William M. Briggs

Statistician to the Stars!

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More On Randomness

Anything could be at the end of this lane!

Anything could be at the end of this lane!

I took this picture yesterday (using my mom’s phone: mine can’t offload photos) at the start of the cul de sac, at the bottom of which lies the first job I ever had: washing dishes in a nursing home (in which my uncle now resides).

Who could have guessed I would have moved from there to where I am now?

Certainly not one of my old teachers, who was shocked when told by my parents of my career (such as it is). The teacher was cornered in the back of a grocery store. This same teacher would have taken in stride news that I was just coming up for parole.

This highlights one of the shades of meaning of random. It’s when an event was not just unpredictable, but that it happened almost against the evidence. “That was random,” we say.

This usage acknowledges random is a measure of information, which at least removes some of the mysticism the words has in scientific and mathematical contexts. But maybe not all. We sometimes almost have the idea Nature is working against our desires, though Her actions in this regard are weak.

Mysticism? Did you know that in classic statistical formula if some numbers aren’t imbued—nobody knows how—with randomness, the formula won’t work?

Oh, the formulas will still spit out answers, of course, but you won’t be allowed to use those answers. It’s kind of like sitting down to a feast and discovering the witch doctor didn’t give his prior blessing to the animals cooked, and therefore nobody is allowed to eat.

It’s not just frequentists who believe in magic, but most Bayesians, too. Whenever you hear somebody say, “X is randomly distributed normally” (or some other thing), you have heard an incantation. There is nothing in the world that makes a number “randomly normal” (or whatever). It’s only that our understanding might be quantified by a normal (or whatever).

How X knows it’s supposed to be normal (or whatever) is never specified either. It’s here that the Deadly Sin of Reification mixes with the mysticism of randomness. The formulas become realer than reality, and it’s the power of mysticism which does the deed. But again, nobody knows how. It’s a question which is never asked.

When I’m done with this mini-vacation, I’ll set out more specifically all the shades of meaning of random.

Up North At The Lake, With No Phone, Computer, TV

Another day at the office.

Chris doesn’t have a computer. And he doesn’t want one. He’s my age and works at the Dobleski Marina as a mechanic. He has a house, family, couple of cars, and of course lives near the lake.

The shop has a few dozen men, and one day the boss switched to a new company to handle everybody’s benefits. This required the men to go on line with their “pass codes” and enter information. One by one the men came into the office to do so.

The first started pecking around with one finger, asking for help with the mouse. The boss asked, “What’s the matter. Don’t you know how to use a computer?”

“Nope. Don’t have one.”

Same thing with Chris—and with about a third of the men. No computer, no internet access at home. Why? They see no need for it. Chris said, “It’s a waste of time.” Costs too much, too.

“My boss said, ‘Why don’t you have the internet. It’s great!’ and he proceeded to show me some thing that took an hour to get it to work. Why do I need that?”

Chris also doesn’t have cable television. He had it once, but the company started raising the rates, raised them some more, and then raised them again. Chris called it quits. Said TV is a waste of time anyway. But to please his daughter he bought an antenna. He now gets five channels, and sometimes six if the weather is just right.

You probably already know, but Chris doesn’t have a smart phone, either. And he isn’t alone. Many people up here just don’t see the need.

Now the lake Chris lives on is a big one and the town is one with a lot of rich folks from down south who have summer mansions, in which they spend a week or four a year. These people aren’t any different than anybody else and like to play, but having orders of magnitude more money than most, their toys are shinier—and most of them float.

It’s Chris’s job to fix these toys. Last week, he had to fetch a 59-foot beauty from point A and drive it to point B, about thirty-some miles away. He drove the work boat over to get it (and towed it back), and took along Mitch who spends most of his days inside. Mitch is a detailer.

Now the person who owned that big boat also drives from A to B every now and then. That trip, a popular route, is the reason he bought the boat, and is why he pays for its docking and maintenance. Since the maintenance is expert, it isn’t cheap. Would you know how to fix the motor of one of these things?

The men at the marina are outside most of the summer, and even into the fall and part of the winter. They try to get the inside work done before January, because the building which houses the boats isn’t heated. And boy can it get cold up here, with plenty of snow.

Another fellow bought a fancy new boat and thought something was funny with it, so he called the marina to have somebody take a look at it. Chris was dispatched. Back out onto the lake, the sun shining, the wind just so. Tigers on the radio.

The man was waiting. He said, “My boat smells like water.”

Chris knew enough not to laugh and tried to get the man to explain more carefully what he meant. Well, he meant what he said. When he went below decks, he thought he smelled water.

Now it was costing plenty for Chris to come down and inspect the boat, and to give the man the feeling that he was getting something for his money, Chris told him that boats tend to smell that way, but if he liked he could run his dehumidifier once in a while.

This advice greatly cheered the man, who paid the hefty fee, and Chris got back into the work boat heading north. The sun was still shining.

Chris is gratefully these rich folk want to play in his back yard. If they weren’t there, the 59-foot boats wouldn’t be there, a source of beauty would go missing, and far fewer people up north could make a living. And although Yours Truly didn’t talk with any, it’s a good bet these rich folks are glad people like Chris are around, too.

The names have all been changed, but the story hasn’t.

Comprehensive List Of Catholic Dogmas Refuted By Science

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In other light reading, see also the leaflet: Famous Jewish Sports Legends.

Summary Against Modern Thought: God Is Not A Body. Update

This may be proved in three ways. The first...

This may be proved in three ways. The first…

See the first post in this series for an explanation and guide of our tour of Summa Contra Gentiles. All posts are under the category SAMT.

Previous post.

Update I haven’t any idea how I did it, but I somehow turned off comments on this post. They are now restored.

The conception of what God is went downhill after Aquinas. And, dear atheist reader, shouldn’t you know what it is you claim to reject? New Atheists in particular have been shockingly Would it surprise you to learn that the Church rejects the same gods, or same weakened conception of God, you reject? This chapter, which is broken over multiple posts, shows that God is not a physical body, that God is not a creature.

Chapter 20: That God is not a body

1 FROM the foregoing we are also able to prove that God is not a body.

2 For since every body is a continuous substance, it is composite and has parts. Now God is not composite, as we have shown.[1] Therefore He is not a body.

3 Further. Every quantitative substance is somehow in potentiality: for that which is continuous is potentially divisible to infinity; and number can be infinitely augmented.i Now every body is a quantitative substance. Therefore every body is in potentiality. But God is not in potentiality, but is pure act, as shown above.[2]ii Therefore God is not a body.

4 Again. If God were a body, He would needs be a physical body, for a mathematical body does not exist by itself, as the Philosopher proves,[3] since dimensions are accidents.iii Now He is not a physical body; for He is immovable, as we have proved,[4] and every physical body is movable. Therefore God is not a body.

5 Moreover. Every body is finite, which is proved in regard both to spherical and to rectilinear bodies in 1 Coeli et Mundi.[5] Now we are able by our intellect and imagination to soar above any finite body. Wherefore, if God were a body, our intellect and imagination would be able to think of something greater than God: and thus God would not exceed our intellect: which is inadmissible. Therefore He is not a body.iv

6 Furthermore. Intellective knowledge is more certain than sensitive. Now among natural things we find some that are objects of sense: therefore there are also some that are objects of intellect. But the order of powers is according to the order of objects, in the same way as their distinction. Therefore above all sensible objects there is an intelligible object existing in natural things. But every body that exists among things is sensible. Therefore above all bodies it is possible to find something more excellent. Wherefore if God were a body, He would not be the first and supreme being.v

7 Again. A living thing is more excellent than any body devoid of life. Now the life of a living body is more excellent than that body, since thereby it excels all other bodies. Therefore that which is excelled by nothing, is not a body. But such is God. Therefore He is not a body.vi

8 Moreover. We find the philosophers proving the same conclusion by arguments[6] based on the eternity of movement, as follows. In all everlasting movement the first mover must needs not be moved, neither per se nor accidentally, as we have proved above.[7] Now the body of the heavens is moved in a circle with an everlasting movement. Therefore its first mover is not moved, neither per se nor accidentally. Now no body causes local movement unless itself be moved, because moved and mover must be simultaneous; and thus the body that causes movement must be itself moved, in order to be simultaneous with the body that is moved. Moreover no power in a body causes movement except it be moved accidentally; since, when the body is moved, the power of that body is moved accidentally. Therefore the first mover of the heavens is neither a body nor a power residing in a body. Now that to which the movement of the heavens is ultimately reduced as to the first immovable mover, is God. Therefore God is not a body.vii

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iWho knew St Thomas was familiar with analysis! (The first argument above I left uncommented, it being obviously sound.)

iiDon’t forget to review what these terms mean, particularly act and potential. Don’t assume you know how St Thomas and Aristotle meant them.

iiiFrom The Philosopher, lovely as always (yes, but was this peer-reviewed?):

A question connected with these is whether numbers and bodies and planes and points are substances of a kind, or not. If they are not, it baffles us to say what being is and what the substances of things are. For modifications and movements and relations and dispositions and ratios do not seem to indicate the substance of anything; for all are predicated of a subject, and none is a ‘this’…

But if this is admitted, that lines and points are substance more than bodies, but we do not see to what sort of bodies these could belong (for they cannot be in perceptible bodies), there can be no substance. Further, these are all evidently divisions of body, one in breadth, another in depth, another in length…

iv(Heaven and Earth.) St Anselm, anyone? Don’t let’s forget that Contra Gentiles came before Summa Theologica in Aquina’s thinking. See 2c here.

vAs a sound argument, this bullet is shaky, assuming what it seeks to prove, it seems to me, at the end, in much the same way as the ontological argument fails. But, the first premise is certainly true: “Intellective knowledge is more certain than sensitive.” One can mistake cold for hot, but not that you know. This is why many also say mathematical knowledge is supreme.

viThis one is too telegraphic, maybe. We have “Therefore that which is excelled by nothing, is not a body”, which we can grant. But angels are not bodies, and we haven’t yet shown that these are lesser than God. Certainly, this argument is weak. But. If, as he does, St Thomas offers two dozen arguments for a proposition, and one or two fail, this does not imply the others fail, which (as shown) they do not. Do not be intellectually lazy and ponder only that which is admitted to fail. And anyway, like the ontological argument, much can be learned from the failures of these arguments.

viiIf you key in on the heavens moving circularly bit, you’ll be missing the point. This argument, which does not for a mote rely on that contention, is really no different than the proof of God’s existence because in order for anything to move—here and now—we need a first unmoved mover. Go back and read Chapter 13, as St Thomas himself commands in the footnotes.

[1] Ch. xviii.
[2] Ch. xvi.
[3] 2 Metaph. v. [This is a typo; it should be 3 Metaph. v.]
[4] Ch. xiii.
[5] Ch. v. seqq.
[6] 7 and 8 Phys. See above, ch. xiii.
[7] Ch. xiii.

[6] 7 and 8 Phys. See above, ch. xiii.

Yet Another Author Claims Statistically Significant Temperature Change. 99.999%!

Statistical significance is even uglier than this painting, which is pretty darn ugly.

Statistical significance is even uglier than this painting, which is pretty darn ugly.

Update 6 Sep 2014 Yet another another another study has claimed “statistical significance”, this one by Philip Kokica, Steven Crimpc, and Mark Howdend. “A probabilistic analysis of human influence on recent record global mean temperature changes.” I haven’t had a chance to look at that study in any detail yet, but I imagine many of the remarks below hold. If I find the new paper needs a new post, I’ll do one in the future.

Update 12 Apr 2014 This originally ran 28 May 2013, but given Shaun Lovejoy’s latest effort in Climate Dynamics to square the statistical circle, it’s necessary to reissue. See the Lovejoy update at the bottom.

My Personal Consensus

I, a professional statistician, PhD certified from one of the top universities in the land—nay, the world—a man of over twenty years hard-bitten numerical experience, a published researcher in the very Journal of Climate, have determined that global temperatures have significantly declined.

You read that right: what has gone up has come back down, and significantly. Statistically significantly. Temperatures, he said again, have plunged significantly.

This is so important a scientific result that it bears repeating. And there is another reason for a recapitulation: I don’t believe that you believe me. There may be a few of you who are suspicious that old Briggs, well known for his internet hilarity, might be trying to pull a fast one. I neither josh nor jest.

Anyway, it is true. Global warming, by dint of a wee p-value, has been refuted.

Which is to say that according to my real, genuine, mathematically legitimate, scientifically fabricated scientific statistical scientific model (calculated on a computer), I was able to produce statistical significance and reject the “null” hypothesis of no cooling. Therefore there has been cooling. And since cooling is the opposite of warming, there is no more global warming. Quod ipso facto. Or something.

I was led to this result because many (many) readers alerted me to a fellow named Lord Donoughue, who asked Parliament a question which produced the answer that “the temperature rise since about 1880 is statistically significant.” Is this right?

Not according to my model. So who’s model, the Met Office’s or mine, is right?

Well, that’s the beauty of statistics. Neither model has to be right; plus, anybody can create their own.

Statistical model

Here’s the recipe. Grab, off the shelf or concoct your own with sweat and integrals, a model. The more scientific sounding the better. Walk into a party with “Autoregressive heteroscedastic GARCH process” or “Coupled GCM with Kalman-filtering cloud parameterization” on your lips and you simply cannot fail to be a hit.

Don’t despair of finding a model. They are as dollars to a bureaucracy: they are infinite! Thing is, all models, as long as they are not fully deterministic, have some uncertainty in them. This uncertainty is parameterized by a lot of knobs and switches which can be throw into any number of configurations.

Statistical “significance” works by tossing some data at your model and hoping that, via one of a multitude of mathematical incantations, one of these many parameters turns out to be associated with a wee p-value (defined as less than the magic number; only adepts know this figure, so if you don’t already have it, I cannot tell you).

If you don’t get a wee p-value the first time, you keep the model but change the incantation. There are several, which practically guarantees you’ll find joy. Statisticians call this process “hypothesis testing.” But you can think of it as providing “proof” that your hypothesis is true.

Funny thing about statistics is that you can always find a model with just the right the set of parameters so that one, in the presence of data, is associated with a wee p-value. This is why, for example, one scientist will report that chocolate is good for your ticker, while another will claim chocolate is “linked to” heart disease. Both argue from a different statistical model.

Same thing holds in global warming. One model will “confirm” there has been statistically significant cooling, another will say statistically significant warming.

Say What?

The global temperature (as measured operationally) has certainly changed since the 1800s. Something, or some things, caused it to change. It is impossible—as in impossible—that the cause was “natural random variation”, “chance” or anything like that. Chance and randomness are not causes; they are not real, not physical entities, and therefore cannot be causes.

They are instead measures of our ignorance. All physical and probability models (or their combinations) are encapsulations of our knowledge; they quantify the certainty and uncertainty that temperature takes the values it does. Models are uncertainty engines.

This includes physical and statistical models, GCMs and GARCHes. The only difference between the two is that the physical models ties our uncertainty of temperatures to knowledge of other physical processes, while statistical models wed uncertainty to mysterious math and parameterizations.

A dirty, actually filthy, open secret in statistics is that for any set of data you can always find a model which fits that data arbitrarily close. Finding “statistical significance” is as difficult as the San Francisco City Council discovering something new to ban. The only evidence weaker than hypothesis tests are raw assertions and fallacies of appeal to authority.

The exclusive, or lone, or only, or single, solitary, sole way to check whether any model is good is if it can skillfully predict new data, where “new” means as yet unknown to the model in any way—as in in any way. The reason skeptics exist is because no know model has been able to do this with temperatures past a couple of months ahead.

The Dramatic Conclusion

There isn’t a soul alive or dead who doesn’t acknowledge that temperatures have changed. Since it cannot be that the observed changes are due to “natural variation” or “chance,” that means something real and physical, possible many different real and physical things, have caused temperature to take the values it did.

If we seek to understand this physics, it’s not likely that statistics will play much of role. Thus, climate modelers have the right instinct by thinking thermodynamically. But this goes both directions. If we have a working physical model (by “working” I mean “that which makes skillful predictions”) there is no reason in the world to point to “statistical significance” to claim temperatures in this period are greater than temperatures in that period.

Why abandon the physical model and switch to statistics to claim significance when we know that any fool can find a model which is “significant”, even models which “prove” temperatures have declined? This is nonsensical as it is suspicious. Skeptics see this shift of proof and rightly speculate that the physics aren’t as solid as claimed.

If a statistical model has skillfully predicted new temperatures, and of course this is possible, then it is rational to trust the model to continue to do so (for the near horizon; who trusts a statistics model for a century hence?). But there is not a lot that can be learned from the model about the physics, unless the parameters of the model can be married to physical concepts. And if we can do that, we should be able to create skillful physical models. Good statistical models of physical processes thus work toward their own retirement.

Ready for the punch line? It is shocking and deeply perplexing why anybody would point to statistical significance to claim that temperatures have gone up, down, or wiggled about. If we really want to know whether temperatures have increased, then just look. Logic demands that if they have gone up, then they have gone up. Logic also proves that if they have gone down, then they have gone down. Statistical significance is an absurd addition to absolute certainty.

The only questions we have left are—not whether there have been changes—but why these changes occurred and what the changes will be in the future.

Lovejoy Update To show you how low climatological discourse has sunk, in the new paper in Climate Dynamics Shaun Lovejoy (a name which we are now entitled to doubt) wrote out a trivially simple model of global temperature change and after which inserted the parenthetical words “skeptics may be assured that this hypothesis will be tested and indeed quantified in the following analysis”. In published comments he also fixated on the word “deniers.” If there is anybody left who says climate science is no different than politics, raise his hand. Anybody? Anybody?

His model, which is frankly absurd, is to say the change in global temperatures is a straight linear combination of the change in “anthropogenic contributions” to temperature plus the change in “natural variability” of temperature plus the change in “measurement error” of temperature. (Hilariously, he claims measurement error is of the order +/- 0.03 degrees Celsius; yes, three-hundredths of a degree: I despair, I despair.)

His conclusion is to “reject”, at the gosh-oh-gee level of 99.9%, that the change of “anthropogenic contributions” to temperature is 0.

Can you see it? The gross error, I mean. His model assumes the changes in “anthropogenic contributions” to temperature and then he had to supply those changes via the data he used (fossil fuel use was implanted as a proxy for actual temperature change; I weep, I weep). Was there thus any chance of rejecting the data he added as “non-significant”?

Is there any proof that his model is a useful representation of the actual atmosphere? None at all. But, hey, I may be wrong. I therefore challenge Lovejoy to use his model to predict future temperatures. If it’s any good, it will be able to skillfully do so. I’m willing to bet good money it can’t.

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