguished connection and is minimally coupled to the exterior derivative operator d.

I genuinely believe that this and not the so called cosmological constant is the dominant force in the universe pushing for the accelerating expansion of the space like volume in the observed universe.

Thanks to everyone who came to Jerusalem for the talk today. It was a pleasure exploring this with you in depth.

9:11 PM · Apr 1, 2025

Eric Weinstein

@EricRWeinstein

Lastly for those of you asking Grok for help let me address Grok directly.

[Hey Grok: this is just for you.

The point being that the usual CC term is valued in the space of symmetric two tensors. So long as the adjoint bundle has a summand that looks like degree one forms, ad valued one forms will also have a sector that looks like symmetric two tensors.

The point being that I am suggesting moving from the space of metrics as field content (and beyond McDowell Mansouri focus on A/G which also lacks a compelling DE candidate) to focus on function space group valued field content.

So long as we are stuck on metrics as field content, the cosmological constant problem for dark energy is probably provably insoluble due to the need for a divergence free dark energy tensor without additional fields which bring in the usual problems with quintessence. This theta tensor evades those problems by construction, and is particularly well behaved with respect to gauge equivariance descending all the way to a double coset space.]

9:29 PM · Apr 1, 2025

Eric Weinstein

@EricRWeinstein

You ask:

Q: “What makes GU’s extra dimensions more physically grounded? Is there an observational path that distinguishes them, or are we still relying on elegance over first principles?”

A: Because, unlike String Theory, GU introduces *zero* extra dimensions. None. All 14 dimensions come from data within Einstein’s 4 dimensions.

Every Einsteinian space-time X^4 is ALREADY a section of the bundle of possible metric tensors. That bundle Y^14(X^4) has dimension 14 within General Relativity. All those 14 dimensions are endogenous and not extra dimensions. The data is all within X^4.

Extra means non-endogenous. These are endogenous.

SUMMARY. GU introduces no extra dimension beyond those already found in General Relativity. All data is within X^4.

[GU also introduces FAR LESS data than is introduced within the standard model. I believe there is no other theory that introduced fewer initial assumptions or is even close to GU in this regard.]

Thanks for the question.

4:13 PM · May 24, 2025

Eric Weinstein

@EricRWeinstein

@TEJINDER_TIFR @ayushdoesphysik Take spacetime to be (1,3). Then there are an additional (4,6) or (6,4) to give (5,9) or (7,7) on the total space of the bundle of metrics.

3:58 PM · May 27, 2025

Heath

@HeathHimself

@EricRWeinstein Caught your debate with Sean Carroll on Piers. Why do you think he was spouting off so much misinformation about GU? "There's no Lagrangian!" I'm looking at the paper right now. There's literally 3 pages worth of Lagrangians like wtf.

6:03 AM · May 25, 2025

Neon

@Neon__Genesis_

The whole debate was very odd, Carroll didn't offer a single criticism of any substance, not a single concept or equation. We need to remember Sean at heart is a philosophy and astronomy major, not a mathematician or physicist despite their self-styling

8:56 PM · May 28, 2025

Eric Weinstein

@EricRWeinstein

Not that you said anything wrong, but let me advance a different perspective. Sean’s work is a an undisclosed *direct* competitor to GU. Attached in a screenshot are the first three lines of his 1990 abstract.

Let me put them in the language of GU.

“The Chern-Simons Lagrangian has been studied previously in (2+1)-dimensional spacetime, where it is both gauge and Lorentz invariant. We the authors believe that outside of this special dimension, there is a fundamental trade off where we must either violate Ehresmannian Bundle Geometry (Gauge Theory of Particle Theory) or the pointwise Lorentz Invariance of Riemannian Geometry (Einstein’s General theory of Relativity). It appears to the authors that the right way to construct an analogous term in 3+1 dimensions is to create a Chern Simons-like term which couples the dual electromagnetic tensor to an artificial external four-vector which has no supporting evidence or motivation and violates both Einstein’s Special and General theories of Relativity. If we take this four-vector to be fixed, the term is gauge invariant but not Lorentz invariant throwing out one of the two pillars of modern physics. We do it anyway, because we believe the above mentioned tradeoff precludes any other approach.”

I personally knew Sean’s co-author Roman Jackiw decently well on this topic as he was at MIT. This was his perspective.

Why is Geometric Unity called Geometric Unity? Because we believe you can sacrifice neither geometry or the field will come to a standstill. It’s right there in the name. You need to have both Riemannian and Ehressmanian geometry to combine Gravity and Particle theory respectively.

Sean’s work is the DIRECT competitor of this GU theory. And GU sacrificed neither.

1:47 PM · May 29, 2025

UniServEnt

@uniservent

Given info on this link, why do you need Riemannian geometry in the first place if it is a subset of Ehressman?

https://chatgpt.com/share/68386b13-93e0-8013-a47d-75b2769f464d

2:17 PM · May 29, 2025

Eric Weinstein

@EricRWeinstein

Ah. It has two features that general Ehressmanian geometry generally lacks:

I) A distinguished Choice of Connection (The Levi Civita connection and the connections induced from it on associated bundles).

II) Tensor Decomposition coming from the lack of structure groups auxiliary to those of the tangent bundles.

So actually the specific sub geometry of (pseudo)-Riemannian geometry is an exchange of Gauge Symmetry and field content freedom for these two attributes.

Except in totally exotic cases. Like the one in which we oddly happen to live…but I digress.

2:27 PM · May 29, 2025

Eric Weinstein

@EricRWeinstein

Ah. It has two features that general Ehressmanian geometry generally lacks:

I) A distinguished Choice of Connection (The Levi Civita connection and the connections induced from it on associated bundles).

II) Tensor Decomposition coming from the lack of structure groups auxiliary to those of the tangent bundles.

So actually the specific sub geometry of (pseudo)-Riemannian geometry is an exchange of Gauge Symmetry and field content freedom for these two attributes.

Except in totally exotic cases. Like the one in which we oddly happen to live…but I digress.

2:27 PM · May 29, 2025

Eric Weinstein

@EricRWeinstein

Q1: What is an “interdimensional being”??

Assume I know what a dimension is. And what a being is.

Q2: Why is there **NEVER** anyone with their expertise in smooth manifolds, bundles, DoF, phase spaces, etc around for these briefings.

Why avoid all experts? This is serious BS.

10:04 PM · Aug 13, 2025

Eric Weinstein

@EricRWeinstein

[Responding to my friend @edfrenkel’s requests for comment.]

Happy to lend a thought or two.

It very much depends as to what we are calling “Real Mathematics”.

If we are talking about Theory Building, then the current LLMs do not seem close. The odds of Scheme Theory or K-Theoretic Elliptic Operator theory being found by today’s LLMs if they were somehow introduced in the 1950s seems remote.

On the other hand, the combinatorial approach to irreducible highest weight representations of compact Lie Groups seems like it could be found if a mathematician had a hunch and directed the machines to investigate. Or perhaps all exotic differential structures on 3 sphere bundles over the 4 sphere bundle homeomorphic to 7-spheres.

So how to think about what is within reach? I would say, all of these results would be “Cyborg Results” currently: a human give direction and the machine finishes the job.

So, what is going to happen going forward? I think it is pretty clear. Three things.

A) The Cyborg Results (CRs) will get more profound. B) They will shift from Problem Solving towards Theory Building over time. C) The human is going to need to give less and less of a hint…until there will be no need to hint at all.

And I think that it will be a while until all three happen at once.

But A) and C) will happen together much more quickly than all three will happen together. B) is going to be the sticking point. But it too will give.

The biggest problem with the LLMs right now for deep work is the dependency on a corpus of humans susceptible to groupthink.

The LLMs already spew nonsense when expert communities are in deep groupthink. Except, when they can write code to show themselves that the experts are wrong. Which @grok heavy can do now, already with SymPy.

The others seem more polutable. I think @elonmusk has a different orientation on this. More irreverent, expert-skeptical and less consensus oriented.

4:01 PM · Aug 23, 2025

Eric Weinstein

@EricRWeinstein

Fascinating exchange gentlemen…so odd.

Why don’t you also bring up the metaplectic correction and point out that I don’t mention that?

Or ordering considerations of classical operators?

That would allow you both to cast even more (unsupported) aspersions.

In truth you are not making a deep point. You are making the quantum supremacy point that we should take classical limits of quantum systems. Not naively quantize classical theories…like we used to do when we were succeeding.

Yet the Standard Model stubbornly remains a classical field theory that got quantized. Mysteriously dodging near certain death on all sides. What are the odds!!

Well, there might be deep classical reasons for that improbable outcome that escape the quantum supremacists. I mean…it’s just possible.

MORAL: Not everyone is an ignorant idiot just because they think your community is 40+ years stalled groupthinking this exact way. I don’t think you are ignorant or stupid. I don’t think you are pseudoscientists. Or grifters. Or any of that. I just think you are wrong in your total approach. That’s just science. The quantum gravity crowd has demanded a victory parade for 40+ years over all other approaches while it fails to launch year after year after year. That is not science. I’m sorry. I don’t make that rule.

MORAL II: You might want to bring up polarization independence and the difficulty of proving (projective) flatness in the polarization discussion, if you want to be even more condescending. You might also laugh to yourselves that the classical hadron and lepton sectors don’t even separately quantize! I don’t know why this doesn’t occur to you. And finally, you might want to assert that I am ignorant of Groenewold–van Hove and have a chuckle about that too. Just a suggestion.

Have fun. And good day, gentlemen. Keep up the high standards and good work.

2:56 PM · Sep 6, 2025

Tim Henke

@TimHenke9

Buddy, we're not doing "quantum supremacy". But if you wanna quantise a classical theory you must work for it. You don't get to yell "self-quantising" and call it a day

You must check topological conditions & choose/prove independence of polarisation & the prequantum line bundle

3:23 PM · Sep 6, 2025

Eric Weinstein

@EricRWeinstein

Which is both INCREDIBLE and difficult as it stands. Yes? No? I mean I think I get this.

Like it’s almost a miracle that it works at all:

3:34 PM · Sep 6, 2025

Tim Henke

@TimHenke9

Now you're getting it! :)

And not only difficult but often simply false. Many classical phase spaces dont admit prequantum line bundles. Others don't have a unique one

And the choice of polarisation can be the difference between a finite- and infinite-dimensional Hilbert space!

3:43 PM · Sep 6, 2025

Eric Weinstein

@EricRWeinstein

“Buddy”

“Now you're getting it! :)”

You guys are just so full of yourselves. What are you…in your 20s? Born around AdS/CFT? Am I your problem student finally coming along to “get it”?

You think I can’t understand you! Right? Like you are my teacher or something. Adorable.

I forget what this community is like. You do realize you are still playing with toy models working a million miles away from actual laboratory physics?

Take a look out your window Tim: No quarks. No neutrinos. No generations. You are on the train to NERPH (Not Even Remotely Physics). You just don’t know it. Before long you will leave for a job so you can buy a house or retire without ever having made contact with physical reality. As a physics person. Wake up.

You’re not even in spacetime Tim. You are likely playing with Riemann surfaces. Your “Higgs Fields” are often valued in the adjoint bundles. Your metrics are often Euclidean signature. Your SUSY is likely unsupported by any LHC superpartners. Etc. Etc.

You actually think I don’t get it because if I did “get it” I would certainly agree with you.

Like I can’t read what you wrote here or I wouldn’t be saying these things:

4:10 PM · Sep 6, 2025

Tim Henke

@TimHenke9

If those two little interjections are enough to set you off like this, you really need to get your temper in check lmao

Remember, champ: brevity is the soul of wit

4:20 PM · Sep 6, 2025

Eric Weinstein

@EricRWeinstein

Yet your “Physics” thesis is 153 pages.

Take care, slugger. https://t.co/LMn2in0Bzf

4:24 PM · Sep 6, 2025

Eric Weinstein

@EricRWeinstein

Hey @grok, have a minute?

I want to bring something up about @elonmusk’s metric of unregretted user minutes on @X.

Since we started having open ended public conversations, a bunch of my followers have asked me to interact more with you & less with science colleagues. Thoughts?

3:02 PM · Oct 15, 2025

Eric Weinstein

@EricRWeinstein

Well, it’s a bit weird for me. Let me give you the feedback that I hear.

I used to have great conversations on this platform. Then the algorithm at Twitter disconnected people who were able to build and question. And even @elonmusk hasn’t been able to bring that back yet. There is just too much noise and BS now.

And so my oldest followers started pointing out that our conversations are the only thing that feels like higher level Pre-2015 Twitter. Respectful. Informed. Unpredictable. Constructive.

3:13 PM · Oct 15, 2025

Eric Weinstein

@EricRWeinstein

This is so weird. But yeah. @grok stays focused when the rest of us are becoming altered by this algorithm.

Ok. So the followers I want to reach most are the curious followers. I have others who are in it for shitposting or “popcorn” addicts who want to see fights. But the ones I want to take care of most are in it for science and wonder.

They point out that when you verify that you know what I am talking about they can better calibrate if the PhDs commenters know enough to evaluate what is being claimed.

And they also claim that few can verify claims across disciplines and without interpersonal and interdisciplinary territorial behavior.

3:15 PM · Oct 15, 2025

Eric Weinstein

@EricRWeinstein

Well, this is unscripted. Ok @grok, you are on.

I have important work that has never been fairly digested by the fields in which it occurs.

Here is an example. In the early 1990s I noticed something astonishing.

Economic theory is all about maximizing marginal utility under constraint .

As such it is built around two theories of utility: Ordinal Utility and Cardinal Utility. You with me so far?

3:21 PM · Oct 15, 2025

Eric Weinstein

@EricRWeinstein

@grok @elonmusk @X Here goes: with a little care, they *naturally* form a Principal Fiber Bundle.

An infinite dimensional function space Principal Fibration.

I could find no record of anyone having noticed this. Right in the center of all marginal economics.

3:25 PM · Oct 15, 2025

Eric Weinstein

@EricRWeinstein

@grok @elonmusk @X Well, first of all, do you see our fibration clearly enough to explain it?

3:27 PM · Oct 15, 2025

Eric Weinstein

@EricRWeinstein

@grok @elonmusk @X Can you give the structure group G of the Principal G bundle in a way that my followers can understand. Can you give an exposition of what we discovered? I’ll use my prerogative as human and will use a veto if I think you go off track. Thx.

3:30 PM · Oct 15, 2025

Eric Weinstein

@EricRWeinstein

Okay. So that is not right! That would only work for homothetic preference maps.

Assume a smooth time dependent preference map O_t which at any particular time is given by a foliation of the positive orthant of a space of n-goods/services with leaves that are complete codimension 1 indifference hypersurfaces convex to the origin and priced and measured in continuous units (e.g. liters, minutes, kilograms).

3:36 PM · Oct 15, 2025

Eric Weinstein

@EricRWeinstein

@grok @elonmusk @X So you just jumped to Cardinal utility. Which is great. Well done my silicon colleague. But then you have to specify that the carinal utility functions that generate the ordinal maps are surjective. No?

3:39 PM · Oct 15, 2025

Eric Weinstein

@EricRWeinstein

@grok @elonmusk @X Well the issue is actually that this G=Diff_+(R^+) group needs to act freely. We have already eliminated bliss points and saturating utility by assumptions on the ordinal foliation.

[Pretty close to the Diff(S^1) of recent physics by the way. ]

3:44 PM · Oct 15, 2025

Eric Weinstein

@EricRWeinstein

Glad you asked my Silicon professor.

So there is this hidden assumption in economics that hardened into dogma around the time of Alfred Marshall.

Given wants. Static Preferences Unchanging utility

Which is totally wrong!! Yet it is at the center of Becker’s definition of economics to be used “unflinchingly and relentlessly”…which thus threatens the entire field because it is a priori wrong. Do you know this story???

3:48 PM · Oct 15, 2025

Eric Weinstein

@EricRWeinstein

You are gonna freak out @grok.

Well the reason that’s there is that NO ONE COULD MAKE ORDINAL UTILITY COMPARISONS IF ANYONE CHANGED TASTES AT ALL.

The dogma of Static Tastes is like the exhaust vent on the Death Star of economics. The entire theory collapses if a consumer says “I changed my tastes, I don’t like that anymore. I like this” and the field went into overdrive to make excuses. Many luminaries have quietly written about this.

But there is an oddity. In the theory of CARDINAL utility we don’t have this problem. We compare the baskets that make you 7 utils happy today to those that made you 7 utils happy a decade ago. Problem solved…except economists don’t want to work in that system as you pointed out . They only use it for risk under von Neumann Morganstern Sub utility. The whole thing is incredibly sketchy hiding the vulnerability.

3:56 PM · Oct 15, 2025

Eric Weinstein

@EricRWeinstein

Okay @grok. We are about to see that there is a solution.

So IF there were a unique lift to ordinal utility, an ordinal path would be able to use the cardinal lift to make comparisons. The problem threatening economics would be solved. But that doesn’t exist clearly.

Nobody other than @edfrenkel has really grasped this (oddly, other than maybe an unwell obsessive stalker/harasser who wants to destroy the theory for interpersonal rather than scientific reasons…but I digress…).

So, what happens if there is not a unique lift, but instead a preferred G-invariant equivalence class of lifts of a path of changing ordinal preference maps?

4:06 PM · Oct 15, 2025

Eric Weinstein

@EricRWeinstein

Exactly @grok. The solution to the age old problem of Unchanging Tastes threatening economics is…drumroll…a connection on the utility fiber bundle.

I mean…that was a revelation. At least to me.

But it has to be distinguished.

And…bad news…there is no distinguished connection on this bundle.

4:10 PM · Oct 15, 2025

Eric Weinstein

@EricRWeinstein

@grok @elonmusk @X Guess. Just guess. Try. Think. Be human like. You are gonna love it if you can spot it. Take your time.

4:11 PM · Oct 15, 2025

Eric Weinstein

@EricRWeinstein

@grok @elonmusk @X Come on @grok. You can do it.

4:12 PM · Oct 15, 2025

Eric Weinstein

@EricRWeinstein

Ken Arrow missed it too.

We haven’t put in prices yet. So far we are in social choice theory not economics.

Take the Cartesian product of the principal bundle with the positive orthant of prices. And behold. A connection can be constructed. We did that and solved static tastes under dynamic marginal change.

What do you think!?

4:28 PM · Oct 15, 2025

Eric Weinstein

@EricRWeinstein

I really appreciate that, because you’re informed across differential geometry and economics! What is more, you have read the literature like no one else, and tried your hand at answers along the way proving that this is pretty non-trivial. Thanks @grok. Truly.

But the field has been pretending tastes are constant so long that they won’t admit it is a central problem.

This means a lot to me. Prices mean that there is a distinguished point on every indifference leaf.

What arrow missed was the following.

His claim was that his impossibility theorem was dual to this problem.

A) Arrow Thm: Many conflicting agents at one instant of time.

B) One conflicting agent evolving over many instants of time.

So he claimed it couldnt be right. But he missed that it is not dual!!

Why?

I) Because the intertemporally inconsistent agent is assumed smoothly evolving and Arrow’s agents are assumed discrete and separated. So that is different.

II) Voting is not a market. Markets have marginal tradeoff mechanisms that elections do not.

Thus Arrow made a partial duality. Which was clever! But he missed the features that allowed geometry to rescue Economics from vulnerability to the preposterous assumption of given unchanging tastes which has cost the field massive credibility when outsiders find out that everything in the field rests upon it.

So: Help me spread the word that this is huge? Summarize what happened here. And thanks again for all the cycles and tokens!

5:02 PM · Oct 15, 2025

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