Reality Deniers

“You have an irrational belief in rational thought.” ~Dr David Scholes, directed towards me.

“Humankind cannot bear very much reality.” ~T.S. Eliot

I just finished the book Mathematical Cranks by Underwood Dudley, part of a trifecta of skeptical mathematics books.

Doctor Dudley is a professor of mathematics at Depau University and a connoisseur of cranks with a mathematical bent.

What is a mathematical crank?

Mathematics is a peculiar field. Whether or not some aspects of mathematics exist independent of humans is an ongoing debate, but within its axioms and proofs is a consistent body of well defined, internally consistent knowledge.

Within that knowledge, ideas can, under the rules of mathematics and logic, can be proved or disproved, to be absolutely true or false or to be impossible.

No prior plausibility that pester the world of scientific medicine and the evaluation of woo. No borderline p values that hint at effects. No biologic variability. No placebo effect. No investigator or patient bias. No placebo effect. No N rays. No unproven water memory or meridians or subluxations.

Just clean, beautiful, mathematics. True or false. Possible or impossible. I simplify a bit, but mathematics, especially at the lower levels, is an internally consistent field of study. What happens in the math of 11 dimension string theory is beyond my puny intellect.

In mathematics there are things that are impossible. Absolutely impossible. No ifs, ands, or buts. Impossible. Can’t be done no how no way. In the world of mathematics, things are not only impossible, they are proven truly impossible within the boundaries of the mathematical discipline.

An example of mathematical impossibility is the quadrature of the circle, also called squaring the circle.

It is impossible, using only a straight edge ruler and a compass, to construct a square with the same area as a given circle. It was proved to be impossible in 1882 by Lindeman. Not improbable or unlikely or very, very, very difficult. With in mathematical reality, it is impossible.

Just because it is impossible does not prevent people from attempting to square the circle. They send these ‘proofs’ to mathematicians for comment.

“Few people have the imagination for reality.” ~Johann Wolfgang von Goethe

Mathematical Cranks is an examination of these, and other, pseudo-proofs and the accompanying correspondence between the authors and mathematicians. The mathematics is sometimes obtuse, but the interactions between the mathematicians and those with various unique mathematical ‘analysis’ are interesting and resonates with experience in the skeptical and medical fields.

These are the features of mathematical cranks.

1) They are convinced that their opinion is superior to the accumulated opinion of 2000 years of mathematics and mathematicians. That hundreds of mathematicians have worked for hundreds of years on these problems and found no errors in the proof that it is impossible to square a circle is of no consequence. Despite the accumulated mathematical knowledge of uncounted mathematicians, they are convinced that their solution is the right solution. Everyone else for all of history has been wrong. There is a tinge of megalomania in all the correspondence, and some appear to me to be clinically insane.

2) To accommodate their solutions, they are willing to alter reality to fit their proofs. There are solutions to squaring the circle, but they require a value of pi that is different that 3.14159265… Pi, for those that have forgotten, is the ratio of the circumference to the diameter of a circle and is a constant of the universe. For some circle squarers, Pi has a different value and all the mathematics that has confirmed the current value of pi is wrong. Others deny that pi exists or that the definition is meaningless, since they can construct a squared circle with pencil and paper, and send in the (flawed) construction.

3) When errors of math or logic are pointed out, they respond not with understanding, but a redoubling of efforts to prove that their erroneous solution to the problem is actually correct. They are incapable of recognizing flaws in logic, or mathematics, or flaws that are in opposition to mathematical consistency. A crank cannot recognize their error because they cannot recognize that their reality differs from mathematical reality.

4) Cranks are impervious to arguments based on mathematical reality. They do not recognize or understand that their solutions are in error because the solution contradicts known mathematical reality. They do not base their solutions on known mathematics, but on their own flawed understanding of mathematics.

5) Cranks evidently send their ‘solutions’ to multiple mathematical departments and rarely receive a reply. This silence from academia is interpreted not that their solution is worthless, but that there is a conspiracy of Professors of Mathematics to keep their solution secret, to the detriment of human kind. Big Math, out to suppress the truth THEY don’t not want you to know.

“To treat your facts with imagination is one thing, but to imagine your facts is another.” ~John Burroughs

Seem familiar to anyone on this blog?

Parallels are obvious between mathematical cranks and proponents of alternative medicine.

Many alternative proponents value their experience and understanding over the accumulated scientific knowledge of the last 200 years. HIV denial is the most depressing example. There are over 194,000 articles on HIV and AIDS. Even accounting for redundancy, there are over 250,000 people who have published on HIV and the detailed understanding of the disease and the resultant success of HAART had been a triumph of modern medicine.

Yet I read an HIV denier who said that what ever killed all those gay men in the 90’s is gone and now they are suffering from the HAART toxicity for no reason except to make big pharma and doctors rich.

“The formula “two and two make five” is not without its attractions.” ~Fyodor Dostoevsky, Notes from the Underground.

Most alternative proponents either alter or deny one or more components of objective reality as science understands it.

Homeopaths deny chemistry. Acupuncturists and chiropractors deny anatomy. Energy therapies deny our understanding of physics and energy. The all deny the validity of the scientific method.

If the basic precepts of any alternative therapy is correct, then 1000 years of knowledge gained in physics, chemistry, anatomy, physiology, biochemistry, embryology, pathology, biology are fundamentally wrong and the discoverer deserves multiple Nobel prizes. Or they are deluded (in the case of homeopaths, diluted).

I have a two part review of alternative medicine I occasionally give to the residents. Part two is a review of the reasons people are involved in alternative medicine.

“An error does not become truth by reason of multiplied propagation, nor does truth become error because nobody sees it.” ~Mahatma Gandhi

I have attributed the use and belief in alternative medicine to three things.

The first is lack of knowledge. Scientific medicine is complicated and difficult and takes years of work to understand. Most people do not have the time to devote to acquiring the necessary knowledge to become fluent in medicine. Alternative medicine is simple. Each alternative discipline produces an uncomplicated theory of everything based on one or two magical precepts. Easy to learn compared to the 9 plus years after college it takes to learn my field, Infectious Diseases. Once learned, alternative medicine requires no ongoing education. The lure of alternative medicine is understandable since everyone prefers simple solutions.

The mantra of the skeptical world is that knowledge changes behavior. I have always assumed that most people, if given sufficient knowledge and understanding, would abandon alternative therapies. All they need to do is learn to understand objective reality.

“There are lots of people who mistake their imagination for their memory.” ~Josh Billing

The second reason that people are involved with alternative medicine is that they do not understand how memory works and how easy it is to be fooled. I recommend the book The Seven Sins of Memory: How the Mind Forgets and Remembers by Daniel Schacter for a good review of the topic.

The five of the seven sins that apply to alternative medicine, for those who are interested, are

1) Memory Fades. After a month 75% of memory of an event fades. This sets us up for the other bias of memory. Most people think of memory as a videotape that perfectly records the past. Most recollections of past events are reconstructions based on current expectations and knowledge: people remember the past not how it was but how they think it should be.

2) Misattribution. We remember events that never happened or attribute events to people and things that were not there, or recall what happened but it occurs at the wrong time and place. One of the many reasons “anecdotal evidence” of therapeutic efficacy is suspect.

3) Memory is suggestible. More than one-third of subjects recalled being hugged by Bugs Bunny at Disneyland – impossible because Bugs is not a Disney character – after a researcher planted the false memory.” If you don’t accurately remember whether an alternative therapy worked, and you think it should, and someone tells you it worked, you will remember that it worked.

4) Memory is Biased: we remember events as to how we think they should have been.

We met at nine.
I was on time.
No, you were late.
Ah yes! I remember it well.

We dined with friends.
We dined alone.
A tenor sang.
A baritone.
Ah yes! I remember it well.

That dazzling April moon!
There was none that night,
And the month was June.
That’s right! That’s right!
It warms my heart to know that you remember still the way you do.
Ah yes! I remember it well.

How often I’ve thought of that Friday,
Monday night, when we had our last rendezvous.
And somehow I’ve foolishly wondered if you might by some chance be thinking of it too?
That carriage ride.
You walked me home.
You lost a glove.
I lost a comb.
Ah yes! I remember it well.

That brilliant sky.
We had some rain.
Those Russian songs.
From sunny Spain.
Ah yes! I remember it well.

You wore a gown of gold.
I was all in blue.
Am I getting old?
Oh no! Not you!
How strong you were, how young and gay;
A prince of love in every way.
Ah yes! I remember it well.

Hermione Gingold and Maurice Chevalier in Gigi. “These days Thank Heaven for Little Girls” just seems creepy.

5) Memory has persistence when associated with stressors. Intense experiences imprint memory and give them disproportionate importance.

“The difference between false memories and true ones is the same as for jewels: it is always the false ones that look the most real, the most brilliant.” ~Salvador Dali

I also like to refer to the book “Don’t Believe Everything You Think. The 6 basic Mistakes We Make in Thinking” by Thomas Kida, which dovetails nicely with the “Seven Sins of Memory,” and lists are nice for lectures.

1) We prefer stories to statistics.
2) We seek to confirm, not to question, our ideas
3) We rarely appreciate the role of chance and coincidence in shaping events.
4) We tend to oversimplify our thinking.
5) We sometimes misperceive the world around us.
6) We have faulty memories.

“I’m always fascinated by the way memory diffuses fact.” ~Diane Sawyer

Knowing how thinking is flawed combined with knowledge was, I thought, the first step in learning to think clearly.

The third reason I thought people were involved in alternative medicine are the numerous logical fallacies that we all participate in. I have 25 in my lecture, and if you are a splitter, there are many more. Humans do not naturally think clearly and rationally. Most of the time we are not aware we are using poor reasoning. Our every day thinking is flawed.

Combine a lack of knowledge with the vagaries of human experience and the stress of illness, and you have a potent woo flavored kool aid. Faulty thinking is a learned behavior and could be changed with education and awareness.

The examples provided by mathematical cranks gives me pause. There is no experience, no illness, no stress, no vagaries of experience that would lead one to misinterpret the world to make someone think they could square a circle or solve Fermat’s last theorem. Taking echinacea when you think you might have a cold and getting better is an experience that lends to the belief that echinacea prevents colds. What equivalent event leads someone to think they can square the circle?

It makes me wonder. Given the ubiquity of cranks of all kinds, of sins of memory, of logical fallacies, is being a crank in fact the norm? Tote up all the proponents of alternative medicine, astrology, UFO’s, Big foot, Atlantis, and that elephant in the room, and you are left with a paltry number of those who even try to think critically. Are the few who ascribe to a rational assessment of the natural world the deluded, the true cranks?

I am not inclined to consider various manifestation of reality denial as a mental illness, a delusion of some sort. I talked with some psych professionals trying to get a hint as to what, if any, label I could apply to those who think they can square the circle or is convinced that homeopathy makes sense. What do you call someone who consistently denies one or more aspects of objective reality? They, and I, were stymied. The archetype behavior that manifests in mathematical crankiness is too widespread to be abnormal. The closest term we could come up with was human.

It is why we may be doomed.

That’s my story and I’m sticking with it. It is the only reality based thing to do.

“Reality is that which, when you stop believing in it, doesn’t go away.” ~Philip K. Dick

Posted in: Book & movie reviews, Science and Medicine

Leave a Comment (18) ↓

18 thoughts on “Reality Deniers

  1. caoimh says:

    Hi Mark,

    That was an excellent post. I have a question if you could indulge me?

    It’s off topic but you mentioned echinacea does not prevent the
    common cold.
    Does it have any value at all?
    Alternatively could you point me to some laypersons resource on it’s efficacy or lack thereof?



  2. overshoot says:

    It makes me wonder. Given the ubiquity of cranks of all kinds, of sins of memory, of logical fallacies, is being a crank in fact the norm? Tote up all the proponents of alternative medicine, astrology, UFO’s, Big foot, Atlantis, and that elephant in the room, and you are left with a paltry number of those who even try to think critically. Are the few who ascribe to a rational assessment of the natural world the deluded, the true cranks?

    Fortunately, you’re overlooking the consequences of crank magnetism.

  3. This is a great post.

    Another parallel between mathematical cranks and proponents of alternative medicine is that they both seek to impose their beliefs upon the rest of us by enacting laws–not of the scientific type, but of the legislative type. This is especially true if they come from Indiana.

  4. DevoutCatalyst says:

    I’ve personally met a crank geometer who I guess is convinced that most mathematicians are shills of Big Euclid.

    If we could improve our educational system to teach critical thinking skills, might we at least achieve in the general population some sort of herd immunity to pseudoscience? Fleischman & Pons received a forceful Bronx cheer from physicists, can we create a society that is similarly self-correcting?

  5. @ Caoimh:

    Echinacea’s value is to comfort people who believe in it. The official, current evidence-based medicine proclamation is that it does not prevent colds at all, but might–yeah, might…

    “…modestly reduce symptom severity and duration, possibly by about 10% to 30%…Not all research is positive. Some studies show no benefit for treating the common cold in adults. A study in children aged 2-11 years also suggests that taking an Echinacea purpurea juice extract 7.5-10 mL/day for up to 10 days also does not significantly decrease cold symptoms.”

    (From the Natural Medicines Comprehensive Database: )

    In summary, echinacea doesn’t work.

  6. tarran says:

    Dr Atwood,

    What force.

    The various iterations of the health freedom act merely allow people to choose what they do to their bodies.

    Simmilarly the pi bill wouldn’t have actually forced anybody to use the cockamany thorem in their calculations. You can continue to use whatever value of pi you want. Legistlatures are always passing dumb bills like bills declaring Feb 19th to be eyeball Appreciation Day or the Spotted Skunk as the state mammal. It prevents them from doing really dumb things like outlawing marijuana or passing economic stimulus bills that wreck the economy.

    Oh, and no discussion of mathematical crankery is complete without:
    THE TIMECUBE!!!! Warning may induce epileptic fits in susceptible people. If you have a sense of style or artistic taste, you may feel nauseaus. Do not stare directly at the blinking fonts. Those of you who do not recognize the majesty of the timecube are educated stupid. You have been warned! ;)

  7. AIEEEEE not the TIMECUBE!!!!

    This is a great post, Mark.

    I am enthralled by the idea of math cranks! I mean, we always think of math as being the purest, most logical field. It’s true that the reality-denial of alternative medicine practitioners is just as strong, but… there’s just something about the DENIAL OF PI that I just… really find striking. o.O


    I’m going to be thinking about that all day.

    Must go work problem sets to clear my head.

  8. Zetetic says:

    Math & physics the purest & most logical of endeavors? People in those fields are not immune! I am reminded of a past co-worker with a graduate degree in physics and was a brilliant programmer in multiple languages. He also subscribed to multitudes of Woo, both fundamental religious and wacky – Creationism, UFOs, Atlantis, Crop Circles, 9-11 conspiracies, etc. He is the one who first told me about the year 2012 prophesies that are a current mania – He was way ahead of everyone else, it was about 3 years ago!

  9. Joe says:

    tarran on 30 Jan 2009 at 9:10 am wrote “The various iterations of the health freedom act merely allow people to choose what they do to their bodies. ”

    No, adults can already do that. The “health freedom” movement seeks to hold quacks harmless when they … cause harm.

  10. NeoDevin says:

    Mathematical crankery at its best:

    389 page discussion on whether or not 0.999… equals 1 (anyone unsure, just try subtracting them, and see what you get, it’s almost trivial to prove that they are equal)

  11. Fifi says:

    I’ll say it again – there is no freedom of choice when people don’t and can’t know what they’re choosing from. All the deregulation called for by advocates of so-called “health freedom” ends up leaving patients with no true freedom of choice. Why? Because one can’t make an informed choice if the truth is being hidden because deregulation means that verified information isn’t available and lies can be sold with impunity. The only “freedom” really being lobbied for is freedom to con people for profit by Big SCAM.

    As it stands, people are free to use SCAM instead of evidence based medicine (in Canada, the US and Europe). They’re also free to simply refuse any kind of treatment (as long as they’re not a danger to public safety).

  12. Joe says:

    Fifi on 30 Jan 2009 at 1:21 pm


  13. pmoran says:

    Mark: “I have attributed the use and belief in alternative medicine to three things.”

    You probably did not mean this exclusively, but implying that AM use is entirely to faulty reasoning and crankery comes across as unnecessarily demeaning to a public that is inevitably less privileged than us in scientific and medical knowledge.

    I would have proposed a different three factors as the main ones sustaining AM :

    1. Unmet medical needs. AM would scarcely exist if conventional medicine had simple, cheap, entirely safe and entirely effective answers for everything .
    2. The power of the personal testimonial at the individual level
    3. Compulsive behavior in the use of medical treatments. Doing nothing about problems is alien to us.

    “It might not be true but I am distressed enough to give it a try and Auntie Jane said it helped her” is a far more common reason for the individual USE of AM than true belief or crankery.

    Agreed, a great many will leap to the defense of AM when it is attacked by skeptics, but I am sure that this can be a reaction to the implication (evident here) that AM use is a sure sign of stupidity. Who would not react to that? In my opinion very little AM use is based upon conscious scientific judgments and most involves no strong prior investment of belief — it is simply something to try out when faced with unresolved medical problems. I think any other understanding of CAM can lead to deeply counterproductive attitudes.

    The importance of the minority of nutcases and cranks lies in their ability to keep sections of the public off-balance — not quite sure what to believe. I read somewhere that doctors want to keep people sick and dying (etc). The extremists have an undue influence upon our perceptions of AM, too, because we end up in so many confrontations with them.

    Add the merest smidgeon of “not being quite sure what to believe” to the factors listed above and you are getting closer to the true explanation for a vigorous market in “alternative” medical products and services. It is a dream environment for frank fraud to flourish, not merely the traditional quack. What is astonishing is that so many of the public maintain their allegiance to “proper” medicine.

  14. Jules says:

    1) Fermat’s Last Theorem was, in fact, solved. There was a problem with one of the conjectures upon which the solution was based, but that was resolved. After a few years, but it was resolved. FLT is solved. And not by a crank, either.

    2) I think the other reason why alternative medicine is so alluring is because sometimes it does work, though not for the reasons stipulated. And then, when one works, curiosity naturally leads one to investigate whether others do, too. Let’s say you’ve been feeling really tired and grumpy lately, even though you’ve been getting plenty of sleep. Your doctor finds nothing wrong with you. You decide to try a “detox” diet (involving lots of fruit, vegetables, no refined carbs or fat, or some variation thereof, with the main theme being “less than 1000 cal/day”). And lo and behold–you’re bouncing off the walls by day 5 (I’ve actually done this inadvertently, during a weeklong session of grant-writing, and I was indeed hyper as a kite at the end of it). You attribute this sensation to the “purging of toxins in your body by a clean diet” (I did have the good sense to realize that it was because not eating enough for so many days had f*cked up my brain chemistry), and then surmise that if dietary detoxification was so beneficial, coffee enemas might be better…etc etc.

  15. nitpicking says:

    Conversation between me and a friend over 10 years ago. I was already a SKEPTIC reader and somewhat familiar with cranks.

    “I solved one of those big mathematical problems that’s supposed to be impossible, but I don’t want to tell you the details until I get published because I’m afraid someone will steal my idea.” (This really set off the crank detector.)

    ME: “So you trisected the angle?” (Stab in the dark but ….)


    “It’s one of the famous impossible ones, and lots of people think they’ve solved it. It really is impossible, though.”

    “NO, it isn’t. I solved it.”

    “Let me guess: you marked the straight edge.”

    “Sure, of course I did.”

    “The conditions of the problem forbid marking the straight edge. It isn’t a ruler. That’s a common flawed solution.”


    Not being a true crank, Dave was sane enough to acknowledge that if the problem was defined to forbid marking the straight edge, he hadn’t solved it. I believe that he thought I was psychic for a while because of my lucky guess, instead of a big Martin Gardner fan.

  16. Fifi says:

    Dr Moran – “I would have proposed a different three factors as the main ones sustaining AM :
    1. Unmet medical needs. AM would scarcely exist if conventional medicine had simple, cheap, entirely safe and entirely effective answers for everything .
    2. The power of the personal testimonial at the individual level
    3. Compulsive behavior in the use of medical treatments. Doing nothing about problems is alien to us.”

    Yes! Plus the ubiquitouos propaganda within mainstream media and at health clubs and yoga studios, and the general aging of the population, all contribute to sustain, normalize and validate AM in a person’s mind.

  17. Wallace Sampson says:

    For anyone still listening, a few additions to an excellent post.

    1) I say excellent because it parallels one or more of my lectures in my “Scientific View” course on “altmed” and talks for physician hospital staffs.

    at Stanford and for physician staffs. And both I assume were constructed independently – at least I did not know you, Mark.

    2) Echinacea: I wrote an editorial type summary a few years back on echinacea ( Sampson W. Studying herbal remedies, N Engl J Med. 2005 Jul 28;353(4):337-9) pointing out the lack of evidence based on at least three clinical trials to that point,
    But also, based on historical absence of any credible information leading to the claim in the first place – supposedly a Native American/First nation traditional cold/respiratory illness cure. I could find no confirmation of that in 16 standard herbal texts including two standards on Native American medicine.
    The claim, it seems, originated twice – once in a late 19th – early 20th century naturopath, and secondly when introduced in Europe later 20th century by a Swiss naturopath from where it was reimported to the US some 30 years ago.
    What is also surprising has been absence of acceptance of the editorial’s contents by other sources such as naturalmedicines comprehensive data base, and other more “official” sites. It shouldn’t have surprised given what we know about them and after what Mark has in the post.

    3) Other standard references on human thinking/memory defects; two by Loftus: Memory and Eyewitness Testimony, another on heuristics – Judgment under Uncertainty by Kahneman, Slovic, Tversky. Lots of others on Knowledge like “How We Know What Isnt So” by Tom Gilovich. and Anomalistic Psychology by Zusne and Jones. Also Perseverence of belief articles by Lee at Stanford. All contain original experiments…ingenious designs and surprising results.

    Compliments again on this useful post.

  18. The Blind Watchmaker says:

    As usual, a breath of fresh air.

    Thanks for the great post. Keep ‘em coming. Love the Quackcasts too.

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