Martin Gardner (1914-2010) was one of the foremost anti-pseudoscience polemicists of the 20th and early 21st century. His 1957 book “Fads and Fallacies in the Name of Science” became a classic and seminal work of the skeptical movement. In 1976 he joined with fellow skeptics, including Paul Kurtz, Ray Hyman, James Randi, and Marcello Truzzi to found the Committee for the Scientific Investigation of Claims of the Paranormal (CSICOP), an organization promoting the use of science and reason in examining extraordinary claims. In the early days of CSICOP there was a discussion as to whether believers in PSI would be invited to join, with Truzzi taking the position that investigating PSI should be part of its mission. Gardner was supposedly against it, stating that Truzzi "conferred too much respectability to nonsense." Although Gardner was not an academic (and did not have a PhD), he was thought to be a mathematical genius. Douglas Hofstadter is reportedly to have said, “Martin Gardner is one of the greatest intellects produced in this country in this century.” Stephen Jay Gould is reportedly to have said that Gardner has been “the single brightest beacon defending rationality and good science against the mysticism and anti-intellectualism that surround us.” In any event, Gardner was second to no one in his outspoken criticisms of pseudoscience and the paranormal in all its forms.

But there was one problem. Gardner believed in God. In a famous essay called Science and the Unknowable, Gardner stated his beliefs about the limitations of science:
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“If one is a theist, obviously there is a vast unknowable reality, transcending our universe, a "wholly other" realm impossible to contemplate without an emotion of what Rudolph Otto called the *mysterium tremedum.* But even if one is an atheist or agnostic, the Unknowable will not go away. . . The emotion behind all religions, aside from their obvious superstitions and gross beliefs, is one of awe toward the impenetrable mysteries of the universe.”

“No matter how many levels of generalization are made in explaining facts and laws, the levels must necessarily reach a limit beyond which science is powerless to penetrate.”

(Martin Gardner, Science and the Unknowable, Skepical Inquirer, Vol. 22, No. 6 (November 1998) Reprinted in Paul Kurtz (ed.) Science and Religion: Are They Compatible, pages 323-331)
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So, how could this diehard skeptic believe in God? Was this the God of Spinoza, or Einstein’s God? No. Gardner believed or had faith in a traditional God, and in an immortal soul! It is worth quoting Gardner at length. The following is from a 1997 interview with Michael Shermer for for Skeptic Magazine:
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Skeptic: Inevitably skepticism leads to asking the God question. You call yourself a fideist.

Gardner: I call myself a philosophical theist, or sometimes a fideist, who believes something on the basis of emotional reasons rather than intellectual reasons.

Skeptic: This will surely strike readers as something of a paradox for a man who is so skeptical about so many things.

Gardner: People think that if you don’t believe Uri Geller can bend spoons then you must be an atheist. But I think these are two different things. I call myself a philosophical theist in the tradition of Kant, Charles Peirce, William James, and especially Miguel Unamuno, one of my favorite philosophers. As a fideist I don’t think there are any arguments that prove the existence of God or the immortality of the soul. Even more than that, I agree with Unamuno that the atheists have the better arguments. So it is a case of quixotic emotional belief that is really against the evidence and against the odds. The classic essay in defense of fideism is William James’ The Will to Believe. James’ argument, in essence, is that if you have strong emotional reasons for a metaphysical belief, and it is not strongly contradicted by science or logical reasons, then you have a right to make a leap of faith if it provides sufficient satisfaction. It makes the atheists furious when you take this position because they can no more argue with you than they can argue over whether you like the taste of beer or not. To me it is entirely an emotional thing.

Skeptic: Couldn’t someone make this same argument for belief in New Age hokum? Couldn’t they quote you in support of their beliefs?

Gardner: They could use that argument, except New Agers also have a whole series of beliefs that can be empirically refuted. Like reincarnation — the evidence against that is overwhelming. Most New Agers also accept most of the beliefs of the parapsychologists. They believe in ESP and PK and channeling. We have very strong empirical evidence against these beliefs. So I think there is a big difference between belief in God and belief in the paranormal. William James made this clear in The Will to Believe. In the first place, it has to be a leap of faith about something that has overwhelming importance to an individual. Second, it has to be something for which there isn’t any strong empirical evidence or logical argument against it. So there is something radically different about belief in a mind behind the universe and the whole cluster of beliefs that the New Age movement presents.
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Now I think Gardner is entirely wrong in his assessment about the evidence for and/or against the paranormal. But that is another post. What is more important as far as I am concerned is the obvious inconsistency, if not logical absurdity, of his position. The “leap of faith” he acknowledges as legitimate is based upon a negative assumption that “there isn’t any strong empirical evidence or logical argument against it.” The evidence against the paranormal that he constantly cites is *entirely* based upon the laws of materialist science, which laws insist that such things cannot happen. These same laws preclude any notion of a non-physical, causally efficacious, mind in humans (free will); and presumably even more so in some vague idea of a personal God.

When Gardner states: “No matter how many levels of generalization are made in explaining facts and laws, the levels must necessarily reach a limit beyond which science is powerless to penetrate,” he is inviting all sorts of phenomena into reality, including the paranormal that he emphatically denies. And once this door is open, he cannot slam that door shut whenever it suits him. Moreover, the “feelings and emotions” he claims to justify a “leap of faith” are explained by the laws of materialist science as the effects of the limbic system of the brain. There is no room in neuroscience for *any* justification for a “leap of faith” in the reality of God from such emotions and feelings.

Now, a true and honest skeptic might respond to Gardner’s theism with a ruthless and relentless attack on such “nonsense;” similar to his own ruthless and relentless attacks on the paranormal. But Gardner is one of their prophets, so there has been a “hands-off” policy against such attacks for decades. However, for me the lesson is not that Gardner’s theism was wrong, or unjustified. After all, science *is,* as Gardner claimed, severely limited in its access to reality. Rather what was wrong was first, his (and others) unbridled, and narrowly focused skepticism on those aspects of human experience that simply do not fit into their own favored worldview, and thus by fiat cannot count as evidence for any reality not confirmed by science; and second, the underlying scientism that states that current materialist science is, or should be, the final arbiter and gatekeeper of what can count as the reality behind usual forms of human experience. Gardner's feelings about God were intuitions of the transcendent that were too strong to be dismissed--even by one of the worlds most notable skeptics.

And your point is ?

It's ghawd as a style choice (the outward, nonessential) v. ghawd as a fundamental building block.

Dave the Atheist Wrote:
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> And your point is ?


I guess he's competing with Steve Benson to see who can post the longest.

At least Steve posts original stuff.

Read it again Dave, it's in there somewhere.

You have to bring it down to our level Henry or you won't have much of audience.

Because Terry Jones died recently, I've been looking up some of his content on Youtube. His series Medieval Lives is fun and each episode deals with a character from those times.

In this episode he deals with "the Philosopher" which back in those times referred to scientists too. It is interesting to note that contrary to modern popular opinions of the time, churchmen were at the forefront of scientific research and scientists were mixed up in astrology, alchemy etc but did yield some results. Jones also points out that most medieval people did not think the world was flat (although they did think the sun went round the Earth).

https://youtu.be/LVdA4gs-z8A

Science and Religion? What is an oxymoron, Alex.

Making the post falsely true?

Thanks for the information on Martin Gardner. I wasn't aware of much of that. I think the very first book I ever bought was a collection mathematical puzzles he published in 1957. I stumbled across it a decade or so ago, and was surprised at the date. I also had to throw it out. The high acid cheap paper had basically eaten itself, and the pages were too brittle to turn.

Gardner got me reading his column in Scientific American, which got me reading the rest of the magazine, which gave me enough of a science background as a kid to start to seriously question the BoM and especially the BoA. Gardner, along with all the math programs thrown together in the US after the Russians beat us into space with Sputnik, and an outstanding math teacher that I had for 10th thru 12th grade, was what got me into being a math major.


Some other quotes along the same lines that you might add you your repertoire:

If I should ever die, God forbid, let this be my epitaph: The only proof he needed for the existence of God was music.
- Kurt Vonnegut (famously atheist)

This Vonnegut quote you will be less fond of. :)
Those who believe in telekinetics, raise my hand.

Another person, who if you are not familiar with him, you ought to be (by you, I mean anyone reading this)
https://en.wikipedia.org/wiki/Donald_Knuth

From the religion subheading of his wikipedia article:
In addition to his writings on computer science, Knuth, a Lutheran,[30] is also the author of 3:16 Bible Texts Illuminated,[31] in which he examines the Bible by a process of systematic sampling, namely an analysis of chapter 3, verse 16 of each book. Each verse is accompanied by a rendering in calligraphic art, contributed by a group of calligraphers under the leadership of Hermann Zapf. Subsequently, he was invited to give a set of lectures on his 3:16 project, resulting in another book, Things a Computer Scientist Rarely Talks About, where he published the lectures "God and Computer Science".

He is arguably the godfather of Computer Science. He started on an epic series of books called The Art of Computer Programming (acknowledging it is at least as much art as science), a 7 volume magnum opus. He is in his late 80s, and still working on volume 4, which has turned out to be 3 hardcover volumes itself. So far. He still hopes to finish the series. I am doubtful. I jumped into the middle of computer science after my mission. It was a field that didn't even exist before my mission. "Knuth volume 1" as it was universally known was my baptism by fire. It was the text for my second course in CS.

He stopped writing those books temporarily because he felt typesetting software for printing mathematical text was awful, and there was no good software to aid people in designing fonts. He created TEX and MetaFont, now the 2 standard software packages in math typesetting, and font design. That was how he got to know so many calligraphers, and got into the 3:16 project, which he wrote about in some detail (including about his belief in God) in his book "Things a Computer Scientist Rarely Talks About". I recommend the first book simply as a piece of thought-provoking art, and the second as a nontechnical introduction to a great mind.

He still lives in Palo Alto, and wanders over to Stanford now and then to hold forth. I suspect it is always an SRO crowd.


And now I am out of time, and will be gone all day. I will return to add my commentary on the quoted material from Gardner. The short version is summed up by my second Vonnegut quote above.



Edited 4 time(s). Last edit at 02/08/2020 12:56PM by Brother Of Jerry.

Thanks for this. I will look forward to your further thoughts.

Fascinating.

Do you know him or ever go hear him?

I have never seen Knuth in person, but have read much of his work. He did a math book, essentially a book length "more leisurely" presentation of the math preliminaries in Chapter 1 of TAOCP. Read some of the Amazon reviews for Concrete Math. Hard to believe people would get that excited about a math book.

I was working at a company in Utah, and a group of 7 of us decided to get together for lunch once a week and assign ourselves reading and problems from Concrete Math. Everybody in this group had at least the equivalent of a college minor in math, and most had 40 credit hours or more. Two of them had PhDs in physics, which has a ton of math.

Anyway, we got to chapter three, and the problem we assigned ourselves for what turned out to be our last week, took everybody 5 to 7 hours to solve. Between all the members of the group, we came up with two fairly different approaches to solving it, both of which worked. We dropped the project after that week because we had families and demanding jobs, and taking an extra 7 or so hours to read the material and solve one bloody problem was more time than we were willing to sacrifice. We were actually quite pleased with ourselves at having correctly cracked a very tough nut, and thought we should quit on a high note, rather than waiting until we were trapped in the quicksand, a fate that was looking more and more likely each week.

And for all you people who "can't do math", even people who can do math sweat long and hard on some problems. You put in your 10,000 hours of practice, and you too can be way better than the average bear at math.

Things Knuth does in his books:
Cites authors names in their English orthography, and as written in their native language.
Cites sources for exercises when he can find them. I have NEVER seen that in any other math book.
Lists all the TAs who helped teach the course when he was writing the text.
In Concrete Math, students reviewed the manuscript and wrote comments in the margins. He included many of them in the margin of the finished book. Some were smart-ass, some were helpful to other students (e.g. "start skimming here, for the rest of this section"). Some were quotes from people in the field.
Speaking of which, he now does quotes in English and the author's original language. I have seen that in other author's books.
His indexes are legendary. Even the comments in the margin are indexed.

In short, the attention to detail is jaw dropping.

I have seen Steve Jobs in several of his reality-distortion presentations in San Jose, and I've met Grace Hopper, who is not an academic like Knuth, but kind of the godmother of CS and remarkable in her own right. Stories for another day.

Interesting.

I am not a mathematician, as you know, but I have what is for normal mortals a strong background in the discipline and work in a related field. I am also nerd enough to have bought math books--linear algebra, stochastic processes, probability theory, option pricing, game theory--for vacation reading.

People like Knuth are fascinating to me: their (your) brains are wired differently, sort of like the prevalence of dyslexics in certain sorts of advanced physics.

"I am not a mathematician, as you know, but I have what is for normal mortals a strong background in the discipline and work in a related field. I am also nerd enough to have bought math books--linear algebra, stochastic processes, probability theory, option pricing, game theory--for vacation reading."

COMMENT: Most of my knowledge of mathematics is self-taught, and on the theoretical side rather than the problem solving side. Although I think I have a pretty good understanding of mathematical theory, and mathematics as it relates to physical theory, I do not --and in complex cases cannot-- *do* the math so to speak.

Having said that, my experience is that when mathematicians move away from applied mathematical problem solving, and engage the more theoretical issues, including such issues involving mathematics itself, theoretical physics or biology, philosophy, or theology, they often stumble on the broad facts, theories, and conceptual logic that is necessary for such engagement. I don't know why, and there are, of course, many notable exceptions. (And, of course, it may be me that is doing the stumbling!)

No doubt that Knuth's technical writings are over my head mathematically, but I am skeptical as to whether he has anything new and meaningful to say about religion. His book, is "Things a Computer Scientist Rarely Talks About (2001)" which is described as follows:

"Things a Computer Scientist Rarely Talks About (2001)is a book by Donald E. Knuth, published by CSLI Publications of Stanford, California. The book contains the annotated transcripts of six public lectures given by Donald E. Knuth at MIT on the subject of relations between religion and science (particularly computer science).[1] Knuth gives credence to the concept of divinity."

I think the book applies computer algorithms to Biblical scripture in some way. I can see how this might result in some interesting statistical facts, but fail to see how this might be theologically interesting, and much less some level of Biblical justification or support of religious faith. But, I have not read this book, so don't know. Maybe BoJ has read it and would offer a comment on it.
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People like Knuth are fascinating to me: their (your) brains are wired differently, sort of like the prevalence of dyslexics in certain sorts of advanced physics.

COMMENT: Interesting observation. It reminds me of autistic savants, or people with Asperger's, who are exceptional geniuses in one area, e.g. mathematical calculations or calendar counting, but who come up short in less rigid and more open theoretical endeavors. I am not saying this about Knuth, of course, or others with mathematical gifts, but there is a temptation to suggest that they *are*, as you say, "wired differently."

Finally, do you have any thoughts about the post generally? Or am I just too far off base for you to comment? :)

On being wired differently: I don't know if the type of people who go into STEM fields, particularly software engineering has changed over the years. I suspect it has normalized somewhat, but back in the early days, I would not be at all surprised if 5 to 10% of the people who went into computing, and maybe even higher percentage than that, were somewhere in the Aspie spectrum.

In fact, I am of the opinion that "Aspie" is just an extreme version of the Meyers-Briggs personality type INTJ, a type which is relatively rare in the general population, and are a dime a dozen in university tech departments (and on RFM, which is rife with INTJs. In the general population, they are about 3% if I recall correctly)

Aspies clearly do not make good Mormons! ;)

"Different wiring" is truly a thing. The reason people have the standard learning disabilities is because their brains are structured in non-standard ways.

I don't know much about autism although savants appear to function as they do because the parts of the brain normal people use to register others' emotions (and other things) are wired into different mental systems. Dyslexics are like that as well: reading centers in the brain are wired into three-dimensional thinking. The world expert on dyslexia is a Yale academic who notes that 1/3 of software engineers "suffer" from the "disorder," which she calls "the MIT disease."

This "wiring" explains why people with basically the same intellectual firepower have such different strengths and weaknesses. Society does better, and will do better, when it recognizes the strengths concomitant with the differences in brain structure rather than just consigning those with learning differences to the "stupid class" as was routinely done decades ago.

My only problem with this is the suggestion that "wiring" or "brain structure" provides a meaningful "explanation" when neuroscientists really have little understanding of what such "structures" are and how such structures account for human experience and behavior. Typically, to fill this out, neuroscientists turn to neural imaging, where very course "structures" seem evident, but in most cases only loosely tied to specific experiences. My own skepticism in this regard was fueled by the writings of William R. Uttal, in particular his book, The New Phrenology: The Limits of Localizing Cognitive Processes in the Brain.

In short, all such structural "explanations" are merely place holders that are dependent upon Crick's astonishing hypothesis that essentially all of human experience and behavior is explainable solely by appeal to the brain. In the case of savant syndrome this hypothesis is strained because in some cases the heightened abilities of the savant do not have a clear neurological corollary.

This is well-established science. Imagery showing how different centers of the brain use energy are scientific facts as are patterns by which different parts of the brains communicate with each other. When those patterns line up with phenomena like dyslexia with predictive ability, the findings are real.

I don't care about "Crick's astonishing hypothesis that essentially all of human experience and behavior is explainable solely by appeal to the brain." It would be a mistake to let an emotional recoil from that extreme hypothesis get in the way of more prosaic, and reliable, discovery.

"This is well-established science. Imagery showing how different centers of the brain use energy are scientific facts as are patterns by which different parts of the brains communicate with each other. When those patterns line up with phenomena like dyslexia with predictive ability, the findings are real."

COMMENT: Read the book.

https://mitpress.mit.edu/contributors/william-r-uttal

"There is thus an enormous chasm between what can and cannot be done to solve the localization problem, on the one hand, and what has actually been concluded from well-intentioned, but inadequately reasoned research, on the other. Whatever specialization and localization may occur in the brain, and however isolated the dimensions of a sensory code may be in the peripheral transmission pathways, it seems far more likely that the mind, consciousness, or self-awareness represent the merging or binding of many different underlying processes and mechanisms into an integrated singular experience. It should be understood that the unity of subjective experience therefore contradicts the hypothesis of cognitive localization in a fundamental way. Whereas the unity hypothesis emphasizes how the brain puts together mental events, the localization hypothesis emphasizes how it takes them apart. There is thus a tension between our subjective experience-- the most direct evidence of our own mental activity-- and the analytic assumption on which all of the work in the field of localization is premised. The attempt to marshal arguments for mental modules and cerebral region associations must assume something that does not seem, at least to a first approximation, to be so -- that mental activity can be analyzed into separable components."
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"I don't care about "Crick's astonishing hypothesis that essentially all of human experience and behavior is explainable solely by appeal to the brain." It would be a mistake to let an emotional recoil from that extreme hypothesis get in the way of more prosaic, and reliable, discovery."

COMMENT: It sounds to me like the "emotional recoil" is coming from you!

This is crazy.

I don't care about the philosophical implications of specific scientific analysis. A fact does not cease to be such simply because someone doesn't like where that analysis might ultimately lead. You are arguing backwards; you might as well dismiss the heliocentric description of the solar system because it diminishes the stature of God's creation.

Uttal was a well-regarded psychologist with a Ph.D. from the 1950s. He had no academic training in neuroscience. I'm hardly going to reject rigorous studies done by people with current credentials and publications in the world's best journals in deference to an elderly curmudgeon no matter how important a skeptical view of the literature is as a general matter.

You can refuse to entertain material that you believe contradicts your particular weltanschauung, but I am going to proceed from the other direction. I am interested in data and fundamental research, not a priori generalizations.

"Uttal was a well-regarded psychologist with a Ph.D. from the 1950s. He had no academic training in neuroscience. I'm hardly going to reject rigorous studies done by people with current credentials and publications in the world's best journals in deference to an elderly curmudgeon no matter how important a skeptical view of the literature is as a general matter."

COMMENT: William Uttal was a well-respected cognitive scientist and engineer who well understood neuroscience, and was an expert on brain imaging to the day he died. Calling him "crazy" or an "elderly curmudgeon" displays nothing but your own ignorance. I know of no neuroscientist, or any other academic, who has criticized his work or called into question his credentials. Perhaps you can point one out, or provide a link that addresses the issue of brain imaging substantively, instead of your ad hominem nonsense.

Like most scientific skeptics, you are fine with skepticism, so long as it is not directed to your favored theory or subject. Then it must be "crazy." This is essentially what you are saying here.

According to religion skeptic Paul Kurtz:

"By the same token, skeptical inquiry in principle should apply equally to economics, politics, sociology, ethics, and indeed to all fields of human interest."

As with you, this, of course, is nothing but lip service. What he really means is that skepticism should be selectively applied to whatever point of view one is against; or whatever person challenges one's cherished beliefs. His writings prove that repeatedly. I know, because I have actually read his books and essays. (A novel concept!)

Thank you for your contribution to this post, and particularly for inadvertently confirming the point I intended to make.

> Calling him
> "crazy" or an "elderly curmudgeon" displays
> nothing but your own ignorance. I know of no
> neuroscientist, or any other academic, who has
> criticized his work or called into question his
> credentials. Perhaps you can point one out, or
> provide a link that addresses the issue of brain
> imaging substantively, instead of your ad hominem
> nonsense.

I didn't call him "crazy." I called you crazy. As for the term "curmudgeon," that came from his obituary as written by a friend and scientific colleague. But it doesn't really matter insofar as the word is a description of his demeanor, not his research, and hence is not an "ad hominem" attack on his work.


------------
> Like most scientific skeptics, you are fine with
> skepticism, so long as it is not directed to your
> favored theory or subject. Then it must be
> "crazy." This is essentially what you are saying
> here.

You either don't pay attention or you have a poor memory. Have you ever heard me describe myself as an atheist? Hint: no. Why? Because as I have said innumerable times, I do not believe science can disprove the existence of God. Moreover, three or so years ago I posted several things on the limits of human intellect and hence on scientific epistemology. You took exception to that, arguing that my skepticism about science was unwarranted. For you to turn around now and say I am not skeptical about science is, to put it charitably, inconsistent.


------------
> According to religion skeptic Paul Kurtz:
>
> "By the same token, skeptical inquiry in principle
> should apply equally to economics, politics,
> sociology, ethics, and indeed to all fields of
> human interest."

Absolutely true.


-----------------
> As with you, this, of course, is nothing but lip
> service. What he really means is that skepticism
> should be selectively applied to whatever point of
> view one is against; or whatever person challenges
> one's cherished beliefs.

And yet it is you who has a worldview that disregards mundane but consistently demonstrated science contradicting your "cherished beliefs."

I don't have a worldview. What interests me is what actually works. You didn't even address the specifics of my point, which are well-documented in current research and employed effectively in clinics all across the Western world every day. Am I to disregard that work? Am I to refuse to use proven derivative techniques to design learning curricula for people with disabilities because you a priori reject the entire body of science?


--------------
> Thank you for your contribution to this post, and
> particularly for inadvertently confirming the
> point I intended to make.

What I confirmed was that your worldview prevents you from reading clearly what I have written in this thread and many others. I will not join you in denying well-documented science the way a TBM denies Meso-American archaeology or a climate skeptic averts her eyes from the actual data.

The brutal truth, Henry, is that you are an intellectual anti-vaxxer, so confident in your worldview that you deny actual science. That is unfortunate.

To LW - you're better at math than I am at history. Your interests seem to be at the statistics end of math, never my forte. I have been interested in options pricing, because the principle seems so simple. When an option expires, it is worth zero dollars. Ideally, there should be a stable glide path from an option's current price down to zero at expiration date (in calculese, the first derivative should be constant). Any time the option price has fallen too rapidly, or too slowly, there is an opportunity to make money because the option must return to that ideal glide path at some point before the option expires.

Of course changes in the underlying stock price change the glide path, but that does not make it disappear. In fact, I imagine it is changes in the stock price that knock the option price off the glide path in the first place. First Quant that notices the discrepancy makes money. Or so it seems to me.

Me, I struggled in HS algebra. Really. One quarter of algebra II was my one and only D in HS, and may have been my only grade below B. Factoring polynomials drove me nuts. I learned in later life that it drives a great many people nuts. Abstract Algebra in university also drove me up a wall. I was thrilled to find out the Douglas Hofstadter dropped math and went into physics because of the exact same course.

I was interested in calculus, IMHO, the first course where math gets exciting. High school math is the math equivalent of practicing piano scales. Useful tools, but rarely fun. the other subject was number theory, the study of the properties of integers.

Number theory was the darling of theoretical mathematicians, because it had almost no practical applications. People went into it just for the beauty of the theorems. then along came computers, and integers and their properties suddenly became Very Important. Those https secure web sites - serious number theory involved there.

Knuth's Concrete Math book was so named as a pun about being a combination of CONtinuous and disCRETE math (calculus and number theory, respectively). It is a garden of delights for people like me.

COMMENT on Henry's comment on LWs comment: Knuth's book on Bible Text Illuminated and his companion book Things a Computer Scientist Rarely talks about, has very little computer science type math in it. He does explain briefly how one can get a feel for the content of a huge sprawling work like the Bible by using statistical sampling methods, and he chose to examine in depth chapter 3, verse 16 from every book in the Bible, with slight variations when a particular book didn't have 3 chapters or 16 verses in chapter 3. He assigned each verse to a calligrapher to let their imaginations run wild and do something with it. He wrote some back story to put the particular verse in context.

BTW, he picked 3:16 because that means John 3:16 (For God so loved the world that he gave.... y'all know that one) would be inn the list, so he was guaranteed at least one really good verse. So his sampling choice was slightly biased in that he knew in advance what one of the verses was going to be.

The other book is mostly a series of lectures about how the idea for the book formed, and how the process of writing the book proceeded. He was often very surprised and delighted at the artwork he got back. Interwoven in the text are his thoughts on creativity and on religion.

I don't actually recall if I have ever read the second book all the way through. I think it is basically six one hour lectures, committed to print, so it is not that long a read. I should put that at the top of my "to read" list. I will return and report.

I love all math although household and professional things prevent me from reading the way I used to do. But I have to qualify that by saying that the high school math classes were indeed torture. I tell people that Calculus is when math starts getting interesting, where it starts changing your worldview.

A chunk of my life has been consumed by taking big problems and devising models to explain them. This usually involves relatively simple math combined with a lot of big-picture thinking about what variables really matter, the model's weaknesses, etc. Although the clients generally focus on the quantitative outcomes, I learn more from the process in terms of elucidating causes and connections. These exercises are not high-level math per se, but they are assuredly mathematical.

Finance interests me because it is one of the few fields in which math is not only elegant but relevant. Option models are fun because they allow you to break down the components of pricing, meaning gamma, delta, theta, vega, etc., and then to construct portfolios as desired. But then these things verge on philosophy to the extent that "risk" is defined by historical volatility and one wonders whether that assumption makes any sense in a world where systems change by the day.

Math is a discipline but it can also be a way of life!

If you keep banging your head on Concrete Math, you will get a headache.

The preface to the book makes that point. It also calls the book "a concrete life preserver thrown into a sea of abstraction". That metaphor can be read several ways!

All of my posts are accessible to literally everyone on the Board who is interested enough in the subject to make the effort to read them carefully, think about it, and perhaps Google a concept their are not familiar with. (Or, God forbid, ask!) If some of you are not interested in making such an effort, that's fine.

In any event, here is a response to the several respondents who failed to see the point of this post. So, let me make it crystal clear, because it might well apply to you!

A belief is simply a mental state; a psychological mental disposition that some proposition is true or false, or that some entity or event exists, happened, or will happen. The proposition stating such a belief is called a “propositional attitude.” All such beliefs are based upon experience and perhaps neurological predispositions, but they do not have to be rationally based. They are just beliefs that we have, whatever their source, and whether they "make sense" or not.

The above applies to beliefs about “God,” in all their varieties. Some hold a belief that there is such an entity, some hold the belief that there is not. Some have mental states that vacillate between the two in complicated ways. Note, however, that such bare beliefs about God also do not have to have a rational basis. When you merely express a belief you are simply *stating* what your mental disposition is about some proposition. You are not justifying it.

But the game changes when you present an *argument* for your belief; or when you make a claim, express or implied, that your belief is rational, and the opposing belief is irrational. Sometimes such sentiments are expressed by statements exhibiting a pejorative attitude toward the opposing belief, or by insinuating that your belief is based upon “critical thinking,” whereas the opposing belief is not. In these cases you are sticking your neck out, so to speak.

Now, if you are going to make the leap from merely stating your belief, to arguing for it, or denigrating an opposing belief, or ridiculing an opposing belief, you had better not play the fool; i.e. you had better have at least some of your ducks in a row. And when your proposed “rational” belief is challenged, you had better have some kind of a response. If you don’t, perhaps you should just be satisfied by stating your belief and leaving it at that.

Martin Gardner’s whole public life was based upon a stated commitment to rationalism and science, and attacking beliefs he insisted were irrational pseudoscience, including virtually all things paranormal. The basis for these attacks was the claim that such things “lacked evidence,” and/or were inconsistent with scientific fact or theory. That’s all well and good, and one can argue about whether he is right or wrong.

But what is disconcerting is that while he is leaning heavily on rationality and science to attack beliefs in one context (the paranormal), he is perfectly O.K. with embracing what he admits is *irrational* as determined from the same standard, i.e. science and evidence. Is irrationality O.K. or isn’t it? Is it only O.K. for Gardner, when it suits his emotional pleasure, but not for others? In short, Gardner’s position is fundamentally logically inconsistent, as Shermer rather timidly pointed out in the cited interview. Yet, he constantly gets a free pass from his fellow skeptics. Why? Why is this darling of skepticism, an acknowledged mathematical (and presumably logical) genius, allowed this luxury? What’s even worse is that this “looking the other way” is done by the skeptics themselves, who set themselves up on a high and mighty "critical" pedestal as being against all things "irrational" or inconsistent with science!

There is a temptation here to say, well O.K. Gardner is wrong, belief in God, like the PSI and the paranormal, is also irrational and Gardner should be similarly attacked for such beliefs. But, in my view this misses the point where Gardner was wrong. He acknowledges, quite correctly, that science is extremely limited in its access to reality. But he then proceeds to attack on scientific grounds those who speculate beyond science, sometimes when there *is* evidence supporting such speculations. Moreover, he dismisses subjective “evidence,” however credible, as being non-scientific, but he is allowed to fall back on his own “feelings and emotions” as the basis for his own religious commitment.

The "rational" answer, in my view, is to celebrate openness, both with respect to the standard of evidence, and the rationality of beliefs. This does not mean that anything goes, e.g. flat earth creationism. But it *does* mean that credible human experience should be taken seriously —-as evidence-— and not thrown under the bus by materialist science simply because it speaks to some reality that is unusual, and not encompassed by some favored scientific theory.

I think what’s going on with Gardner is that you can’t teach an old dog new tricks. It’s like geneticist James Watson making wildly racist statements. But he’s old as dirt. Those same statements weren’t a problem when he was a young fella of 50 or 60.

Gardner grew up in the rationalist movement. He’s stuck there even though the quantum age says “Not so fast”. His contradictory views just make him look incompetent, which is the same problem the GAs face.

One of these positions involves a personal belief in an unprovable concept, because makes him feel good, while acknowledging that there is no proof.

The other involves skepticism regarding extraordinary claims made by some human beings to other human beings, which can potentially be tested and examined. Claims that are sometimes used to bilk and con.

I don't think the two positions are either very comparable or contradictory. They are just two positions on two things.

"One of these positions involves a personal belief in an unprovable concept, because makes him feel good, while acknowledging that there is no proof."

COMMENT: So, Gardner's belief in the irrational is O.K. because it involves (1) a personal belief; in (2) an unprovable concept because (3) it makes him feel good. As pointed out by Shermer in the interview, and accepted by Gardner, this same justification can be used by virtually any holder of any "unprovable concept." Note that science and evidence are NOT part of this equation. They are ruled out by his admission of "irrationality." Once a claim is acknowledged to be irrational, one cannot then invoke science to argue that it is nonetheless O.K.

So, in order to differentiate between acceptable irrational beliefs, and non-acceptable irrational beliefs, Gardner needs some criteria. But since the "unprovability" of the concept is a pre-requisite to the acceptability of irrational beliefs, just where does science and evidence fit it? After all, according to essentially all skeptics, science and evidence *do* apply to God beliefs just as they do to paranormal beliefs and claims, even if such beliefs are technically beyond scientific disproof.
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The other involves skepticism regarding extraordinary claims made by some human beings to other human beings, which can potentially be tested and examined. Claims that are sometimes used to bilk and con.

COMMENT: So, belief in the paranormal is NOT O.K. because in involves (1) extraordinary *claims* (rather than mere beliefs) that are sometimes used to bilk and con; made (2) by some human beings to other human beings; which (3) can be tested and examined.

Well, in the first place, belief in a personal God, and all that such a belief entails, is, by scientific standards an extraordinary belief, and if presented as a claim, an extraordinary claim. Moreover, such beliefs and claims are sometimes used to con people by presenting them to other human beings. (Even the mere expression of a belief can perpetrate a fraud.) So, the distinction seems to come down to (3) whether there is a distinction between God beliefs and paranormal beliefs based upon the claim that God beliefs cannot be tested, whereas paranormal claims can. This is very strange indeed.

So, Gardner (and you) want to bring in science and evidence to defeat irrational claims that are testable, while reserving the right of a person to hold irrational beliefs that are supposedly untestable. In the first place, God beliefs *are* testable by science. When science applies its theories to God beliefs, they come out false, whether such falsity is provable metaphysically or not. Science has standards of evidence which encompass theories of how the world works. God beliefs are neither supported by such evidentiary standards, or encompassed by such theories. This is essentially equivalent to saying that within science God beliefs are false; i.e. there are no theorems in any scientific theory that support such beliefs.

Second, it is well established that most of the standard paranormal beliefs and claims that Gardner attacks are also NOT *provably* false by science. This includes psi phenomena (clairvoyance, telepathy, precognition, and psychokinesis) You can add to the list, reincarnation and beliefs in a human soul) There are no scientific *proofs* against any of this. (In fact, science is really not in the business of providing logical or metaphysical proofs or disproofs!) Moreover, in each case, there are academics in highly respected institutions (for example, Duke, Stanford, and Princeton) that study, or have studied, such things, most of whom believe psi has some level of validity. So, the scientific evidence as related to the paranormal is highly controversial. But in any event, even assuming such things are "irrational," Gardner's hand-waving, rhetorical dismissals, most certainly do not establish a *criteria* upon which to justify his own irrational beliefs in contradiction to his relentless attacks on the paranormal. On the contrary, it is quite odd--to say the least--that one would favor an irrational belief that is supposedly untestable by science, as against an claimed "irrational" belief that is testable, but where the results of such testability have not been conclusively determined within the scientific community itself.

That said, I appreciate very much you comments, and if you have more to say about this, I would welcome additional feedback.

Sorry to be so late in responding. Been in and out a lot. I actually took several hours this morning and composed a magnum opus, that caused the RFM software to barf for some reason. That was possibly the gods that I don't believe in protecting me from myself! ;)

I had about 4 major topics crammed together. I will try for more bite sized opuses tomorrow. Going to a movie tonight. Been a regular social butterfly this week. Out of character.

I think Henry and I have some common ground. I agree that claiming science proves something false is very problematic. OTOH, I am sure some of my opinions will cause a deep disturbance in The Force™.

Don’t feel bad. Satan controls the waters and much of the Internet.

There's about 5 or 6 different topics in here. I'll pick one to comment on, though I don't think it is the most important. or even solely relevant to this thread, but it is something I have seen repeatedly on RFM, and it rather puzzles me.

Sam Harris seems to be the major vector for this particular meme, though in this thread it is Martin Gardner, and there have been others. Let me use Harris as the example, since the recurring theme about him should be in the memory of most people who read these sorts of threads.

Every now and then someone (or someones - haven't noticed if it is one particular person or not) posts about Sam Harris saying something the OP think is Simply Awful, and aren't all the RFMers who worship at the feet of Harris either feeling silly or appalled at our hypocrisy in hanging on his every word.

The reason I am puzzled is that not only don't I hang on his every word, I haven't read a thing or even heard mention of Sam Harris in years, with the lone exception of right here on RFM.

Yes, he had some interesting things to say back in the day, and made atheism an acceptable topic of conversation in polite society. I didn't agree with everything he said then, and I pay no attention to what he says now. So the way it appears to me, is that some little OCD lapdog is following Sam Harris around online, ready to gleefully pounce at any perceived verbal misstep.

To which my reaction is "oh, good lord, get a life. I don't worship at the feet of Sam Harris, nor do I know anyone who does."

The flips side of the gotcha threads about Sam Harris are the gotcha threads about how we poor not very bright souls are not impressed into worshipfulness by the profound religions insights of Einstein, Neal deGrasse Tyson, Miki Musa or whatever the hell his name is, et al. Ironically, the first part of my reaction to that is exactly the same. "Oh, good lord, get a life."

Since Sam Harris is still alive, the Simply Awful material attributed to him is new material, instead of the eternal Einstein reruns.

I don't put this thread in that category. It is not a recurring theme every couple months for years on end. But still, I read Martin Gardner for years. I am almost certain the first book I ever bought (anyone remember the Scholastic Book Club in grade/high school?) was by him. While I am familiar with Paul Kurtz and James Randi, I was not aware Gardner was part of that academic Rat Pack back in the 60s through 80s (90s?). Now that I look a wikipedia, seems he was indeed.

He may have been an outspoken critic of the paranormal, but I wouldn't characterize him as relentless. He obviously spent a great deal of his time not railing against the paranormal, just as I spend an overwhelming portion of my time not reading Sam Harris.

Anyway, watching all this go by on RFM, I feel like a puzzled dog with its head cocked to one side, wondering what all the fuss is about.

In this particular case, I don't have a problem with Gardner claiming to be a theist. Don Knuth is a practicing Lutheran, which makes him a very specific sort of theist. As long as their theism is not used as justification discrimination or bigotry, its no skin off my nose.

Is his theism inconsistent with his highly rational approach to the paranormal? Yes, of course. He admits that he has no good rational arguments for his theism. I see his position as inconsistent, but I wouldn't call it hypocritical.

There are several other points that I think Henry would like to discuss (like the nature of proof - I agree with Henry completely that science "proving something false" is a very problematic idea. I'll create a separate thread with my ideas on that) but I have gone on long enough here and am starting to wander on to other topics, so good place to pause.

A lesson well worth learning!

I will eventually get it. I have faith...

Thank you BoJ.

I cannot speak for others who might reference prominent philosophers, scientists, or others in a negative way, as I did here with Gardner. My primary intent is not to attack the person for just having beliefs, whether consistent or not. In fact, I suppose we all have a few cherished beliefs that are inconsistent in some sense.

My intent is to draw attention to logical flaws and inconsistencies in the skeptical literature in order to make the point that when one moves away from the fringes, the issues surrounding the Science-Religion debate, or the theism-atheism debate, are complicated and highly nuanced, both scientifically and philosophically. One certainly finds a lot of nonsense in the extremes of religion. But so also in scientism. I am particularly annoyed with those who hold (or held) themselves out as scientific or philosophical "rationalists" who are on a mission to chastise the lowly public for their "irrational beliefs." As I point out, such people often do not have their own logical and scientific ducks in a row.