And of course there is correlation between math knowledge and success at test. The problem is that at the extremes the tails come apart. Kids that are better at multiplication will be better at the tests. But the kids who score maximum at the tests and the kids who win math olympiads, are probably two distinct groups. I am saying this as a former kid who did well at math olympiads, but often got B's at high school, because of some stupid numeric mistake.
This is culture-dependent; e.g. in (some parts of Russian grading culture) making a numeric mistake migh...
The post I commented on is about a justification of induction (unless I have commited some egregious misreading, which is a surprisingly common error mode of mine, feel free to correct me on this part). It seemed natural for me that I would respond with linking the the strongest justification I know -- although again, might have misread myself into understanding this differently from what words were written.
[This is basically the extent to which I mean that the question is resolved; I am conceding on ~everything else.]
I find the questions of "how and when can you apply induction" vastly more interesting than the "why it works" question. I am more of a "this is a weird trick which works sometimes, how and when does it apply?" kind of guy.
Bayesianism is probably the strongest argument for the "it works" part I can provide: here are the rules you can use to predict future events. Easily falsifiable by applying the rules, making a prediction and observing the outcomes. All wrapped up in an elegant axiomatic framework.
[The answer is probabilistic because the nature of the problem is (unless you possess complete information about the universe, which coincidentally makes induction redundant).]
I might have an unusual preference here, but I find the "why" question uninteresting.
It's fundamentally non-exploitable, in a sense that I do not see any advantage to be gained from knowing the answer (not a straightforward /empirical way of finding which one out of the variants I should pay attention to).
Bayesian probability theory fully answers this question from a philosophical point of view, and answers a lot of it from the practical point of view (doing calculations on probability distributions is computationally intensive and can get intractable pretty quick, so it's not a magic bullet in practice).
It extends logic to handle be able to uniformly handle both probabilistic statements and statements made with complete certainty. I recommend Jaynes's "Probability Theory: The Logic of Science" as a good guide to the subject in case you are interested.
Oh, so human diseases in the form of bacteria/viruses! And humans working on gain-of-function research.
Reminds me of a discussion I've had recently about whether humans solve complex systems of [mechanical] differential equations while moving. The counter-argument was "do you think that a mercury thermometer solves differential equations [while 'calculating' the temperature]?"
This one is a classic, so I can just copy-paste the solution from Google. The more interesting point is that this is one of those cases where math doesn't correspond to reality.
In the spirit of "trying to offer concrete models and predictions" I propose you a challenge: write a bot which would consistently beat my Rob implementation over the long run enough that it would show on numerical experiments. I need some time to work on implementing it (and might disappear for a while, in which case consider this one forfeited by me).
One of the rules I propose tha...
It does work for negative bases. Representation of a number in any base is in essence a sum of base powers multiplied by coefficients. The geometric series just has all coefficients equal to 1 after the radix point (and a 1 before it, if we start addition from the 0th power).
Oh, thanks, I did not think about that! Now everything makes much more sense.
Those probabilities are multiplied by s, which makes it more complicated.
If I try running it with s being the real numbers (which is probably the most popular choice for utility measurement), the proof breaks down. If I, for example, allow negative utilities, I can rearrange the series from a divergent one into a convergent one and vice versa, trivially leading to a contradiction just from the fact that I am allowed to do weird things with infinite series, and not because of proposed axioms being contradictory.
EDIT: concisely, your axioms do n...
The correct condition for real numbers would be absolute convergence (otherwise the sum after rearrangement might become different and/or infinite) but you are right: the series rearrangement is definitely illegal here.
It actually would, as long as you reject a candidate password with probability proportional to it's relative frequency. "password" in the above example would be almost certainly rejected as it's wildly more common that one of those 1000-character passwords.
Stamp collecting (e.g. "history" and "English literature") does not count.
Interesting to see your perspective change from this post and it's comments, which suggested that history is a useful source of world models. Or am I misinterpreting past/current you?
You cannot falsify mathematics by experiment (except in the subjective Bayesian sense).
Actually, that's technically false. The statements mathematical axioms make about reality are bizarre, but they exist and are actually falsifiable.
One of the fundamental properties we want from our axiomatic systems is consistency — the fact that it does not lead to a logical contradiction. We would certainly reject our current axiomatic foundations in case we found them inconsistent.
Turns out it's possible to write a program which would halt if and only if ZFC is consis...
I would suggest E.T. Jaynes' excellent Probability Theory: The Logic of Science. While this is a book about Bayesian probability theory and it's applications, it contains a great discussion of entropy, including, e.g., why entropy "works" in thermodynamics.
I would probably move the "spoilers ahead" section before the "Japanese history" one. Unsure if it's possible to make this non-spoilery somehow, but history section is written as if to make the ending twist obvious.
One way to keep bots out is to validate real-world identities.
Currently, the actual use case is more akin to an assistant for human writers, so validating the identity would not do much good. Additionally, if the demand for real-life tethered online identities ever gets high, there would appear a market for people selling theirs. I have a friend, who has found a Chinese passport online, because a (Chinese) online game required one as part of registration data.
Use of social media as a marketing platform for small, tightly-knit communities is probably the way to largely mitigate this problem.
two her brain
This gave me the chills. I have never thought about digital brain modification safety before, although now the idea seems obvious. Wonder what else am I missing.
The meritocratic part is the best are significantly more likely to rise to the top, real world is best thought of as a stochastic place, full of imperfect information and surprises.
Being the best at content creation is not the same as being the best at YouTube: size of one's target demographic matters, the ability to self-promote matters, ability to network matters, ad-friendliness of content matters... Akin to evolution, the system does not select the *best* creators in the conventional sense of creating the best videos, being the best at writing and so o...
I agree, but my reasoning for it is different.
Given that the simulacra levels framework is fake, I care mostly about the way it pumps my intuition. For me it has more impact with less levels. Grouping everything in levels 4+ as a single thing does speed processing up, and doesn't seem to meaningfully change my conclusions.
There likely exists some context where those extra levels are useful and offer new insights, but I've not seen it yet.
Excellent as always!
Throughout the entire process it is implied that words if you specify a value and if you specify a criterion...
By training children in the traditional of adversarial competitive rhetoric...
"Can I get you a coffee?" a young quant named said.
It's really good, am waiting for the next part, keep it up!
There won't be any more harm done to Oliver by spreading the story, so, at least from utilitarian-ish point of view, the case is clear.
Right, but that’s why it’s interesting.
From a utilitarian perspective, is Oliver’s outing morally redeemed by using him as an example in journalistic ethics classes? Or would it be, if it helped reduce the incidence of future privacy invasions?
If so, then Harvey Milk is a hero in this story. He not only made Oliver into a gay hero, probably saving more than one life in the long run by advancing the cause of gay rights, but he also gave us a great example of the consequences of privacy invasion that we can use in ethics classes. A two-fer!
That doesn’t feel ...
I think your list of conditions is very restrictive; to the point at which it's really difficult to find something matching it.
Most (all?) modern
difficult
strategy games rely on some version of "game knowledge" as part of it's difficulty, expecting you to experiment with different approaches to find out what works best -- this is a core part of the game loop, something specifically designed into the game to make it more fun. This is baked into the design on a fundamental level and is extremely difficult to separate out.Combine that with the one-shot natur... (read more)