34 Matching Annotations
  1. Sep 2021
    1. a triple is the smallest irreducible representation for binary relationship

      great explaination

    1. These stages postdate the Permo‐Carboniferous glaciation but retain a moderately steep equator‐to‐pole gradient, judging by the level of floral and faunal differentiation

      overall gradient?

  2. Aug 2021
    1. Even considering all these peculiarities, color is one of the simplest cases of nebulosity

      shades of gray

    1. we find that fixing fossil ages to the midpoint or a random point drawn from within the stratigraphic age range leads to biases in divergence time estimates, while sampling fossil ages leads to estimates that are similar to inferences that employ the correct ages of fossils. Second, we show a comparison using an empirical dataset of extant and fossil cetaceans, which confirms that different methods of handling fossil age uncertainty lead to large differences in estimated node ages

      dealing with uncertainties carefully actually matters

    1. The rate of GMSL rise for 2006–2015 of 3.6 mm yr–1 (3.1–4.1 mm yr–1, very likely range), is unprecedented over the last century

      That's only for 2006-2015 period. So 许艺炜 & 胡修棉 is bullshiting when they write "自工业革命以来,全球海平面以3.6mm/yr速度上升(IPCC, 2019)"

    1. Because the influence of early diagenetic cements on the bulk δ13Ccarb signal can, but need not be synchronized, chemostratigraphy should not be used as a stand-alone method for trans-continental correlation, and especially minor isotopic shifts have to be interpreted with utmost care

      how shall we deal with "local" anomalies

    2. Chemostratigraphic correlation based on bulk sediment carbon isotopes is increasingly used to facilitate high-resolution correlation over large distances, but complications arise from a multitude of possible influences from local differences in biological, diagenetic and physico-chemical factors on individual δ13C records that can mask the global signal

      signal vs. noise

    1. an invitation to readers to invest their time reading it

      structure vs. function. the introduction exists for a purpose; that is, to allure the intended readers.

    1. Some words, like "the" or "a" are pretty unsurprising; in fact they are redundant since you could probably understand the message without them. The real essence of the message lies in words that aren't as common, such as "alien" or "invasion".

      why does natural language has redundancy?

    2. If your string of symbols constitutes a passage of English text, then you could just count the number of words it contains. But this is silly: it would give the sentence "The Sun will rise tomorrow" the same information value as he sentence "The world will end tomorrow" when the second is clearly much more significant than the first. Whether or not we find a message informative depends on whether it's news to us and what this news means to us.

      importantly, information depends on the prior knowledge of the receiver. If we have no idea about the relative frequency of sun rise and world ending, then the two sentences has the same amount of information to the receiver.

    3. To treat them all on equal terms, Shannon decided to forget about exactly how each of these methods transmits a message and simply thought of them as ways of producing strings of symbols

      ultimately it boils down to the transmission of a series of encoded message, whether in the form of spoken language, drums, smoke, or Morse code

    1. There is, however, a major flaw: Hartley's measure gives the same value to every symbol. You could well imagine situations, though, in which one symbol carries a lot more significance than another

      Hartley apparently assumes people have no prior knowledge about the symbols & frequency

    2. Hartley thought, the information content should grow in direct proportion to the length of the string. If every symbol has an information content of, say, , then a string of ten symbols should have an information content of And a string of symbols should have an information content of Writing for the information of the string of length , we need  

      first rule: information content should be proportional to the length of the string

    3. Since we have decided that information content hinges on that total number, our measure of information should allocate the same value to two strings produced on the two different machines

      second rule: the use of alphabetic system shouldn't affect the information content

    4. Hartley realised that, as a measure of information, the quantity has a fatal flaw. If we apply it to our coin example, we see that a string of length has information content while a string of length has information content So adding an extra symbol to the string has added amount of information. This means that adding an extra symbol to a string of length adds only amount if information, while adding an extra symbol to a string of length adds amount of information — the information added grows exponentially with the length of the string. But that’s weird: why should an extra symbol carry much more weight when it is added to a long string than when it is added to a short string?

      typo: "if information" should be "of information"; also good point

    5. When there is only one flip, receiving its outcome only rules out one other possibility. But when there are ten, there are a total of possible outcomes (because there are different strings of Hs and Ts of length 10). Receiving the information of which one it actually was rules out possibilities

      The information content seems abundant; however, any of the 1024 possibilities content the same amount of information,

    6. How informative is this piece of information? Well, it's not that informative really, because there were only two possibilities

      this assumes that the receiver has the same prior knowledge as the send of the message.

  3. Jul 2021
    1. Hayek draws attention to the fact that the most relevant knowledge for economic decision-making is not the general knowledge of the economist or philosopher, but rather the dispersed, local, and often tacit knowledge of myriad individuals in an economy

      will big data change the situation? What used to be impossible now starts to seem likely.

    1. better to have had five stupid ideas than no ideas at all. And if somebody wrongly points out that your idea is stupid, it is even more important not to take offence: just explain gently why their dismissal of your idea is itself stupid

      highlight

    2. My feelings at the moment are that blogs are too linear—it would be quite hard to see which comments relate to which, which ones are most worth reading, and so on. A wiki, on the other hand, seems not to be linear enough—it would be quite hard to see what order the comments come in.

      The same problem exists for paleogeography Q&A forum.

    3. The article starts with a question on the necessity and feasibility of massive collaboration and proceeds with discussion of the two immediate questions. In particular, the author addresses concerns he can think of, such as the problem of a person who tries steal the fruits of labor from others. Doing so makes the article more convincing and sincere. Furthermore, talking about the limitation also helps to gain the readers' trust.

    4. overall, the article proposes a way for massive collaboration in math, and explains the potential advantages which ultimately result from the inherent differences of human race and relativity (not the Einstein relativity, but the philosophical one which relates to the perspectives/angles of viewing the world in general): 1) the tendency of trying out different techniques to solve problems (assuming that we know exactly the same amount of knowledge), 2) the complementing nature of collective knowledge (if we know about different things), and 3) different strategies for approaching problems as people prefer and are good at different aspects of solving the same problem.

    5. it might be quite hard to say on your CV, “I had an idea that proved essential to Polymath’s solution of the *** problem,” but if you made significant contributions to several collaborative projects of this kind, then you might well start to earn a reputation amongst people who read mathematical blogs, and that is likely to count for something. (Even if it doesn’t count for all that much now, it is likely to become increasingly important.) And it might not be as hard as all that to put it on your CV: you could think of yourself as a joint author, with the added advantage that people could find out exactly what you had contributed

      interesting perspective; by contributing to discussions in written format, people can trace the contribution of each author (or participant of a discussion) more accurately in a later published result

    6. The next obvious question is this. Why would anyone agree to share their ideas? Surely we work on problems in order to be able to publish solutions and get credit for them. And what if the big collaboration resulted in a very good idea? Isn’t there a danger that somebody would manage to use the idea to solve the problem and rush to (individual) publication? Here is where the beauty of blogs, wikis, forums etc. comes in: they are completely public, as is their entire history

      The answer isn't that convincing and motivating; we need better stimuli for people to contribute

    7. Different people have different characteristics when it comes to research. Some like to throw out ideas, others to criticize them, others to work out details, others to re-explain ideas in a different language, others to formulate different but related problems, others to step back from a big muddle of ideas and fashion some more coherent picture out of them, and so on. A hugely collaborative project would make it possible for people to specialize

      mechanism 3: it is the difference that makes the human race flourish.

    8. Sometimes luck is needed to have the idea that solves a problem. If lots of people think about a problem, then just on probabilistic grounds there is more chance that one of them will have that bit of luck

      mechanism 1: trying out different techniques for solving the problem at hand

    9. we don’t have to confine ourselves to a purely probabilistic argument: different people know different things, so the knowledge that a large group can bring to bear on a problem is significantly greater than the knowledge that one or two individuals will have. This is not just knowledge of different areas of mathematics, but also the rather harder to describe knowledge of particular little tricks that work well for certain types of subproblem, or the kind of expertise that might enable someone to say, “That idea that you thought was a bit speculative is rather similar to a technique used to solve such-and-such a problem, so it might well have a chance of working,” or “The lemma you suggested trying to prove is known to be false,” and so on—the type of thing that one can take weeks or months to discover if one is working on one’s own

      mechanism 2: collective knowledge of a community is likely to better approximate reality; this applies especially to subjects like paleogeography; also related to relativity

    10. what you would not tend to do, at least if you wanted to keep within the spirit of things, is spend a month thinking hard about the problem and then come back and write ten pages about it. Rather, you would contribute ideas even if they were undeveloped and/or likely to be wrong.

      rules of the game

    11. Suppose one had a forum (in the non-technical sense, but quite possibly in the technical sense as well) for the online discussion of a particular problem. The idea would be that anybody who had anything whatsoever to say about the problem could chip in

      The platform and mechanism for collaboration

    12. classification of finite simple groups, or of a rather different kind of example such as a search for a new largest prime

      types of problems that require huge collaboration

    13. there are certain kinds of problems that lend themselves to huge collaborations

      the same for paleogeographic reconstruction, human genome sequencing, building large colliders, etc.

    14. This suggestion raises several questions immediately. First of all, what would be the advantage of proceeding in this way? My answer is that I don’t know for sure that there would be an advantage. However, I can see the following potential advantages.

      raises several questions immediately