Many of you are familiar with the Müller-Lyer illusion but I will present it anyway because seeing it is useful for my thesis, which I admit is very speculative. Please begin by looking at the diagram.

Now decide which of the horizontal portions of the two lines is longer. If you measure them, you will then KNOW they are identical but you will have difficulty seeing that even after you know it to be true. Can the optical illusion be overcome? With some effort it can be, but our tendency is not to try hard. Constantly questioning our intuitive judgments is unpleasant and often unrewarding. I believe that most of us have an instinctive liking for Barack Obama and a strong intuition that he is a good man who means well. Our trust in Obama is the cognitive analogy to our trust in the perceptual experience of viewing the illusion. We are making a mistake but my merely telling you so without much argument gets me nowhere. You already know some of his his worst policy errors but you have a way of dismissing them as “not his fault.” Because you may be right, my arguments, if I presented them, would strike you as curiously flimsy. “You can’t fight City Hall,” so to speak. So I won’t.

Mental effort is hard for all of us. Just ask students at Harvard, M.I.T, or Princeton to solve this math puzzle: “A bat and a ball together cost $1.10. The bat costs a dollar more than the ball. How much does the ball cost?” Any person smart enough to be admitted to any of these schools can figure out the answer if he allows himself 20 seconds of thought but a study has proved that most of them get the answer wrong because they take the path of least resistance. The intuitive (and wrong) answer is that the ball costs ten cents. This is almost the cognitive equivalent of the Müller-Lyer illusion. Of course it doesn’t take too long to see one’s error in the bat and ball “illusion” but I simply don’t know what can be done about the Obama illusion. The trouble is that it may very well be the case that Obama really is a good man who means well but our intuitive feeling that this is so is not based on a study of evidence but is a hastily formed opinion based on his apparent affability.

Quick judgments are the very stuff of life in a world that crowds us with important decisions that will not wait. Consider this problem: “All roses are flowers. Some flowers fade quickly. Therefore some roses fade quickly.” A person who has a grasp of elementary logic sees this is a fallacious argument and may even be able to name the error. The rest of us require a moment of reflection. But why bother? What would it prove? If we get it wrong, we get it wrong. How does it bear on Obama’s goodness? Answer: I don’t know but I think it is another instance of hasty judgment. Is Obama what he seems to be? My answer is this: Why rush to judgment? If it is too much trouble to think long and hard about it, don’t form an opinion. Let history decide unless you are willing to put your brain in the hands of others. Dangerous business, that.

Diet gurus keep changing their minds. Right now, on top of the leader board, is the much publicized Mediterranean Diet. I believe we should not jump to conclusions. The next 200 years will tell the tale.

Here is the scorecards for the two favorites – The Med diet and the Low Fat diet:

Med Diet……………………………….Low Fat Diet

Recommended

Olive oil 4 tablespoons/day……….discouraged by low fat enthusiasts
Tree nuts & peanuts 3 servings/week..discouraged by LF enthusiasts
Fresh fruits 3 servings/day……….LF: 2 servings/day
Vegetables 2 servings/day…………LF: 2 servings/day
Fatty fish 3/ servings/week………discouraged / LF people like lean fish
Legumes 3 servings/week. Mystery items. Maybe beans, peas… LF enthusiasts: don’t know
Bread and whole grain cereals……..LF enthusiasts – choose wisely.
Wine w/meals 7 glasses/week…….. LF enthusiasts ??? No report card – no guts, no glory, no fun.

Discouraged

Bakery sweets and pastries discouraged by both diets. This proves beyond any doubt these diets are worthless.
Dairy is discouraged by both diets: eggs, cheeses, milk, ICE CREAM! More proof of how ridiculous these diets are.
Red and processed meats discouraged by both diets. [What the hell is red meat? Is that in contrast to green, blue and white meat?]

It is alleged by members of Mediterranean Diet Fan Club that the Diet will allow you to get off your statin and high blood pressure medications and cause you to live longer! [SG: I have one question about this - IS THIS A BOAST OR CONFESSION?]
P.S. The researchers [sic] said the olive oil must be extra virgin! I suspect they were sex maniacs.

At the end of the five year study of 7,447 people, 3.8% of the Med folks had suffered a heart attack, stroke or death. 4.4% of the low fat “control group” had suffered from the same set of adverse events. In other words, assuming I can still do arithmetic, 283 people in the Med Diet ritual were miserable or dead. 328 of the low fat gang were the victims of their diet. Together that totals 611. What happened to the remaining 6836 folks? Here’s what happened to them: They were still eating their ice cream and chocolate candy on the sly, laughing all the way to the grocery store.

The National Institutes of Health is making progress in phasing out government-funded chimpanzee experiments and retiring most federally owned chimpanzees to sanctuaries. But the agency shouldn’t hold 50 chimpanzees for future research.

“The Institute of Medicine made it clear that chimpanzees are neither necessary nor useful research subjects. While they suffer needlessly in laboratories, millions of taxpayer dollars are wasted on inappropriate housing and unproductive research,” says Elizabeth Kucinich, PCRM’s director of government affairs. “While we are happy with the progress this report suggests, we advise that chimpanzee experiments be phased out completely.”

The report from the Council of Councils Working Group on the Use of Chimpanzees in NIH-Supported Research states that the NIH should permanently retire all but 50 of the 360 government-owned chimpanzees to a federal sanctuary program. The Working Group’s report recommends that NIH should not revitalize breeding of chimpanzees for any research, including new, emerging, or re-emerging disease research.

If the NIH accepts the recommendations of this report, the approximately 170 chimpanzees at the Alamogordo Primate Facility (APF) in New Mexico should be sent to sanctuaries. This includes Ken and the 23 chimpanzees, previously housed at APF, who are in poor health facing laboratory procedures at Texas Biomed in San Antonio. Ken, for example, is at risk of sudden cardiac death according to medical records obtained by PCRM through the Freedom of Information Act. Ken and the others should now be removed from the laboratory and reunited with the other Alamogordo chimpanzees in permanent retirement.

To learn more about ending chimpanzee experiments, visit PCRM.org/GAPCSA. That’s the Physicians Committee For Responsible Medicine.
***************************
McDonald’s, Chicken-Fried Steak Served in Top U.S. Children’s Hospitals:

1.Shands Hospital in Florida is a top children’s hospital for heart surgery. But it has at least five fast-food outlets, and the patient menu includes artery-clogging meatloaf with gravy, according to PCRM’s new report on children’s hospitals that serve the most unhealthful foods.

The four other children’s hospitals named in PCRM’s report also host fast-food restaurants and serve young patients foods loaded with cholesterol and fat:

The Five Worst Children’s Hospital Food Environments

1. Shands Hospital for Children at University of Florida Gainesville, Fla. At least 5 fast-food outlets, including Wendy’s; patient menu includes a ham-and-cheese croissant, barbecue chicken, and meatloaf with beef gravy
2. Monroe Carell Jr. Children’s Hospital at Vanderbilt Nashville, Tenn. 4 fast-food outlets, including Taco Bell/Pizza Hut Express; cafeteria features barbecue chicken, cheesesteak wrap, and chicken-fried steak with cream gravy
3. St. Louis Children’s Hospital-Washington University St. Louis, Mo. 2 fast-food outlets, including Pizza Hut; patient menu includes sausage, bacon, ham, grilled chicken, and roast beef with gravy
4. Children’s Hospital Los Angeles Los Angeles, Calif. McDonald’s on first floor of hospital; patient menu features pizza and hot dogs
5. Riley Hospital for Children-Indiana University Health Indianapolis, Ind. McDonald’s in hospital next to cafeteria; patient menu features sausage, bacon, and corn dogs

*************************************
https://www.youtube.com/watch?v=YpBPavEDQCk

If you make the mistake of regularly listening to TV pundits (who know absolutely zilch about mathematics) you find yourself bombarded with the phrase “margin of error.” The phrase is never explained by them for the good reason that they are phonies who don’t know what it means but they are sure (and unfortunately right) in thinking frequent use of the flickendoodle expression will gain them much credibility with the dupes who listen to and watch them with mind-numbing regularity.

However, the fat lady has now sung to the rhythm of Obama jogging down the stairs from the plane to the ground and so it won’t hurt to say a little about what “margin of error” means. For a much more thorough account, turn to any of the 13,465,325 books and articles on probability and statistics. Many of these are actually the work of people who can think and, accordingly, know how to explain their ideas to lay persons. I am particularly fond of one article that is so easy even I understand it: http://www.amstat.org/sections/srms/pamphlet.pdf. I suggest bookmarking it and referring to it often.

The margin of error is a statistical formulation of how well a sample of voters (those voters who took the poll) reflects the general population (all voters), assuming that their voices are chosen randomly within the population you want to know about. It tells us how confident we can be that a poll is accurately reporting how the whole population feels. There is no such thing as THE margin of error despite the fact that Madame Professor Doctor Rachel Maddow hurls it out glibly, knowing full well her audience doesn’t know what she is talking about. Margins of error are determined by the level of confidence one seeks. If I am happy with a 50% level of confidence, (which means I don’t know what the hell I am talking about), my margin of error will be very low. For example, I might predict that if I toss a coin I will get a Head. I’ve got a 50-50 chance of being right and, in saying that I’ve got a 50-50 chance of being right, my margin of error is nonexistent. Since no rational person really cares who wins the presidential election, statisticians want to be very confident of their mathematics or the intended audience will turn away and watch re-runs of Fred Flintstone. Accordingly, when they report margins of error, they report them for the 95% confidence level. That means that one time in 20 they would be wrong. If the pollster says Obama is heading for 49% of the total vote and that this figure lies within “the margin of error,” chances are he is assuming a certain margin he is just too bored to report. However, my spies tell me that the margin of error these guys usually like is 3%. From this, remembering our elementary arithmetic, we may calculate that they think Obama will get between 46% and 52% of the total vote and that they think the chances of being wrong are mighty small – one chance in twenty. Just keep in mind that as the margin of error increases so, too, does our confidence increase. If the pundit says the margin of error is 20% then he is predicting Obama will get between 29% and 69% of the total vote. That’s not much use to us but the statistician can be a lot more certain that he is right than if he aims for a margin of 1%.

So what did Madame, Professor, Doctor Maddow really think? Who the hell knows? But what we do know is what she was hoping for: to bludgeon you with the incomprehensible so that you would feel it would be hopeless to vote against her guy. SHE NEARLY WAS RIGHT.

So far, so good. Bo knows football; these guys know science, social science and HOW TO THINK. I’ll be back tomorrow for more. Again, Rackham Building, UM. All day. I can hardly begin to summarize the presentations or the number of them. Check my previous post for details.

In the light of the statistics below, I suggested to one presenter that if an infected person knows how low the risk of of infection is, he may be encouraged not to inform anyone with whom he is contemplating having sex that he is HIV-positive. Why take the risk of being turned down? We banged that one around for awhile. I think I won.

Estimated Per-Act Probability of Acquiring HIV from an Infected Source, by Exposure Act
Type of Exposure Risk per 10,000

Blood Transfusion 9,000
Needle-sharing during injection drug use 67
Percutaneous (needle-stick) 30

Receptive anal intercourse 50
Receptive penile-vaginal intercourse 10
Insertive anal intercourse 6.5
Insertive penile-vaginal intercourse 5
Receptive oral intercourse low
Insertive oral intercourse low

Biting negligible
Spitting negligible
Throwing body fluids (including semen or saliva) negligible
Sharing sex toys negligible

The hot topic of the day was whether criminalization of HIV makes sense. Some very profound discussion.

Conversation (or interview?) with Johnny Cash’s daughter, Rosanne.

Her appreciation of the harmony of the spheres “led me to light shifts and that led me to theoretical physics.” So she married “a brilliant singer” but divorced him in 1992 to develop “personally and musically and move into self-discovery, culminating in her writing a song titled “Seventh Avenue.” She realized how much she loved her father and reconciled with him via the “haunting and unbearably sad duet she recorded with him shortly before his death, “September When It Comes.” The interviewer most solemnly warns that you should check “with your cardiologist before you listen because once you hear it, you will never recover as long as you live.” [A link is provided]

For musical inspiration, Rosanne likes to spend nearly all her time among the genteel brownstones of Manhattan whose gaslight lampposts still flicker at night, where Edith Wharton, Edna St. Vincent Millay, Mary McCarthy and Djuna Barnes got their own inspiration. She is now writing a song tentatively titled “Particle and Wave” which draws from her deep knowledge of black holes. She had a conversation with her “good friend” the great string theory genius of Stuyvesant High School who now resides at Columbia University when he is not with Rosanne. She tormented him with an example of her own genius: “Is God the unified field?” Brilliantly, Brian answered, “It depends on your definition of God.”

Rosanne mentioned that “theoretical physics is like religion” and so she had another conversation with another “good friend,” Lisa Randall of Harvard who, as you can probably surmise, was a high school buddy of Brian. [Challenge: Name three people in the last thousand years who are first rate geniuses who did not attend Stuyvesant High School.....Just give it up. You can't do it.]

Rosanne inclines to the view that there are parallel universes to our own. They are infinite in number and “encompass all possible eventualities, in which infinitesmal and grand differences play themselves out.” She observes that this idea “is freeing to me.. The choices I am making in another universe might be better but they might be worse. I might be doing pretty well.” Lisa, on the other hand, “is a multiverse skeptic. She thinks it is narcissism.”

Rosanne’s friend, Mark Everett, took a trip to Princeton to ask the resident physicists, “So when you die, do you just go to a parallel universe? Is that what heaven is?” Their collective reply, “It is possible.” Rosanne pushed on: “Is the one in the parallel universe the real you and the one here just a specter?” She grasped the idea of ineradicable unpredictability and rejected, like any good modern physicist, Einstein’s belief in “hidden variables” that unite everything. So she moved on to more songs – great songs are not about love but create love. She met a woman at a dinner party, the anthropologist Helen Fisher, who assured her that love is natural. Some anthropologists think humans are like bonobo chimps, but that sort of thinking does not get us far. Consider the Beatles song, “I want to hold your hand.” Out of reach of bonobo chimps. When Rosanne first heard that song, she was “struck blind and dumb.” Apparently, she has recovered and now writes songs of “morbid joy.” It seems, too, that a country weeper named George Jones wrote a song called “He stopped loving her today” and proceeded to drop dead that very day. Rosanne “can barely pronounce the name of that song without bursting into tears.” Morbid joy is great and “George Jones is better than a pill,”she says. George helps us “not to go crazy because we can put it out there.” WITH THOSE WORDS, WE COME TO THE END OF INTERVIEW OR CONVERSATION OR WHATEVER IT IS.

All that remains – at least if you want to be a great songwriter – is to check out a few parallel universes and see if your life in this one is only a specter.
*******************************
Johnny and Rosanne – strictly for those who have checked with their cardiologist.
http://www.youtube.com/watch?v=J2WilM6ljUg

Albert Einstein Medical College in Philadelphia is one of the few holdouts against rational reform. Only a handful of medical schools retain the medieval torture practice of animal lab as a training technique for students. Perhaps 6-10 colleges (out of the over 200 medical schools) are refusing to admit that the courses in which animals are tortured and then thrown into the garbage are pointless and inhumane. Many physicians, distinguished and unknown, are adding their voices to the protest of what is going on at AEMC. Many laymen are complaining, too.

Einstein should switch to simulation as U. Washington recently did. UW has a state-of-the art simulation center that provides cruelty-free nonanimal training. There are no excuses for using live dogs and cats in invasive procedures.

You can go to PCRM.org/actnow and sign a petition. Thousands are doing this. Why not you?
http://www.pcrm.org/media/blog/august2012/progress-in-ending-animal-abuse-in-medical

The New York Review has published another in its long list of ass-kissing sycophantic wonder accounts of great men in science. For the whole of it, if you have a strong enough stomach, go here: http://www.nybooks.com/blogs/nyrblog/2012/jun/30/kentridge-galison-refusal-of-time/?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+nybooks+%28The+New+York+Review+of+Books%29

The conversation between Peter Galison and William Kentride ends this way: [MK is the NYR reviewer, Margaret K. Koerner (a genius in her own right)] The work under discussion is William Kentridge & Peter L. Galison, The Refusal of Time, available as “100 Notes – 100 Thoughts,” published by Hatje Cantz.

A BLACK HOLE

MK: Is The Refusal of Time about avoiding death?

WK: It ends up there. It starts with: Is a black hole the end of time? As Peter was saying, that is one of the questions that physicists consider. But as soon as you say, right, let’s start having things disappear into a black hole, it is an immediate jump to that being, as it were, a metaphorical description of death. Is any trace left when you are gone? Is there any information, attributes of you that still float around the edge? So it is both from the psychological, or the lived sense of, what is the balance between the finality of death and the continuation of attributes of people afterward?

PG: We can’t live forever, but we can hope that some small trace of our existence might somehow survive. In the black hole debate one side contended that it truly was an end to all things, a portent of the final stage of the universe. The other desperately wanted to prove that somehow all the information swallowed up would survive—coded far beyond easy recognition to be sure, but there nonetheless. And in the black hole battle, in this ultimate refusal of the end of time, there is something that struck me as so evocative that I hoped it could be wound into our story.

WK: So that became clear, that one of the elements of the project was black holes, and there was a procession going into the black hole.

MK: You’re in it, right?

WK: I am in it, eating soup.

****************************************
Some of the many awards given to William Kentridge are:

1994 Loerie Award memo
2004 Carnegie Medal
2004 Honorary Doctor of Literature from the University of the Witwatersrand
2006 Jesse L Rosenberger Medal from the University of Chicago
2010 Kyoto Prize

Meanwhile, Peter Galison has galloped off with:

the Pellegrino University Professorship in History of Science and Physics at Harvard University
and a MacArthur “genius” fellowship in 1986.

Peter has already superseded Newton and Einstein in the Race To The Top as is evidenced by his magnificent work Einstein’s Time. You can glean a little of its magnificence by thrilling to http://www.aip.org/history/einstein/essay-einsteins-time.htm

Here is a neat trick to try on children, especially those under the age of twelve. Ask a child to think of a number from 1 to 4 and to tell you what it is. Then direct to him to some unlikely place such as the butter compartment in the refrigerator and there on a sheet of paper he will find a slip of paper that says, “The number you were thinking of is ….” He will be impressed. Don’t try this with a range of more than ten numbers or you will strain your memory and run out of good hiding places that are far from one another. A nifty variation is to ask him for a number from 1 to 20 and then show him a sheet of paper with your correct guess. If you do this trick often enough, you will get correct hits 1/20th of the time. Shrug off your misses with some clever patter and move on to another trick. In due course, your misses will be forgotten (such is the nature of human psychology) and your successes will assure you of well deserved greatness.
**********************
Your physician, a practitioner of magic for adults, will try this one out on you. He will ask you to put a number down on a form to indicate your level of pain. Since you have been well indoctrinated into the habit of timid obedience, you will feel you have no choice but to play the game. After you comply, he will never explain the meaning of this game because it is pure gibberish. The treatment “modality” he will offer you won’t differ if you say 7 rather than 6. Sophisticated magician that he is, he will not bother to look at the form on which you placed a number and will move on with some clever patter to the exam itself.

But be kind and remember that he is mathematically challenged. He does not understand the pain scale has no natural zero point as some scales do. For example, there is a natural scale on your ruler that runs from zero to 12 inches. It follows that an object laid out on the ruler with length of 8 inches is twice the length of an object of 4 inches. If inches are not your thing, you may convert that to the metric system and you will find that one object is still twice the length of the other. You will not have this luck if you are measuring temperature because there is no natural scale. Mr. Fahrenheit and mr. Celsius had arbitrary starting points. This means that it makes no sense to say that when the temperature is 50 degrees F it twice as hot as when it was 25 degrees F. Test this out by converting your 25 degrees F to its equivalent in centigrade (or as it is usually called nowadays, in celsius). Now convert what you took to be twice the heat when measured in the other scale and observe the great disparity. So much for twice as hot.

However. As you know, and presumably so does your “health care provider,” 212 degrees F (the water boiling point) corresponds to 100 degrees on the celsius scale. So, can we use this to develop a scale showing some invariance between C and F? Yes, in fact, we can. This gets a little tricky and my own math skills, being as shaky as they are, I won’t explore the matter in depth but I can say this much: Temperature scales are examples of interval scales and the relation of differences is left invariant with respect to linear transformations. That is, left invariant with respect to y=ax +b. In a branch of mathematics called game theory, we can use this math to say of three preferences that my preference for B over C is 3 and 1/2 times greater than my preference for A over B if, in fact, we put magnitudes on each of them.

The trouble is that we are still in a whirl of arbitrariness. How, in God’s name, did we put numbers on preferences in the first place? If your health care provider knows why he put certain numbers down to indicate certain levels of pain then he can actually go ahead and do a game theory sort of analysis. Of course, he can’t because, please remember, he does not know what he is doing. the numbers mean nothing to you and, likewise, to him. Do not despair. Hydrocodone is hydrocodone in any language and your provider is licensed to prescribe it. (Actually, to my way of thinking, that is frightening but all you readers know that if imbecility could be licensed, I’d have no trouble gaining my accreditation).

One next-to-last thing and I am done. We haven’t addressed the problem of interpersonal comparisons of utility. Utility theorists are pretty much agreed utilities cannot be compared across persons, at least not quantitatively. The upshot of this is that we have no way of saying my 7 is anything like your 7. I call out “7″ when someone sticks his finger in my eye and you also call out “7″ when someone does likewise to you. So what? The level of intensity of pain you feel may not be much like my feeling of pain. There is no good way to get around this. I can say, “Boy, that hurt a lot more than when you punched me in the arm and that, in turn, hurt more than drinking that spoiled glass of milk. I did an ordinal comparison and you can do the same thing, even creating the same order. If I am sufficiently crazy, I can even say the finger in the eye was 2 and 1/2 times worse than the punch in arm, and you, also being a madman, can come up with exactly the same quantities. We now know the ratio of our dislikes are identical. So what? Pass the hydrocodone, please. Gotta keep the doc happy.

What you need to do is lay down the law. “Listen, Doc, this number game is malarky and I won’t play along. However, if you want, think of a number from 1 to 4 and I’ll tell you what it is.”

**********************************
And now for the last piece of magic, and you’ll never figure this one out. I got up from one level of my house to this one on which my computer is stationed. Given that the pain involved is well beyond any known to mortal man, how did I do it? The only clue I will give you is that I was inspired by love for you.

**************************
Lamont Cranston, The Whistler, and Doris Day know the answer.

I sat on a park bench in Michigan’s vast and great Kensington Park last week at about 7.30 A.M. when who should briskly walk by but Dr. Ringolevio, the great pain specialist of Ann Arbor. We greeted each other cordially and then he asked, “How have you been lately? I mean how has your back pain been since I last treated you two years ago?”
SG: “That problem is over but two months ago a new one set in, and it causes me much misery.”
Dr. R: “Sorry to hear that. You should come to my office for a new evaluation. By the way, for now, what is the level of your pain?”
SG: “33.6, more or less. It could be as low as 33.2 or as high as 35.3. I’m not sure.”
Dr. R: “All the time? ……….SG: “No, at its worse. Sometimes it is only about 9.”
Dr. R.: “That’s bad enough. My own back pain is usually around 6.” ……….SG: “Wow! That’s impressive.”
Dr. R: “I owe it to good eating – kale, turnips radishes. A bit of walking, of course. Plenty of sleep but mainly, I think, to my twice weekly playing of johnny-on-a-pony with the old gang from Brooklyn. I fly in twice weekly just to play.”
SG: “Wow! Impressive and COOL. Let me see if I understand. Does my pain level of 35.3 suggest to you that I am suffering almost 6 times more than you do when you score 6?
Dr. R: “No. It means you are suffering 6 times more than you suffer when you score 6. I can’t directly compare your suffering with mine.”
SG: “So, is it possible that when I score a measly 3, I am suffering 100 times more than you do when you score just 2?”
Dr. R: “Afraid so.”…………SG: “How discouraging. How do you handle this conflicting data? Do you use ordinal scales? Ratio scales? Interval scales? Something else?”
Dr. R: “What do you mean?”…………SG: Well,consider ratio scales. If my thermometer says it is 40 degrees today but yesterday said it was 20 degrees, I cannot conclude that it is twice as warm today as yesterday because my scale is calibrated by Fahrenheit measurements which, after all, are quite arbitrary. Had I used old man Celsius’s Centigrade scale, the readings would have been very different: -6 & 2/3C for Monday and 4 & 4/9C for Tuesday. So, unless I am very confused, ratio scales don’t work well for temperature.” …………….Dr. R: “Come again, please, I don’t get it.”
SG: “Temperature relations seem to shift with different scales. However, I grant that the ratios of different temperatures seem to survive these numerical challenges. For example, if the thermometer says 30 degrees on Wednesday then it could be that the rise of temperature from Monday to Wednesday was twice as much as the fall from Tuesday to Wednesday. If the Centigrade scale read -1 & 1/9 degrees on Wednesday but the rise from Monday to Tuesday was 11 & 1/19 degrees then the fall from Tuesday to Wednesday was 5 7 5/9 degrees, allowing us to say the number is indeed twice the second. Get it?
Dr. R: [Getting frustrated and angry.] “No, I don’t get it.”
SG: Well, let’s retreat a bit. You do see that if magnitudes are given in such a way that one can say of any two things which is larger but can say nothing about the magnitude of the differences, these magnitudes are given on an ordinal scale.
If all you know is that Joe is fatter than Bill and Bill fatter than Sid, you don’t have a clue about the weight disparity among any of these pairs. So, if you say your pain level is 6 and that is better than 9 (speaking strictly for and of yourself) and I say my 110 is worse than my 45, you don’t have the slightest idea how to compare your pain with mine nor even how to compare my own pains with one another.. Get it, now?” Dr. R: ‘No, your explanations are dense and that might be a consequence of the fact that your brain fibers are thin.”……………..SG: “I couldn’t agree more. But I feel committed to plunging ahead.”
SG: “Let’s try this. I say I prefer the music of Mozart to that of Bach and that of Bach to that of the Beatles. Even if I put numbers on these preferences, you won’t learn much because the scales are conventional. If I could tell you that my preference for Mozart was twice as much as much as my preference for Bach over Beatles, we’d make some progress but not a helluva lot. But let’s get fancy because I know you are a doctor and therefore a very brilliant guy. Suppose I say my pain levels on different days are 100, 17, and -25 (never mind what the latter means). Now. comes the part you are going to hate. We can substitute for those numbers any other numbers we want so long as [GULP!] as they are obtained by a monotone transformation – a set of numbers that preserve their relative positions on the axis of real numbers. A mouthful, I know, but don’t blame me. Blame Dedekind and all those other wise guys. Instead of 100, 17 and -25, I could have put down 3, 2, and 21/11. What’s it to you? It’s only ordinality that counts in this mad game you, yourself, have foisted upon me in the first place when you asked me to put a number down for my pain and then asked me to compare it to pains on other days and even threw in your own for “nonsensical reference.” I could have changed all three numbers by use of a mathematical function y=10x. They would have increased or decreased together. That’s a nifty positive monotone for you, if ever you saw one. I could have used y=x cubed but notice I could not have used y=x squared because the order of magnitude would have changed. I swear I am not using dirty language but I have to tell you that ordinal scales are invariant with respect to positive monotone transformations but, sadly, as my colonel friend, Michael, would tell you, y=x square is not a monotone transformation.
Dr R: “I’m beginning to catch on.” SG: “Thank God because I am beginning to get lost and don’t know how much longer I can hang in.”……………….Dr. R: “Take a breather and just tell me if this is right. If we multiply 1,000, 170 and -25 by a factor of 10, the ratios don’t change because we can cancel out the factor. I wouldn’t mind if you told me that the transformation y=ax can be called the similarity transformation because the ratios are invariant.”
SG: “That’s why you’re a doctor and when push come to shove or when we come down to the crunch, or when the going gets tough, I am revealed to be a low grade prick and you are King of the HILL. I love you.”
Dr. R: “As you should, and I will accept your love as payment for my otherwise substantial bill.”
SG: “One last thing, and I swear I will never bother you again. Do you now see why, when you ask me to put a number on my pain, I don’t have a flickendoodle idea of what you want and, worse yet, neither do you?”
Dr. R: “That’s heady stuff. Maybe we should just repeat this whole session.”
SG: SEND ME A BIG FAT BILL, INSTEAD.

****************************
Climbing up several flights of stairs to reach this machine is better proof that I love you than God’s creating beer is proof that he loves mankind. My pain level can only be represented by Godel numbers, and believe me, you don’t want to know that they’re about.

With any luck, I’ll be back within a couple of weeks.