Category Archives: Science & Technology

TLE Syndrome: The God Module, OOBEs, NDEs and Spiritual Experiences




I was wondering if the Out of Body Experiences, Near Death Experiences and Spiritual Experiences associated with the God Module might also happen in our sleep: particularly while dreaming. I found a great article called, “Fear & Loathing in the Temporal Lobes“, by Iona Miller. The following excerpt was especially interesting. Please check out the original article and read the whole thing.

Without further ado, here’s the fascinating excerpt . . .

Rapture of the Neurological Deep

 How do we get from existential anxieties about death to intensely personal spiritual experience?  Many of our spiritual notions come from the reports of the dying, or those with near-death experiences (NDEs).  When the brain begins to shut down certain typical experiences appear as each of the major areas of the brain crash and billions of functional neurons heave their last gasp (McKinney).

Deeply embedded neurons in the brainstem are among the last to go.  Unless the brain is physically destroyed, dying is a process.  It doesn’t instantly collapse, but degrades in a somewhat predictable manner with associated characteristic phenomena.

Meanwhile, there is a regression toward the oceanic feelings of life in the womb as the process of birth gets played in reverse and we return to eternity.  We journey back through earlier forms of consciousness, in a dreamy haze once the frontal lobes cease their rationalizing and abstractions.

As in dreams there are irregular bursts of neural static and discharge (Hobson) that affect the visual, affective, motor, orientation, time, and memory areas.  There is no more chronological sequencing of events.  Our experience of dying is synthesized holistically from the confabulation of all these elements.  We may be unconscious and yet still somewhat aware with scintillating electrical surges creating their last faltering messages as they fail.

We dissociate from the body.  As in deep meditation, attention is withdrawn from the extremities and external senses.  We return to a simpler mode of being, the undifferentiated mind, where time seems endless, if it exists at all.  As oxygen levels drop, and opiate-like endorphins are dumped into the system, the sense of peace and contentment may rise along with our spirits. Phantasmogorical images flood our awareness.

Between the dissociation from the body and the last glimpse of light, we may experience a culturally conditioned transcendence. Some might say the soul leaves the body as it journeys into the Light.  Bright white light may be the melding of all colors of the visual spectrum once the visual cortex is disinhibited.

Perhaps as many as 1/3 of those coming close to death report a characeristic group of experiences.  Bruce Greyson, in a paper in Varieties of Anomalous Experience (Cardena et al), lists the common elements of adult near-death experiences and aftereffects:

  • Ineffability
  • Hearing oneself pronounced dead
  • Feelings of peace and quiet
  • Hearing unusual noises
  • Seeing a dark tunnel
  • Being “out of the body”
  • Meeting “spiritual beings”
  • Experiencing a bright light as a “being of light”
  • Panoramic life review
  • Experiencing a realm in which all knowledge exists
  • Experiencing cities of light
  • Experiencing a realm of bewildered spirits
  • Experiencing a “supernatural rescue”
  • Sensing a border or limit
  • Coming back “into the body”
  • Frustration relating experiences to others
  • Subtle “broadening and deepening” of life
  • Elimination of fear of death
  • Corroboration of events witnessed while “out of the body”

The reports of those with near-death experiences moving through a tunnel toward the light, accompanied by ancestors, deceased friends and their cultural divinities are now well known (Ring; Moody; Sabom).  A minority experience emotional problems requiring psychosocial rehabilitation following NDEs, including anger and depression at having been “returned” perhaps unwillingly, broken relationships, disrupted career, alienation, post-traumatic stress disorder, “social death” (Greyson).

Gradual death is often gentle, creating its own palliative.  Heavens and hells are fully immersive virtual reality constructions of our dying neural networks.  But when the brain comes close to an irreversible coma on the journey towards death, the great endarkening comes before any great enlightenment.  Hence many with NDEs do not report seeing the Light and may even focus on their experiences as being intensely negative in content and tone.

Unable to calm their disoriented mind, their dismal experience is largely one of panic, pain, and terror.  This may be the result of toxins in the blood including carbon dioxide buildup.  If we die a sudden violent death, we may miss heaven, but mercifully we will never know that.

The whole process may be greatly compounded by the release of powerful endogenous hallucinogenic DMT from the pineal gland (Strassman).  In highly stressful situations, such as birth, sexual ecstasy, extreme physical distress, childbirth, near-death and death, the normal inhibitions against the production and circulation of this potent mind-bending “spirit molecule” are over-ridden. Massive DMT dumps may also create intense visions of blinding white light, ecstatic emotions, timelessness, and powerful presence.

A neurobiological model proposed by Saavedra-Aguilar and Gomez-Jeria suggests temporal-lobe dysfunction, hypoxia, psychophysical stress, and neurotransmitter changes combine to induce epileptiform discharges in the hippocampus and amygdala.  They contribute to life review and and complex visual hallucinations.

When the visual cortex begins to crash (Blackmore), there is a cascade of distorted imagery, then a shift down the color spectrum toward primeval redness and impenetrable black.  Maybe there is still a dull glow or scintillating pinpoints of light, like stars in some inner universe.

As the reticular activating system dies there may be a final burst of distant light, somehow familiar from the very dawn of our existence.  As our last cells die, the mind is finally unwound.  We have closed the circle of life and entered the Great Beyond.


© Copyright 2013



Carl Sagan in Marihuana Revisited

All images in this post are from Wikipedia and created by Yves Tanguy.

Dr. X

By Carl Sagan

This account was written in 1969 for publication in Marihuana Reconsidered (1971). Sagan was in his mid-thirties at that time. He continued to use cannabis for the rest of his life.

In a blog entry titled, ‘Inner Space and Outer Space: Carl Sagan’s Letters to Timothy Leary (1974)‘, authored by ‘lisa‘, at the Timothy Leary Archives website, the author explains why Carl Sagan used a pseudonym for the article reproduced, below.

Disguised as “Doctor X,” to protect his reputation,  he wrote this for his friend Lester Grinspoon’s book, Marihuana Reconsidered, in 1977:

“The illegality of cannabis is outrageous, an impediment to full utilization of a drug which helps produce the serendipity and insight, sensitivity and fellowship so desperately needed in this increasingly mad and dangerous world.”

At the time of his visit,  Sagan was surely aware that Leary had been originally sent to prison for possession of less than a joint of cannabis.

Like Leary, Sagan also exemplified the connection between mind-expanding drugs, which increased intelligence, and scientific breakthroughs. In “The Amniotic  Universe,” an article drawn from Sagan’s book Broca’s Brain, and published in the Atlantic Monthly in 1979, Sagan shows a deep and perceptive familiarity with the effects of LSD, MDA, DMT and Ketamine in his review of Stanislav Grof’s extensive and revolutionary LSD research. He writes about the effects of LSD in particular, speculating that “the Hindu mystical experience” of union with the universe “is pre-wired into us, requiring only 200 micrograms of LSD to be made manifest.”   Eminent psychedelic historian Peter Stafford, author of Psychedelics Encyclopedia, placed Sagan in a list of famous people who have taken LSD. Sagan was also number 1 on io9′s recently published list of “10 Scientific and Technological Visionaries Who Experimented With Drugs.”

Without further ado, here’s the article . . .

It all began about ten years ago. I had reached a considerably more relaxed period in my life – a time when I had come to feel that there was more to living than science, a time of awakening of my social consciousness and amiability, a time when I was open to new experiences. I had become friendly with a group of people who occasionally smoked cannabis, irregularly, but with evident pleasure. Initially I was unwilling to partake, but the apparent euphoria that cannabis produced and the fact that there was no physiological addiction to the plant eventually persuaded me to try. My initial experiences were entirely disappointing; there was no effect at all, and I began to entertain a variety of hypotheses about cannabis being a placebo which worked by expectation and hyperventilation rather than by chemistry. After about five or six unsuccessful attempts, however, it happened. I was lying on my back in a friend’s living room idly examining the pattern of shadows on the ceiling cast by a potted plant (not cannabis!). I suddenly realized that I was examining an intricately detailed miniature Volkswagen, distinctly outlined by the shadows. I was very skeptical at this perception, and tried to find inconsistencies between Volkswagens and what I viewed on the ceiling. But it was all there, down to hubcaps, license plate, chrome, and even the small handle used for opening the trunk. When I closed my eyes, I was stunned to find that there was a movie going on the inside of my eyelids. Flash . . . a simple country scene with red farmhouse, a blue sky, white clouds, yellow path meandering over green hills to the horizon. . . Flash . . . same scene, orange house, brown sky, red clouds, yellow path, violet fields . . . Flash . . . Flash . . . Flash. The flashes came about once a heartbeat. Each flash brought the same simple scene into view, but each time with a different set of colors . . . exquisitely deep hues, and astonishingly harmonious in their juxtaposition. Since then I have smoked occasionally and enjoyed it thoroughly. It amplifies torpid sensibilities and produces what to me are even more interesting effects, as I will explain shortly.

Promontory Palace, by Yves Tanguy

I can remember another early visual experience with cannabis, in which I viewed a candle flame and discovered in the heart of the flame, standing with magnificent indifference, the black-hatted and -cloaked Spanish gentleman who appears on the label of the Sandeman sherry bottle. Looking at fires when high, by the way, especially through one of those prism kaleidoscopes which image their surroundings, is an extraordinarily moving and beautiful experience.

I want to explain that at no time did I think these things ‘really’ were out there. I knew there was no Volkswagen on the ceiling and there was no Sandeman salamander man in the flame. I don’t feel any contradiction in these experiences. There’s a part of me making, creating the perceptions which in everyday life would be bizarre; there’s another part of me which is a kind of observer. About half of the pleasure comes from the observer-part appreciating the work of the creator-part. I smile, or sometimes even laugh out loud at the pictures on the insides of my eyelids. In this sense, I suppose cannabis is psychotomimetic, but I find none of the panic or terror that accompanies some psychoses. Possibly this is because I know it’s my own trip, and that I can come down rapidly any time I want to.

While my early perceptions were all visual, and curiously lacking in images of human beings, both of these items have changed over the intervening years. I find that today a single joint is enough to get me high. I test whether I’m high by closing my eyes and looking for the flashes. They come long before there are any alterations in my visual or other perceptions. I would guess this is a signal-to-noise problem, the visual noise level being very low with my eyes closed. Another interesting information-theoretical aspects is the prevalence – at least in my flashed images – of cartoons: just the outlines of figures, caricatures, not photographs. I think this is simply a matter of information compression; it would be impossible to grasp the total content of an image with the information content of an ordinary photograph, say 108 bits, in the fraction of a second which a flash occupies. And the flash experience is designed, if I may use that word, for instant appreciation. The artist and viewer are one. This is not to say that the images are not marvelously detailed and complex. I recently had an image in which two people were talking, and the words they were saying would form and disappear in yellow above their heads, at about a sentence per heartbeat. In this way it was possible to follow the conversation. At the same time an occasional word would appear in red letters among the yellows above their heads, perfectly in context with the conversation; but if one remembered these red words, they would enunciate a quite different set of statements, penetratingly critical of the conversation. The entire image set which I’ve outlined here, with I would say at least 100 yellow words and something like 10 red words, occurred in something under a minute.

Indefinite Divisibility, by Yves Tanguy

The cannabis experience has greatly improved my appreciation for art, a subject which I had never much appreciated before. The understanding of the intent of the artist which I can achieve when high sometimes carries over to when I’m down. This is one of many human frontiers which cannabis has helped me traverse. There also have been some art-related insights – I don’t know whether they are true or false, but they were fun to formulate. For example, I have spent some time high looking at the work of the Belgian surrealist Yves Tanguey (see above). Some years later, I emerged from a long swim in the Caribbean and sank exhausted onto a beach formed from the erosion of a nearby coral reef. In idly examining the arcuate pastel-colored coral fragments which made up the beach, I saw before me a vast Tanguey painting. Perhaps Tanguey visited such a beach in his childhood.

A very similar improvement in my appreciation of music has occurred with cannabis. For the first time I have been able to hear the separate parts of a three-part harmony and the richness of the counterpoint. I have since discovered that professional musicians can quite easily keep many separate parts going simultaneously in their heads, but this was the first time for me. Again, the learning experience when high has at least to some extent carried over when I’m down. The enjoyment of food is amplified; tastes and aromas emerge that for some reason we ordinarily seem to be too busy to notice. I am able to give my full attention to the sensation. A potato will have a texture, a body, and taste like that of other potatoes, but much more so. Cannabis also enhances the enjoyment of sex – on the one hand it gives an exquisite sensitivity, but on the other hand it postpones orgasm: in part by distracting me with the profusion of image passing before my eyes. The actual duration of orgasm seems to lengthen greatly, but this may be the usual experience of time expansion which comes with cannabis smoking.

I do not consider myself a religious person in the usual sense, but there is a religious aspect to some highs. The heightened sensitivity in all areas gives me a feeling of communion with my surroundings, both animate and inanimate. Sometimes a kind of existential perception of the absurd comes over me and I see with awful certainty the hypocrisies and posturing of myself and my fellow men. And at other times, there is a different sense of the absurd, a playful and whimsical awareness. Both of these senses of the absurd can be communicated, and some of the most rewarding highs I’ve had have been in sharing talk and perceptions and humor. Cannabis brings us an awareness that we spend a lifetime being trained to overlook and forget and put out of our minds. A sense of what the world is really like can be maddening; cannabis has brought me some feelings for what it is like to be crazy, and how we use that word ‘crazy’ to avoid thinking about things that are too painful for us. In the Soviet Union political dissidents are routinely placed in insane asylums. The same kind of thing, a little more subtle perhaps, occurs here: ‘did you hear what Lenny Bruce said yesterday? He must be crazy.’ When high on cannabis I discovered that there’s somebody inside in those people we call mad.

When I’m high I can penetrate into the past, recall childhood memories, friends, relatives, playthings, streets, smells, sounds, and tastes from a vanished era. I can reconstruct the actual occurrences in childhood events only half understood at the time. Many but not all my cannabis trips have somewhere in them a symbolism significant to me which I won’t attempt to describe here, a kind of mandala embossed on the high. Free-associating to this mandala, both visually and as plays on words, has produced a very rich array of insights.

Mama, Papa is Wounded!, by Yves Tanguy

There is a myth about such highs: the user has an illusion of great insight, but it does not survive scrutiny in the morning. I am convinced that this is an error, and that the devastating insights achieved when high are real insights; the main problem is putting these insights in a form acceptable to the quite different self that we are when we’re down the next day. Some of the hardest work I’ve ever done has been to put such insights down on tape or in writing. The problem is that ten even more interesting ideas or images have to be lost in the effort of recording one. It is easy to understand why someone might think it’s a waste of effort going to all that trouble to set the thought down, a kind of intrusion of the Protestant Ethic. But since I live almost all my life down I’ve made the effort – successfully, I think. Incidentally, I find that reasonably good insights can be remembered the next day, but only if some effort has been made to set them down another way. If I write the insight down or tell it to someone, then I can remember it with no assistance the following morning; but if I merely say to myself that I must make an effort to remember, I never do.

I find that most of the insights I achieve when high are into social issues, an area of creative scholarship very different from the one I am generally known for. I can remember one occasion, taking a shower with my wife while high, in which I had an idea on the origins and invalidities of racism in terms of gaussian distribution curves. It was a point obvious in a way, but rarely talked about. I drew the curves in soap on the shower wall, and went to write the idea down. One idea led to another, and at the end of about an hour of extremely hard work I found I had written eleven short essays on a wide range of social, political, philosophical, and human biological topics. Because of problems of space, I can’t go into the details of these essays, but from all external signs, such as public reactions and expert commentary, they seem to contain valid insights. I have used them in university commencement addresses, public lectures, and in my books.

But let me try to at least give the flavor of such an insight and its accompaniments. One night, high on cannabis, I was delving into my childhood, a little self-analysis, and making what seemed to me to be very good progress. I then paused and thought how extraordinary it was that Sigmund Freud, with no assistance from drugs, had been able to achieve his own remarkable self-analysis. But then it hit me like a thunderclap that this was wrong, that Freud had spent the decade before his self-analysis as an experimenter with and a proselytizer for cocaine; and it seemed to me very apparent that the genuine psychological insights that Freud brought to the world were at least in part derived from his drug experience. I have no idea whether this is in fact true, or whether the historians of Freud would agree with this interpretation, or even if such an idea has been published in the past, but it is an interesting hypothesis and one which passes first scrutiny in the world of the downs.

I can remember the night that I suddenly realized what it was like to be crazy, or nights when my feelings and perceptions were of a religious nature. I had a very accurate sense that these feelings and perceptions, written down casually, would not stand the usual critical scrutiny that is my stock in trade as a scientist. If I find in the morning a message from myself the night before informing me that there is a world around us which we barely sense, or that we can become one with the universe, or even that certain politicians are desperately frightened men, I may tend to disbelieve; but when I’m high I know about this disbelief. And so I have a tape in which I exhort myself to take such remarks seriously. I say ‘Listen closely, you sonofabitch of the morning! This stuff is real!’ I try to show that my mind is working clearly; I recall the name of a high school acquaintance I have not thought of in thirty years; I describe the color, typography, and format of a book in another room and these memories do pass critical scrutiny in the morning. I am convinced that there are genuine and valid levels of perception available with cannabis (and probably with other drugs) which are, through the defects of our society and our educational system, unavailable to us without such drugs. Such a remark applies not only to self-awareness and to intellectual pursuits, but also to perceptions of real people, a vastly enhanced sensitivity to facial expression, intonations, and choice of words which sometimes yields a rapport so close it’s as if two people are reading each other’s minds.

Cannabis enables nonmusicians to know a little about what it is like to be a musician, and nonartists to grasp the joys of art. But I am neither an artist nor a musician. What about my own scientific work? While I find a curious disinclination to think of my professional concerns when high – the attractive intellectual adventures always seem to be in every other area – I have made a conscious effort to think of a few particularly difficult current problems in my field when high. It works, at least to a degree. I find I can bring to bear, for example, a range of relevant experimental facts which appear to be mutually inconsistent. So far, so good. At least the recall works. Then in trying to conceive of a way of reconciling the disparate facts, I was able to come up with a very bizarre possibility, one that I’m sure I would never have thought of down. I’ve written a paper which mentions this idea in passing. I think it’s very unlikely to be true, but it has consequences which are experimentally testable, which is the hallmark of an acceptable theory.

I have mentioned that in the cannabis experience there is a part of your mind that remains a dispassionate observer, who is able to take you down in a hurry if need be. I have on a few occasions been forced to drive in heavy traffic when high. I’ve negotiated it with no difficult at all, though I did have some thoughts about the marvelous cherry-red color of traffic lights. I find that after the drive I’m not high at all. There are no flashes on the insides of my eyelids. If you’re high and your child is calling, you can respond about as capably as you usually do. I don’t advocate driving when high on cannabis, but I can tell you from personal experience that it certainly can be done. My high is always reflective, peaceable, intellectually exciting, and sociable, unlike most alcohol highs, and there is never a hangover. Through the years I find that slightly smaller amounts of cannabis suffice to produce the same degree of high, and in one movie theater recently I found I could get high just by inhaling the cannabis smoke which permeated the theater.

There is a very nice self-titering aspect to cannabis. Each puff is a very small dose; the time lag between inhaling a puff and sensing its effect is small; and there is no desire for more after the high is there. I think the ratio, R, of the time to sense the dose taken to the time required to take an excessive dose is an important quantity. R is very large for LSD (which I’ve never taken) and reasonably short for cannabis. Small values of R should be one measure of the safety of psychedelic drugs. When cannabis is legalized, I hope to see this ratio as one of he parameters printed on the pack. I hope that time isn’t too distant; the illegality of cannabis is outrageous, an impediment to full utilization of a drug which helps produce the serenity and insight, sensitivity and fellowship so desperately needed in this increasingly mad and dangerous world.

Reply to Red, by Yves Tanguy

The Death of Christian Apologetics


Many Christian apologists try to give the impression that slavery was upheld in the Old Testament only. The fact is, it was also upheld – by none other than Jesus himself – in the New Testament. It’s gospel! Here’s the verse (Luke 12:47 – 48) . . .

Beat slaves who did wrong with many stripes, unless they knew not their wrong, then few stripes.

. . . Paul and Peter also upheld slavery in the New Testament. Come to think of it, there’s not a single word against slavery in the entire Bible.

There’s all kinds of immoral acts condoned, upheld or even encouraged in the Bible: bloodlust, incest, genocide, vengeance, battlefield atrocities, slavery, etc. But, as far as I know, human subjugation (slavery and male dominance over women) is the only one endorsed by BOTH the Old and New Testaments. This fact is important because it preempts the old apologist cop out: “That was the old covenant of the Old Testament but Jesus changed things with his new covenant of the New Testament”. They can discount the Old Testament all they want but slavery is also upheld in the New Testament by the ultimate authority: Jesus himself . . . God in the flesh.

Apologists are persistent, so next they’ll likely attempt to claim the word, ‘slave’, is a mis-translation. But it’s not. The Greek word, ‘doulos’, plainly means slave and is used unambiguously in the Bible. Some translations of the Bible soften the word into ‘servant’ but that’s an intentional attempt to mask an obvious weakness.

Once you shoot down that lame claim, you’re likely to be told slavery was kinder and gentler back in the Biblical era. The other day, one such apologist claimed slaves were better treated because their masters knew that, by law, they had to manumit their slaves after 7 years (some experts claim it was actually 6 years) . . . and this foreknowledge “tempered the master’s temper”. However, that claim was a conscious, calculated, misrepresentation. The fact is: only indentured Jewish MALE slaves – Hebrew MEN who sold themselves into bondage because of extreme poverty or debt – had to be manumitted. But non-Jewish slaves (mostly Canaanites) were chattel for life and could be passed from generation to generation through inheritance. And guess what? Females sold into slavery by their families – even if they were Jews – were slaves for life! That’s right, Hebrew male slaves get manumitted after 7 years . . . but Hebrew female slaves were chattel slaves for life. The human subjugation double-whammy, in the Bible, is reserved for women.

The bottom line is that real slaves (not the indentured, Jewish, MALE, slaves) were property for life and could be whipped or raped at the discretion of his/her master. Chattel slavery is chattel slavery: human subjugation is not kind or gentle. Or moral.

Some will claim that, when Jesus spoke (in Luke 12:47 – 48) about beating slaves, he was telling a parable. That’s not true. He wasn’t telling a parable – he was explaining one (Luke 12:35 – 40): clarifying a point about responsibility and accountability. But even if he was . . . parables take commonplace ideas to convey, by comparison or analogy, deeper ideas. So, if Jesus used the beating of slaves to convey lessons about responsibility and accountability . . . what does that say about his concern for slavery? It says he doesn’t give it a second thought! It’s a natural part of the order of things as far as Jesus is concerned.

The final, desperate, maneuver of the Christian apologist is to claim the “culture” or “prevailing attitudes” were different in the Biblical era. And that is the final nail in the coffin of the hapless apologist. By suggesting slavery is morally relative – justified by prevailing attitudes – one is admitting the immutable word of God is subjective, not objective, and not immutable or perfect or moral after all. Besides, God had always upheld slavery . . . nobody needed “prevailing attitudes” to make it okay.

Apologists can’t have it both ways. Either God’s word is immutable or it’s not. Either God is good and perfect, or he’s not. Either God is the source and final arbiter of morality or he’s not. Either the holy Bible is true and the divinely inspired word of God or it’s not.

And if God and the Bible are moral, true and perfect, then so is the slavery they uphold. But we know better. Don’t we? Slavery can no longer be upheld. We’ve grown beyond that. There’s no way in hell we will ever re-normalize slavery in order to align mankind’s morality with God’s. That slave ship has sailed. It’s over.

This fact puts slavery out of reach of Christian apologetics. Anybody can see – unless they refuse to – that if God’s morality grows outdated, it was never true or perfect to begin with. Clearly, God’s word is not the objective truth. In fact, God stands corrected by us ALL: believers and nonbelievers alike. If we must overrule God, we’re better off without him.

The single issue of slavery is all it takes to prove God is not moral, timeless or perfect – and neither is his split-personality scripture. If the allegedly omniscient, omnipotent, God or his scripture can’t stand the test of time, they’re frauds.

Of course, all this presumes the Biblical God exists in the first place.

© Copyright 2012

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Google and YouTube: Too Big for Their Britches

First Google filtered out a lot of anti-Islamic content from its search engine. Then they enforced a “no pseudonym” policy on Google Plus — making anonymity difficult for whistle-blowers, corporate and government protest organizers and those who would risk their safety to criticize Islam. Now they’re removing videos critical of Islam from YouTube. Google/YouTube are near-monopolies who have no problem, whatsoever, throwing their weight around. These social networking giants need a lesson in social responsibility.

I don’t know about you, but censorship of freethought is unthinkable to me. How dare they silence our freedom of expression! The world NEEDS our perspective, our concerns, our voice. Google has repeatedly demonstrated a wrong-headed, accommodationist, cowardly, propensity to forfeit democratic ideals to placate vocal majorities. As the great American, Adlai Stevenson, once pointed out: “My definition of a free society is a society where it is safe to be unpopular.” Being a minority should not mean being expendable.

If you value freedom of expression and hate censorship, please let Google and YouTube know that you will not tolerate our inalienable rights taken away so cavalierly. They’re big now but they’re establishing a history of cowardice that will come back to bite them on the ass. Their continued success is not guaranteed and it will be the users they alienated that will boost the fortunes of their competitors.

Something else you can do is to download all the freethought videos you can from YouTube, before they disappear, and repost them over and over. Or you can make your own freethought videos and post them over and over. Actually, I’m not sure that’s workable but you get my gist . . . punish YouTube. We could learn a lesson from the “squeaky wheel” religious zealots and make a big noise of our own.

The Unreasonable Effectiveness of Mathematics

“The most incomprehensible thing about the universe is that it can be comprehended” ~Albert Einstein

I stumbled across this essay at the Dartmouth website. It’s copied below for your convenience. It’s written by Eugene Wigner, the 1963 Nobel Prize winner for physics. Written over 50 years ago, it is still very much germane to modern physics.

This subject is another one of those scientific curiosities that give reason to pause and to ponder ultimate sources (as I recently did in the post, “A New Argument for God?“)

Something else I really like about this article is that Wigner referred to “the laws of inanimate nature”, “knowledge of the inanimate world” (twice), “properties of the inanimate world” and “theories of the inanimate world”. With these 5 references to the inanimate, Wigner clearly takes it for granted that the laws of physics are not intended to deal with the animate parts of the universe (i.e. life and living things). This fact is central to the many posts I’ve written about self-determinism, here at, and not something that materialists like to admit.

Anyway, without further ado, here’s the essay . . .

The Unreasonable Effectiveness of Mathematics in the Natural Sciences
by Eugene Wigner

Mathematics, rightly viewed, possesses not only truth, but supreme beauty – beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.

BERTRAND RUSSELL, Study of Mathematics

THERE IS A story about two friends, who were classmates in high school, talking about their jobs. One of them became a statistician and was working on population trends. He showed a reprint to his former classmate. The reprint started, as usual, with the Gaussian distribution and the statistician explained to his former classmate the meaning of the symbols for the actual population, for the average population, and so on. His classmate was a bit incredulous and was not quite sure whether the statistician was pulling his leg. “How can you know that?” was his query. “And what is this symbol here?” “Oh,” said the statistician, “this is pi.” “What is that?” “The ratio of the circumference of the circle to its diameter.” “Well, now you are pushing your joke too far,” said the classmate, “surely the population has nothing to do with the circumference of the circle.”

Naturally, we are inclined to smile about the simplicity of the classmate’s approach. Nevertheless, when I heard this story, I had to admit to an eerie feeling because, surely, the reaction of the classmate betrayed only plain common sense. I was even more confused when, not many days later, someone came to me and expressed his bewilderment (the remark to be quoted was made by F. Werner when he was a student in Princeton) with the fact that we make a rather narrow selection when choosing the data on which we test our theories. “How do we know that, if we made a theory which focuses its attention on phenomena we disregard and disregards some of the phenomena now commanding our attention, that we could not build another theory which has little in common with the present one but which, nevertheless, explains just as many phenomena as the present theory?” It has to be admitted that we have no definite evidence that there is no such theory.

The preceding two stories illustrate the two main points which are the subjects of the present discourse. The first point is that mathematical concepts turn up in entirely unexpected connections. Moreover, they often permit an unexpectedly close and accurate description of the phenomena in these connections. Secondly, just because of this circumstance, and because we do not understand the reasons of their usefulness, we cannot know whether a theory formulated in terms of mathematical concepts is uniquely appropriate. We are in a position similar to that of a man who was provided with a bunch of keys and who, having to open several doors in succession, always hit on the right key on the first or second trial. He became skeptical concerning the uniqueness of the coordination between keys and doors.

Most of what will be said on these questions will not be new; it has probably occurred to most scientists in one form or another. My principal aim is to illuminate it from several sides. The first point is that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it. Second, it is just this uncanny usefulness of mathematical concepts that raises the question of the uniqueness of our physical theories. In order to establish the first point, that mathematics plays an unreasonably important role in physics, it will be useful to say a few words on the question, “What is mathematics?”, then, “What is physics?”, then, how mathematics enters physical theories, and last, why the success of mathematics in its role in physics appears so baffling. Much less will be said on the second point: the uniqueness of the theories of physics. A proper answer to this question would require elaborate experimental and theoretical work which has not been undertaken to date.


Somebody once said that philosophy is the misuse of a terminology which was invented just for this purpose. In the same vein, I would say that mathematics is the science of skillful operations with concepts and rules invented just for this purpose. The principal emphasis is on the invention of concepts. Mathematics would soon run out of interesting theorems if these had to be formulated in terms of the concepts which already appear in the axioms. Furthermore, whereas it is unquestionably true that the concepts of elementary mathematics and particularly elementary geometry were formulated to describe entities which are directly suggested by the actual world, the same does not seem to be true of the more advanced concepts, in particular the concepts which play such an important role in physics. Thus, the rules for operations with pairs of numbers are obviously designed to give the same results as the operations with fractions which we first learned without reference to “pairs of numbers.” The rules for the operations with sequences, that is, with irrational numbers, still belong to the category of rules which were determined so as to reproduce rules for the operations with quantities which were already known to us. Most more advanced mathematical concepts, such as complex numbers, algebras, linear operators, Borel sets – and this list could be continued almost indefinitely – were so devised that they are apt subjects on which the mathematician can demonstrate his ingenuity and sense of formal beauty. In fact, the definition of these concepts, with a realization that interesting and ingenious considerations could be applied to them, is the first demonstration of the ingeniousness of the mathematician who defines them. The depth of thought which goes into the formulation of the mathematical concepts is later justified by the skill with which these concepts are used. The great mathematician fully, almost ruthlessly, exploits the domain of permissible reasoning and skirts the impermissible. That his recklessness does not lead him into a morass of contradictions is a miracle in itself: certainly it is hard to believe that our reasoning power was brought, by Darwin’s process of natural selection, to the perfection which it seems to possess. However, this is not our present subject. The principal point which will have to be recalled later is that the mathematician could formulate only a handful of interesting theorems without defining concepts beyond those contained in the axioms and that the concepts outside those contained in the axioms are defined with a view of permitting ingenious logical operations which appeal to our aesthetic sense both as operations and also in their results of great generality and simplicity.

The complex numbers provide a particularly striking example for the foregoing. Certainly, nothing in our experience suggests the introduction of these quantities. Indeed, if a mathematician is asked to justify his interest in complex numbers, he will point, with some indignation, to the many beautiful theorems in the theory of equations, of power series, and of analytic functions in general, which owe their origin to the introduction of complex numbers. The mathematician is not willing to give up his interest in these most beautiful accomplishments of his genius.


The physicist is interested in discovering the laws of inanimate nature. In order to understand this statement, it is necessary to analyze the concept, “law of nature.”

The world around us is of baffling complexity and the most obvious fact about it is that we cannot predict the future. Although the joke attributes only to the optimist the view that the future is uncertain, the optimist is right in this case: the future is unpredictable. It is, as Schrodinger has remarked, a miracle that in spite of the baffling complexity of the world, certain regularities in the events could be discovered. One such regularity, discovered by Galileo, is that two rocks, dropped at the same time from the same height, reach the ground at the same time. The laws of nature are concerned with such regularities. Galileo’s regularity is a prototype of a large class of regularities. It is a surprising regularity for three reasons.

The first reason that it is surprising is that it is true not only in Pisa, and in Galileo’s time, it is true everywhere on the Earth, was always true, and will always be true. This property of the regularity is a recognized invariance property and, as I had occasion to point out some time ago, without invariance principles similar to those implied in the preceding generalization of Galileo’s observation, physics would not be possible. The second surprising feature is that the regularity which we are discussing is independent of so many conditions which could have an effect on it. It is valid no matter whether it rains or not, whether the experiment is carried out in a room or from the Leaning Tower, no matter whether the person who drops the rocks is a man or a woman. It is valid even if the two rocks are dropped, simultaneously and from the same height, by two different people. There are, obviously, innumerable other conditions which are all immaterial from the point of view of the validity of Galileo’s regularity. The irrelevancy of so many circumstances which could play a role in the phenomenon observed has also been called an invariance. However, this invariance is of a different character from the preceding one since it cannot be formulated as a general principle. The exploration of the conditions which do, and which do not, influence a phenomenon is part of the early experimental exploration of a field. It is the skill and ingenuity of the experimenter which show him phenomena which depend on a relatively narrow set of relatively easily realizable and reproducible conditions. In the present case, Galileo’s restriction of his observations to relatively heavy bodies was the most important step in this regard. Again, it is true that if there were no phenomena which are independent of all but a manageably small set of conditions, physics would be impossible.

The preceding two points, though highly significant from the point of view of the philosopher, are not the ones which surprised Galileo most, nor do they contain a specific law of nature. The law of nature is contained in the statement that the length of time which it takes for a heavy object to fall from a given height is independent of the size, material, and shape of the body which drops. In the framework of Newton’s second “law,” this amounts to the statement that the gravitational force which acts on the falling body is proportional to its mass but independent of the size, material, and shape of the body which falls.

The preceding discussion is intended to remind us, first, that it is not at all natural that “laws of nature” exist, much less that man is able to discover them. The present writer had occasion, some time ago, to call attention to the succession of layers of “laws of nature,” each layer containing more general and more encompassing laws than the previous one and its discovery constituting a deeper penetration into the structure of the universe than the layers recognized before. However, the point which is most significant in the present context is that all these laws of nature contain, in even their remotest consequences, only a small part of our knowledge of the inanimate world. All the laws of nature are conditional statements which permit a prediction of some future events on the basis of the knowledge of the present, except that some aspects of the present state of the world, in practice the overwhelming majority of the determinants of the present state of the world, are irrelevant from the point of view of the prediction. The irrelevancy is meant in the sense of the second point in the discussion of Galileo’s theorem.

As regards the present state of the world, such as the existence of the earth on which we live and on which Galileo’s experiments were performed, the existence of the sun and of all our surroundings, the laws of nature are entirely silent. It is in consonance with this, first, that the laws of nature can be used to predict future events only under exceptional circumstances; when all the relevant determinants of the present state of the world are known. It is also in consonance with this that the construction of machines, the functioning of which he can foresee, constitutes the most spectacular accomplishment of the physicist. In these machines, the physicist creates a situation in which all the relevant coordinates are known so that the behavior of the machine can be predicted. Radars and nuclear reactors are examples of such machines.

The principal purpose of the preceding discussion is to point out that the laws of nature are all conditional statements and they relate only to a very small part of our knowledge of the world. Thus, classical mechanics, which is the best known prototype of a physical theory, gives the second derivatives of the positional coordinates of all bodies, on the basis of the knowledge of the positions, etc., of these bodies. It gives no information on the existence, the present positions, or velocities of these bodies. It should be mentioned, for the sake of accuracy, that we discovered about thirty years ago that even the conditional statements cannot be entirely precise: that the conditional statements are probability laws which enable us only to place intelligent bets on future properties of the inanimate world, based on the knowledge of the present state. They do not allow us to make categorical statements, not even categorical statements conditional on the present state of the world. The probabilistic nature of the “laws of nature” manifests itself in the case of machines also, and can be verified, at least in the case of nuclear reactors, if one runs them at very low power. However, the additional limitation of the scope of the laws of nature which follows from their probabilistic nature will play no role in the rest of the discussion.


Having refreshed our minds as to the essence of mathematics and physics, we should be in a better position to review the role of mathematics in physical theories.

Naturally, we do use mathematics in everyday physics to evaluate the results of the laws of nature, to apply the conditional statements to the particular conditions which happen to prevail or happen to interest us. In order that this be possible, the laws of nature must already be formulated in mathematical language. However, the role of evaluating the consequences of already established theories is not the most important role of mathematics in physics. Mathematics, or, rather, applied mathematics, is not so much the master of the situation in this function: it is merely serving as a tool.

Mathematics does play, however, also a more sovereign role in physics. This was already implied in the statement, made when discussing the role of applied mathematics, that the laws of nature must have been formulated in the language of mathematics to be an object for the use of applied mathematics. The statement that the laws of nature are written in the language of mathematics was properly made three hundred years ago (it is attributed to Galileo); it is now more true than ever before. In order to show the importance which mathematical concepts possess in the formulation of the laws of physics, let us recall, as an example, the axioms of quantum mechanics as formulated, explicitly, by the great physicist, Dirac. There are two basic concepts in quantum mechanics: states and observables. The states are vectors in Hilbert space, the observables self-adjoint operators on these vectors. The possible values of the observations are the characteristic values of the operators – but we had better stop here lest we engage in a listing of the mathematical concepts developed in the theory of linear operators.

It is true, of course, that physics chooses certain mathematical concepts for the formulation of the laws of nature, and surely only a fraction of all mathematical concepts is used in physics. It is true also that the concepts which were chosen were not selected arbitrarily from a listing of mathematical terms but were developed, in many if not most cases, independently by the physicist and recognized then as having been conceived before by the mathematician. It is not true, however, as is so often stated, that this had to happen because mathematics uses the simplest possible concepts and these were bound to occur in any formalism. As we saw before, the concepts of mathematics are not chosen for their conceptual simplicity – even sequences of pairs of numbers are far from being the simplest concepts – but for their amenability to clever manipulations and to striking, brilliant arguments. Let us not forget that the Hilbert space of quantum mechanics is the complex Hilbert space, with a Hermitean scalar product. Surely to the unpreoccupied mind, complex numbers are far from natural or simple and they cannot be suggested by physical observations. Furthermore, the use of complex numbers is in this case not a calculational trick of applied mathematics but comes close to being a necessity in the formulation of the laws of quantum mechanics. Finally, it now begins to appear that not only complex numbers but so-called analytic functions are destined to play a decisive role in the formulation of quantum theory. I am referring to the rapidly developing theory of dispersion relations.

It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of the existence of laws of nature and of the human mind’s capacity to divine them. The observation which comes closest to an explanation for the mathematical concepts’ cropping up in physics which I know is Einstein’s statement that the only physical theories which we are willing to accept are the beautiful ones. It stands to argue that the concepts of mathematics, which invite the exercise of so much wit, have the quality of beauty. However, Einstein’s observation can at best explain properties of theories which we are willing to believe and has no reference to the intrinsic accuracy of the theory. We shall, therefore, turn to this latter question.


A possible explanation of the physicist’s use of mathematics to formulate his laws of nature is that he is a somewhat irresponsible person. As a result, when he finds a connection between two quantities which resembles a connection well-known from mathematics, he will jump at the conclusion that the connection is that discussed in mathematics simply because he does not know of any other similar connection. It is not the intention of the present discussion to refute the charge that the physicist is a somewhat irresponsible person. Perhaps he is. However, it is important to point out that the mathematical formulation of the physicist’s often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena. This shows that the mathematical language has more to commend it than being the only language which we can speak; it shows that it is, in a very real sense, the correct language. Let us consider a few examples.

The first example is the oft-quoted one of planetary motion. The laws of falling bodies became rather well established as a result of experiments carried out principally in Italy. These experiments could not be very accurate in the sense in which we understand accuracy today partly because of the effect of air resistance and partly because of the impossibility, at that time, to measure short time intervals. Nevertheless, it is not surprising that, as a result of their studies, the Italian natural scientists acquired a familiarity with the ways in which objects travel through the atmosphere. It was Newton who then brought the law of freely falling objects into relation with the motion of the moon, noted that the parabola of the thrown rock’s path on the earth and the circle of the moon’s path in the sky are particular cases of the same mathematical object of an ellipse, and postulated the universal law of gravitation on the basis of a single, and at that time very approximate, numerical coincidence. Philosophically, the law of gravitation as formulated by Newton was repugnant to his time and to himself. Empirically, it was based on very scanty observations. The mathematical language in which it was formulated contained the concept of a second derivative and those of us who have tried to draw an osculating circle to a curve know that the second derivative is not a very immediate concept. The law of gravity which Newton reluctantly established and which he could verify with an accuracy of about 4% has proved to be accurate to less than a ten thousandth of a per cent and became so closely associated with the idea of absolute accuracy that only recently did physicists become again bold enough to inquire into the limitations of its accuracy. Certainly, the example of Newton’s law, quoted over and over again, must be mentioned first as a monumental example of a law, formulated in terms which appear simple to the mathematician, which has proved accurate beyond all reasonable expectations. Let us just recapitulate our thesis on this example: first, the law, particularly since a second derivative appears in it, is simple only to the mathematician, not to common sense or to non-mathematically-minded freshmen; second, it is a conditional law of very limited scope. It explains nothing about the earth which attracts Galileo’s rocks, or about the circular form of the moon’s orbit, or about the planets of the sun. The explanation of these initial conditions is left to the geologist and the astronomer, and they have a hard time with them.

The second example is that of ordinary, elementary quantum mechanics. This originated when Max Born noticed that some rules of computation, given by Heisenberg, were formally identical with the rules of computation with matrices, established a long time before by mathematicians. Born, Jordan, and Heisenberg then proposed to replace by matrices the position and momentum variables of the equations of classical mechanics. They applied the rules of matrix mechanics to a few highly idealized problems and the results were quite satisfactory. However, there was, at that time, no rational evidence that their matrix mechanics would prove correct under more realistic conditions. Indeed, they say “if the mechanics as here proposed should already be correct in its essential traits.” As a matter of fact, the first application of their mechanics to a realistic problem, that of the hydrogen atom, was given several months later, by Pauli. This application gave results in agreement with experience. This was satisfactory but still understandable because Heisenberg’s rules of calculation were abstracted from problems which included the old theory of the hydrogen atom. The miracle occurred only when matrix mechanics, or a mathematically equivalent theory, was applied to problems for which Heisenberg’s calculating rules were meaningless. Heisenberg’s rules presupposed that the classical equations of motion had solutions with certain periodicity properties; and the equations of motion of the two electrons of the helium atom, or of the even greater number of electrons of heavier atoms, simply do not have these properties, so that Heisenberg’s rules cannot be applied to these cases. Nevertheless, the calculation of the lowest energy level of helium, as carried out a few months ago by Kinoshita at Cornell and by Bazley at the Bureau of Standards, agrees with the experimental data within the accuracy of the observations, which is one part in ten million. Surely in this case we “got something out” of the equations that we did not put in.

The same is true of the qualitative characteristics of the “complex spectra,” that is, the spectra of heavier atoms. I wish to recall a conversation with Jordan, who told me, when the qualitative features of the spectra were derived, that a disagreement of the rules derived from quantum mechanical theory and the rules established by empirical research would have provided the last opportunity to make a change in the framework of matrix mechanics. In other words, Jordan felt that we would have been, at least temporarily, helpless had an unexpected disagreement occurred in the theory of the helium atom. This was, at that time, developed by Kellner and by Hilleraas. The mathematical formalism was too dear and unchangeable so that, had the miracle of helium which was mentioned before not occurred, a true crisis would have arisen. Surely, physics would have overcome that crisis in one way or another. It is true, on the other hand, that physics as we know it today would not be possible without a constant recurrence of miracles similar to the one of the helium atom, which is perhaps the most striking miracle that has occurred in the course of the development of elementary quantum mechanics, but by far not the only one. In fact, the number of analogous miracles is limited, in our view, only by our willingness to go after more similar ones. Quantum mechanics had, nevertheless, many almost equally striking successes which gave us the firm conviction that it is, what we call, correct.

The last example is that of quantum electrodynamics, or the theory of the Lamb shift. Whereas Newton’s theory of gravitation still had obvious connections with experience, experience entered the formulation of matrix mechanics only in the refined or sublimated form of Heisenberg’s prescriptions. The quantum theory of the Lamb shift, as conceived by Bethe and established by Schwinger, is a purely mathematical theory and the only direct contribution of experiment was to show the existence of a measurable effect. The agreement with calculation is better than one part in a thousand.

The preceding three examples, which could be multiplied almost indefinitely, should illustrate the appropriateness and accuracy of the mathematical formulation of the laws of nature in terms of concepts chosen for their manipulability, the “laws of nature” being of almost fantastic accuracy but of strictly limited scope. I propose to refer to the observation which these examples illustrate as the empirical law of epistemology. Together with the laws of invariance of physical theories, it is an indispensable foundation of these theories. Without the laws of invariance the physical theories could have been given no foundation of fact; if the empirical law of epistemology were not correct, we would lack the encouragement and reassurance which are emotional necessities, without which the “laws of nature” could not have been successfully explored. Dr. R. G. Sachs, with whom I discussed the empirical law of epistemology, called it an article of faith of the theoretical physicist, and it is surely that. However, what he called our article of faith can be well supported by actual examples – many examples in addition to the three which have been mentioned.


The empirical nature of the preceding observation seems to me to be self-evident. It surely is not a “necessity of thought” and it should not be necessary, in order to prove this, to point to the fact that it applies only to a very small part of our knowledge of the inanimate world. It is absurd to believe that the existence of mathematically simple expressions for the second derivative of the position is self-evident, when no similar expressions for the position itself or for the velocity exist. It is therefore surprising how readily the wonderful gift contained in the empirical law of epistemology was taken for granted. The ability of the human mind to form a string of 1000 conclusions and still remain “right,” which was mentioned before, is a similar gift.

Every empirical law has the disquieting quality that one does not know its limitations. We have seen that there are regularities in the events in the world around us which can be formulated in terms of mathematical concepts with an uncanny accuracy. There are, on the other hand, aspects of the world concerning which we do not believe in the existence of any accurate regularities. We call these initial conditions. The question which presents itself is whether the different regularities, that is, the various laws of nature which will be discovered, will fuse into a single consistent unit, or at least asymptotically approach such a fusion. Alternatively, it is possible that there always will be some laws of nature which have nothing in common with each other. At present, this is true, for instance, of the laws of heredity and of physics. It is even possible that some of the laws of nature will be in conflict with each other in their implications, but each convincing enough in its own domain so that we may not be willing to abandon any of them. We may resign ourselves to such a state of affairs or our interest in clearing up the conflict between the various theories may fade out. We may lose interest in the “ultimate truth,” that is, in a picture which is a consistent fusion into a single unit of the little pictures, formed on the various aspects of nature.

It may be useful to illustrate the alternatives by an example. We now have, in physics, two theories of great power and interest: the theory of quantum phenomena and the theory of relativity. These two theories have their roots in mutually exclusive groups of phenomena. Relativity theory applies to macroscopic bodies, such as stars. The event of coincidence, that is, in ultimate analysis of collision, is the primitive event in the theory of relativity and defines a point in space-time, or at least would define a point if the colliding panicles were infinitely small. Quantum theory has its roots in the microscopic world and, from its point of view, the event of coincidence, or of collision, even if it takes place between particles of no spatial extent, is not primitive and not at all sharply isolated in space-time. The two theories operate with different mathematical concepts – the four dimensional Riemann space and the infinite dimensional Hilbert space, respectively. So far, the two theories could not be united, that is, no mathematical formulation exists to which both of these theories are approximations. All physicists believe that a union of the two theories is inherently possible and that we shall find it. Nevertheless, it is possible also to imagine that no union of the two theories can be found. This example illustrates the two possibilities, of union and of conflict, mentioned before, both of which are conceivable.

In order to obtain an indication as to which alternative to expect ultimately, we can pretend to be a little more ignorant than we are and place ourselves at a lower level of knowledge than we actually possess. If we can find a fusion of our theories on this lower level of intelligence, we can confidently expect that we will find a fusion of our theories also at our real level of intelligence. On the other hand, if we would arrive at mutually contradictory theories at a somewhat lower level of knowledge, the possibility of the permanence of conflicting theories cannot be excluded for ourselves either. The level of knowledge and ingenuity is a continuous variable and it is unlikely that a relatively small variation of this continuous variable changes the attainable picture of the world from inconsistent to consistent. [This passage was written after a great deal of hesitation. The writer is convinced that it is useful, in epistemological discussions, to abandon the idealization that the level of human intelligence has a singular position on an absolute scale. In some cases it may even be useful to consider the attainment which is possible at the level of the intelligence of some other species. However, the writer also realizes that his thinking along the lines indicated in the text was too brief and not subject to sufficient critical appraisal to be reliable.] Considered from this point of view, the fact that some of the theories which we know to be false give such amazingly accurate results is an adverse factor. Had we somewhat less knowledge, the group of phenomena which these “false” theories explain would appear to us to be large enough to “prove” these theories. However, these theories are considered to be “false” by us just for the reason that they are, in ultimate analysis, incompatible with more encompassing pictures and, if sufficiently many such false theories are discovered, they are bound to prove also to be in conflict with each other. Similarly, it is possible that the theories, which we consider to be “proved” by a number of numerical agreements which appears to be large enough for us, are false because they are in conflict with a possible more encompassing theory which is beyond our means of discovery. If this were true, we would have to expect conflicts between our theories as soon as their number grows beyond a certain point and as soon as they cover a sufficiently large number of groups of phenomena. In contrast to the article of faith of the theoretical physicist mentioned before, this is the nightmare of the theorist.

Let us consider a few examples of “false” theories which give, in view of their falseness, alarmingly accurate descriptions of groups of phenomena. With some goodwill, one can dismiss some of the evidence which these examples provide. The success of Bohr’s early and pioneering ideas on the atom was always a rather narrow one and the same applies to Ptolemy’s epicycles. Our present vantage point gives an accurate description of all phenomena which these more primitive theories can describe. The same is not true any longer of the so-called free-electron theory, which gives a marvelously accurate picture of many, if not most, properties of metals, semiconductors, and insulators. In particular, it explains the fact, never properly understood on the basis of the “real theory,” that insulators show a specific resistance to electricity which may be 1026 times greater than that of metals. In fact, there is no experimental evidence to show that the resistance is not infinite under the conditions under which the free-electron theory would lead us to expect an infinite resistance. Nevertheless, we are convinced that the free-electron theory is a crude approximation which should be replaced, in the description of all phenomena concerning solids, by a more accurate picture.

If viewed from our real vantage point, the situation presented by the free-electron theory is irritating but is not likely to forebode any inconsistencies which are unsurmountable for us. The free-electron theory raises doubts as to how much we should trust numerical agreement between theory and experiment as evidence for the correctness of the theory. We are used to such doubts.

A much more difficult and confusing situation would arise if we could, some day, establish a theory of the phenomena of consciousness, or of biology, which would be as coherent and convincing as our present theories of the inanimate world. Mendel’s laws of inheritance and the subsequent work on genes may well form the beginning of such a theory as far as biology is concerned. Furthermore, it is quite possible that an abstract argument can be found which shows that there is a conflict between such a theory and the accepted principles of physics. The argument could be of such abstract nature that it might not be possible to resolve the conflict, in favor of one or of the other theory, by an experiment. Such a situation would put a heavy strain on our faith in our theories and on our belief in the reality of the concepts which we form. It would give us a deep sense of frustration in our search for what I called “the ultimate truth.” The reason that such a situation is conceivable is that, fundamentally, we do not know why our theories work so well. Hence, their accuracy may not prove their truth and consistency. Indeed, it is this writer’s belief that something rather akin to the situation which was described above exists if the present laws of heredity and of physics are confronted.

Let me end on a more cheerful note. The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.

Is the Universe Made of Math?

The following is excerpted from a Discover Magazine interview, by Adam Frank, with cosmologist Max Tegmark. The full article can be found here.

Is the Universe Actually Made of Math?

Unconventional cosmologist Max Tegmark says mathematical formulas create reality.

Let’s talk about your effort to understand the measurement problem by positing parallel universes—or, as you call them in aggregate, the multiverse. Can you explain parallel universes?

There are four different levels of multiverse. Three of them have been proposed by other people, and I’ve added a fourth—the mathematical universe.

What is the multiverse’s first level?

The level I multiverse is simply an infinite space. The space is infinite, but it is not infinitely old—it’s only 14 billion years old, dating to our Big Bang. That’s why we can’t see all of space but only part of it—the part from which light has had time to get here so far. Light hasn’t had time to get here from everywhere. But if space goes on forever, then there must be other regions like ours—in fact, an infinite number of them. No matter how unlikely it is to have another planet just like Earth, we know that in an infinite universe it is bound to happen again.

You’re saying that we must all have doppelgängers somewhere out there due to the mathematics of infinity.

That’s pretty crazy, right? But I’m not even asking you to believe in anything weird yet. I’m not even asking you to believe in any kind of crazy new physics. All you need for a level I multiverse is an infinite universe—go far enough out and you will find another Earth with another version of yourself.

So we are just at level I. What’s the next level of the multiverse?

Level II emerges if the fundamental equations of physics, the ones that govern the behavior of the universe after the Big Bang, have more than one solution. It’s like water, which can be a solid, a liquid, or a gas. In string theory, there may be 10500 kinds or even infinitely many kinds of universes possible. Of course string theory might be wrong, but it’s perfectly plausible that whatever you replace it with will also have many solutions.

Go far enough out and you will find another Earth with another version of yourself.

Why should there be more than one kind of universe coming out of the Big Bang?

Inflationary cosmology, which is our best theory for what happened right after the Big Bang, says that a tiny chunk of space underwent a period of rapid expansion to become our universe. That became our level I multiverse. But other chunks could have inflated too, from other Big Bangs. These would be parallel universes with different kinds of physical laws, different solutions to those equations. This kind of parallel universe is very different from what happens in level I.


Well, in level I, students in different parallel universes might learn a different history from our own, but their physics would still be the same. Students in level II parallel universes learn different history and different physics. They might learn that there are 67 stable elements in the periodic table, not the 80 we have. Or they might learn there are four kinds of quarks rather than the six kinds we have in our world.

Do these level II universes inhabit different dimensions?

No, they share the same space, but we could never communicate with them because we are all being swept away from each other as space expands faster than light can travel.

OK, on to level III.

Level III comes from a radical solution to the measurement problem proposed by a physicist named Hugh Everett back in the 1950s. [Everett left physics after completing his Ph.D. at Prince­ton because of a lackluster response to his theories.] Everett said that every time a measurement is made, the universe splits off into parallel versions of itself. In one universe you see result A on the measuring device, but in another universe, a parallel version of you reads off result B. After the measurement, there are going to be two of you.

So there are parallel me’s in level III as well.

Sure. You are made up of quantum particles, so if they can be in two places at once, so can you. It’s a controversial idea, of course, and people love to argue about it, but this “many worlds” interpretation, as it is called, keeps the integrity of the mathematics. In Everett’s view, the wave function doesn’t collapse, and the Schrödinger equation always holds.

The level I and level II multiverses all exist in the same spatial dimensions as our own. Is this true of level III?

No. The parallel universes of level III exist in an abstract mathematical structure called Hilbert space, which can have infinite spatial dimensions. Each universe is real, but each one exists in different dimensions of this Hilbert space. The parallel universes are like different pages in a book, existing independently, simultaneously, and right next to each other. In a way all these infinite level III universes exist right here, right now.

That brings us to the last level: the level IV multiverse intimately tied up with your mathematical universe, the “crackpot idea” you were once warned against. Perhaps we should start there.

I begin with something more basic. You can call it the external reality hypothesis, which is the assumption that there is a reality out there that is independent of us. I think most physicists would agree with this idea.

The question then becomes, what is the nature of this external reality?

If a reality exists independently of us, it must be free from the language that we use to describe it. There should be no human baggage.

I see where you’re heading. Without these descriptors, we’re left with only math.

The physicist Eugene Wigner wrote a famous essay in the 1960s called “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” In that essay he asked why nature is so accurately described by mathematics. The question did not start with him. As far back as Pythagoras in the ancient Greek era, there was the idea that the universe was built on mathematics. In the 17th century Galileo eloquently wrote that nature is a “grand book” that is “written in the language of mathematics.” Then, of course, there was the great Greek philosopher Plato, who said the objects of mathematics really exist.

How does your mathematical universe hypothesis fit in?

Well, Galileo and Wigner and lots of other scientists would argue that abstract mathematics “describes” reality. Plato would say that mathematics exists somewhere out there as an ideal reality. I am working in between. I have this sort of crazy-sounding idea that the reason why mathematics is so effective at describing reality is that it is reality. That is the mathematical universe hypothesis: Mathematical things actually exist, and they are actually physical reality.

OK, but what do you mean when you say the universe is mathematics? I don’t feel like a bunch of equations. My breakfast seemed pretty solid. Most people will have a hard time accepting that their fundamental existence turns out to be the subject they hated in high school.

For most people, mathematics seems either like a sadistic form of punishment or a bag of tricks for manipulating numbers. But like physics, mathematics has evolved to ask broad questions.These days mathematicians think of their field as the study of “mathematical structures,” sets of abstract entities and the relations between them. What has happened in physics is that over the years more complicated and sophisticated mathematical structures have proved to be invaluable.

Can you give a simple example of a mathematical structure?

The integers 1, 2, 3 are a mathematical structure if you include operations like addition, subtraction, and the like. Of course, the integers are pretty simple. The mathematical structure that must be our universe would be complex enough for creatures like us to exist. Some people think string theory is the ultimate theory of the universe, the so-called theory of everything. If that turns out to be true, then string theory will be a mathematical structure complex enough so that self-awareness can exist within it.

But self-awareness includes the feeling of being alive. That seems pretty hard to capture in mathematics.

To understand the concept, you have to distinguish two ways of viewing reality. The first is from the outside, like the overview of a physicist studying its mathematical structure. The second way is the inside view of an observer living in the structure. You can think of a frog living in the landscape as the inside view and a high-flying bird surveying the landscape as the outside view. These two perspectives are connected to each other through time.

In what way does time provide a bridge between the two perspectives?

Well, all mathematical structures are abstract, immutable entities. The integers and their relations to each other, all these things exist outside of time.

Do you mean that there is no such thing as time for these structures?

Yes, from the outside. But you can have time inside some of them. The integers are not a mathematical structure that includes time, but Einstein’s beautiful theory of relativity certainly does have parts that correspond to time. Einstein’s theory has a four-dimensional mathematical structure called space-time, in which there are three dimensions of space and one dimension of time.

So the mathematical structure that is the theory of relativity has a piece that explicitly describes time or, better yet, is time. But the integers don’t have anything similar.

Yes, and the important thing to remember is that Einstein’s theory taken as a whole represents the bird’s perspective. In relativity all of time already exists. All events, including your entire life, already exist as the mathematical structure called space-time. In space-time, nothing happens or changes because it contains all time at once. From the frog’s perspective it appears that time is flowing, but that is just an illusion. The frog looks out and sees the moon in space, orbiting around Earth. But from the bird’s perspective, the moon’s orbit is a static spiral in space-time.

The frog feels time pass, but from the bird’s perspective it’s all just one eternal, unalterable mathematical structure.

That is it. If the history of our universe were a movie, the mathematical structure would correspond not to a single frame but to the entire DVD. That explains how change can be an illusion.

Of course, quantum mechanics with its notorious uncertainty principle and its Schrödinger equation will have to be part of the theory of everything.

Right. Things are more complicated than just relativity. If Einstein’s theory described all of physics, then all events would be predetermined. But thanks to quantum mechanics, it’s more interesting.

But why do some equations describe our universe so perfectly and others not so much?

Stephen Hawking once asked it this way: “What is it that breathes fire into the equations and makes a universe for them to describe?” If I am right and the cosmos is just mathematics, then no fire-breathing is required. A mathematical structure doesn’t describe a universe, it is a universe. The existence of the level IV multiverse also answers another question that has bothered people for a long time. John Wheeler put it this way: Even if we found equations that describe our universe perfectly, then why these particular equations and not others? The answer is that the other equations govern other, parallel universes, and that our universe has these particular equations because they are just statistically likely, given the distribution of mathematical structures that can support observers like us.

These are pretty broad and sweeping ideas. Are they just philosophical musings, or is there something that can actually be tested?

Well, the hypothesis predicts a lot more to reality than we thought, since every mathematical structure is another universe. Just as our sun is not the center of the galaxy but just another star, so too our universe is just another mathematical structure in a cosmos full of mathematical structures. From that we can make all kinds of predictions.

So instead of exploring just our universe, you look to all possible mathematical structures in this much bigger cosmos.

If the mathematical universe hypothesis is true, then we aren’t asking which particular mathematical equations describe all of reality anymore. Instead we have to figure out how to separate the frog’s view of the universe—our observations—from the bird’s view. Once we distinguish them we can determine whether we have uncovered the true structure of our universe and figure out which corner of the mathematical cosmos is our home.

Google Plus Requirement for Real Names

Google Plus (Google+) stirred up a controversy by deleting, wholesale, accounts created under pseudonyms instead of under real names.  Google+ acknowledged their mistakes and is now formulating an official policy for naming conventions on their new social network.

There are legitimate reasons that users might need to use pseudonyms.  Perhaps you don’t want your parents or ex-spouse to contact or follow you in any way.  The most obvious and crucial one is anonymity for political dissidents and social activists. Without that anonymity, activism can be too dangerous to pursue.  Social networks like Facebook and Twitter have changed the face of activism by facilitating historic movements for democratic reforms and human rights.  The whole world needs social networks to provide this service to help keep governments honest and accountable to their citizens. If Google+ wants to be a leader in social networking, they have no business abdicating such a crucial role by requiring the display of real names for their accounts, thus making activism too dangerous.  Google+ can require our real names for their internal records but they do not need to display our real names against our will.

Google+ can suspend, delete or ban accounts that violate their terms of service (TOS) whether or not those accounts use real names.  The purpose of requiring real names is to provide a deterrent against violating their TOS in the first place and to have the real names of culprits to provide to authorities should their violations rise to the level of criminal activity (fraud, cyber bullying, hacking, etc.).

But the deterrent is not about the display of real names . . . it’s about the possession of real names.  The deterrent is just as effective whether or not violators display their real names — as long as they know that Google+ has their real names on record.

And how will Google+ know if the name of an account is the real name unless they require proof of identity from everybody? Unless they do, many people will simply supply legitimate-looking false names. The requirement for real names is virtually unenforceable to begin with.

So the whole controversy over the requirement of real names is unnecessary as long as Google+ allows its users to hide their real names and substitute pseudonyms if they want to.  Google+ only needs to possess our real names: they don’t need to display them.  In theory, not only would they have the deterrent they want but they would also have the real names authorities will need to pursue criminal activity perpetrated on the Google+ network.  But most importantly, Google+ will be able to follow the example set by Facebook and Twitter and provide a desperately needed service to dissidents and activists around the world.  If Google+ is going to require our real names, then we should require them to shoulder their responsibility, as a social networking leader, to facilitate activism.

Let Google+ know that requiring our real names is okay as long as they don’t FORCE us to display them!

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