My understanding is that cellophane generally does biodegrade in most settings. Polylactic acid (those cornstarch-derived bags) mostly biodegrades in hot enough compost or (after several years) in ambient-temperature soil, but not very well in cooler water (One study: "The half-life period of degradation [of polylactic acid in artificial seawater] is 12 [days at 90° C] or 468 days [at 60° C]").
Those temperatures are certainly hard to find in nature, outside of hot springs! Even if this is an error and we are talking about 90°F/60°F, the higher temperature is pretty much constrained to the tropics, so we're talking a year+ to degrade in real conditions. It is better than centuries, but not exactly rapid?
Yeah, I imagine it's considerably slower at ambient ocean temperature. Don't throw your PLA bags in the ocean or a river. Here's a different paper:
> For example, PLA is not biodegradable in freshwater and seawater at low temperatures [32,36–39]. There are two primary reasons for this: (i) The hydrophobic nature of PLA, which does not easily absorb water [40–42]. In aqueous environments, the lack of hydrophilicity diminishes the hydrolysis process, which is crucial for the initial breakdown of PLA into smaller, more degradable fragments. (ii) Resistance to enzymatic attack; the enzymes that degrade PLA are not prevalent or active under typical freshwater and seawater conditions [39,43,44]. The microbial communities in these environments may not produce the necessary enzymes in sufficient quantities or at the required activity levels to effectively breakdown PLA. Additionally, the relatively stable and crystalline domains of PLA can further resist enzymatic degradation.
Also:
> It should be emphasized that neat PLA cannot be classified as a completely biodegradable polymer, as it generates microplastics (MPs) during biodegradation.
BART is full of white-collar people who use it to commute and to travel around the area (alongside all sorts of other kinds of people, as you would expect for a broadly used service).
Ridership collapsed in 2020 because of the pandemic, for obvious reasons, but it's hard to really blame that on the service itself, or the riders.
Ridership has been gradually recovering since then. Total trips are now up to something like 70% of 2019 levels, and continuing to rise. Number of unique riders is actually above the 2019 level now.
Maybe you haven't tried riding BART again within the past several years?
I left SF ~2021, but even in 2019 it was kind of in a death spiral. Hopefully it's better now, loved it back when I lived there. But still hear mixed reports from friends.
For a bit of context, the Phaenomena was a book by Eudoxus (c. 400 BC) explaining the then-current knowledge of astronomy; unfortunately there are no extant copies. A poem (also called Phaenomena) by Aratus (c. 300 BC) made the content more accessible, and was extremely popular. The only surviving work by Hipparchus (c. 150 BC) is a critical commentary on these two books, and it only survived because it was bundled together with several other commentaries on Aratus' poem which were copied as a group. Hipparchus synthesized Mesopotamian astronomical observations and measurement techniques with Greek spherical geometry, founding the subject we now call trigonometry. All of his other works are lost, but much of the content of Ptolemy's Syntaxis (a.k.a. Almagest, c. 150 AD) was taken from Hipparchus' astronomical and mathematical works.
Any additional fragments of Hipparchus' works is of great interest to the history of mathematics and astronomy.
Sanger was originally hired to edit Nupedia, a web encyclopedia project with a strict peer review process, and only worked for Wales for about a year. Wikipedia was started as a side project (with Sanger contributing to the concept and some early organizing), but Wikipedia quickly became much more successful while Nupedia basically never got off the ground. My impression is that Sanger wanted to impose his own vision on Wikipedia, but couldn't because the community of volunteer editors disagreed, and when Wales stopped paying him as a full time Nupedia editor (Wales's company was tight on cash at that time), he stopped any involvement. This was long before most of the actual work of Wikipedia happened, and that should have been the end of the story.
But ever since, Sanger has been trash talking Wikipedia as a project and community ("broken beyond repair") and trying to undermine it. A few years later he started a competing project (which was predictably a total failure). For two decades he has been promoting himself as "cofounder of Wikipedia". Interviewer after interviewer asks the same lazy questions about the subject, without ever adding any new insight. (You can see that Sanger's ghost is chasing Wikipedia even into this discussion.)
It's beating a dead horse, and entirely off the topic of what the interview was supposed to be about. Answering the question clearly and accurately takes a lot of time and finesse, which is wasted on the interviewer and most of the audience. Wales clearly screwed up in that interview, but it's not hard to see where he's coming from, psychologically.
The articles about Fourier series and Fourier transform currently begin with:
> A Fourier series is a series expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood.
and
> In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input, and outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex valued function of frequency. The term Fourier transform refers to both the mathematical operation and to this complex-valued function. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical chord into the intensities of its constituent pitches.
That is much more as it used to be in english. Anyway I stated clearly, it was a time ago, and now may be better, that it was just an example. In german is still shooting mathematical symbols that anybody who does not already know what FT is, will 99% not even start to understand what is it about.
The only way anything ever changes in a volunteer project is if someone feels motivated and makes the effort. Please contribute changes to German Wikipedia articles (or English ones) when you notice possible improvements. If you are not personally capable of improving an article about a topic you don't know about, please try to contribute to the articles about topics you do know something about. Or you can try to leave a talk page message asking for help.
It's extremely difficult to write math articles for a general audience which are both accessible and accurate, and the number of excellent writers working on Wikipedia math articles is tiny.
Please get involved if you want to see improvement. There are some math articles which are excellent: readable, well illustrated, appropriately leveled, comprehensive; but there are many, many others which are dramatically underdeveloped, poorly sourced, unillustrated, confusing, too abstract, overloaded with formulas, etc.
there are many math teachers teaching math to people who don't know the subject, basically all mathemeticians. and wikipedia has guidelines for how to serve the audience, the math articles ignore it.
I (got into and) went to MIT (and graduated several times) in engineering and also in finance. I am way beyond the average wikipedia reader in math knowledge. the mathematics wiki articles are imho worthless. the challenge is not how to write articles that are explanatory and reasonable, the challenge is all the gatekeeping of the wiki editors who make it the way it is, that is an unreasonable fight. I tried to make a change a couple of weeks ago to correct an error that was in an article. I got reverted by a person who wanted to collaborate on making the article more abstruse as a solution. "but the error" I said. It's still there.
The thing about Wikipedia is that no one cares what you have done outside Wikipedia. It is like showing up at a new work place and saying something that is factually correct, it can go any way.
I have a fair amount of edits on Wikipedia and the wikis that preceded it. Whenever I read this sentiment here I never really understand what the problem is. I never have it myself. The only fight I have been involved in was if Wikipedia should have an article on Bitcoin. Which was not obvious in the beginning.
You could always link to the article and we can have a look. I have no clout on Wikipedia but I do understand why facts can be problematic in any text book. It once took me a week to correct an article about a Russian author.
I'd say there's significantly less gatekeeping on Wikipedia than most parts in academia. YMMV.
But: there are a bunch of random clueless people trying to promote their obscure papers to boost their citation counts, push weird nationalist POVs, add fringe pseudoscience, make "fixes" that turn out to be wrong, add vague explanations which they find personally helpful but nobody else can make sense of, remove clarifications and explanations in the name of rigorous purity, change the wording of sentences that have been subject of years-long dispute and careful compromise, and so on. Wikipedia maintainers are constantly fighting against these agents of entropy (or when an article is not actively maintained, it tends to get a lot worse over time), which unfortunately can sometimes also negatively color interactions with helpful contributors. They're also part-time volunteers, and fallible humans; try to cut them some slack.
To the extent that there is "gatekeeping", it is mostly along the lines of: you can't use Wikipedia primarily for self promotion, you can't add your own new claims that have no published source, and you have to abide by existing norms of project/community engagement. In general, people are judged by their contributions and behavior, not their credentials (though editors also include a bunch of world-class experts in the topics they contribute about, and it does have some pull when someone can say "I literally wrote the top cited paper about this" or whatever).
But beyond that, the difficulty is that there's no one correct way to explain difficult topics, no single audience for Wikipedia articles, a lot of strong opinions about how things should be one way or the other. Trying to satisfy everyone takes discussion and compromise and sometimes a minority is still unhappy with the resolution. The biggest problem though is that there are not enough active participants (including in mathematics) to write great articles about every topic, and writing a really excellent article about something takes a huge amount of work; there are many mediocre articles that have never really had the time put in to make them great.
When someone new to the project gets into a heated dispute about a minor point, they routinely get extremely frustrated and occasionally then run around the web complaining about how awful the people on Wikipedia are. Several times times in the past few years I have asked such complainers for specifics, and remarkably I have gotten a reply ~4 times. In all but one case, when I went to investigate further it turned out that they were clearly in the wrong. In the last example there was a misunderstanding and I fixed the issue. If you want to provide a specific article and error, I'm happy to go take a look.
Alternately, when people run into an unresolvable dispute on one local article talk page, they can seek opinions from wider groups of Wikipedia editors, e.g. on the math "wikiproject" talk page https://en.wikipedia.org/wiki/Wikipedia_talk:WikiProject_Mat.... If you make a post there about your issue, you will get more eyes on your problem, and it will likely be resolved correctly.
The Greeks "notation" was a diagram full of points labeled by letters (Α, Β, Γ, ...) with various lines connecting them and a list of steps to do with an unmarked ruler and a compass, some of which added new points. But those tools alone can't be used to describe cube roots of arbitrary numbers (or, equivalently, trisections of arbitrary angles).
> What is this [statisticians' function]?
The integral of the bell curve (normal distribution) is called its cumulative distribution function (CDF). The CDF of the normal distribution is closely related to a special function called the "error function" erf(x).
> Is there a good intro to [the symmetry interpretation of the quadratic formula]?
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