In the course of checking whether Ramez Naam's GDP figures (in Decoupling Growth From Energy and Carbon) were inflation adjusted, I came across nice looking site about visualizing economics. The graph there matches Naam's and is clearly identified as illustrating an inflation-adjusted real per-capita GDP growth rate of about 2% per year (pretty consistently over about 150 years). This led me to wonder if I am really twice as materially "well off" as I (or rather the social peer of my presentself) was in 1970. The quality of my life as a whole is hard to compare but that of my communications and entertainment infrastructure is certainly well beyond the purchasing power of any normal member of society at that time, and it is indeed of real value to be able to easily and freely connect by video link with children half a world away. Then I had about a dozen or so close friends who I engaged with regularly in person and now I have about half of that; but also, through this website, I have an audience of as many thousands of eager readers. Yeah right! Actually 5994 of those readers are spambots and the half dozen real people who have ever commented here may barely make up for the less close half dozen of my more local friends.
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David Brin cheers on The Coming Transparent World while Jaron Lanier is decidedly less enthusiastic.
Lanier's solution is to implement ownership of personal data with the right to deny access and charge whatever price we want for such access. Of course, although that might be built in to the protocols for transfer of digital information, it could never be made effective for traditional means of communication. Or can you envisage a way of preventing me from telling someone else your phone number that I just purchased?
Ophelia Benson picks up on an interesting minor point in an essay by Conor Friedesrorf where he attributes some of the goodness of his friend to the influence of religion: "Nick happens to be one of the best people I know. Even though I don’t have faith in the same things that he does, I see how his faith makes him a better person. I see how he makes the world a better place, and how his belief system drives him to do it. And whenever I think about Nick, I think to myself, you know, I disagree with the Catholic faith on a lot of particulars, but there must be nuggets of truth within it if it inspires people like Nick to be this good."
At first it seems odd that Mr Friedersorf does not give his friend full credit for his own goodness. Does he really suspect that it’s only the benign influence of the church that gives us Saint Nicholas instead of Old Nick? But actually that’s not so impossible. The same religions that enable some people to be far more evil than they would otherwise have been may also support increased goodness in others. There’s really no contradiction in that and it’s not obvious where the overall balance lies. (It may also be true that religion played an essentially positive role at some stages in our cultural development but that it no longer does so. )
The "Dear Muslimo" scorn being heaped on Richard Dawkins over his lost honey would be undeserved were it not for his own earlier mockery of Rebecca Watson's mild complaint on behalf of women who feel uncomfortable as a result of unwanted attention at a convention. Dawkins' sarcastic "Dear Muslima" letter implying that Watson and her ilk should shut up about their little issues because they’re not the biggest issues was offensive at the time, but his blindness to the parallel is quite amazing.
In Why Falsifiability, Though Flawed, Is Alluring: Part I , William M. Briggs argues that "most theories scientists hold are not falsifiable" because "if the predictions derived from a theory are probabilistic then the theory can never be falsified. This is so even if the predictions have very, very small probabilities. If the prediction (given the theory) is that X will only happen with probability ε (for those less mathematically inclined, ε is as small as you like but always > 0);, and X happens, then the theory is not falsified. Period. Practically false is (as I like to say) logically equivalent to practically a virgin."
I think he's right - at least if "falsifiable" means "provable to be false". But I don't think most scientists really demand scientific theories to be falsifiable in that sense. And many don't even try to use that word any more; they are more inclined to use a less binding word like "testable".
A theory might then be considered adequately testable if it can be used to predict that in some repeatable experiment there are outcomes of very low probability. If we see such outcomes we say that the theory fails the test (though it could in principle still be true) and we reject it (ie strongly doubt it) - at least until the relative frequency of failure events in repeated experiments falls to somewhere near the predicted probability.
There has been a lot of heated reaction recently to a couple of incidents in which people have apparently denied the sincerity of others' statements of belief.
Oprah Winfrey responded to atheist swimmer Diana Nyad's expression of wonder and awe at the universe with "Well, I don't call you an atheist then. I think if you believe in the awe and the wonder and the mystery, then that is what God is. That is what God is. It's not a bearded guy in the sky." And Richard Dawkins, in conversation with Bill Maher, declared that Barack Obama and Pope Francis must really be atheists.
Most of the commentary has been outrage expressed with less restraint than by Paul Brandeis Raushenbush in How Not to Talk About the Beliefs of Others where he at least acknowledges a positive aspect in both cases. "Oprah and Dawkins/Maher are being simultaneously arrogant and complimentary. Arrogant, in that they assume that anyone who has a similar world view as they do is secretly 'one of them'; and complimentary, in that they are saying I admire you enough to claim you for my own belief system." And "What we can learn from these two vivid examples is that we all have the right to decide how to identify ourselves in terms of religion or lack thereof. It is not for others to affix their identity upon us, or strip ours from us."
But rather than interpret these two events as someone claiming to know the content of another's mind better than they do themselves, it may be more charitable to interpret both as explaining that their own professed label is actually more inclusive than perceived by the other.
With this interpretation it is not denial or stripping of identity but just a clarification that the speaker's own identity label is intended to be more encompassing than may have been thought.
The downside, which is there of course, is that defining one's own view as a 'Big Tent' is often used as a strategy for discouraging self-identification with the alternative label. Oprah discouraging self-declared atheism, and Dawkins discouraging self-declared religious feeling, may not be denying the actual beliefs of the other but are threatening them with censure for their choice of label.. You may not be a bad kid, but if you dare to wear the wrong colours then you belong with the gang from the other side of the street.
Kloor says "it’s worth asking at this stage in his career if Lomborg is a voice of reason, a professional pot stirrer, or a trollish ankle-biter. The answer probably depends on where you sit in these debates." I suspect from his tone in Cosmos that Kloor sees it as maybe an 80,20,0 mix, but for my part I would put it as more like 30,50,20.
Maybe I should revisit the 2002 controversy in more detail to see if a deeper look would change my view.
Newcomb’s paradoxis the name usually given to the following problem. You are playing a game against another player, often called Omega, who claims to be omniscient; in particular, Omega claims to be able to predict how you will play in the game. Assume that Omega has convinced you in some way that it is, if not omniscient, at least remarkably accurate: for example, perhaps it has accurately predicted your behavior many times in the past.
Omega places before you two opaque boxes. Box A, it informs you, contains $1,000. Box B, it informs you, contains either $1,000,000 or nothing. You must decide whether to take only Box B or to take both Box A and Box B, with the following caveat: Omega filled Box B with $1,000,000 if and only if it predicted that you would take only Box B.
What do you do?
(If you haven’t heard this problem before, give it some thought first and maybe read the post linked to above before going on to my own thoughts on the matter)
To follow up on my previous post: since the occurrence of an event having low probability according to some model is not always reason to doubt the model, it becomes natural to ask what would be reason to doubt the model. And for this, some of the negative examples from last time may help to bring things into focus.
In the case of a continuously distributed variable (with absolutely continuous probability density) the probability of any particular value is zero, so whatever we observe is a case of something that had low probability in the model. (And the same applies in the case of a discrete variable with a large number of equally likely values.)
When we throw an icosahedral die, whatever face we see on top has a probability of only 1/20 of being there, but we don't take that as evidence that the die is not a fair one. However, if someone specific had correctly predicted the result then we might be more suspicious - and that is the key to how p-values work. (By "someone specific" here I mean specified in advance - not the same as having 20 people place bets and being surprised to see one of them get it right.)
Similarly, in my silly example from last time, although a value very close to the predicted mean should not cause us to doubt that that predicted mean is correct, it may well cause us to doubt that the variance is as large as proposed in the model. (And in fact there are several historical examples where data clustered too close to the predicted mean has been taken as convincing evidence of experimental malfeasance.)
So in order to be made suspicious by a low p-value it seems to be important that we know in advance what statistic we will be interested in and what kind of results we will consider significant.
This does not answer the question of exactly what that significance means or how we quantify it, but I think it does suggest that there is a valid intuition behind the idea that seeing something actually occur right after asking whether it will happen makes us doubt the claim that it actually had very low probability.
Now when I buy a lottery ticket I do wonder if I will actually win. So if I do win the jackpot I will be faced with something that to me would be a significant indication that there was more than chance involved. Of course in that case I will probably be wrong, but the probability of my being forced into that error is so small as to be of little worry to me.
Similarly, if I reject a null hypothesis model on seeing a pre-described outcome to which the model assigns a probability of p (whether it's an extreme value of some statistic or just a value very close to some specific target) then if the hypothesis is actually true I have a probability p of being wrong.
That's what the p-value really is. It's the probability that the model predicts for whatever outcome we choose to specify in advance of checking the data. Period. If we decide to reject the model on seeing that outcome then we can expect to be wrong in the fraction p of cases where the model is true.
Of course if we just choose a low probability event at random we probably won't see it and so will have nothing to conclude, so it is important to pick as our test event something that we suspect will happen more frequently than the model predicts. (This doesn't require that we necessarily have any specific alternative model in mind, but if we do then there may be more powerful methods of analysis which allow us to determine the relative likelihoods of the various models.)
Note: None of this tells us anything about the "probability that the model is true" or the "probability that our rejection is wrong" after the fact. (Noone but an extremely deluded appropriator of the label "Bayesian" would attempt to assign a probability to something that had already happened or which actually is either true or false.)
To repeat: What the p-value is is the frequency with which you can expect to be wrong (if you reject at level p) in cases where the null hypothesis is true. This is higher than the frequency with which you will actually be wrong among all the times you apply that rule, because the null hypothesis may not actually be true and none of those cases will count against you (since failure to reject something is not the same as actually accepting it and it is never factually wrong to withhold judgement - though I suppose it may often be morally wrong!).
P.S. Significance should not be confused with importance! Anyone who speaks English correctly should understand that significance refers to strength of signification - ie to the relative certainty of a conclusion - not to the importance of that conclusion. So it is possible to have a highly significant indication of a very small or unimportant effect and estimating the "size" of whatever effect is confounding the null hypothesis is something that cannot be done with the p-value alone.
P.P.S. There is of course a
significant quite large non-zero probability that a randomly chosen pronouncement from my repertoire may be flawed. So if you find something to object to here you could get lucky.
UPDATE7:45pm Oct22: See the end of my long comment below re the common practice of computing a "p-value" after the fact from an actual observation rather than from a target event specified in advance.
One of my favourite betes noires claims to have put everything wrong with P-Values under one roof.
My response started with "There’s nothing wrong with p-values any more than with Popeye. They is what they is and that’s that. To blame them for their own abuse is just a pale version of blaming any other victim."
Briggs replied saying "This odd because there are several proofs showing there just are many things wrong with them. Particularly that their use is always fallacious." which is odd itself as it seems to be just a reworking of exactly what I said, namely that what is "wrong" with them is just the (allegedly) fallacious uses that are made of them.
My comment continued with the following example:
Now the joke here is really based on Briggs mis-statement of what a p-value is. Not that there would be anything wrong with the thing he defined but it just wouldn't be properly called a p-value. And in order to criticize something (or even just the use of that thing) you need to know what it actually is. So for the enlightenment of Mr Briggs, let me explore what a p-value actually is.
What Briggs defined as a p-value is as follows: "Given the model used and the test statistic dependent on that model and given the data seen and assuming the null hypothesis (tied to a parameter) is true, the p-value is the probability of seeing a test statistic larger (in absolute value) than the one actually seen if the experiment which generated the data were run an indefinite number of future times and where the milieu of the experiment is precisely the same except where it is “randomly” different." This has a number of oddities (excessive and redundant uses of the word "given" and the inclusion of an inappropriate repetition condition being among them) but the most significant thing wrong with it is that it only applies to certain kinds of test statistic - as demonstrated by my silly example above.
A better definition might be: Given a stochastic model (which we call the null hypothesis) and a test statistic defined in terms of that model, the p-value of an observed value of that statistic is the probability in the model of having a value of the statistic which is further from the predicted mean than the observed value.
With this definition, it becomes clear that if the null hypothesis is true (ie if the model does accurately predict probabilities) then the occurrence of a low P-value implies the occurrence of an improbable event and so the logical disjunction that Briggs quotes from R A Fisher, namely "Either the null hypothesis is false, or the p-value has attained by chance an exceptionally low value" is indeed correct.
Briggs claim that this is "not a logical disjunction" is of course nonsense (any statement of the form "Either A or B" is a logical disjunction), and this one has the added virtue of being true. Of course if the observed statistic has a low p-value then the disjunction is essentially tautological, but then really so is anything else that we can be convinced of by logic.
But Briggs is right to wonder if it has any significance - or at least, if it does then what is the reason for that.
we some people consider the occurrence of a low p-value to be significant (in the common language sense rather than just by definition)? In other words, why and how should it reduce our faith in the null hypothesis?
The first thing to note is that the disjunction "Either the null hypothesis is false, or something very improbable has happened" should NOT actually do anything to reduce our faith in the null hypothesis. It certainly matters what kind of improbable thing we have seen happen. For example a meteor strike destroying New York should not cause us to doubt the hypothesis that sex and gender are not correlated - so clearly the improbable observed thing must be something that is predicted to be improbable by the null hypothesis model. But in fact, in any model with continuously distributed variables the occurrence of ANY particular exact observed value is an event of zero probability. One might hope to talk in such cases of the probability density instead, but the probability density can be changed just by re-scaling the variable, so that won't do either.
What is it about the special case of a low p-value, ie an improbably large deviation from the expected value of a variable, that reduces our faith in the null hypothesis?
...to be continued
Clean Slate? Asking Bjorn Lomborg To Help Figure Out 'The Most Pressing Issue Facing' America Is Like... | ThinkProgressOctober 7th, 2013
one of the most pressing issues facing America is the media’s over-reliance on widely-debunked, non-credible sources, which poisons the atmosphere for a genuine discussion of our biggest problems and their best solutions
In Whos Afraid of Peer Review? 'Science' magazine publishes a purported bit of "research" into the failings of open access journals which starts by selecting those of less repute and fails to do any comparable study of the population (of traditional subscription-based journals) against which the open access journals are being compared. This has generated a lot of negative reaction, including a tongue-in-cheek suggestion that the writer who submitted to 'Science' his story of a "sting" on the open access journals was actually engaged in a sting on the 'Science' magazine itself.
Tunisia’s Islamist party to step down after talks - The Hindu. If only the Egyptians had waited to see how the Tunisians do it they might have been a lot better off than they are now. ...more »
Richard V. Reeves, in The Glass-Floor Problem - NYTimes.com concludes with:
This is delicate territory. Nobody wants parents to stop trying hard for their children. But nor do we want a society in which the social market is rigged in favor of those born into affluence. If we want a competitive economy and an open society, we need the best and brightest to succeed. This means some of the children of the affluent must fail.
Well actually, I do want parents whose wealth and position gives their children an advantage over mine to "stop trying hard for their children". Of course I do! And I want any person or child whose natural talent exceeds mine or my children's to be hobbled by whatever encumbrances can ensure the eventual success of me and mine. But that doesn't make it right.
So when Reeves earlier on bleats out that:
Even the most liberal parents are unlikely to be comfortable with the idea that their own children should fall down the scale in the name of making room for a smarter kid from a poorer home.They invest large amounts of economic, social and cultural capital to keep their own children high up the social scale. As they should: there is nothing wrong with parents doing the best by their children.
I have to reply "Oh yeah? Sez who?" Of course I may do it myself (to the best of my own meagre ability), but that doesn't make it admirable or even not wrong. Perhaps there is something wrong with valuing our own children more highly than others'. And perhaps the world would be better if we each sought out the most admirable of our peers and devoted our lives to increasing their fertility at the expense of our own.
But this is too complicated for me. So bring on Sam Harris's "scientific" total well being accumulator to tell us what it is that we really ought to do.
Ever since whatever happened at the Obama/Putin meeting at the G10 it's been an amazing time for optimism regarding the future of humanity. But of course the election of Hassan Rohani actually precedes that meeting.
Ophelia Benson. quoting Stephen Pinker in paraphrase of Stephen Jay Gould to the effect that "Science gets the empirical universe; religion gets the questions of moral meaning and value" struck me as identifying the key point on which Gould's idea of “non-overlapping magisteria” is often misinterpreted.
It is true that science "gets" the empirical universe because science is defined as including anything useful that can be said about the empirical universe (whether or not it comes from "peer reviewed" journals or people with academic appointments in specific disciplines at specially annointed institutions). But religion does not "get" the questions of moral meaning and value - it may be restricted to those questions but it doesn't own them. The fields of ethics and aesthetics "get" these questions by definition in the same sense as science "gets" the empirical world, but anyone who wants to is empowered to participate. To compare science and religion is like comparing values and academic departments or journals. (Or dogs and vegetables, or animals and weeds)
Sam Harris has issued a "public challenge" to those who think his book is silly.
To wit: "Anyone who believes that my case for a scientific understanding of morality is mistaken is invited to prove it in 1,000 words or less. (You must refute the central argument of the book—not peripheral issues.) The best response will be published on this website, and its author will receive $1,000. If any essay actually persuades me, however, its author will receive $10,000, and I will publicly recant my view."
Fujitsu and MIT Announce First-of-its-kind Breakthrough Higher Education Learning Platform ~ Stephen's WebJuly 12th, 2013
He (at DLORN) and I (at the CMR site) have both proposed something similar back in the first decade of the millennium, but this second decade team have added some interesting new wrinkles. I don't know if there's anything new in a "navigation technology, which can organize massive online learning materials into multi-layer topics" "with multi-layer topics having different granularity based on a probabilistic topic model (Latent Dirichlet Allocation) framework", but their "students’ learning behavior simulation based on an advanced probabilistic learner model",via a "stochastic, Bayesian Knowledge Tracing algorithm" may be something new. And the "implicit rating system for learning materials, in which learning nuggets are not rated by learners directly, and instead their ratings are calculated based on learning outcome of learners" may also be a good idea so long as there is some user input into the identification and prioritization of learner outcomes.(Otherwise it seems little different from the choosing one side in the perennial debate about whether instructors and their materials should be rated more on the basis of student opinion surveys or on exam performance.)
Anyhow, it will be interesting to see what the product actually looks like when it finally comes out of the box.