Dangerous Knowledge
Beneath the surface of the world, are the rules of science. But beneath them, there is a far deeper set of rules – a matrix of pure mathematics which explains the nature of the rules of science and how it is way we can understand them in the first place. 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.
Part 1
Part 2
To Part 1: to treat mathematical infinities as a “mythical something” and to be baffled about them is silly from the get go. Confusion and paradoxes disappear when you treat every “infinity” as a target of a process with a finite description, a target which has no empirical equivalent whatsoever in Nature (and is just an idealized, thought up model = a description of something that we wish to describe). The “amazing” different infinities simply correspond to different finite generating processes. It is thus again silly to talk about one infinity being bigger than the other AS IF they had dimensions (an empirical concept). Rather, we should just admit that the different generating processes are, well, different.
When I posted the above comment, I was unaware that Poincaré and Gauss essentially stood by my intuitive interpretation of infinity, as did Wittgenstein later on. Having informed myself, I’m even more confident that Cantor’s treatment of “infinite sets” is ******** and that it’s not ME who is a looney having trouble to accept the obvious. How reassuring.
silkop – you sound like a second year student in some vaguely related discipline. Very pretentious and very shallow. Read more, think harder and type less.
The first mistake,Cantor made was trying to define an infinitesimally small point. The only
way to define such a point is to factor out,infinity.
The second mistake,obsessing about,”Pi” on the number line,with infinite digits.
Doesn’t the next number after 1.000…(infinite zeros)0,also have infinite points?
1.000…(infinite zeros)1
Thank you
I really liked this documentary.
I am no Math person, but still feel a resemblance that 'Life = Continuum Hypothesis'
You have reached one goal in life……and you will find that there is still a bigger goal that you want to achieve !!
Isn’t this show supposed to be about good mathematicians who go insane? In that case, it seems to me that telling these stories with a romantic yet melancholy tone is what they are trying to teach us. Of course the math is important too, and i’m learning lots as i watch this, but i kind of like the humanity aspect of these people. I remember when i finally, absolutely realized that religion was all just fairy tales made up by uneducated people from the distant past in order for them to feel like there was something worth living for so that they could face the hard lives they had to endure. In creating a fantasy they could live out “after death” made them feel like their lives were worth living. Of course religion eventually evolved into something that quit helping humanity and began to harm it, but people didn’t, and still don’t want to give up the fantasy. After I got away from all the religion of my childhood and could finally think clearly, even though i was very willing to shed that religion because of how horrible it had been to endure, that religion had been in my head since i was a baby, crammed in day after day. So, when i was able to get away from that religion and let it go, i was surprised at how difficult it was to still let go of the concepts i’d been taught. Even though i knew none of it was true, even when i was a kid it was obvious religion, all religion, is false, yet when i finally had to clear my mind and let reality seep in, i was still sad to see my fantasy go away. knowing i would die and that was it wasn’t easy to let myself accept. today i’ve had time to become used to the truth and i no longer feel like i did, nor am sad that lies are not true true. What I think happened to these math men was that they had a view of how the universe was, and when they learned it wasn’t going to be the way they once believed, nor had it ever been the way they once thought, these men suffered more than most when they realized that they not only had to let go of old concepts, they actually were the ones who had to bring the change to the world. And they coudln’t help knowing they themselves wrought the change, and that everyone on earth would eventually have to suffer the loss of their original thinking, or fantasy, in order to know the truth. And i suppose these men suffered more because they knew of the suffering they were delivering to the world. Change is difficult to accept. Men of science, i suppose, must bear it first and bear it well if it is to be accepted by others. these men i guess had a hard time being the bearers of truth.
excellent J. Miller – couldn’t have said it better myself. I tend to think that the human lacking of quantitative knowledge and certainty lead us into abstraction (pain does this as well). It is then that we create our own one word answers to explain what we do not understand, thereby putting our minds at ease. In my case this answer was always God. Mathematics is a tool for human understanding of the relationships in the universe and is imperfect as physics has failed to find the smallest parts – the discovery of atoms was supposed to satisfy this requirement but there are yet smaller pieces.
I also think human tenancies of pattern finding can often cause us to end up heading down the wrong path. Especially if one holds preconceptions. The opposite pitfall is to label anything that doesn’t as an anomaly, coincidence, and fail to follow your instincts even if it is based off circumstantial evidence. Every theory must be looked into. “Lets get messy” as the yellow school bus teacher miss frizzle always say. Yep the truth is messy.
This being said I haven’t watched the documentary yet. ^^
J Miller, i’m 100% agree
very well said
Do unto others as you would have them do unto you.
Is this not an equation that explains infinity as;
infinity sustaining itself by keeping other infinities alive therefore, to exist there must be other infinities that don’t take care of others as unto themselves and thus wither away into themselves and create the difference necessary to hold an opposing view and thus LIFE.(…that thinks about itself)?
:)
silkop, like your description! “idealized, thought up model = a description of something that we wish to describe.” Sadly, “Dangerous Knowledge” does seem to describe four unhappy lives that thoughtful peers were unable to ameliorate.
The date is late so you have my apologies for taking exception to the “********” remark. This may indicate the encumbered nature of my condition. Unable to complete the Sunday Crossword yours truly has learned to just put it down and move on. This makes me humble.
Trapped in a fragile and imperfect Allegory, dominated by the infinitely divisible Continuum, the Entropic, the Incomplete, the Uncertain … my life is in Chaos. How is a mere human (hobbled by constant Change) able to assume that languages like Physics, Mathematics or English may be able to provide answers to the chaotic puzzle?
Is what follows not the mathematical definition of “a perfect circle”? “A set of points all exactly equidistant from a single center point?” In grade school Cantor must have learned that since that single center point is infinitely divisible, the circle cannot in reality be perfect.
Why didn’t these great men just put down the puzzle? What’s that? Don’t wish to preach my dear silkop but here goes. Surely I’m not putting words in your mouth when it is said that good direction dictates we should still be proud of those who refuse to believe in our imperfection and entrapment? Those who, having a simple proof of imperfection, are willing to again take up the chaotic puzzle, following tangent after tangent in an innocent search for the completion of our mathematically perfect circle?
Now this is ********!
Beautiful documentary!
Here,here!
>>”It is thus again silly to talk about one infinity being bigger than the other AS IF they had dimensions”
If you work with sets it’s very easy to show two sets A and B
each with infinite elements where A is a subset of B
and at the same time B has elements in it that are not elements of A
thus showing that B has more elements than A even if both have infinite elements.
Similar example as mentioned in this docu:
Think the two sets of natural numbers and integers.
You can even show that that #Z = 2*#N – 1 since for every natural number there is a negative number with equal numbers between itself and zero f.e. -10 and 10.
If you accept that -0 is diffrent from 0: #Z = 2*#N.
So you can not only “rank” infinities but also show some exact relations.
“these men i guess had a hard time being the bearers of truth.” – J. Miller
J, you forgot – there IS NO truth.
Remember, from your rant – you “absolutely realized” the progression of history is merely the selling of fairy tales by snake oil salesmen to a ******** populace.
Drink up.
Science is no different.
The temple has been relocated to MIT.
The gowns now include pocket protectors.
Still, the (new?) clergy dabbles with the same old Strange Fire.
Or is the Big Bang theory not a creation myth?
What can science and a clip board prove True?
Please stop confusing the activity of compiling statistical probability, with Truth.
Just because Infinity may or may not appear in nature does not mean that it should not be described and/or used in mathematics.
There are many examples in the history of math where seemingly crazy ideas are brought into the subject for the simple reason that they work (examples include complex numbers and infinity) where at a later date some application has been found. Furthermore if you ask most pure mathematitions you will find that they could’t give two hoots about applications, just that there ideas are consistent within the axiomatic system. Someone will invariably find and apllication 500 years down the line!
@you were warned – often
Human Knowledge, by Bertrand Russell.
I love the conclusion of part 2, truly insightful it is.
“Are we grown up enough to live with uncertainty or will we again pledge blind allegiance to another certainty” – repeating the horrors of history. Just watching this is infinitely more educational than spending a million sabbaths listing to the ranting preacher say the same conjecture based on ancient myths and call it somehow perfect and logical (in this case my father). That is the great fallacy so many people have – faith – the truly great have ideas that swing back and forth like pendulums while retaining an anchor (often a family) in the ocean of the abstract.
I would also like to say that even though there is uncertainty – theories that describe the uncertainty can be true. Mathematics and Science are collectively a framework paradigm that is attempting to describe as best as possible through probabilities what has happen what is and what will happen. Perhaps instead of talked about the truth it is better to talk about the best truth right now. Remember though that a paradox can be described and by doing so will become another unit of truth. We will gain certainty in the foundations being uncertain – therefore our solutions will be more realistic. It is good to say what we no, better to admit and classify what we do not no, so that eventually we may understand what we do not know we do not know.
So, things are uncertain. Since we have no authority or certainty, what is wrong with claiming divine inspiration? Often when science “proves” something beyond a doubt, they find it actually isn’t true; the equation is of a higher order. Yet, if there is a God, then He understands everything and can make it clear. If Cantor was inpired by God, then Cantor might have actually known some real truths.
Absolute Perfection, Certainty and Infinity can only be percieved at the cost of time, evolution and entropy. They are contradictions. Although time, evolution and entropy are simply concepts born of agreement as are Perfection, Certainty and Infinity. There is only Perpetual now.
The part which makes the great thinkers a little tilted is Through our agreements on these concepts, The Mind can grow in its assessment of existance and accumulated understanding while everything around it is in a constant state of creative evolutionary renewal, devolution and Thermodynamic entropy. If this were not true, we would be able to build pyramids equal to those of Giza and we would have taken care of the ones already there using them for their original intent. What ever that might have been. WhoaHaHaHa
This is why most questions on subjects of agreed upon existance can only be answered with more questions begging for new or continued agreements. The more extended and powerful the agreement, the more effective words of agreement are on the Light which fills the void and agrees to condense from light matrix, Mind, into material existance. Everything is Alive, There is only Now. And down the rabbit hole we go HaHa.
Thought is Telepathy. The first language or Original form of communication. The original sin was to use words to try to describe infinity. Words all being containments or finite in their nature. The tree of knowlege was a devloved form of communication incapable of describing The tree of life because it is infinite. If you ever get a glimpse of it, you will be at a loss for words. We can never know anything, The minute we do it changes. The veil between this Tree of Knowlege side and that Tree of Life side is only a smoke screen which we can step through by accepting more and more of what we are being consatntly fed by the telepathic stillness which lies between the finite words. Like the spaces between the notes in music, there in lies Life. All the words, notes and numbers are the confusion, the insanity, the smoke screen. Be still and merge with god.
Maths is a formal system for understanding nature but it is a product of the Human Mind. The universe is not the product of the Human mind only to the extent that any individual observes it. The universe all matter and all systems cannot be defined absolutely by maths as such things exist unaware of these notions and have no necessity to conform to them, we seek to make the universe conform to our understanding this does not mean that our conclusions are correct. Science and mathematics can only offer us an ever more refined and predictable method of observing and ‘predicting’ Natural phenomena. It is curious that the notion of infinity still stands unresolved at the subatomic and larger cosmological scales. It is still in my mind linked closely with the notion of God. My belief is if all things are at the subatomic scale infinite, then there is a god if not the the opposite is the case, cant rationally explain that one but its just a hunch. NASA are 99% certain that the Universe is flat but we have been wrong about such notions before! I’d like to believe there was no God and that we could prove it but I think we will never be free of the Notion and perhaps there is a reason for this.
Just finished pt1..and am doing 2 ..good doc on these unfortunates..anybody ever look into the Chudnovsky brothers? The 2 Russkies computing pi out to 2 billion digits on a supercomputer they’ve built from mail order parts in their NY apt?….strange days indeed!
pt2 finis! makes me wonder if Jobs named his co. per Turing rather than a variety. great doc Vlatko..a most impressive site.