As an engineer, this and the principle of least action occupy my wall of “things I think are super deep and maybe mysterious* and interesting and I wish I understood deeply”
A big part of what’s impressive about Noether’s theorem is that it’s not at all mysterious. At its core, it’s a mathematical proof that’s possible to fully understand. It doesn’t depend on any magic constants in our universe, or indeed anything in the universe at all. It should apply to all possible universes in any situation that satisfies its conditions. The PLA is similar.
Some people see a mystery at the point where these mathematical constructs are applied to our physical universe. Eugene Wigner wrote about “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.”
There are explanations for many of the points he raised in that paper. Perhaps the one that remains most unresolved is the question of why universal law or behavior isn’t messier, more chaotic - why it should so often correspond so neatly to physical phenomena. Intuitively, this doesn’t seem surprising to me, but Wigner correctly points out that we don’t really know why this is the case.
Answering that gets deeper into philosophy: structural realism, the anthropic principle, and so on. But one possible explanation is an extension of ideas like Noether’s: that the various mathematical constraints collapse the space of possibilities enough to make it likely, if not inevitable, that the universe ends up embodying relatively simple mathematical structures.
Indeed. I'd suggest Susskind's Theoretical Minimum: Classical Mechanics if someone wants an introduction. He doesn't explicitly prove Noether but he demonstrates the connection between symmetry and conservation laws building the intuition to properly appreciate Noether.
I've also written a series on Abstract Algebra for computer programmers if you're serious about learning it:
In physics textbooks the usual presentation is to posit Hamilton's stationary action, followed by demonstration that F=ma can be recovered from it.
Now: we have that in physics you can often run derivations in both directions.
Example: the connection between the Lagrangian formulation of mechanics and the Hamiltonian formulation.
The interconversion is by way of Legendre transformation. Legendre transformation is it's own inverse; applying Legendre transformation twice recovers the original function.
Well, the relation between F=ma and Hamilton's stationary action is a bi-directional relation too: it is possible to go _from_ F=ma _to_ Hamilton's stationary action.
The process has two stages:
- Derivation of the work-energy theorem from F=ma
- Demonstration that in circumstances such that the work-energy theorem holds good Hamilton's stationary action holds good also.
Knowing how to go from F=ma to Hamilton's stationary action goes a long way towards lifting the sense of mystery.
General remark:
Of course, in physics there are many occurrences of hierarchical relation. Classical mechanics has been superseded by Quantum mechanics, with classical mechanics as limiting case; the validity of classical mechanics must be attributed to classical mechanics emerging from quantum mechanics in the macroscopic limit.
But in the case of the relations between F=ma, the work-energy theorem, and Hamilton's stationary action: the bi-directionality informs us that the relations are not hierarchical; those concepts are on equal par.
Thinking of doing the same! Which kit did you order? I see a FNG, FNG+ Bundle, and "Learn lockpicking bundle". 3rd one seems the most likely candidate. Any tips you can share? Thanks!
Start with a cheap kit from e.g. Amazon which includes a couple of perspex locks so you can see what you're doing. Get a real set of picks for real money once you graduate from that.
I got the Learn Lockpicking bundle a few years back, it's a solid customizable lock - six slots, a few different pin styles, and the springs to make it work. I got practiced enough to get a 3-pin opened, but I'm definitely out of practice now.
I did the same (also during COVID, after doing it for a bit in my youth). I haven't tried Covert Instruments gear, I bought some other pack from China, but whatever pack you can find with the basics (and maybe some variety so you can try different techniques) plus a training padlock so you can see what's going on inside, and it'll be a walk in the park.
Sorry - what do you mean by yud-cult? Searching google didn’t help me (as far as I can tell) - I view LW from an outside perspective as well, but don’t understand the reference
They're referring to the founder of that website, Eliezer Yudkowsky, who is controversial due to his 2023 Time article that called for a complete halt on the development of AI.
Yudkowsky is controversial for much more than an article from 2023.
Yudkowsky lacks credentials and MIRI and its adjacents have proven to be incestuous organizations when it comes to the rationalist cottage industry, one that has a serious problem with sexual abuse and literal cults.
It was not so much the call for a complete halt that caused controversy, but rather this part of his piece in Time (my emphasis):
"Make it explicit in international diplomacy that preventing AI extinction scenarios is considered a priority above preventing a full nuclear exchange, and that allied nuclear countries are willing to run some risk of nuclear exchange if that's what it takes to reduce the risk of large AI training runs.
That's the kind of policy change that would cause my partner and I to hold each other, and say to each other that a miracle happened, and now there's a chance that maybe [our daughter] will live."
No, he's controversial because he runs an online sex cult centered around the idea that 1. if you do a specific kind of math in your head instead of regular thinking you'll automatically be correct about everything 2. computers can do math faster than you 3. therefore computers are going to take over the world and enslave you 4. therefore you should move to Berkeley and live in a group home.
I understand that, but the guidelines don't get relaxed because the topic seems important to you. It's common for people to think that a particular issue is so important that the normal rules shouldn't apply or should be interpreted differently in that case, but we can't run the site like that.
Purely empirical observation, in my own life, make no claim as to humanity/society/etc.:
It's interesting how often fermi estimation problems are used as proxy's for "intelligence". Something like: 'let's assess how well "they can think" - how many golf balls fit in a baseball stadium?' etc.
Often, doing well in these kinds of problems can more than makeup for a lack of specific knowledge in something someone is interested in assessing!
I’ll simplify for manhattan and extrapolate for the four outer boroughs. Ten avenues, a hundred streets. A thousand blocks? One cab per block? One thousand cabs in manhattan? 5,000 total?
That sort of estimation feels a lot easier to me than the "golf balls in a baseball stadium one" that was mentioned by the parent because it's dealing with quantities I can recall having heard before like "how many streets are there in Manhattan" rather than measurements that personally would never stick in my head like "how wide is a golf ball". I'm not sure why, but I've always been awful at making even rough estimates of units. If you gave me the diameter of a golf ball and the dimensions of the stadium, I could do some basic calculations, but even though I physically know about how large a golf ball is, I couldn't tell you whether it's more likely that its diameter is 0.5 or 1.5" (and not having looked it up, I would believe you if you told me it wasn't even within that range)! This gets worse with units I can't visualize (like weight), and when the sizes get larger than I can easy relate to; if you asked me questions like how much a car weighs or how long the Brooklyn Bridge is, I'm doubtful I'd even be within a factor of 2 more often than not.
I'm probably taking this more seriously than it was intended above, but the idea that this is some sort of proxy for "thinking" or "intelligence" feels off to me; doing the math given the size of something might be thinking or intelligence, but knowing roughly "how big" something is seems more like intuition.
I kind of figure a centimeter is about the width of a pinky, then I try to gauge how many pinkies fit in some distance, and go by that. I'd imagine a golf ball is about 4cm in diameter, though I haven't seen one in years.
Yeah, I don't feel confident in the idea that my pinky is around 1/4 of a golf ball. It could be 1/6, or 1/2, or nowhere close to either. A lot of this seems to be an exercise in how confident someone is about arbitrary guesses, and it seems weird to me that a higher willingness to make assumptions is somehow correlated with raw intellect. If someone wants me to do the math with a completely made up number, I can do that, but at that point it seems like the true test is figuring out whether the person asking the question actually cares about the accuracy of the answer or not, and that seems more about the social aspect of an interview. That isn't to say that what it's measuring isn't useful, but I think as someone on the spectrum, it's hard for me not to have a strong reaction to the idea that it's purely a measure of intelligence.
I had a great boss who really liked that kind of question. I disagreed with him. I would rather have someone who knows how to find the official answer online and verify the quality of the source.
The ability to estimate within an order of magnitude or within 2X is vastly more valuable, and beyond being able to have a sense of whether the "official" answer is likely accurate or off by orders of magnitude.
During most of the process of designing anything in or that touches the physical world, you are using rough figures.
Taking time to get the fully accurate and precise answer for every question is a waste of time as you don't need that many decimals of precision to move forward. Every decimal of precision in the answer takes more time and there are MANY of those questions, so being 100% accurate in every answer does not scale.
Of course, when it gets to the end of the process, the accuracy & precision requirements increase, but the emphasis needs to be placed where needed, not everywhere.
Plus, you are not going to find the "official" and accurate number of golf balls in the particular school bus you want to model. You'll find some vaguely similar answer or set of sub-answers, so sure, those will be fully accurate and precise, but THEN you must take those as inputs for your estimate, and we're back to the skill of estimating being most critical.
Being able to estimate and do sound back-of-the-envelope calculations is the far more critical skill, at least on any team I'm building.
Ideally I think the ability to come up with a quick off-the-cuff guess that is correct to one order of magnitude and then find and verify the specific answer are nicely complementary.
Not downplaying or defending - but I don’t understand the failure mode here - presumably hegseth had to ask someone in pentagon IT to set this up? Submit a form etc. sure he asked for something illegal* but someone actually following a set of rules had to enable this, no?
The failure mode is that the Secretary of Defense unilaterally bypassed security protocols to use technology that had not been evaluated for that use case in a national security context by the appropriate experts.
It doesn't matter if he happened to use something that has a solid security model. The problem isn't Signal, it's that he ignored all the rules.
And it does have an impact, as we see in other news, because one failure mode of Signal is that it's super easy to add the wrong people to a group. Which has actually happened. Twice (at least.)
Of course it’s not approved for classified use. There is a leap here until it’s been proven it’s been used for classified communications. There is no proof yet. Open to changing my mind if an authority on the topic says it is classified.
> "Michael Waltz has learned a lesson, and he’s a good man," Trump said Tuesday in a phone interview with NBC News.
> Asked what he was told about how Goldberg came to be added to the Signal chat, Trump said: “It was one of Michael’s people on the phone. A staffer had his number on there.”
—-
“The Secretary of Defense is the original classification authority," Ratcliffe said, "and my understanding is that um his comments are that any information that he shared was not classified.”
—-
So, I am back to what I have been saying from the beginning.
This is an AP hit piece via corrupt MSM and until someone can point to further evidence from these unknown “sources” then this story can’t be trusted.
Hit piece! Sec of Def can say anything he wants, it was automagically cleared for release, and his wife applying for clearance as soon as story leaked is just a coincidence!
I 100% agree - I’m only saying hegseth didn’t run an unsecured line into his office himself no?
Why didn’t some automated system say “installation of unsecured lines in this building is not possible” or similar
To be course : I didn’t think something so obviously wrong would have been allowed and enabled by several people who made this possible - removing absolutely no accountability from the person who asked for this to happen
If this happened the way it's being reported, yeah, several people should lose their jobs.
I suspect this is a case of being more afraid of saying "no" to the boss than of facing consequences for violating policy. Policies are unfortunately not self-enforcing.
Trump's been firing Inspectors General and dismantling mechanisms of internal accountability across the government, so perhaps that's a correct calculus in this case.
Not downplaying or defending - but I don’t understand the failure mode here
Like so many others, this particular 'failure mode' doesn't exist if you're a Republican. What if Hillary Clinton did it? Now that would be a democracy-threatening 'failure mode.'
I'd note that he's not subject to them. It's a civilian position, and he's no longer serving in the military. You're obviously allowed to wear makeup as a former soldier.
I agree he's a clown, but not for this. Politicians frequently wear makeup. It's part of the job.
Just to clarify - I am not presuming to shift blame - I am asking about a failure mode here- absolutely hold hegseth accountable (he should have never been in this position and is completely unqualified in my opinion).
I am also not suggesting we hold an IT person accountable-
I am only saying there should be rules/systems in place so that if someone else asks for something obviously wrong like this again, there’s a clear stop gap to say “that’s not possible”
Maybe there already is one(several) - if so, then of course the chain of accountability continues to ensnare…
Why are you so upset about men wearing makeup? I mean clearly he is not a member of any of the armed services anyway. Your whole comment is essentially a rant about how this guy should adhere to gender norms. You have a point about spending the money for a studio, but that has nothing to do with the article.
No software—whether on a secure or non-secure (dirty-line) government computer—can be installed without IT being alerted within milliseconds. Likewise, absolutely no unauthorized hardware can be connected to a military system without immediate detection.
There is simply no realistic scenario in which PH could have operated an unknown system with unapproved software inside one of the most secure facilities in the United States without it being known and approved. If I’m proven wrong, I’ll gladly apologize for doubting. But when it’s confirmed I’m right, I hope you’ll extend the same courtesy to those your post may have misled or unfairly accused.
Edit: I wonder if the vim community can contribute to a feature bounty like this? Hmm
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