"Pure Mathematics" seems remote from a lot of practical and "artful" techniques, but PM is usually how hidden mechanisms are discovered. Sometimes it's the other way around, for patterns of chaos in paintings and transmission of data. Focused interest attracts others simply by curiosity.
Once again arts is described as theater or music or similar. It isn't, it's so much more than that. I agree that his starting point is flawed and biased especially with relation to the composer who applied mathematics to his work. The Beatles discredited and put to bed this deconstruction of the tonal scale. He then adds that an insect also sings in a mathematically pattern. The quote of Henri Poincare so depicts the mathematically minded view of creativity it is embarrassing, and we are living with its consequences today. Sorry, you might be correct, but you think in a way that many of us don't, like a labyrinth, and we all know what lurks here.
The title of this video (and of the talk) is misleading. The two cultures referred to by C. P. Snow are the sciences and the humanities, not science and art. There is a difference, there. Especially, the link between mathematics (patterns, mostly) and music has been acknowleged for ages - take, for instance, the famous book "Gödel, Escher, Bach", by Douglas Hofstadter (1979). This guy's central message is nothing new. Personally, I would say that the great devide is between science and theology (no, I don't agree with Stephen Jay Gould's "non overlaping magisteria"). Art is compatible with both. Within science, there is, perhaps, some tension beween physical sciences and social sciences (and postmodernism is bullshit - google the "Sokal affair"). I have the impression that the lecturer in this video didn't spend too much time thinking about the "two cultures". He didn't get the point. In any case, I see no problem at all between science and art. Hell, we even have "science fiction" as a literaly genre!
He made his point well. I don't know the context of the entire event, but he spoke directly to mathematics and art as the two cultures in the beginning. Then showed and spoke upon many ways that they do combine in positive ways. It may be nothing new but it helped me to understand some of what I've been feeling as I move into mathematics after almost a quarter century of writing poetry and stories.
deadeaded Yeah, I see what you mean. Is it bad that I'm not overly impressed though? So, I read up about the one that re-proved a section of the principia mathematica, then I read a bit of the principia itself and, well I can see why Russell said that writing it deadened his mind! I don't know how to put this other than it's very symbolic and derivational, so it doesn't surprise me all that much that a computer could churn it out. If you told the computer to give a result when it derives an equation you already know is significant, and give it a preference to simplify when it can, it seems that you could just set it off to combine all the rules you start it off with in as many ways as possible. It feels a bit monkeys on typewriters. Could the program, on the other hand, find one off the more inventive proofs of something like Pythagoras' theorem though, without giving it some major hints that you know the computer can take its trial and error technique to eventually get there?
There are computer proofs now that humans find rather hard to read (and, quite to the point, classification of finite simple groups seems to be one of them - do you know the order of Monster Group btw.?)
"Pure Mathematics" seems remote from a lot of practical and "artful" techniques, but PM is usually how hidden mechanisms are discovered. Sometimes it's the other way around, for patterns of chaos in paintings and transmission of data. Focused interest attracts others simply by curiosity.
Once again arts is described as theater or music or similar. It isn't, it's so much more than that. I agree that his starting point is flawed and biased especially with relation to the composer who applied mathematics to his work. The Beatles discredited and put to bed this deconstruction of the tonal scale. He then adds that an insect also sings in a mathematically pattern. The quote of Henri Poincare so depicts the mathematically minded view of creativity it is embarrassing, and we are living with its consequences today. Sorry, you might be correct, but you think in a way that many of us don't, like a labyrinth, and we all know what lurks here.
I wonder, what is the density of true statements in the set of all statements?
is the set of all statements finite
Why this man getting so much hate
The title of this video (and of the talk) is misleading. The two cultures referred to by C. P. Snow are the sciences and the humanities, not science and art. There is a difference, there. Especially, the link between mathematics (patterns, mostly) and music has been acknowleged for ages - take, for instance, the famous book "Gödel, Escher, Bach", by Douglas Hofstadter (1979). This guy's central message is nothing new.
Personally, I would say that the great devide is between science and theology (no, I don't agree with Stephen Jay Gould's "non overlaping magisteria"). Art is compatible with both. Within science, there is, perhaps, some tension beween physical sciences and social sciences (and postmodernism is bullshit - google the "Sokal affair"). I have the impression that the lecturer in this video didn't spend too much time thinking about the "two cultures". He didn't get the point. In any case, I see no problem at all between science and art. Hell, we even have "science fiction" as a literaly genre!
He made his point well. I don't know the context of the entire event, but he spoke directly to mathematics and art as the two cultures in the beginning. Then showed and spoke upon many ways that they do combine in positive ways.
It may be nothing new but it helped me to understand some of what I've been feeling as I move into mathematics after almost a quarter century of writing poetry and stories.
A literary genre? As in literature? As in the humanities?
Computers can't churn out proofs. I they could we would have perfected AI
minch333 Not only can they, they do. The problem is that we don't have a way of knowing which proofs will end up being relevant or important.
deadeaded Evidence?
minch333 google automated theorem proving.
deadeaded Yeah, I see what you mean. Is it bad that I'm not overly impressed though? So, I read up about the one that re-proved a section of the principia mathematica, then I read a bit of the principia itself and, well I can see why Russell said that writing it deadened his mind! I don't know how to put this other than it's very symbolic and derivational, so it doesn't surprise me all that much that a computer could churn it out. If you told the computer to give a result when it derives an equation you already know is significant, and give it a preference to simplify when it can, it seems that you could just set it off to combine all the rules you start it off with in as many ways as possible. It feels a bit monkeys on typewriters. Could the program, on the other hand, find one off the more inventive proofs of something like Pythagoras' theorem though, without giving it some major hints that you know the computer can take its trial and error technique to eventually get there?
There are computer proofs now that humans find rather hard to read (and, quite to the point, classification of finite simple groups seems to be one of them - do you know the order of Monster Group btw.?)