William M. Briggs

Statistician to the Stars!

Author: Briggs (page 151 of 407)

The Probability Of Nonsense In Science: Complexity & Verification

This is a work in progress, and today is a busy day. This is just for fun and for you to play with.

The more complex the field of study, the more likely that any result, finding, or theory in that field is wrong. I am only considering science, i.e. that which explains and is subject to empirical verification. I exclude fields such as ethics, morality, philosophy which are fields that tell us “that empirical verification is a good”, and other statements which are not subject to verification.

There are three broad areas, or groupings, of complexity in science. Not uncoincidentally, this laddering also correlates with the fields’ dependence on statistics for evidence, from most to least. The groups are also, from least to most, though somewhat more loosely, ordered by connections with observation via prediction.

  1. Behavioral: Education, Sociology, Politics, Psychology.
  2. Biological: Economics, Evolutionary Psychology, Psychiatry, Neurology, Medicine (doctoring), Genetics
  3. Physical: Climatology, Meteorology, Chemistry, Physics, Engineering, Mathematics

The demarcations between these areas are not abrupt, nor is the ordering within each group anything more than a crude, but still somewhat useful, guide.

Some explanation is needed. Why is Physics, the mother of all sciences, the field requiring the biggest brains, listed near the end and is therefore one of the least complex fields? Because Physics is not complicated in the sense I mean complex.

Physicists study the fundamental properties of the universe, it’s true, but it’s also so that these basics are not complex. They are amazingly difficult to comprehend, yes, but not convoluted. If under your consideration is just the interaction between two electrons, themselves encased in forces that are as precisely defined as possible, then your world view is narrow, constrained, and quite simple. It might be true, and usually is, that this simplicity is difficult to express and to understand, and that to reach this bare pinnacle requires years dedicated to its singular purpose, but that does not render the process under consideration complex in the sense we use that word here. We are only talking about what electron A and electron B will do in strikingly limited terms.

Too, the physicist has ample opportunity to verify his theories. If, under the circumstances he explicated, electron A goes where he predicted it to go, and electron B behaves as he expected, then the physicist has learned that the theory he entertained is probably right—but only probably. But if the particles go their own way, then the physicist must also venture down a new path and toss out or modify his theory. This deep, lasting, and intimate connection with observation is what keep physics honest.

Engineering tops physics because this field is defined as all sciences exposed completely and continuously to reality. It is less complex in the sense that the rules which govern the field are more worked out in advance, but it is also more complex in that engineering implies building something for human use, and human behavior is the most difficult thing of all to predict. More on that in a moment.

I cheated by putting Mathematics as the field which gives us our most certain beliefs, because math is not a science. Mathematics more properly belongs to philosophy. If you think not, and since science is that which is testable, try empirically verifying that, say, a triangle’s interior angles sum to 180o or that, in reality, (if I may abuse the notation) alpeh0 < aleph1, which is to say one kind of infinity is larger than another kind of infinity. Report back to me when you reach aleph0. Math is used in science and openly, but so are the other areas of philosophy and ethics, etc. It is just that these other branches more typically remain unacknowledged.

Now, a chemist can tell us with great precision what will happen when Na hits H2O, but his, or any other scientist’s, ability to predict what John Smith (43) of Cleveland, OH will have for lunch next week Thursday is no better than any unschooled layman. The conceit of the sociologist is to abandon the question and substitute for it one which he believes he can answer: what will the “average person” will eat for lunch in OH. Enter statistics, through which, perhaps (but only perhaps), the sociologist can build a model which will do slightly better than just guessing. And only do better if the prediction is not too far out into the future. Or where the circumstances do not change, it being more of less a mystery what those circumstances are.

Plus the sociologist probably won’t bother to verify his model: won’t use it to make actual predictions. And neither will most of the educationists, psychologists, and so forth. Of course I do not mean all sociologists etc. nor do I claim the fields are sterile.

It is just that the probability of speaking nonsense is greater the more complex the field and the further that field is from empirical verification. Which is why climatology, which is simpler than meteorology, ranks below that field because climatology is further from empirical verification.

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Note: I tried everything I could think of to get the HTML to properly render the Hebrew letter aleph: render it it would, but it would put it in strange places, nowhere near where I put it, and super- or sub-scripted at random.

Sleeping Beauty Probability Problem

Update This has been moved up from its original 29 Feb 2012 date on 23 March 2012 to allow additional comments.

Update This has been moved up from its original 29 Feb 2012 date again on 21 May 2012 to allow additional comments.

sleeping beautyAre you awake? I copied and pasted this direct from Wikipedia (I know, I know):

Sleeping Beauty volunteers to undergo the following experiment and is told all of the following details. On Sunday she is put to sleep. A fair coin is then tossed to determine which experimental procedure is undertaken. If the coin comes up heads, Beauty is awakened and interviewed on Monday, and then the experiment ends. If the coin comes up tails, she is awakened and interviewed on Monday and Tuesday. But when she is put to sleep again on Monday, she is given a dose of an amnesia-inducing drug that ensures she cannot remember her previous awakening. In this case, the experiment ends after she is interviewed on Tuesday.

Any time Sleeping beauty is awakened and interviewed, she is asked, “What is your credence now for the proposition that the coin landed heads?”

I interpret credence as probability. Think about the answer before reading further.

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Suppose she is awakened on Monday. She knows it is Monday, she knows that if the coin landed heads she would have been awakened. She also knows that if the coin landed tails she would have been awakened. In other words, regardless of the way the coin landed, she will be awakened on Monday.

Formally, her evidence is C = “A coin with two sides, labeled head and tail, will be flipped and only one side can show”, M = “It is Monday”, and also E = “The details of the experimental protocol.” She is asked to compute (or form):

     Pr( head | C & E & M) = 1/2.

Since knowledge that it is Monday and of the experimental protocol tells her she will be awakened on Monday no matter what happens with the coin, the probability is numerically (but not logically) equivalent to Pr( H | C ), which everybody agrees is 1/2.

Now suppose T = “it is Tuesday.” Here the problem becomes ambiguous (at least, as Wikipedia has it). If the coin originally came up heads she will have been awakened Monday. There are then no words, i.e. no evidence, which tells us what she does Monday night into Tuesday. Perhaps she stays awake all Monday night celebrating Barack Obama’s defeat (we’re imagining this experiment taking place in November). Therefore, when it is Tuesday she will know that she was awakened Monday, because she will have recalled all the events which took place since her awakening; in particular, she will know she was not awakened on Tuesday.

So if queried on Tuesday about the coin she will have a different response than when she was queried on Monday. That is,

     Pr( head | C & E & T & Up all night with memories) = 1,

and this will be the same if she goes to sleep on Monday but remembers being awakened on Monday, because of course she was not administered any drugs. So really all we need is her memory of what happened on Monday; she needn’t stay awake. That is,

     Pr( head | C & E & T & Memories of Monday) = 1.

But if it is Tuesday and she is awakened and she hasn’t any memory of what happened on Monday, then

     Pr( head | C & E & T & No memories of M ) = 0,

because she knows she was awakened on Tuesday and she knows she has no memory of Monday, whereas she would have those memories if the coin was heads. So she knows the coin was tails.

Since all that was too easy, I suspect the problem has been stated poorly. More evidence for this is that the Wikipedia discussion of other authors’ solutions appear to suggest that Sleeping Beauty has no idea what day it is. If that is so, her only knowledge is that she was awakened. Actually, not quite. She still knows that the day(s) she is awakened will be one of two, M or T.

We have already worked out the solutions conditional on her knowing the day. So we need to fit in the uncertainty in the day. She knows (and remember, we’re going on her information)

     Pr( M | C & E ) = Pr( T | C & E ) = 1/2.

Here we don’t need memories, because if it’s M there aren’t any to be had, and if it’s T they’ve been wiped away (this is implicit in our new understanding of E). So what she wants is

     Pr( head | C & E & M ) x Pr( M | C & E) + Pr( head | C & E & T ) x Pr( T | C & E) = 1/4.

Now Pr( head | C & E & M ) = 1/2 since if she assumes it is Monday, she knows by C & E that she will be awakened no matter what, just as above. But, Pr( head | C & E & T ) is different, since if she assumes it is Tuesday she knows that the coin must have been tails, so Pr( head | C & E & T ) = 0.

This is different than the other solutions, which were 1/3 and 1/2, so it’s possible that I have misinterpreted the experiment or that I have made a bone-headed mistake. What do you think?

The Implications Of Moral Insignificance

In her piece “In Praise of Insignificance” in Scientific American, Jennifer Ouellette says,

If one embraces an atheist worldview, it necessarily requires embracing, even celebrating, one’s insignificance. It’s a tall order, I know, when one is accustomed to being the center of attention. The universe existed in all its vastness before I was born, and it will exist and continue to evolve after I am gone. But knowing that doesn’t make me feel bleak or hopeless. I find it strangely comforting.

A cockroach is insignificant even to the extent that squashing it, i.e. depriving it of its life in an expedient and, for the roach anyway, awful manner, cannot be considered wrong. It can even be said to be good or necessary for the “greater good.” What, after all, is the life of one small bug when compared with the wellbeing of even one human being?

But then if that human being has admitted herself to be insignificant, to have willingly placed herself on the same moral and ontological plane as a filthy bug, why is her good to be placed above the roach’s? Don’t just pass this sentence by with a quick nod. Insignificant is a strong word, none stronger. Taken at its definition—which is what we are doing here, to see where it leads us—means meaningless, valueless, of no use, disposable.

Now it might appear to imply that if all accepted that they were insignificant, all would be allowed; that is, any behavior would be acceptable. But this is false; indeed, the opposite is true. No behavior would be allowed or acceptable.

When we examine questions of morality we quite naturally think about what our behavior would do or mean to somebody else; that is, we imagine ourselves acting in some way and then in some person or persons reacting. If we decided that “we are insignificant” then it appears that if I wanted to (say) hit you upside the head with a baseball bat, then that would be fine because your life is insignificant. (Richard Dawkins, for instance, famously admits that rape isn’t “wrong” in this sense.)

That is true in a weak sense, but we stepped over the hard part. The problem is that I have already admitted that I am insignificant too, which entails that I have no justification for my initial act. My pleasure is nothing, even the physical exercise gained in hefting the wood is meaningless. If I realize this, then I cannot justify to myself why I should act. Not just in swinging the bat, but for walking, talking, eating, any activity at all that isn’t automatic (eating is not automatic; it implies you have judged that to feed yourself is good, which admits significance). If I am to be logically consistent, then I must remain entirely impotent and always motionless.

You’ll notice that in these arguments, I sling around the word I, as if I have deduced that I exist, and the same for you. But if I exist, if I am aware of me and that there is a me, then this automatically implies significance (I at least know there is the rational creature me). It remains to be seen what are the limits and implications of this significance, of course, but that there is some significance, that there is an absence of insignificance, necessarily follows.

So it cannot be that we are insignificant nor can we imagine ourselves insignificant (we can say it, but we’re always either lying or deluded), though it is easy, as history has repeatedly proven, to think the other guy insignificant. Ouellette does not really believe she is insignificant, despite her claims. She informs us that she tells her husband daily that she loves him, a very nice thing. But it is only nice if she admits to being significant, which we have seen she must do. Of course, we haven’t proven that because are are significant saying “I love you” to somebody (and meaning it) is nice, though all of us believe it (and it can be proven).

Ouellette’s first argument is right, though: “If one embraces an atheist worldview, it necessarily requires embracing, even celebrating, one’s insignificance.” I mean her argument is right if you strike out the “celebrating” bit, for to celebrate and to enjoy a celebration presupposes significance. A real world running on atheist lines would contain no celebrations, indeed nothing but non-moving bodies, frozen in realization that nothing—as in no thing—they did matters or is justified.

Another Academic Says Climate Skeptics Criminals Against Humanity And Other Name Calling

Donald BrownIn a talk at some “sustainability” something-or-other seminar—one this is sure: we’re not going to soon run out of climate conclaves—academic Donald Brown told his audience (25 min. mark) that the people who are not as afraid as he that the world will soon end are committing crimes against humanity. If Brown is right, this put yours truly well into the company of such noted transgressors as Mao, Stalin, Pot and other socialist dictators.

Or maybe Brown hadn’t meant that level of heinousness and instead envisioned lesser culprits, such as the guy who invented the car alarm or whoever it was that thought up the Sony Walkman (which has morphed into our ubiquitous present-day thinking suppression devices).

Anyway, here’s what happened.

Marc Morano at Climate Depot placed Brown’s image and his email in earlier articles on that site in posts which outlined Brown’s views on this and that climate topic. Brown thought that showing his publicly available email and head shot—which are not hidden and are trivially easy to find at Penn State—represented “intimidation.”

This, so Brown claims, led to him receiving emails some of which were scatological and others which threatened death. I unfortunately believe him. There are a lot of knuckleheads out there and the (pseudo) anonymity of the internet fills some with a pathetic false bravery. I wish these foolish souls would think better.

Of course, Morano himself hauls in plenty of scathing missives daily, as do others who run blogs expressing doubt that we should let government “solve” climate change.

Your truly hasn’t received any death threats, but I get plenty of things like this one from yesterday, “I know you are an extreme political right winger, but now you’ve become a ringleader of a hate group.” Ringleader—I presume my interlocutor did not mean in the Tolkienian sense—is a promotion of sorts, up from Lone Wolf. But I’ve still got a ways to go before I reach Mastermind.

Brown, who was dressed a priest (without the collar), early in his talk said that skepticism about climate change should be “encouraged.” But he wants it separated from “disinformation,” which he defines as that which departs from the “consensus.” Brown’s position is thus like that of the dictatorship which claims voting is every citizen’s right, but which produces ballots on which there is only one candidate.

He says that those who speak against the consensus are engaged in an organized “campaign” funded by oil companies and “right wing” groups. This might be true, but none of those funds have managed to trickle down my way. But now that I’m a Ringleader, perhaps I can expect a raise in pay?

Somehow Brown forgot to mention that the funding to spread the “climate catastrophe” message dwarfs, by at least one, possibly two, maybe even three, orders of magnitude any monies skeptics receive. Nearly every government dumps tens and tens and more tens of millions each year on the “problem,” a good chunk of which ends up in the pockets of people like Donald Brown. And then there’s the money sucked in and pumped out by Greenpeace, the Environmental Defense Fund, Sierra-blah-blah-blah. Skeptics run on alms, consensus members and their hangers on are clothed in gold.

The whole of his talk is to convince that a conspiracy exists to gull the public. In a separate work he hints of dark rooms and speaks of a “climate change disinformation campaign.” He claims skeptics “are guilty of exacerbating risks to our collective well-being and of undermining society.”

He claims the “moral outrage” caused by skeptics “should motivate a movement at least as ferocious as the Occupy Wallstreet movement.” And in his talk he says that climate skeptics are guilty of a “new crime against humanity. [Skepticism] is really evil stuff. It is nasty.”

Donald Brown is not the first to croak out this tune. He accepts the “consensus” as a given, as unquestionable in its outline, its warnings certain. But he is not simply filled with wonder that others doubt his faith, which would be natural. He is instead outraged. He wants action. He walks up to the line, over which is to ask that government silence his enemies, and hovers there. He would cross that line if he could be sure of support from enough of his colleagues.

All Forecasts, Predictions, & Prophecies Are Contingent

Yesterday I made the point that Jim Hansen’s latest threat of doom was a conditional one. I also said that there was nothing wrong with this. And there isn’t. Nothing wrong with the structure of a contingent—which is to say conditional—prediction. I hinted, in a way, that better predictions were not so conditional. This is true in a sense which I did not include in my essay, because in fact, all predictions are contingent. And so is everything else.

To clarify, but briefly.

Any prediction is a statement that, given some set of information or evidence or revelation or knowledge, that “Y will happen” or that “There is a P% probability Y will happen.” You cannot just step onto to the street and announce, “The end is nigh” without there being some shared, or assumed shared, conditional set of knowledge which your listeners hold.

It also goes without saying that your audience must understand what “end” and “nigh” mean. If your prediction fails, there are more way to escape responsibility by disputing what you really meant by “end” than there are Democrats in San Francisco.

The knowledge of word (or mathematical or whatever) definitions are thus also part of the conditional knowledge which is at least tacitly assumed or sometimes explicitly given. For example, Hansen said (I’m paraphrasing) “If Canada sells it oil and the USA doesn’t do something, the Four Horseman begin their ride.” The conditionality is explicit in part, and stated boldly—in part.

The parts that are missing are where the trouble arises. Firstly, Hansen does not make it clear what “USA doing something” means. What exactly is “something”? This kind of seemingly precise vagueness is the trade secret of five-dollar psychics who pass off cold readings as genuine paranormal knowledge. Hansen’s prediction is in the form of, “I see a U. Maybe with an S or an A. Does that mean anything to you?” He lets his listeners fill in the meaning, which invariably is done in the most charitable way.

Secondly, Hansen’s unleashing of the apocalypse (this is his word) is blurry. He mentions food prices rising to “unprecedented” levels. What does that mean exactly? He also says that we’ll see more bad weather. Well, given inflation and the assumption that we’ve seen bad weather in the past, neither of these events can be said to be rare. Lack of specificity plagues his predictions of plague.

Now I suggested yesterday, in poor, even rotten, language that Hansen should have issued his prognostication in unconditional form. Since this is a logical impossibility, I was as wrong as can be. What I meant, but was too lazy or stupid to clarify, is that he should make his conditions explicit, testable, verifiable, measurable, real.

As should anybody who makes a prediction. This includes people who try to pass off failed predictions as “scenarios.” A scenario is a prediction like any other, but usually issued as a cluster. “If A happens, then Y_A will happen”, “If B happens, then Y_B will happen”, and so on. Well, in the end, if it clear what time horizon is meant, we look to see which of Y_A, Y_B, … actually occurred. Suppose Y_R did. We then look to see if R happened, too. If so, then we have a good prediction. If instead B happened, the forecast is a bust.

In other words, you cannot issue any statement without there being something to back it up. This is the conditionality. Regular readers met this earlier when we spoke of statements of knowledge and of probability. There are no unconditional statements of either, except in one sense, to be explained in a moment.

Above I gave a conditional statement of probability “There is a P% probability Y will happen” but left off the conditions though said they were always there. That means the true statement is really “Given X, there is a P% probability Y will happen.” If you doubt this, I challenge you to discover even one instance of a probability which is not conditional, which does not require a set of evidence or knowledge for its definition. (JH, this one’s for you.)

And the same with knowledge. As we’ve used a hundred times, we know it is true that “Socrates is mortal” only because we accepted the conditions that “All men are mortal. And Socrates is a man.” And because we knew that arguments like this lead to true conclusions. (We also knew what the words meant.)

But how did we know about arguments like this? Well, we just knew. There are some basic, or base truths, which we just know are true. I have earlier said that even these are conditional, and this is so. We say we know that “If x = y then y = x” is true conditional on our intuition.

Our friend Luis objected to the use of the word “intuition.” I can see his point. Let us instead say that all men have these basic truths written in their hearts.

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