A resource can be anything that has identity. Familiar examples include an electronic document, an image, a service (e.g., "today's weather report for Los Angeles"), and a collection of other resources. Not all resources are network "retrievable"; e.g., human beings, corporations, and bound books in a library can also be considered resources.

Competent scientists do not believe their own models or theories, but rather treat them as convenient fictions. ...The issue to a scientist is not whether a model is true, but rather whether there is another whose predictive power is enough better to justify movement from today's fiction to a new one. Steve Vardeman, 1987. Comment. Journal of the American Statistical Association 82 : 130-131. [kw]

a triple is the smallest irreducible representation for binary relationship

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

Even considering all these peculiarities, color is one of the simplest cases of nebulosity

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

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

790 kyr for OAE2

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

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

an invitation to readers to invest their time reading it

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".

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.

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

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 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  

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

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?

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

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

Information and the logarithm

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

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

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.

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

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

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

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

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

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.

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

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

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

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.