William M. Briggs

Statistician to the Stars!

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The Scientific Ethicist: Mathematics & Logic Edition

The Scientific Ethicist, PhD

The Scientific Ethicist, PhD

This week, three letters from concerned readers.

Can I Skip College?

Dear Scientific Ethicist,

I am a junior in high school and will graduate in the first semester of my senior year. Someday I would like to be a stay-at-home mom. I have no interest in going to college. I feel it would be a waste of money for me to go when I don’t intend to use my degree.

To say my parents are disappointed in me over this is putting it mildly. They have a life planned for me that includes college. I would also like to move away to somewhere where it’s warm year-round, and they don’t like that idea either.

How do I make them understand that this is MY life and everything will be OK?

Uninterested in Idaho

Dear Uninterested,

This is obviously related to the Fundamental Theorem of Calculus. Let me quote Wikipedia, “The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that an indefinite integral of a function[1] can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions.

The second part, sometimes called the second fundamental theorem of calculus, is that the definite integral of a function can be computed by using any one of its infinitely many antiderivatives. This part of the theorem has key practical applications because it markedly simplifies the computation of definite integrals.”

As you can see, the rest follows easily. That’s the power of mathematics!

The Scientific Ethicist

P.S. See also the first, second, and third laws of thermodynamics in reference to your comment about heat.

Dating Woes

Dear Scientific Ethicist,

The school year has started and many high school girls like me are faced with a similar problem: how to politely decline when a boy asks you to a dance.

Whether it be homecoming, winter formal or prom, some boys go all out and ask girls in elaborate and creative ways. I don’t know what to do in these situations if I don’t want to go with the boy who is asking me. I feel bad saying “no” because of all the work they put into it, and also sometimes there is an audience watching. Should I just go anyway?

Saratoga Teen

Dear Saratoga,

Meta logic is the answer here, especially formal systems. A formal system must have a finite alphabet, a listing of the strict rules of grammar (exceptions aren’t allowed), a specified list of inference rules, and finally a set of indubitable axioms. The latter may be made up because, of course, science has no way of externally checking the validity of any set of axioms.

The point for you, and I’m sure you already see it, is that since you can create this formal system any way you like, the next time to you attend a formal you can act any way you like. Logic guarantees this.

Truly there is nothing more logical than logic!

The Scientific Ethicist

Social Media Prayers

Dear Scientific Ethicist,

I frequently receive requests via Facebook and other social media sites asking for prayers for people who are ill or suffering a loss. I’m not a religious person, but I would like to acknowledge their pain and extend my sympathy. Any suggestions?

Challenged in Tucson

Dear Challenged,

Have you considered that e is irrational? Every schoolgirl ethicist knows that

e = \sum_{n = 0}^{\infty} \frac{1}{n!}\cdot .

Now if e were rational, it would have the form a/b where the two numbers are integers, and where obviously b does not equal 1. Then

\frac{1}{1}\ + \frac{1}{1}\ < e = \frac{1}{1}\ + \frac{1}{1}\ + \frac{1}{1\cdot2}\ + \frac{1}{1\cdot2\cdot3}\ + ...  < \frac{1}{1}\ + \frac{1}{1}\ + \frac{1}{1\cdot2}\ + \frac{1}{1\cdot2\cdot2}\ + ... = 3.

Well, we repeat a procedure like this, working with infinite series, manipulating this way and that, and we finally conclude that e cannot be rational.

But you can be, using math, logic, and science!

The Scientific Ethicist

Be sure not to miss other penetrating installments of The Scientific Ethicist. Or send in your questions today!

Summary Against Modern Thought: God Is Not The Universe

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.

Pantheism is the belief that the universe (or multiverse or whatever is all that exists) is identical with God. It is an ancient and current belief. See inter alia Star Wars or attend any yoga class. Atheists speak like pantheists (see discussions about “spontaneous” effects, creation from “nothing”, etc.).

Chapter 26: That God Is Not The Formal Being Of All Things

1 FROM the foregoing we are able to refute the error of some who have asserted that God is nothing else than the formal being of everything.[1]

2 For this being is divided into substantial and accidental being. Now the divine being is neither the being of a substance nor the being of an accident, as shown above.[2] Therefore it is impossible for God to be the being whereby everything is formally.i

3 Again. Things are not distinct from one another in that they have being, since in this they all agree. If, then, things differ from one another, it follows that either being itself is specified by certain differences added thereto, so that different things have a specifically different being, or that things differ in that being itself is attached to specifically different natures. But the former of these is impossible, because an addition cannot be attached to being in the same way as a difference is added to a genus, as already stated.[3] It remains, therefore, that things differ because they have different natures, to which being is attached in different ways. Now the divine being is not attached to another nature, but is the nature itself, as shown above.[4] If, therefore, the divine being were the formal being of all things, it would follow that all things are simply one…ii

5 Further. That which is common to many is not something besides those many except only logically: thus animal is not something besides Socrates and Plato and other animals except as considered by the mind, which apprehends the form of animal as divested of all that specifies, and individualizes it: for man is that which is truly an animal, else it would follow that in Socrates and Plato there are several animals, namely animal in general, man in general, and Plato himself.iii Much less therefore being itself in general is something apart from all things that have being; except only as apprehended by the mind. If therefore God is being in general, He will not be an individual thing except only as apprehended in the mind. Now it has been shown above[6] that God is something not merely in the intellect, but in reality. Therefore God is not the common being of all.iv

6 Again. Generation is essentially the way to being, and corruption the way to not-being. For the term of generation is the form, and that of corruption privation, for no other reason than because the form makes a thing to be, and corruption makes a thing not to be, for supposing a certain form not to give being, that which received that form would not be said to be generated. If, then, God were the formal being of all things it would follow that He is the term of generation. Which is false, since He is eternal, as we have shown above.[7]v

7 Moreover. It would follow that the being of every thing has been from eternity: wherefore there would be neither generation nor corruption. For if there were, it would follow that a thing acquires anew a being already pre-existing. Either then it is acquired by something already existing, or else by something nowise pre-existing. In the first case, since according to the above supposition all existing things have the same being, it would follow that the thing which is said to be generated, receives not a new being but a new mode of being, and therefore is not generated but altered. If on the other hand the thing nowise existed before, it would follow that it is made out of nothing, and this is contrary to the essence of generation. Consequently this supposition would wholly do away with generation and corruption: and therefore it is clear that it is impossible…vi

We skip the next six arguments, which refute an error not of main interest to us.


[1] Sum. Th. P. I., Q. iii., A. 8.
[2] Ch. xxv.
[3] Ch. xxv.
[4] Ch. xxii.
[5] Ch. xv.
[6] Ch. xiii.
[7] Ch. xv.

i“This being” is the pantheistic deity, if it existed. Obviously, the universe is made of parts, is in potential, and all those things we already know God cannot be. This is probably the simplest proof in the whole book! So obvious is this that we’ll skip around the remaining arguments, though there is plenty there that is of interest.

iiThere was some confusion about this in the past. If you exist and I exist (and we do) then we both share existence, or being. But after that, we begin to differ. That’s all this means, and Aquinas draws the implication in the next sentence. There are not different kinds of to exist. The takeaway point is that in God existence is essence, or nature.

iiiThat is, we can know the essence of animal, and other essences, too! Once you grasp this seemingly simple point, boy howdy do things change.

ivIn other words, God cannot be a thing which only exists in your imagination.

vA good review: things which are in existence, have being, have form and matter. Take away the form of you and what is left? Nothing but dust. The form of man is his soul.

viI find this argument beautiful. Put another way around, if the universe were God, then nothing could change; things change; therefore the universe is not God. Being cannot alter into new ways of being Being, and nothing can come from nothing. If God were there universe, it would be a dull constant unchanging void with not even a seething quantum “vacuum” to liven it up.

Predicting Doom—Guest Post by Thomas Galli

Some treatments are more efficacious than others.

Some treatments are more efficacious than others.

I am not a statistics wizard; an engineer, I value the predictive power of statistics. Indeed, if one can precisely control variables in the design of an experiment, statistics-based prediction of future material properties is remarkably accurate. The joy of predicting end strength for a new carbon nanotube concrete mix design in minutes versus days melts the heart of this engineer.

This predictive power has a foreboding downside. It attaches to other projections, including those used by the medical profession to forecast life after diagnosis with late-stage cancer. Unfortunately, I have first-hand experience with this. I was granted but 6 months of remaining life nearly 11 years ago! My doom was predicted with certainty, and for a while, I believed it.

In the dwell time between treatments, I searched for methods used to generate projections of doom. Each patient’s type, stage, age, ethnicity and race were reported to the National Cancer Institute upon diagnosis. Deaths were also reported but not the cause of death. Nothing was captured on complicating health problems like cardio-pulmonary disease, diabetes or other life-threatening diseases. The predictive data set appeared slim.

My battle turned while mindlessly searching web pages of the American Cancer Society. Ammunition in the form of a powerful essay from the noted evolutionary biologist Stephen Jay Gould—“The Median Isn’t The Message”—contained the words: “…leads us to view statistical measures of central tendency wrongly, indeed opposite to the appropriate interpretation in our actual world of variation, shadings, and continua.”

The statistician seeks to aggregate and explain. I’d forgotten that I was in a “world of variation,” was but one data point in about 1.4 million Americans diagnosed in 2004. I might be “the one” on the right-shifted curve prohibiting intersection with the x-axis.

There was one benefit from my encounter with predictive doom. I found hope—something no statistician can aggregate or explain.

Gould survived 20 years beyond his late-stage, nearly always statistically fatal, abdominal cancer diagnosis. Ironically, he passed after contracting another form of unrelated cancer. A distinguished scientist, Gould eloquently described the limits of science and statistics by suggesting that “a sanguine personality” might be the best prescription for success against cancer. There is always hope, with high confidence.


Editor’s Note I have long been interested in working with physicians who routinely make end-of-life prognoses. The concepts of rating such judgments are no different than, say, judging how well climate models predict future temperatures. I mean predictions should be rated on their difficulty. I haven’t yet discovered docs willing to conduct these experiments, but if anybody happens to know somebody, let me know.

Nonpolitical Images Evoke Neural Predictors Of Political Ideology?

From the paper.

From the paper.

The study

Another day, another dreary study purporting to show that the brains of “conservatives” are different than those of “liberals.”

This one hooked up to an electrical phrenology device (fMRI) 83 people1 and had them look at disgusting pictures (still shots from The View?) and other sorts of pictures and then rate them “using a nine-point Likert scale”. I’ve asked this before, but on a scale of -2 to 52.7, how good are these faux numerical scales at quantifying things like disgust or pleasantness? Never mind.

The peer-reviewed paper is by Read Montague and a slew of others in Current Biology, and has the same name sans question mark as today’s post.

To discover “conservatives”, “liberals”, and “moderates” questions were asked about how strongly participants supported items like “Biblical truth” (do no liberals believe this?) and “Foreign aide”. These were scored, the scores separated, and the results assumed infallible. Yes, really. There is no indication—which is to say, no indication—the uncertainty from these arbitrary questions arbitrarily scored and arbitrarily busted up was carried through in any analyses. But since everybody makes this mistake, we shouldn’t question it.

Anyway, the main result is no result. The three “groups did not significantly differ in subjective ratings of disgusting, threatening, or pleasant pictures”. Also turned out that “there were no significant group differences on [other] self-report measures”.

End of story? No, sir. Scientists do not let the absence of wee p-values discourage them. Out came the “penalized regression method called the elastic net” applied to the fMRI data. The theory was that even though there were no real differences in behavior, maybe the brains were different after all, which is a strange thing to think given there were no real differences in behavior. I hope my repeating that isn’t annoying.

Is this a good point to remind us the fMRI data are not pictures of the brain but are themselves output of models and heuristics (“Functional data were first spike-corrected to reduce the impact of artifacts using AFNI’s 3dDespike”, etc., etc.) which themselves are subject to uncertainty which should be carried forward in any analysis but which usually aren’t, and weren’t here? If not, let me know when is.

The analysis

I hesitate to describe the authors did next not because it’s difficult, but because I don’t think anybody will believe it. I will first remind us that we are to again lament that most statistical practice is designed around model fit, which tell the world how closely a model fits to the data at hand, and that the more models tried the better success of discovering one which fits.

The authors showed each person sets of neutral (whatever the hell that is), pleasant, threatening, and disgusting photos. There weren’t any reported differences in fMRI manipulated data between people seeing these images in the three different groups.

Next up was to form “contrasts”, which was to sort of difference the fMRI manipulated data from times when people looked at disgusting, threatening, and pleasant images against so-called neutral images. These same differences were applied to averages between “conservative” and “liberals.” The “moderates”, sad folks, were thereafter forgotten.

Incidentally, the types of people in the “conservative” and “liberal” groups were not the same: “liberals” averaged 33 years old, 39% female; “conservatives” 27 years old, 61% female. Might these biological differences account for differences in fMRI manipulated data? The authors admit (in supplementary material) that “religiousness”, age, and sex “were significantly correlated with political attitudes”. But they put this down to “false alarms” and carried on.

Now came generalized linear models—we still haven’t reached the elastic net—where for each individual “a temporal high-pass filter (128s) and order 1 temporal autocorrelation (AR(1)) was assumed”. And “The onsets for each picture subcondition (core/contamination disgust, animal reminder disgust, actual threat, no actual threat, social pleasure, nonsocial pleasure) and fixation crosses were convolved with a canonical hemodynamic response function…using a delta function of zero duration”, etc.

And that wasn’t all. “Six head motion parameters were also included in the first level GLM as covariates.” So were age and sex. Uh oh. Then they “separately examined the maps of [Disgusting – Neutral], [Threatening – Neutral], and [Pleasant – Neutral] contrasts”. Then some t-tests and some other things.

Result? “The contrasts with threatening or pleasant pictures revealed no regions surviving multiple corrections. However, in the [Disgusting > Neutral] contrast, the Conservative group showed greater activity than the Liberal group in several regions” (hint: amygdala! amygdala!). Yet, sadly, “No regions survived correction for multiple comparisons for the
[Liberal group > Conservative group] comparison.”

Another no result. So back to the computer and the “penalized logistic regression analysis”, a.k.a. “elastic net”.

“First, we extracted a map of the [Disgust > Neutral] contrast for each participant. Then, we applied an a priori mask, which was generated from the Neurosynth website”. Then they “obtained the union of meta-analytic (positively correlated and both forward and reverse inference) maps of ‘Emotion’ and ‘Attention'” and then finally formed up all the voxels into a matrix and submitted all to the “elastic net.”

That creature is so cumbrous I don’t dare describe it. But it was, in the end, fit to the “individual scores on a standard political ideology assay” and, mirabile dictu, the model fit was reasonable. But only for those time disgusting images were viewed (and leaving out “moderates”). Would young females dislike disgusting images more than older males? Just asking.

The true test: How well does their model predict political attitudes for people not used to fit the model? [INSERT CRICKET CHIRPS HERE]

The End

The authors conclude “Neuroscience has started to provide rich information about the neurophysiological processes underlying political behavior.” No, it hasn’t. It is true that a spate of flawed papers are appearing, each borrowing the mistakes of the other. Yet the authors don’t even blush when the say “Our results have important implications for the links between biology, emotions, political ideology, and human nature more fundamentally.”

Here’s where it gets scary, folks. They suggest “people are born with certain dispositions and traits that influence the formation of their political beliefs”. This seems trivially true; after all, some of us are men and some women, and that difference means a lot. But the differences the authors means refer to flawed ad hoc idiotically scaled questionnaires. How long until some bright academic produces “the” list of questions which separate the sheep from goats?

Next: “A wide range of brain regions contributed to the prediction of political ideology (Figure 3A), including those known from past work to be involved in the processing and interoception of disgust and other stimuli with negative affective valence, but also those involved in more basic aspects of attentive sensory processing”.

The mistake here is to assume we are our brains, slaves to them somehow, that these curious organs can make us do what they like, and that we have little to say about it. The lack of philosophical training tells again.

Nowhere do these authors (or any other that I have seen) betray any lack of confidence in their convoluted analyses. It seems as if—I’m just guessing—that all these authors think that because their analyses are complex they are therefore right. We need a name for this fallacy.


1In supplementary material the authors say 12 people were removed from the analysis, but it’s not clear if these were before or after the 83.

Thanks to Rexx Shelton, Robert, and one anonymous reader for suggesting this topic.

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