The Limits of Understanding

  • Published on: 15 December 2014
  • This statement is false. Think about it, and it makes your head hurt. If it’s true, it’s false. If it’s false, it’s true. In 1931, Austrian logician Kurt Gödel shocked the worlds of mathematics and philosophy by establishing that such statements are far more than a quirky turn of language: he showed that there are mathematical truths which simply can’t be proven. In the decades since, thinkers have taken the brilliant Gödel’s result in a variety of directions–linking it to limits of human comprehension and the quest to recreate human thinking on a computer. This program explores Gödel’s discovery and examines the wider implications of his revolutionary finding. Participants include mathematician Gregory Chaitin, author Rebecca Goldstein, astrophysicist Mario Livio and artificial intelligence expert Marvin Minsky.

    This program is part of The Big Idea Series, made possible with support from the John Templeton Foundation.

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    Original Program Date: June 4, 2010
    MODERATOR: Paul Nurse
    PARTICIPANTS: Gregory Chaitin, Mario Livio, Marvin Minsky, Rebecca Newberger Goldstein

    Paul Nurse's Introduction. 00:00

    Who is Kurt Godel? 03:36

    Participant Introductions. 07:22

    What was the intellectual environment Godel was living in? 10:57

    Godel's beliefs in Platonism. 19:45

    Gregory Chaitin on the incompleteness theorem. 22:30

    Platonism vs. Formalism. 27:18

    The unreasonable effectiveness of mathematics in the world. 40:53

    The world is built out of mathematics... what else would you make it out of? 47:44

    Mathematics and consciousness. 53:29

    What are the problems of building a machine that has consciousness? 01:01:09

    If math isn't a formal system then what is it? 01:07:40

    Explaining math with simple computer programs. 01:18:33

    Its hard to find good math. 01:25:40
  • Runtime : 1:33:
  • The Limits of Understanding what is consciousness the science of consciousness mathematics philosophy limits of human comprehension astrophysicist recreate human thinking Gregory Chaitin Mario Livio Marvin Minsky Rebecca Newberger Goldstein Paul Nurse Kurt Godel New York City NYC World Science Festival biology John Templeton Foundation full program 2010 Big Ideas Series

COMMENTS: 40

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  • James McDonald
    James McDonald   1 days ago

    A plausible response to Chaitin is that he might be looking at the problem in the wrong direction, from axioms to theorems, vs. theorems to axioms.The power of formal mathematics is that given a field of stuff to be explained, you can abstract away a lot and then reduce the remaining structure to a set of much more condensed axioms. In a s sense, the axioms distill the essence of all the complexity seen in the system being modeled (physical or mathematical). Viewed that way, there is little practical mystery associated with Godel's theorem -- it effectively refers to things you don't care about. If you did, those concerns would be in the system being modeled, you would have a richer set of axioms to capture those additional notions, and then Godel's theorem would refer to yet more distant things you do not care about. There is an ever-receding horizon of things any given set of axioms won't handle, but if the axioms were never chosen to handle those things, maybe that's nothing to lie awake worrying about.The implausible effectiveness of mathematics then boils down to noticing that the universe seems to be very parsimonious -- it doesn't use 445,944,222 rules when 3 (or 30) will suffice. It's not so much that mathematics can explain the patterns we see, but that such simple mathematics (maybe not to us, but simple in the grand scheme of things) can explain so much.

  • Brian Azmy
    Brian Azmy   1 weeks ago

    So, a barber, a jellyfish, and a priest all walk into a bar and...Great show and thanks to WSF for a well spent hour and a half 👍

  • [ CMV ] America
    [ CMV ] America   1 weeks ago

    Until humans evolve to a point where they have an average IQ of about 500, they will never understand that they can never completely understand.

  • [ CMV ] America
    [ CMV ] America   1 weeks ago

    All the knowledge of every person who has ever lived, and all the recorded knowledge, is only a small fraction of what is contained in the infinite and eternal universe.

  • Sam Re
    Sam Re   1 weeks ago

    man scientist don't know how to dress up. but i have to say Minsky's tie is cool

  • Sam Re
    Sam Re   1 weeks ago

    ok we know that women can do math too. just don't force them into the scene

  • marco biagini
    marco biagini   1 weeks ago

    I am a physicist and I will provide solid arguments that prove that consciousness cannot be generated by the brain (in my youtube channel you can find a video with more detailed explanations). Many argue that consciousness is an emergent property of the brain, but it is possible to show that such hypothesis is inconsistent with our scientific knowledges. In fact, it is possible to show that all the examples of emergent properties consists of concepts used to describe how an external object appear to our conscious mind, and not how it is in itself, which means how the object is independently from our observation. Let me show this with an example of emergent property, such as the function of a biological organ, like the heart that has the function of pumping blood. Actually, the function of pumping blood is just an abstract concept through which we approximately describe what is really happening, that is billions of linked chemical reactions and moving molecules. In other words, the function of the heart is only a subjective description of the organ from a macroscopic point of view, which neglect many microscopic details. Besides, the concept of pumping is directly connected to the concepts of force and movement, which are fundamental physical properties. Therefore, the function of the heart is not a new real property, but only a conceptual model through which we approximately describe the reality; this means that the function of the heart is just an idea. If we were smarter and could solve the equations of quantum physics for a macroscopic system, we could know all the processes that take place in physical reality without the need to consider simplified models. It is only because of the limitations of our intelligence that we have devised simplified conceptual models to describe natural phenomena. All the classifications used by biologists respond to the need to overcome the limits of our intelligence. Through biology, we describe natural phenomena in order to make them appear consistent with our way of reasoning; biological models are in fact very intuitive, unlike quantum physics. Emergent properties are then ideas conceived to describe or classify, according to arbitrary criteria and from a subjective point of view, certain processes or systems; emergent properties are intrinsically subjective, since they are conceptual models based on the arbitrary choice to focus on certain aspects of a system and neglet other aspects, such as microscopic structures and processes; emergent properties consist of ideas through which we describe how the external reality appears to our conscious mind: without a conscious mind, these ideas (= emergent properties) would not exist at all. Here comes my first argument: arbitrariness, subjectivity, classifications and approximate descriptions, imply the existence of a conscious mind, which can arbitrarily choose a specific point of view and focus on certain aspects while neglecting others. It is obvious that consciousness cannot be considered an emergent property of the physical reality, because consciousenss is a preliminary necessary condition for the existence of any emergent property. We have then a logical contradiction. Nothing which presupposes the existence of consciousness can be used to try to explain the existence of consciousness. I specify that by consciousness I refer to the common property of all our psychical experiences, such as sensations, emotions, thoughts and even dreams. Here comes my second argument: our scientific knowledge shows that brain processes consist of sequences of ordinary elementary physical processes; since consciousness is not a property of ordinary elementary physical processes, then a succession of such processes cannot have cosciousness as a property. In fact we can break down the process and analyze it step by step, and in every step consciousness would be absent, so there would never be any consciousness during the entire sequence of elementary processes. It must be also understood that considering a group of elementary processes together as a whole is an arbitrary choice. In fact, according to the laws of physics, any number of elementary processes is totally equivalent. We could consider a group of one hundred elementary processes or ten thousand elementary processes, or any other number; this choice is arbitrary and not reducible to the laws of physics. However, consciousness is a necessary preliminary condition for the existence of arbitrary choices; therefore consciousness cannot be a property of a sequence of elementary processes as a whole, because such sequence as a whole is only an arbitrary and abstract concept that cannot exist independently of a conscious mind. Here comes my third argument: It should also be considered that brain processes consist of billions of parallel sequences of elementary processes that take place in different points of the brain; if we attributed to these processes the property of consciousness, we would have to associate with the brain billions of different consciousnesses, that is billions of minds and personalities, each with its own self-awareness and will; this contradicts our direct experience, that is, our awareness of being a single person who is able to control the voluntary movements of his own body with his own will. Consciousness is in fact the only phenomenon that we know from direct experience, and from direct experience we know that consciousness is characterized by the immediate and intuitive awareness of being an indivisible subject, of being an "I". If cerebral processes are analyzed taking into account the laws of physics, these processes do not identify any unity; this missing unit is the necessarily non-physical element (precisely because it is missing in the brain), the element that interprets the brain processes and generates the unitary conscious state that characterizes all our psychic experiences, i.e., the human mind. Here comes my forth argument: Consciousness is characterized by the fact that self-awareness is an immediate intuition that cannot be broken down or fragmented into simpler elements. This characteristic of consciousness of presenting itself as a unitary and non-decomposable state, not fragmented into billions of personalities, does not correspond to the quantum description of brain processes, which instead consists of billions of sequences of elementary incoherent quantum processes. When someone claims that consciousness is a property of the brain, they are implicitly considering the brain as a whole, an entity with its own specific properties, other than the properties of the components. From the physical point of view, the brain is not a whole, because its quantum state is not a coherent state, as in the case of entangled systems; the very fact of speaking of "brain" rather than many molecules that have different quantum states, is an arbitrary choice. This is an important aspect, because, as I have said, consciousness is a necessary preliminary condition for the existence of arbitrariness. So, if a system can be considered decomposable and considering it as a whole is an arbitrary choice, then it is inconsistent to assume that such a system can have or generate consciousness, since consciousness is a necessary precondition for the existence of any arbitrary choice. In other words, to regard consciousness as a property ofthe brain, we must first define what the brain is, and to do so we must rely only on the laws of physics, without introducing arbitrary notions extraneous to them; if this cannot be done, then it means that every property we attribute to the brain is not reducible to the laws of physics, and therefore such property would be nonphysical. Since the interactions between the quantum particles that make up the brain are ordinary interactions, it is not actually possible to define the brain based solely on the laws of physics. The only way to define the brain is to arbitrarily establish that a certain number of particles belong to it and others do not belong to it, but such arbitrariness is not admissible. In fact, the brain is not physically separated from the other organs of the body, with which it interacts, nor is it physically isolated from the external environment, just as it is not isolated from other brains, since we can communicate with other people, and to do so we use physical means, for example acoustic waves or electromagnetic waves (light). The brain is actually an arbitrary set of quantum particles involved in billions of parallel sequences of linked chemical reactions. This necessary arbitrariness in defining what the brain is, is sufficient to demonstrate that consciousness is not reducible to the laws of physics. Besides, since the brain is an arbitrary concept, and consciousness is the necessary preliminary condition for the existence of arbitrariness, consciousness cannot be a property of the brain. Based on these considerations, we can exclude that consciousness is generated by brain processes or is an emergent property of the brain; the brain is not even a sufficient condition for the existence of the most elementary psychical experience, such as a simple sensorial perception. Marco Biagini

  • Steve Seamans
    Steve Seamans   2 weeks ago

    Somebody give the poor lady a drink of water. She looks like nobody gave her a bottle on stage.

  • Rooster Crows
    Rooster Crows   2 weeks ago

    Never been change of kind . GOD the creator gets all the credit.

  • Fetishannabella bella

    1; 20 something, yes my Ex GF ... had the same sh*** God is a Maschin... Ahm... yes`? No , dream on

  • Fetishannabella bella

    I do love the sh*** they talk about... but? do talk "one day fly" (fem 3 male) diskuss life , sience, evolution ? Explain me Musik and love? can you?

  • Kyle Mullins
    Kyle Mullins   2 weeks ago

    Fallen angels arent aliens. Ishtar became a man for her father, god and jesus are one. Lucifer is catholic and false, satan is a tyrant and chose to be king of the gentilles. The great falling away has happened and the 144 are being sealed right now. Dont take the mark of the beast if they come for you, let them take you. Dont worship the statue.✝ENERGIES NOT ALIENS✝

  • Ramaraksha
    Ramaraksha   2 weeks ago

    We see this dichotomy - highly intelligent people a bit crazy or a lot crazy, killing themselves or ending up in institutions. We don't see this happening to less intelligent peopleThe answer is obvious - highly intelligent people think too much - they overburden their brains - way too many thoughts crowding their brains, giving them no peaceWe see this with ourselves - after a hard day's work we want to unwind - we open a beer and watch a ballgame - guess what? Our brains are at rest then, no more thinkingWe are happy & at peaceAnd that is what Heaven is all about - it is for the less intelligent - no more thinking - no need for brains - just sit and relax! What happens is that those who chase after Heaven end up as lower life formsWhat does a Dog think? Not much. How about a sheep? Again not muchA dog or a sheep is not going to go crazy, it is not going to overburden its brainThey live in peace and joy - Heaven!Fools chasing after fools Gold called Heaven, end up as lower life forms

  • Melk en Honing
    Melk en Honing   2 weeks ago

    I wish Chaitin wasn't so defensive and crippled by his ego so we could hear more interesting things from him

  • Victor Yankov
    Victor Yankov   2 weeks ago

    Bring those guys in 1 building plus some chaos lovers and you will get a god somewhere there haha! They will point the heck out of things what we didnt even ever imagine we can ask and they will first give the answers then the questions seems like. They will define the chaos what will give the order no point. And if this problem goes solved so all others will be just a paradoxal jokes and the barber will develop a gene what will stop his beard from growing (he will never need to shave heh)

  • Kenneth chamberland
    Kenneth chamberland   2 weeks ago

    Gods hand is of the number One,And mans hand is of the number zero... Universal math...Gods math of the one is as one tree or a man himself...As man is of the zero such as any machines or anything put together from Gods living creations...Just as God came into being when all Universal Matter had its first conscious thought...KNIGHTStEMPLAR...SLEEPERCELL...Till Mankind Addresses this fact World WIDE,It will be ...Same Old...Same Old...HOW CAN MAN EVER TURLY LEAD MANKIND,HONESTLY AND TURLY...WHEN WE ALL HAVE THE SAME,WANTS AND NEEDS...KNIGHTSTEMPLAR...SLEEPERCELL...Oldest war trick in book...Turn all God’s Prophets into Gods Themselves...[WORLD WIDE]...KNIGHTStEMPLAR...

  • Andrew Denis
    Andrew Denis   3 weeks ago

    Great discussion. I love how Minski is the only panel member who gets applause, despite the fact that he has repeatedly, confidently, and so consistently shot down the work and direction of other scientists for decades and repeatedly turned-out to be wrong. It’s fine to be wrong, especially while pushing boundaries, but his hubris has cost us decades of important research across thousands of great scientists. Worse yet, he still argued for his disproven approaches, and against validated and verified science such as the perceptron/neural networking; denying basic reality along the way in favor of his disproven beliefs.

  • Stephaine Johnston
    Stephaine Johnston   3 weeks ago

    "The limits of understanding?" Mathematics says that as population values increase, thought on the sums of life are increased as well...... So..... It would say that although we live in an infinite universe we still lead finite lives and conclusions to our time.... Time, ah yes, time is such a quantitively measured sphere of influence... It influences our lives, it influences our thoughts, it influences our advances and/or decay..... Take heed of time, it is an immeasurable paradox that has no bearing on our destiny........

  • Ask why?
    Ask why?   3 weeks ago

    Its beautiful, yet there is no caption :(

  • Jesus lopez
    Jesus lopez   3 weeks ago

    They talk to much about something that they know that they don't know.

  • Stephen chadd
    Stephen chadd   3 weeks ago

    Mathematics works in straight lines, biology works in curved lines.

  • joseph Timpanaro
    joseph Timpanaro   3 weeks ago

    The guy on the extreme left and the extreme right are a$$holes, full of themselves. The answer seems to be that the more you know the more certain it becomes you will never really know.

  • Jerry Yager
    Jerry Yager   1 months ago

    But the real question is, where can I get a crocheted tie?

  • Larry Roth
    Larry Roth   1 months ago

    humans remember every single thing every book every thought we never forget

  • Tudor Lucian
    Tudor Lucian   1 months ago

    19 as gold for gods to jump from 4tee5v to Vic Thor E ,., But 18sil ver soon 🥄 n for adding sugar to Plate ON.🤣.,. philosophy make s the testing of😂IT.,. from popular ET down to earth geography.,.🤑

  • Kurtis Erikson
    Kurtis Erikson   1 months ago

    Anyone who thinks that math is just an illusion or an abstraction, charge them a thousand dollars for a loaf of bread.

  • Derivativesjunkie
    Derivativesjunkie   1 months ago

    The mathematician needs to let the physicist explain himself Jesus Christ.

  • Adithya Ajoy
    Adithya Ajoy   1 months ago

    I wonder in my opinion, why in the move towards finding the hidden mystery of universe, we don't give much importance to philosophers view point??Let me know your opinion.....I love philosophy personally!!!

  • Stephen Thompson
    Stephen Thompson   1 months ago

    The 60 Hz hum of the microphone is terribly distracting and can be filtered out if the owner of this video was willing :(