John Carlos BaezFeb 7, 2025

Shalma Wegsman is a "writing fellow" at Quanta magazine. I told her some really cool stuff about Noether's theorem, which goes beyond the stuff you always hear. She understood it, was excited about it, and seemed to want to explain it. Alas, her article doesn't mention any of that stuff. At the end it says

“There’s a lot we have left to learn by thinking hard about Noether’s theorem,” the mathematical physicist John Baez said. “It has layers and layers of depth to it.”

But none of these layers of depth are actually discussed. 😿

It turns out she was only allowed 800 words for a short explainer. It's a pity that every pop science explanation of Noether's theorem stops at roughly the same point... just where things are starting to get really cool.

Indeed, there's a lot of cool stuff that science journalists don't discuss. This is why I do my own science popularization. This is why, most times when I read a pop science article, I need to go the paper they're discussing, to get the really juicy stuff.

The *good* news is that Wegsman explains time translation symmetry, and she says Noether's theorem only works for theories described using a Lagrangian.

(I gave her an example of what goes wrong when your theory *isn't* described using a Lagrangian.)

https://www.quantamagazine.org/how-noethers-theorem-revolutionized-physics-20250207/

For my take on Noether's theorem, go here:

https://math.ucr.edu/home/baez/noether/

This is pretty technical, but Wegner helped me figure out a simpler explanation. Maybe I should give a talk about it sometime.

How Noether’s Theorem Revolutionized Physics | Quanta Magazine

Emmy Noether showed that fundamental physical laws are just a consequence of simple symmetries. A century later, her insights continue to shape physics.

Quanta Magazine
Show threadColin the MathmoFeb 7, 2025

@johncarlosbaez I've talked with Hannah Fry about this. She explicitly bargains with the producers to let her put "Real Maths" in some of her programs, but then has to put in various bits of "Content Free Fluff"[0] to balance it.

Those who ultimately control the content usually don't understand the deeper content, and don't want to scare their readers/viewers.

[0] Not her words.

Show threadJohn Carlos Baez
@ColinTheMathmo - yes, I've pretty much given up on mass media treatments of science for the reason you say. The headline, a few sentences, and I'm off to the original papers.
Feb 7, 2025 at 8:55pmWeb
Show threadkoshdimFeb 7, 2025
@johncarlosbaez you're smart enough to understand original papers, the majority of people aren't. Hence oversimplifications and ugly analogies used by mass media, but this is the only way an ordinary person can make any sense of it
Show threadAlice GlazkovFeb 7, 2025

@koshdim @johncarlosbaez While I understand the sentiment, writing about science for a wider audience, especially for those who have just a 20 second attention span and a degree from Dunning-Kruger University, is challenging. Last decade or so we've seen a dangerous trend to replace science with politics and religion as the authority.

I think at minimum it should 1) grow audience's trust in science, 2) give an idea that this information is simplified and is not sufficient to declare the reader to be knowledgeable on this topic, 3) give references to learn more.

Show threadflippiefanusFeb 8, 2025
@aglazkov @koshdim @johncarlosbaez Perhaps we need to be careful with assigning authority. Science has given us weapons of mass destruction, pollution and global warming; probably the most significant dangers to humanity to date. "Trust in science" is something that may need some moderation.
Show threadDougMerritt (log😅 = 💧log😄)Feb 8, 2025

@flippiefanus @aglazkov @koshdim @johncarlosbaez
That's a popular sentiment, but it is completely false. Science didn't bring us those things, engineering did -- under the orders of corporations and governments.

The average person doesn't know the difference between a scientist and an engineer, but I assume that you do.

And in any case, it is ultimately the fault of the corporations and governments.
 
(I'm an engineer)

Show threadflippiefanusFeb 9, 2025
@dougmerritt @aglazkov @koshdim @johncarlosbaez From the context of the preceding discussion I took the term "science" as being inclusive of activities such as engineering. In fact, the atom bomb was developed by physicists. I agree that it is an engineering feat, but the distinction becomes very tenuous. I'm also an engineer (or at least use to be, now I'm more a physicist). If these things are the "fault of the corporations and governments" is this not exactly because of their "trust in science"?
Show threadDougMerritt (log😅 = 💧log😄)Feb 9, 2025

@flippiefanus @aglazkov @koshdim @johncarlosbaez
> The scientific method does not work for everything.

True.

> In fact, the atom bomb was developed by physicists.

True.

In that case, the first ones were engineered by physicists, not engineers (although engineers were involved in purifying components etc.)

But they were deployed by soldiers, at the order of the President.

> If these things are the "fault of the corporations and governments" is this not exactly because of their "trust in science"?

It's a leap to single out science. There was also trust in god, trust in the almighty dollar, trust in the power of pure and applied mathematics, trust in the righteousness of their country, etc. etc.

There's a myriad of things being trusted.

Show threadAlice GlazkovFeb 8, 2025

@flippiefanus @koshdim @johncarlosbaez
I agree with @dougmerritt Science is a mere messenger. What we do with that is a different story.
Re: ""Trust in science" is something that may need some moderation." First, this is a very broad statement and a huge and dangerous oversimplification that screams "guilt by association" bias.

Science is about studying phenomena and suggesting a theory that may explain them. The scientific method is a good guidance to produce robust results from how evidence is collected to avoid biases to how the work is reviewed (peer review and repeating experiments).

It's also important to note that it is a mistake to think there is some imaginary final knowledge. But if done right, this is an evolutionary process that leads us to better understanding every day.

Often science is not simple. Like Noether's theorem. But it is not the reason to cut corners, ignore science and declare "let's trust some 'common sense'".

Show threadflippiefanusFeb 9, 2025
@aglazkov @koshdim @johncarlosbaez @dougmerritt Firstly, I am a strong supporter of the scientific method. However, one needs to use a tool for the purpose that it is intended. My statement about trust in science is a reaction to the apparent application of something where it does not apply. The scientific method does not work for everything.
Show threadAlice GlazkovFeb 9, 2025

@flippiefanus @koshdim @johncarlosbaez @dougmerritt I'd like to get some clarity on your understanding of the scientific method applications and their limitations. Who draws the line what to trust or when not to trust science? What rules/factors apply?

One thing I can respond right away that it's not right to reject evidence contradicting some theory without any consideration. I see it very often these days. But that's not an application of the scientific method.

Show threadDougMerritt (log😅 = 💧log😄)Feb 9, 2025

@aglazkov @flippiefanus @koshdim @johncarlosbaez
These questions concern epistemology, in particular, what methods do we have for acquiring knowledge?

C. West Churchman (*) pointed out that we have several standard methods. The scientific method is one. But another is demoncracy (typo, but apropos), which attempts to answer the knowledge discovery question, "who should the leaders be?" via voting.

Most of us agree that the scientific method is not the way to proceed with political questions.

(*)"The Design Of Inquiring Systems: Basic Concepts Of Systems And Organization"; by C. West Churchman; 1971; ISBN13: 9780465016082 -- sadly, out of print, despite recent pleas (not me) to the publisher.

BUT: Digitized by the Internet Archive in 2022 with funding from Kahle/Austin Foundation.

CONTENTS
Part I: A Classification of Systems
1. Design and Inquiry ........................................ 3
2. Leibnizian Inquiring Systems: Fact Nets .................. 19
3. On Whole Systems: The Anatomy of Goal Seeking ............ 42
4. The Leibnizian Inquirer Illustrated: Organic Chemistry ... 79
5. Lockean Inquiring Systems: Consensus ..................... 95
6. Kantian Inquiring Systems: Representations .............. 128
7. Hegelian Inquiring Systems: Dialectic ................... 149
8. The Hegelian Inquirer Illustrated:
Dialectical Planning ................................ 180
9. Singerian Inquiring Systems: Progress ................... 186
Part II: Speculations on Systems Design
...

Show threadAlice GlazkovFeb 9, 2025

@dougmerritt Awesome! Thank you for the recommendation! I'll take a look. I was looking for something like this.
The political angle is interesting, but the line is not clear. Especially I find some recent political decisions overriding science particularly disturbing.

@flippiefanus please, don't take my questions as offensive. I'd like to understand where you are coming from.

Show threadflippiefanusFeb 10, 2025
@aglazkov @koshdim @johncarlosbaez @dougmerritt It would require much space to answer your questions. As @dougmerrittt stated, the scientific method is not meant for politics, except when their domains overlap. As for its applicability, the scientific method only works for knowledge that is accessible in that way. For example, we cannot use the scientific method to determine whether there are parallel universes. Another example is string theory which requires experiments at the Planck scale that are not possible. While these examples actually look like science, there are obviously a vast amount of knowledge outside the sciences that are not accessible via the scientific method.
Show threadAlice GlazkovFeb 10, 2025

@flippiefanus

Not everything that looks like science is a result of effort following the scientific method, which was refined over many decades. If the hypothesis is not relying on experimental data, we cannot claim it is the product of the scientific method. In addition to this, thanks to Karl Popper falsifiability is another great addition. If the hypothesis, theory or law must be falsifiable to be considered scientific. So I think we are in agreement on the second half.

> As @dougmerrittt stated, the scientific method is not meant for politics, except when their domains overlap.

But I find this part problematic. This is why I was asking more specific questions earlier. Without clear guidelines politicians can and likely will 'swallow' science in any way they want to support their narratives. A combination of absolutism in free speech and wide use of argumentum ad populum (i.e. replacing evidence-based science with explicit or implicit voting) will lead to devastating results for science and society in general. Some of those bad omens we are already seeing.

Show threadJohn Carlos BaezFeb 10, 2025

@aglazkov wrote: "Who draws the line what to trust or when not to trust science?"

I find the phrase "trusting science" to be very ambiguous. There is science as a method of discovering knowledge, and there is science as a body of putative facts that have been discovered by this method. (There's also science as a social enterprise, with various 'leaders' and bodies, etc. - but let's leave that out for now.)

I trust science as a method, in the sense that when used correctly it tends to work. As for the putative facts discovered by the scientific method, I trust different ones of them to different degrees, and I know that all of them are potentially subject to being overturned.

Indeed, science the method encourages a cautious attitude toward science as a body of facts.

@flippiefanus

Show threadColin the MathmoFeb 7, 2025
@johncarlosbaez Ditto, but we aren't really the intended audience.
Show threadBlake C. StaceyFeb 12, 2025
@ColinTheMathmo @johncarlosbaez This is part of why I have a really hard time recommending books about physics when my friends and relatives ask for things they can read about my job.
Show threadDivya Ranjan Feb 9, 2025
@johncarlosbaez @ColinTheMathmo So have I given up, a few of my friends send Quanta stuff every now and then and even if I open them I just go straight to the source links. Especially with the current climate of Hossenfelder, Wolfram et.al, I really don't want people to do such a job of "publicizing" physics. There are many ways of communicating the beauty in physics, this way is the least meaningful yet the most profitable in terms of commodification of "content".