Dangerous Knowledge
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Dangerous Knowledge

2007, Science  -   125 Comments
8.54
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Ratings: 8.54/10 from 218 users.

In this one-off documentary, David Malone looks at four brilliant mathematicians - Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing - whose genius has profoundly affected us, but which tragically drove them insane and eventually led to them all committing suicide.

The film begins with Georg Cantor, the great mathematician whose work proved to be the foundation for much of the 20th-century mathematics. He believed he was God's messenger and was eventually driven insane trying to prove his theories of infinity.

Ludwig Boltzmann's struggle to prove the existence of atoms and probability eventually drove him to suicide. Kurt Gödel, the introverted confidant of Einstein, proved that there would always be problems which were outside human logic. His life ended in a sanatorium where he starved himself to death.

Finally, Alan Turing, the great Bletchley Park code breaker, father of computer science and homosexual, died trying to prove that some things are fundamentally unprovable.

The film also talks to the latest in the line of thinkers who have continued to pursue the question of whether there are things that mathematics and the human mind cannot know. They include Greg Chaitin, mathematician at the IBM TJ Watson Research Center, New York, and Roger Penrose.

Dangerous Knowledge tackles some of the profound questions about the true nature of reality that mathematical thinkers are still trying to answer today.

Directed by: David Malone

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June VanDerMark
June VanDerMark
2 years ago

Alan Turing probably committed suicide because of the homophobia he suffered in that era.

pj
pj
4 years ago

The theme inside the opening music is from the film Threads

I felt that fear in my teeth again....

David
David
4 years ago

Intellect and emotion would, ideally, work together in peace or the creative cannot be free but remain caged by confusion, indecision and depression.

Rob
Rob
5 years ago

Boltzman, Cantor, Godel and Turing help us understand that there is a cultural domain that operates in prior unity or serves the sociopolitical or economic domain of humankind.

Mathematics, 'mind' or attention itself, is only one of four faculties that make up the cultural domain of humankind.

Body or service
Mind or attention
Emotion or feeling
Breathe or energy

What Boltzman, Cantor, Godel, Turing help us to do is understand that there are other faculties operating prior to mind or attention such as feeling or energy.

!DA

adzkia21
adzkia21
5 years ago

Bottom line we invented language and numbers to represent everything that can be observed . so how could there be something we cant prove, regardless of medium its told through...? We made up the rules observable to us through sight....with somthing that is not found in nature. (words and numbers) to represent the splendor..of course we can make up some new words if we need to or plug in some numbers in a graph. We invented and tweaked these things based on what happened physically first so of course theres always an ability to clarify mistakes or make revalations using language or numbers.... we invented them! I havent even wwatcheds this yet lol but as far as peoples minds, the ability to interperate the system thats been forged by the geniuses before us is the adaptation of todays great minds that is being tested. We have to evolve with the graph or system because it seems to me like gravity pressure speee force what have you....pretty muchc links up to the point where we caan control those things to such accuracy it cant be wrong or we wouldnntbave been able to create the internet or put people in space with massive rockets.

Urban dweller
Urban dweller
5 years ago

Reading the above review of the doc doesn't seem to indicate exploring how society treated them might have played a larger role in their demise other than their endeavors to solve and understand the mysteries of life.

Nik
Nik
6 years ago

Probably the best documentary in mathematics. Watched in many times. Unfortunately haven't seen any more such by David Malone.

Lance
Lance
6 years ago

"He who knows does not speak, and he who speaks does not know" . . . or something like that . . . from ancient Chinese wisdom . . . .

Hemanth K
Hemanth K
7 years ago

silkop....I hope you will one day take a course in something like discrete mathematics and get an opportunity to realize how there can be different levels of infinities(of course it will appear silly if we do not have prerequisite knowledge), one above the other. Those guys are all geniuses....don't try to judge them without proper knowledge...
Consider the infinities of natural numbers and real numbers...it is very easy to show that they are different levels of infinities....you should properly understand how infinities are defined and measured...it might seem upsurd but it's fun ones you start learning

Johnny Blu
Johnny Blu
8 years ago

I'm not sure if math is even real. I think they figured out it's all a hoax and off'd themselves because they wanted to relive with the astral gods above.

G=uncertainty
G=uncertainty
10 years ago

The way to judge this documentary in proper context is to realize how
outside the box thinking these great men were. Consider how modern
mathematical physicists, like religious zealots who take for granted a
perfection in creation, also seek a perfection in proving a calculus based order in the universe that does not exist. The irony of these tragic figures is that when their contrary views were rejected by a
mechanical materialist establishment, they had breakdowns or went mad like so many computers that crash from problem solving. What to take away from this is that great thinkers need not be one track minded and must be in touch with heart, soul and intuition to solve existential questions beyond our comprehension. And whether or not infinity or eternity can answer the unanswerable, the concept of God is not a math equation.

awful_truth
awful_truth
10 years ago

This is a terrific documentary that needs to be viewed by everyone, especially those who can only accept that which can be proven. Einstein, and Gödel were both correct, but this thinking can only be embraced by those who possess creativity, and intuition. Definitely a good watch. I leave the readers with a quote from Einstein:
"For me, it is enough, just to wonder at the possibilities of existance".

JMDinOKC
JMDinOKC
10 years ago

This is a fascinating documentary that taught me about people and things I never knew about; but I agree with "Guest" who dismisses Malone's premise that "what these men saw" through their unorthodox thinking drove them into madness. I agree with his/her statement that "Sensitively balanced minds have been known to go over the edge." These were brilliant men who happened to have either concurrent psychiatric problems or in Turing's case, a lifestyle that was taboo in 1950s Britain. The psychologist whom Malone interviews himself contradicts Malone's premise in the film when he remarks that in his opinion, it's not so much that these men "could not look away" from the reality they perceived with their innovative thoughts, but that it takes a certain type of personality to go that way in the first place. Malone seems not to have realized that this may well be inconsistent with his premise. There have been lots of brilliant physicists and mathematicians who were psychiatrically more or less normal, e.g. Christian Gauss and Richard Feynman to name but two. Isaac Newton started out peculiar and then seemed to get MORE normal later in life after he'd published his Principia.

drew
drew
10 years ago

Bottom line we invented language and numbers to represent everything that can be observed . so how could there be something we cant prove, regardless of medium its told through...? We made up the rules observable to us through sight....with somthing that is not found in nature. (words and numbers) to represent the splendor..of course we can make up some new words if we need to or plug in some numbers in a graph. We invented and tweaked these things based on what happened physically first so of course theres always an ability to clarify mistakes or make revalations using language or numbers.... we invented them! I havent even wwatcheds this yet lol but as far as peoples minds, the ability to interperate the system thats been forged by the geniuses before us is the adaptation of todays great minds that is being tested. We have to evolve with the graph or system because it seems to me like gravity pressure speee force what have you....pretty muchc links up to the point where we caan control those things to such accuracy it cant be wrong or we wouldnntbave been able to create the internet or put people in space with massive rockets.

Charlie137
Charlie137
10 years ago

This is the most beautiful science documentary I have ever seen(and I have seen many hundreds) True, the emphasis on the sociological aspects may have been overly dramatic, nonetheless, it points out the very deep truth that the need for an anchor or security blanket is one of the primary forms of attachment spoken of by Nagarjuna in his three poisons. It is very interesting to me that Einstein saw Schopenhauer as one of his guiding lights and that Schopenhauer and Nietzsche were students of Buddhism(certainly a long ways from being arhats). Godel and Einstein could imagine mathematical intuition but unfortunately they did not have a Bodhi tree to discover Bodhicitta. Martin Heidegger, a contemporary, conceived of emptiness but failed miserably to realize the Bodhisattva vow. This all goes to show the ethical sterility of Western philosophy. It has only been the mystics like Meister Eckhart who had the vision(intuition?) to look beyond the slavish devotion to the written word(Logos) to see a larger reality. Rupert Sheldrake exposes this hypocrisy in his book "Science Set Free: 10 Paths to New Discovery" ISBN 978-0770436728. Hopefully, we will all awaken from this multi-millenial sleep to embrace the truly infinite potential of being human and the exquisite beauty of living with a spirit of love and compassion.

Muhd Abdullah
Muhd Abdullah
10 years ago

Is it absolutely true there are no absolute truth?

YES or NO

Educate Yourself
Educate Yourself
10 years ago

Why would someone want to solve a problem that made people go berserk? On the other hand if that was my purpose in life I will go for it.

Neo Cool`
Neo Cool`
11 years ago

wow Amazing!

Ch H
Ch H
12 years ago

I get tired of the sentimental thesis that genius spurs this romantic thing called madness.

Sensitively balanced minds have been known to go over the edge. So-called madness also results from bipolar disorder, which is found disproportionately among keenly intelligent and creative people. It is a severe illness that can extend to psychosis and puts its sufferers at high risk of suicide.

Did much learning make these men mad? Doubtful.

For the record, Alan Turing died a martyr not to mathematical theory but to British anti-sodomy laws. I note that the posts here are from mathematicians arguing mathematics, not making psychiatric speculations. That suggests to me that they weren't too impressed with the film's thesis.

Leonid Basin
Leonid Basin
12 years ago

Beautiful!

shane scallan
shane scallan
12 years ago

ignorance is bliss but only for the weak willed.

innnocent
innnocent
12 years ago

George Cantor theory of trans-infinities is right and wrong simultaneously. this calls on the flaw of our basic logic that a statement is either true or false but not both. with infinities and infinitesimals our logic is doomed to failure. in fact it is our logic that is aleph-null and there are higher logics; aleph-one aleph-two e.t.c

innnocent
innnocent
12 years ago

1.George Cantor was wrong: The flaw in his theory of trans-infinities is within the ideal of one to one correspondence comparison.
Your monthly salary is twice mine and we are to work forever and ever adinfinitum. the pension is proportional to salary. Who earns more pension?
Very sorry, the question itself is contradictory; there is no pension to infinity employees.
2. Me and you are to race and you can run twice my speed. The race is adinfinitum in time. who wins? 'wins' means there is an end at which we are to be compared who has moved longer distance at that time which endless.

Francisco Mendivil
Francisco Mendivil
12 years ago

Mathematics is not for finding certainty, but for proving that there are no boundaries for the human brain, when it comes to possibilities.

knowledgeizpower
knowledgeizpower
12 years ago

Certain things are better left unknown it could be too much for the mind to handle.

Jeremiah
Jeremiah
12 years ago

the beginning is the end. the end the beginning. life deaf infinite circle

Craigzz
Craigzz
12 years ago

There are many pieces of the jigsaw of everything still waiting to be put in place by all too few with the ability to do so.

10jwalton
10jwalton
13 years ago

@Crypticfreak You speak of an infinitely big circle.
But an infinite sized circle does not and can not exist.

As a Circle gets bigger it's curvature decreases.
So as a circle tends to infinity it's curvature tends to 0. A staright line has curvature of 0 and nothing else does. So therefore an infinitely large circle cannot exist.

msafwan86_nnss
msafwan86_nnss
13 years ago

This doc evade too many question! For example: If you mentioned Cantor's work then you must explain the work first before rambling about its significance, and similarly with Boltzman's work. The only thing that excite me in this doc is the Pythgorean's idea of infinity: which the host can explain himself (other stuff is just too bland)

uncontinuous
uncontinuous
13 years ago

the film was brilliant. the academia making the commentary underneath the screen section is perfect example of intellectual incompleteness.

Pyrrhus
Pyrrhus
13 years ago

@Robert Allen
Now I am more acquainted with your background, I will work in accordance. Meanwhile, indulge in no-nonsense math history. I think you will find doing so not only edifying, but toughly enjoyable, as well. Fortunately, in this area, there are many fine publication to choose amongst. I also encourage a re-read of Hardy's 'Apology'. It's a quick read, most especially for one with your remarkable literary acumen (yes, it does show!).

Pyrrhus
Pyrrhus
13 years ago

I have NOT received your "missives."

Did you prefix the subject line with 'XYZ'? (I get so much junk.)

Would you please re-encrypt for me, so that I can be sure I got it right in my posting to you? All this word play is so silly, I know; but it's the only way I can think of. Thanks, Robert.

Robert Allen
Robert Allen
13 years ago

@Pyrrhus

To the general and the lion:

Not only did I take the time yesterday to decrypt your post, but have also written you there. Please let me know if you have received my missives.

I have ordered "The World of Mathematics" and eagerly await its arrival. I also plan to read the Penrose introduction.

In college, I started off as a math/music major and came to realize that at that time I lacked the maturity, and perhaps the discipline, to pursue math. After dropping the math part of my major (I graduated with a major in music/comparative literature), I did not look at a math book, much less think about math, for well over 30 years--then I saw the movie "Pi," which though I realized it was total nonsense, for some strange reason rekindled my interest in math. As a result, I have gone or tried to go through texts on calculus (first and second year), linear algebra,abstract algebra, analysis and differential equations and finally determined that although the willingness and effort were there, the talent was not--the biggest hurdle was trying to follow the textbooks and working all the problems. All I can say about the level of my mathematical expertise is that I am dissatisfied with it and disappointed with my understanding of the subject. So, therefore, you have no competition from me as far as mastery. This is as clean as I can come.

I don't mean to cause you further pain by alluding to the distasteful, but I would still like to find out if your opinion of Dembski is the same as mine.

P.S. I think it's terrible that Cauchy "misplaced" Abel's paper. While Cauchy was certainly a fine mathematician, everything I've read about him suggests--well, you know. Anyway the mathematics comes first.

P.P.S. T.S. Eliot is one of the few poets in the English language I like; the others are Blake, Dryden and for the sake of doggerel, Robert Service and Samuel Hoffenstein. I have no use for either the English or the American romantics.

Pyrrhus
Pyrrhus
13 years ago

I hope you realize, Robert, that our discussion is taking away ALL time intended for the math's outline. I do not mind, not at all; but please forgive, in advance, "the Shadow" (as T.S. Eliot would have it) which "Falls:
"Between the idea
"And the reality
"Between the motion
"And the act"
Too, for me, at any rate:
"Life is [not] very long."

As to viewing 'Jesus Camp', I have not, nor intend to. I know enough to fear coming away angry, frustrated, and depressed. Doubtless, 'Jesus Camp' would present me additional information, at a cost: additional depression, elevated blood pressure, heaped atop depressive pathologies in whose caste-iron grip I find myself. Avoidance of 'Jesus Camp' type exposures, in exchange for maintenance of whatever fragments of mental stability are left me, is a chosen trade-off.

With all respect that can be mustered, I request you make no further mention of potential 'shocks-to-the-system'. Amplifications of the 'horror' are intolerable. I am confident you will honor my request, and am grateful.

Now, the mundane:

1) I urge you to read the Penrose introduction, in its entirety. (Upon doing so, one is often tempted to read on :)

2) 'The world of Mathematics' is a comprehensive, historical overview of mathematics' evolution from zero B.C.E. to the late forties. Within its class, I know of no superior program. Its very existence is a tribute to all who contributed. Naturally, one is free to read, linear-fashion, covers to covers; though highly recommended, this is by no means necessary. Any readings in the collections invariably enrich. I love it.

3) I've yet to locate anything, at all, remotely accessible concerning groups' isomorphic nature vis-à-vis groups of permutations; but I've by no means given up trying.

4) Robert, if you can find the time, and are so inclined, would be so kind as to describe for me your level of mathematical expertise. At times I am of the impression you are a beginner. At other times, I come away vaguely suspicious you are far more advanced than I. Structure layouts facilitating endeavors useless to you would waste both your time, and mine. (With no reference to Cauchy intended), 'couched' in the vulgate vernacular, would you kindly: 'come clean'?

I think I like you, Robert, though we each know so very little of the other. Have you taken time to decrypt the post of mine, meant for your eyes, to be seen here, four up preceding this posting? In closing: Pyhrrus' name is Leon.

Robert Allen
Robert Allen
13 years ago

@Pyrrhus

Another question more in your field, although I believe I know the answer. What do you think of William Dembski?

Talk about religioius ravings. Here's someone in academia who lies and misrepresents just for his church and who, to boot, resorts to a faith healer to cure his autistic son.

Even I who cannot begin to qualify as an amateur immediately saw through his ostensibly probabilistic refutation of evolution.

Robert Allen
Robert Allen
13 years ago

@Pyrrhus

Amen! And we don't need to know anything about biology to appreciate what Dawkins stands for. It's not so much what he says about reason; it's his presentation. The man is a born teacher of sterling eloquence and an inspiration, especially to the young.

Religious rant--I like a good hell-fire, brimstone tirade a la Jonathan Edwards as well as the next man, but I treat it like what it is, a diversion. In this regard, at least, Peter Popoff is creative. In one of his perorations, he exclaimed that he had lent Jesus $500.00 from his credit card and exhorted his flock to do likewise. (To raise the hackles, see "Jesus Camp" which is on this site.)

It is chilling when this type of non-thinking (intelligent design) essays to insinuate itelf into the classroom as it did in Kitzmiller v. Dover Area School District. While ID is another view, it is not a scientific one and has no place in a science class any more than numerology has in a mathematics course. To take this digression further, why do its proponents have to lie, misrepresent, etc. to "prove" it.
So your arrogance is as justified as Dr. Dawkins'.

To answer your question, I asked you about Dr. Dawkins to ascertain if we were in the same camp.

Pyrrhus
Pyrrhus
13 years ago

I like Richard Dawkins (in fact, he's my kind of people!); it's just that my knowledge of biology is not 'next to nothing', it IS nothing (if 'nothing' can 'exist', that is). Dawkins is an evolutionary biologist and his work veers to the theoretical. I am completely ill-equipped to appreciate his scholarship. That is sad, but it also is true.

In these, his retirement years, Dr. Dawkins is fighting the 'good fight' on behalf of rational thought and debate, in opposition to what, at times, appears as an all-pervasive resurgence of superstition and willful ignorance in politics, culture -- public discourse, at large. The likes of Dr. Dawkins, and our poor friend, Christopher Hitchens, are all too few in number. I wish I were able to lend a hand, but I am not.

You ask what I think of Richard Dawkins. Concerning the merits of his scholarship, I am unable to comment. As to his valiant strivings to stop this world returning to superstitions it has taken our species tens of thousands of years to conquer, I am, needless to say, in concurrence; but, frankly, there really is not much Dr. Dawkins says on behalf of reason that I do not already know. That sounds arrogant. But I think the same might be true for you and countless others who are sickened by religious ravings.

Well, I have spoken my mind. May I ask you, Robert, why you asked me? And, please, share your thoughts, if you wish.

Robert Allen
Robert Allen
13 years ago

@Pyrrhus

I don't quite understand your comment on Richard Dawkins and would appreciate your view even if it differs from mine, but like him (and obviously you) I'm no theist either.

I'm sorry, I do not speak or read German, but I have read a mountain of German literature. Again, I do not speak or read Russian, but I have read an equal mountain of German literature. Which makes me wonder why most Americans have not read Tom Sawyer, for just about every German and Russian I have met has.

Pyrrhus
Pyrrhus
13 years ago

What do I think of Richard Dawkins? I don't. However, I do share one thing with the man: I am not a theist, nor have I been since leaving a minor seminary, aged thirteen.

By the way, do you happen to speak or read German?

Robert Allen
Robert Allen
13 years ago

@Pyrrhus

As I wrote, if you could find a lucid presentation of Cayley's theorem which seems to be basic to group theory, I would appreciate it.

What do you think of Richard Dawkins? I realize he is not a mathematician, but all the same, I am curious.

Robert Allen
Robert Allen
13 years ago

@Pyrrhus

Congratulations. We're contemporaries.

I will take a look at "Road to Reality." Thank you for the reference.

Pyrrhus
Pyrrhus
13 years ago

Cayley’s Theorem. Got it.

Pyrrhus
Pyrrhus
13 years ago

I turned 63 four days ago!

Pyrrhus
Pyrrhus
13 years ago

P.S.:
Rather than attempting a full print-out, it is probably best to just save the Roger Penrose, 'Road to Reality', PDF file to your hard drive for viewing, as printing it would require 1,094 pieces of paper!

Robert Allen
Robert Allen
13 years ago

@Pyrrhus

Thanks for trying, but what I meant by Cayley's theorem is the one which states, "Every group is isomorphic to a group of permutations."

As far as being a young stallion, I am 63 years old.

Pyrrhus
Pyrrhus
13 years ago

re: Arthur Cayley, am looking for expository intro to graph theory

Meanwhile, do search on "Road to Reality" "Roger Penrose"
It's a PDF file which you can print upon download at:

student 'dot' fizika 'dot' org 'forwardslsh' 'tilde' dzoljom 'forwardslsh' Roger_Penrose_ 'hyphen' _The_Road_to_Reality 'dot' pdf

Decided to start out 'Serial Fashion' and have something in the works. Coming soon!

Robert, you're like a young stallion galloping in all directions at once (lol)!

Robert Allen
Robert Allen
13 years ago

@Pyrrhus

Thank you. I have ordered it.

Do you know of any good, clear expositions of Cayley's theory?

Pyrrhus
Pyrrhus
13 years ago

World of Mathematics 1956

auntiem ecrater c o m "forwardslash" p "forwardslash" 6655682 "forwardslash" 1956-world-of-mathematics-box-set-simon#

Robert Allen
Robert Allen
13 years ago

@Pyrrhus

I knew it was some sport.

Wasn't there a professor, I believe his name was Aiken and I believe he taught at Princeton, who, among other things, could recite Pi to several hundred places, both the correct and incorrect versions? He seems to be just about the only mathematical idiot savant who became a true mathematician.

Pyrrhus
Pyrrhus
13 years ago

Second only to mathematics, stood Hardy's passion, not for rugby but, rather, for cricket, as spectator. He was in the habit of carrying an umbrella to matches born of the conviction that God would have it rain only were he to come unprepared.