Starting at an initial density of air, suppose you descend a distance D such that the air density doubles. Now your air is twice as dense, which doubles the pressure underneath it, meaning if you descend a further D the density will double again. Continue ad infinitum (or at least until the ideal gas law stops being a good approximation).
> Pressure (P), mass (m), and acceleration due to gravity (g) are related by P = F/A = (m*g)/A, where A is the surface area. Atmospheric pressure is thus proportional to the weight per unit area of the atmospheric mass above that location.
It's very common for tech companies to go public without being profitable. As long as their growth is good and they have a reasonable story for how they will achieve profitability, then it typically makes sense. Of course every company is different and not all will reach their profitability goals post-IPO, but in many cases, it wouldn't make sense to wait for profitability before going public.
I've noticed that since I've started using ChatGPT, I've almost entirely stopped using Google (except for the rare case where I need a specific website but don't remember the URL). In addition to a bunch of technical questions related to my work, my ChatGPT chat log has the most mundane things like:
- What is platos frios
- Can you download Netflix videos to your local device
- Who composed the Top Gun theme
- Who have been the most successful American Idol winners
- If I check-in the day before a United Airlines flight, can I still buy additional checked bags when I go to the airport
- If I'm buying a Schwinn IC4 indoor spin bike, do I need a floormat for it also
- What is pisco
- In the US, what is the format for EINs?
- Is it bad to use tap water in your humidifier?
- Which NBA players are on supermax contracts
- What are some of the best steakhouses in Manhattan?
- How much and how long does it take to procure a DUNS number?
- In terms of real estate, what is historic tax credit development
LLMs give me the answers I want immediately. Before, I would use Google basically as a proxy to find websites that I'd then have to sift through to find the answers to these questions. It was another layer of indirection. Now that I can have an LLM just tell me the answer (you still need to approach it with a skeptical eye, since it can certainly get some things wrong), I don't need to "search" the search results pages themselves and read multiple articles and blog posts to hopefully find the answer to my question.
The problem with this approach is that LLM gives me unreliable answers. I know this because sometimes I ask things that I used to knew but forgot and needed to refresh my memory - and sometimes the answers were incorrect. So, unfortunately, a search engine validation step is still a necessity.
Asking LLM to provide a link does NOT work, as they hallucinate links just fine, and give links that are either broken or do not contain the information LLM says it should. Using search tools through a LLM (like ChatGPT's "search" function) sort of works (at least the link will be correct - still need to check if the contents means what LLM says it does), but it's quite limited and cannot be fine-tuned (I don't use Google but rather prefer Kagi, and I tend to heavily rely on Kagi's lenses, site: queries and negative terms to scope and refine searches).
In other words: please do NOT trust LLM's answers, even if they sound plausible. Always verify.
After some experience and testing, I've become well aware not to use LLMs to ask questions like "who did X" and "what is company Y's policy about Z", because they tend to hallucinate responses (even for well-known people).
What I've not yet figured out how to deal with is how to handle being surrounded by a society of people who go ahead and trust LLMs for their factual answers anyway. I think even if I'm careful about selecting my sources, the background noise floor is going to climb up to the point that there's no signal-to-noise ratio left.
People used to criticise Wikipedia for being bad due to being crowdsourced (at least in school they did). Now, Wikipedia looks like one of the best antidotes to LLMs.
I suspect this is more of a case of garbage-in garbage-out. The existing web results have invented answers.
People created websites to "answer" people's search queries about celebrity net worth, if some celebrity is gay, if they are in a relationship, etc. They obviously frequently did not know, and made a guess, or relied on tabloids as a source, who also frequently make things up.
Yes but it is quite obvious that you are on a site like that so you can ignore it. How am I meant to know if ChatGPT was trained on those websites? How do I know when it is effectively drawing from that vs drawing from a reliable source?
Does it matter to you whether the answers you are given are correct? Google results are sometimes wrong but the web gives you signals about reliability, like the author, etc. If I want to know who wrote a paper, I can google the paper's name and get an ACM page about the paper or a PDF of the paper and read the author's name. Very reliable. If ChatGPT says the name I have no clue if it is right.
Multiple sources is a good thing. Using just ChatGPT is like only ever using Wikipedia as a source of all information, but put through a filter that removes all sources and attribution information and cross linking and history and those notices at the top of pages saying the article has issues AND normalising the writing style so that you can't even use bad spelling and grammar as a signal of inaccuracy.
I really like having the site where the answer came from so I can instantly judge how likely the answer is to be correct.
Chat GPT does correctly answer your question about airline bags, but I have no way of knowing if it made that answer up or not because so many airlines have the same policy.
Google at least gives you links to the United baggage policies. The AI overview in Google also "cites its sources", which sort of gives you the best of both worlds. (I'm sure the accuracy of Google's AI vs. ChatGPT is up for debate)
I might misunderstand, but can't you just ask for the reference? I've also been using (Gemini) a lot to basically replace my search engine, but I always tell it to give me a reference. I've had pretty good results with this approach.
I wonder how many new, strange, surprising and wonderful things you indirectly stumbled into during those sifting exercises. Hyper-optimized search has some downsides. I love getting answers to my specific questions, but that always encompasses the "known unknowns" space. Through skimming and sifting using websites as proxies, I enjoyed surprises from the "unknown unknowns" space.
10 years ago I'd agree with you completely. I definitely get your point and share some of that same sentiment, but search results these past 10 uears have become overwhelming absurd, shallow, and barely tangentially related to what I'm looking for
Clocks run at "normal" speed (i.e. "1x" speed) in the absence of a gravitational field. The stronger the gravity, the slower they run (i.e. less than "1x" speed).
This has always felt to me like evidence of a sort of computationalism. I am not a computationalist, but the thought is the "universal CPU" needs cycles for each particle. Mass is what takes time to process, so the voids experience no/less computational delay. This reads like the simulation author is messy and constrained, not godlike.
To me it's not about mass, but more like "maximum information density". There's a limit on the information density (rate of happening?), so when a parameter X changes too much, it affects other parameters -- they become constrained so that the total information density stayed within the maximum limit. That would indeed sound like some kind of computational limit if the universe was a massive CPU with constrained resources...
But I'm a layperson and I have no idea what I'm talking about :)
Right so is the paper saying that lambda CM completely ignored clock differences due to heterogeneity in mass distribution in the universe where isolated galaxies would be experiencing less time slowing than galaxies near other galaxies which would experience more time dilation?
In the standard cosmology the Integrated Sachs-Wolfe effect captures the redshift/blueshift of distant light sources (up to the Cosmic Microwave Background) as it traverses relatively dense regions and relative voids.
Note that in the next paragraph I depart significantly from the vocabulary that the Timescapes programme proponents have been using for the past twenty years.
ISW and comparable spectroscopy is easy enough to think about in terms of an accelerating cosmic expansion, i.e., relative voids are becoming spatially bigger with the expansion. It becomes much less intuitive how to fit the data if one keeps relative voids at roughly constant volume instead implying that there is a significant false vacuum above the ground state and in voids the false vacuum is slowly decaying to that state. (Outside the supervoids, near matter, this false vacuum decays much more slowly still). Because "vacuum" in the voids isn't really vacuum, one is stuck with a running function on the constant c (it gets faster with time from the formation of the CMB; this is because the false vacuum evolves towards a real vacuum) or adapting lightlike geodesics by imposing refraction (since the false vacuum is a medium).
The usual terminology is reasonably capture in the first paragraph here at <https://en.wikipedia.org/wiki/Inhomogeneous_cosmology#Inhomo...> ("Inhomogeneous universe"). The following short section ("Perturbative approach") is what is done in the standard cosmology when one wants to do detailed studies of filamentary distributions and other structures that are lumpy at some (larrrrrge) length scale of interest: the perturbed homogenous background is practically always the standard FLRW.
The justification for perturbation theory on FLRW is that even though there are dense spots (notably most galaxies' central black holes), principles like the Birkhoff theorem capture the idea that as you get far enough away from a galaxy it behaves more and more like a small shell, and this happens at intragalactic scales for these SMBHs: gravitationally, even to its arms' structure, it makes practically no difference whether Andromeda's central bulge has a lot more stars/gas/dust or whether it has one, two, or six central SMBHs (at enough spatial separation that they're not mutually orbiting in a way that would generate gravitational radiation our observatories are sensitive to).
The same idea applies to galaxies->galaxy clusters->filamentary structures: as you "zoom out" the density variations become less important: filaments are pretty sparse on average.
The Timescapes programe wants a sharper difference in matter sparseness between voids and filaments, and proposes that gravitational backreaction by the matter is responsible for generating that: the presence of matter steepens the density of matter over time (without the visible matter clearly becoming denser). I don't personally see how that's much different from a false-vacuum decay in the voids, conceptually. (ETA: well, it depends somewhat on how the Timescape void fraction evolves, but the local universe VF doesn't run void clocks fast enough, unless we do violence to the Copernican principle.)
Finally, I think the most important result of this latest Timescapes paper is a reminder to everyone that supernova data are a mess. A good X-mas present would be a couple readily visible Milky Way supernovae.
T CrB is a recurrent nova (RN), not a supernova (SN).
There is only a microscopic chance of the white dwarf member undergoing runaway fusion becoming a Type Ia SN. So microscopic it would be truly surprising astrophysically.
Aren’t the spherical harmonics functions with domain S^2, the sphere? I think the solutions to the (time-independent) Schrödinger equation for an electron in a hydrogen atom are given by like, a product of a function of distance from the center with one of the spherical harmonics, or something like that?
you are correct. The Schrödinger equation for the hydrogen atoms in spherical coordinates demonstrates separability which allows you to separate the radial and angular coordinates. The radial term, which is most interesting due to the 1/r potential is typically a Laguerre polynomial. The angular term is 'free' from any potential is typically a spherical harmonic.
The spherical harmonics in general are typically derived as part of the solution to the Laplace equation in spherical coordinates. A bit of a semantic point (though perhaps the distinction is important) though, since the Laplace equation's angular dependence is identical to that of the Schrödinger equation for the hydrogen atom.
It's actually more confusing IMHO, because these graphs overload the radial dimension to show probability as "distance from the origin". You have to multiply that by the radial function to get an actual probability distribution, which kinda/sorta looks like these pictures but not really.
Really the harmonics are best understood as something like "wave height on the surface of a sphere". They tell you how the electrons (or whatever) are going to distribute themselves radially, not where they're going in 3D space.
Also FWIW: the much harder thing to grok here (at least it was for me), and that no one tries to tackle, is why the "l" number corresponds directly to angular momentum. In particular "l==0" doesn't look like there's any rotation going on at all.
Simply speaking, "l" describes the number of nodes. In the same sense that a particle in a box with sin(nx) wave function has more nodes the higher energy (or momentum) state it is in.
As for why l==0 has no rotation going on at all, one would say that this should be expected. Qualitatively, the symmetric sphere does not change with rotation, so how would we tell if it is rotating or not? And perhaps the next step is controversial, but if there is no way to tell, maybe there is no dependence? This is a similar argument to why the electric field of an infinite plane is constant with respect to distance from it.
Wait, the US overall is ranked 18th out of approximately 50 countries (on the first chart for Math + Science). Obviously some American demographics are doing better, but across all demographics, the US scores are not excellent and not near the top.
According to the chart, the American scores amongst the internationally high performing demographic categories are exceptional. The overall score is only dragged down due to demographic categories that perform low internationally.
It's nice that that partition (ie: ethnicity) seems to cheer people up (or perhaps not, depending on how one thinks about it).
On the other hand, there's probably some partition - even if it's preference of {boxers, briefs, lingerie, 'commando'} - for any academic field by which one nation is better for each part.
It is possible that every group of immigrants to America is better at baking strudel than its corresponding group in Germany. Still more likely to find good German strudel.
> On the other hand, there's probably some partition - even if it's preference of {boxers, briefs, lingerie, 'commando'} - for any academic field by which one nation is better for each part.
This is not at all self-evident and if any such factor so strongly correlated with academics, it would be born out in real life and society. "Smarter people like vanilla over chocolate ice cream." The only reason race has come to matter so much is that it IS such a massive factor on one's life experience, whereas having brown hair vs. blonde hair does not and causes far less controversy.
The list of attributes that correlate to academic performance is long and picking from them is arbitrary. Eg:
{ People who study, people who cut class }
Country A: one freak Nobel laureate who likes to study, and a million citizens who scrape by but cut class.
Country B is the inverse: a million studious citizens, and one class-cutting deadbeat.
A's single Nobel laureate scores better at Math than than B's million nerds, and A's million deadbeats score better than B's sole deadbeat. Now country A is better at Math.
The point is that euopean americans perform strongly compared to europeans, asian americans perform strongly among asians, and black americans perform strongly compared to majority-black countries. Each demographic as the top of demographic peers internationally.
Most countries don't release fine-grained data but yes when you compare against other countries that are essentially ethnostates – Japan, Poland, few others.
Yes, and I don't think this is racism any more than other DEI/education initiatives that focus on one demographic more vs. another. Everyone talks about trying to get more blacks into gifted programs or selective high schools like Stuyvesant. This is scoping the problem, nothing more.
San Francisco uses RCV, and it’s not much better, maybe worse. Yes you get run off elections and more candidates. But now voters have to use strategy in how they vote and it’s complex to understand the implications. There’s a higher chance of winding up with unpopular candidates simply because nobody actually wanted their second or third choice candidates.
Canada has FPTP and has 5 parties represented in parliament.
Right now the governing party is a Liberal/NDP alliance, and it's possible that the next election will result in a Conservative government with a Bloc opposition.
The bloc only exist because Quebec is special. The NDP only exist because the liberals just pander and then do whatever they want once elected and everyone knows it.
(and Canadians in the east are afraid to vote conservative federally because they are mostly a western thing)
And greens having one seat is not anything real
The bloc only exist because Quebec is special. The NDP only exist because the liberals just pander and then do whatever they want once elected and everyone knows it.
(and Canadians in the east are afraid to vote conservative federally because they are mostly a western thing)
Weak probably means too much VC competition relative to the number of good investment opportunities, leading to higher valuations, fewer investments in top companies, and lower expected returns.
Look at the revenues per quarter. It was growing in 2023, but declined in the first quarter of 2024, but I wouldn't say you can make conclusions for 2024 from one quarter.
No one is comparing year over year, there's been barely a year since the acquisition. I said the "arrow" over the latest few quarters was generally UP, in response to a mistaken argument that Twitter/X has collapsed. I am not trying to say Elon is great or something like that, I am making an observation of what the charts say, that's all. I don't know if the charts are 100% accurate, but I have no reason to doubt either... Why anything that may be positive about X is so controversial, even something as uncontroversial as the direction of an arrow on a damn graph? People seem to lose all rationality over this guy, what the hell is going on?! Do you actually have figures showing completely different results?? IF no, why all of a sudden people are so completely skeptical of it?! Sounds like discussions about climate change: someone shows a chart with temperatures way up, all of a sudden everyone is an expert and points out it was higher 60 million years ago or whatever, or the data cannot be fully trusted because they learned in high school that these are just estimates or other crap on the same vein. It's embarrassing for the human race.
The point has nothing to do with Elon. It's just the correct way to analyze revenue graphs due to seasonality. Whether or not X is "collapsing" isn't obvious from the graphs either, and I made no such claim. We'd need to know other things that aren't public, and it's probably too early to tell anyway. But it's incorrect to say that revenue is growing. It's down quarterly YoY, which is the only real meaningful way to look at it.
Further, everything after Musk bought it is just a guess. Without public audited numbers, who knows what is going on. If I had to bet, I would guess the numbers are even lower than estimated - if things were hunky dory, I doubt they would be suing their customers (advertisers).
