I can't help but think that there was a certain special something that existed among that generation of late modern intellectuals immediately preceding and proceeding from the first world war. There's an intensity, a level of discipline and seriousness with which they engaged in their work that seems unique in human history. The twelve-tone music of Schoenberg, the Cubism of Picasso, Einstein's field theories, and Wittgenstein's Tractatus. All strove to break new ground and push the state of the art beyond what was comprehensible at the time with an air of complete seriousness that seems so lacking today. They treated all of their endeavors, even the creative, with the rigor of a hard science and sought to construct theoretical frameworks around what had always been ephemeral, intangible notions.
One theory is something like this: early modernism was so fruitful because those participating in it were still trained in classical methods. They mastered the rules before breaking them.
Picasso is a good example. He broke the rules of art in creative ways because he had such a firm understanding of artistic methods. Nietzsche, with his deep grounding in Ancient Greek and Latin philology, is another modern innovator.
Today, however, we’ve largely adopted the conclusions of the innovators. Rather than try and recreate what led to these breakthroughs in the first place. Discipline and training are mostly irrelevant in a world that is more concerned with novelty and shock value.
Also, perhaps the fruits that can be masterly picked by single individuals have been picked already.
Yeah, this. And this IMHO is one of the reasons science is in crisis today, because in many ways it is still being conducted according to the late-19th- and early-20th-century models. Scientists are not generally rewarded for doing good science (e.g. replicating previous results or engaging in pedagogy), but rather for making Big Discoveries, because that’s what all the great scientists did before. Trouble is that as time goes by there are fewer and fewer Big Discoveries to be made, and making them gets more and more expensive, while at the same time there are more and more people graduating with STEM Ph.D’s. So you have more and more people chasing fewer and fewer opportunities for career rewards. Another perverse consequence of this dynamic is the pressure to publish any old crap because Big Discoveries are presented in papers and so it is assumed that papers will lead to Big Discoveries despite the obvious logical fallacy. Often it becomes a full-fledged cargo cult [1]. (I once made a very successful career by publishing a lot of crap, so I’m in a position to know.)
Getting this right is a Really Hard Problem because there are entrenched interests for whom this poses an existential threat. There is a lot of power that comes from being an arbiter of truth in a society.
(I think one of the great unsung heroes of humanity is Jimmy Wales. He could have cashed in bigly on Wikipedia, but he chose not to, and as a result Wikipedia is one of the greatest repositories of objective knowledge ever assembled. And it’s free. It’s a freakin’ miracle. Arxiv is also big step in the right direction IMHO.)
[1] https://phys.org/news/2018-10-real-fake-hoodwinks-journals.h...
To give my thoughts about the term 'Big Discoveries': I think it's mainly from the influence of the Enlightenment to focus on discovering absolute, simple laws of nature, and analytically using these laws to obtain a greater understanding of the world. But recently we are now discovering that most of the phenomenon we empirically observe (whether it be chemistry, biology, or society) can't be deduced straightforwardly from those laws, and conversely there is a limit to how we can deduce absolute laws from empirical data, due to the complex nature of large dynamic systems (interplay between molecules, interplay between cells, interplay between humans). The grand problem of Complexity still haunts us to this day.
I think that in the near future there will be a mode shift about how we think about science and technology in general. Simulation will start to replace analytic reasoning (since logical deduction inside our heads has reached its limits of analyzing complex systems), and science will become more and more indistinguishable from engineering (The question of 'what is possible?' will begin to replace 'why is this possible?'). I'm both terrified and excited about this new era.
I'd love to read a book about this, do you have any suggestions?
It's not from a single book, I've personally come to the conclusion after reading about various topics on both science and philosophy, as well as thinking about some current trends in science and engineering. I can't really give you a simple answer, I'm still studying and trying to figure this out.
But to give you a bunch of unorganized links if you want to follow a similar line of thought:
- Cybernetics (https://en.wikipedia.org/wiki/Cybernetics)
- Systems theory (https://en.wikipedia.org/wiki/Systems_theory)
- Seeing how theoretical physics has been left behind in progress for many decades in favor of fields like chemistry, biology, and earth sciences - which all seem to use those discovered laws of physics, and is increasingly trying to arrive at conclusions through computer simulation of those physical laws.
- Thinking about the relationship between computer graphics (which brings the virtual to the real) and computer vision (which brings the real to the virtual) - and its interplay between the two.
- Continental philosophy (I'm currently reading Batallie's The Accursed Share and it's giving lots of good insights about 'societal' systems and the general economy. Deleuze & Guattari also talks a lot about cybernetics, although their books are notoriously hard to decipher and I've only read second-hand explanations of it. And a few writings from Nick Land (preferably something before his breakdown) seems quite illuminating. Marx also seems to have some surprising proto-insights about the cybernetics of capitalism - it's an area of research I might delve into it later.)
I wrote a blog post about the same idea just last week, hope it’s ok to share here: https://choxi.github.io/three-body-problems
The Grand Problem of Complexity is a good name for it.
This is all exactly correct. What too often is left out of these discussions is the labor pool and incentives. Too many cooks in the kitchen, because there are incentives to keep adding more cooks, as though increasing the researcher labor supply were a goal in itself, rather what it truly is, an obstacle to progress. Eternal September comes to academia too, a side effect of scale.
I think science is in a crisis today for the same reason society is: the underlying ethics is a scientific realism have yet to be established. That's to say science, or the advancement of organized knowledge and the corresponding cultural realities are still oriented around anthropomorphic biases that were formed during the advent of global culture and embodied by the mystery religions. This made sense when the planet was a conquest, but not so much as a management strategy. Instead the ethics of science and culture need to be organized around ecological ethics: the reality of planetary stewardship is the challenge of the Anthropocene. This is a problem for scientific culture, because it's easy to build complexity on existing paradigms, it's harder to reorganize ones fundamental belief system. Example is being able to describe the surface of a black hole while people starve in the street. The problem of modern scientific progress is a problem of ethical reorganization, and once that is done (if it succeeds) then again we will be able to build systems of thought that appear new and foundational like the classical ones.
That is a really excellent and concise analysis of the situation.
"This made sense when the planet was a conquest, but not so much as a management strategy" is such a powerful phrase! Thank you
Curiously I think Jimmy Wales contribution was not that store of knowledge, but the community which keeps it alive. He has curated a sphere of unusual individuals working for free.
Otherwise somebody has likely already cloned or mirrored Wikipedia.
I think that argument, which I hear a lot, is a rather poor excuse. Currently it may seem like we're so far in our development, but in the future people will probably look back at our time and make the same argument. I think one big problem is 'hindsight is always 20/20', that is to say, great solutions may seem very simple and almost obvious in hindsight, while we ignore the fact that making the leap to get there was very hard at the time.
But is it a poor excuse?
I mean, in the past there could be a guy alone that discovers 10 math theorems alone and his proofs can be understood by highschool students.
Today we hail new proofs in maths that require 30 pages of proof that few people on Earth can understand.
The same for physics.
To me, the trend is clear.
This trend presupposes an ever-growing accumulation of knowledge and a view of mathematics as a collection of discoveries of "facts". I think most people nowadays hold such a view and it is intimately connected with the idea of progress. Wittgenstein himself was quite suspicious of such an idea, however:
"This book is written for such men as are in sympathy with its spirit. This spirit is different from the one which informs the vast stream of European and American civilization in which all of us stand. That spirit expresses itself in an onwards movement, in building ever larger and more complicated structures; the other in striving after clarity and perspicuity in no matter what structure. The first tries to grasp the world by way of its periphery -- in its variety; the second at its centre -- in its essence. And so the first adds one construction to another, moving on and up, as it were, from one stage to the next, while the other remains where it is and what it tries to grasp is always the same."
- Wittgenstein, "Philosophical Remarks", Preface
Will the current trend continue so that future discoveries are more and more intricate but also more and more specialised and thus perhaps less interesting? Or will there be a paradigm shift so that we lose interest in many of our "fundamental" results and there will be new low hanging fruits waiting to be "discovered"? Wittgenstein was more sympathetic to the latter view and often countered the view that mathematical results are discovered with the idea that mathematical results are invented (which does not make him a naive constructivist, however).
I mostly agree with you, but I'm not sure Picasso would have.
IIRC he expressed the opinion that his mastery of traditional painting was a burden and had to be unlearned before he could make his best work.
I think you're referring to this quote:
It took me four years to paint like Raphael, but a lifetime to paint like a child.
...or this one:
All children are artists. The problem is how to remain an artist once he grows up.
But he also did this:
It always reminds me of the story about the woman who approached Picasso in a restaurant, asked him to scribble something on a napkin, and said she would be happy to pay whatever he felt it was worth. Picasso complied and then said, “That will be $10,000.”
“But you did that in thirty seconds,” the astonished woman replied.
“No,” Picasso said. “It has taken me forty years to do that.”
Ultimately, Picasso made a lot of witty, silly comments. I'm not sure I'd read much into them. Here's one of my favorites, although I can't seem to find an actual source:
Art is the currency of the infinite. I’m rich, I should know.
Ultimately, though, I'm not sure it's quite relevant to what I mean. Today, artists are still "taught" a lot of theory (too much, probably) and the educational goal isn't usually to be childlike.
Wittgenstein's take:
>I was walking about in Cambridge and passed a bookshop, and in the window were portraits of Russell, Freud and Einstein. A little further on, in a music shop, I saw portraits of Beethoven, Schubert and Chopin. Comparing these portraits I felt intensely the terrible degeneration that had come over the human spirit in the course of only a hundred years.
Here's another take by Wittgenstein from the preface of the Philosophical Remarks:
"This book is written for such men as are in sympathy with its spirit. This spirit is different from the one which informs the vast stream of European and American civilization in which all of us stand. That spirit expresses itself in an onwards movement, in building ever larger and more complicated structures; the other in striving after clarity and perspicuity in no matter what structure. The first tries to grasp the world by way of its periphery -- in its variety; the second at its centre -- in its essence. And so the first adds one construction to another, moving on and up, as it were, from one stage to the next, while the other remains where it is and what it tries to grasp is always the same."
I can't help but feel that this description of the "vast stream" captures the current trend in most of software development and academia quite well...
There is a beautiful give-and-take between the experience of variety (either consuming or producing) and the grasping of essence. They do not exist independently of each other, nor is one better inherently better than the other. They must be kept in balance, and yet the world seems to favor variety over understanding at every turn.
Consider yourself lucky to be in the minority of those who appreciate what is truly rare and precious about humans, who are in turn a rare and precious part of life, which is in turn a rare and precious part of the universe.
> at its centre -- in its essence
This desire is precisely what leads Faust to become so frustrated with the limits of human knowledge that he makes an ill-advised bet with (more or less) the Devil, trading an option on his immortal soul for the keys to that essence.
In Goethe's Faust anyway:
https://en.wikipedia.org/wiki/Goethe%27s_Faust
>with an air of complete seriousness that seems so lacking today.
Jaded cynicism, crass commercialism, and the dissapearance of a cultured class that is above mass market culture, they way high/upper middle class, academics, doctors, etc., one were.
Believe it or not, for example, once there was a class of people, more so in Europe, that not only went to the Opera, but also actually liked it, followed it, could get the references, and knew its history and the history of classical/romantic/etc music, the way their today's equivalent will know the pop stars of the day.
Given the above, it's easy that soem of them would take e.g. the twelve-tone music of Schoenberg or Stravinsky's innovations seriously, even if only to be offended by them - and some of, course, to be inspired.
Today's equivalent would at best read something like the New Yorker and the hacks featured in NYT best-selling books of the day, but will seldom have the wide culture that once was quite widespread across parts of the middle and upper middle classes.
People also seem more desperate to sell out quick for a quick buck - even artists today just want to play the game, go ahead with the galleries and agents, and give out much more easily than an early 20th century artist. This diminishes the period between "serious work" and "selling out", often to zero (whereas for Picasso it took decades, and for Van Gogh, it never happened).
Believe it or not, not all of those people were middle class. The UK and the US both had programs which made classical music accessible to the working classes, and they had a significant cultural impact.
In the UK the post-war BBC carried on with (what is called) the Reithian tradition (after Lord Reith) until marketisation started to overwhelm everything in the 80s.
This isn't to say that classical music is somehow always utterly superior to pop. It was about giving people experiences they wouldn't have had otherwise, and to give them more choices about what to listen to and maybe enjoy.
The UK also had an art school track for bright creative working class kids, some of whom went on to make a living in music and/or fashion. Marketisation also destroyed that, because of course student debt destroys your choices and limits your options so you literally can't afford to take risks.
>This isn't to say that classical music is somehow always utterly superior to pop.
Today it's almost forbidden culturally to even suggest that it coule even be (superior).
The thing is, to say such a thing, you need some kind of shared cultural basis (of what's superior and what's not), one that even those who don't "like X" (the way we might like peanut butter or not), nonetheless agree on (and whether they care or not, feel like it's somewhat their loss for not liking it).
Those times, had that (shared cultural agreement).
In more modern times, after the 60s especially, and in the US doubly so, culture is whatever one makes it, the mass consumer is king (because everybody wants his/hers money, so they treat them as such), and personal taste is the be all end all, end of discussion.
Whereas in another era, to say Bieber or Drake are inferior to Bach, for example, would be so self-evident and accepted by all (for the Bieber's and Drake's of their era), as to not even be worth saying.
> Whereas in another era, to say Bieber or Drake are inferior to Bach
This is a strange comparison though. It's like saying strawberries are inferior to lobster. Sure, they're both eaten as food, but they serve very different purposes, and comparing them doesn't really make sense.
BBN, Bolt, Beranek Newman the original ARPANET contractors started out in computational acoustics, tasked to build for the American people concert halls to rival those of Europe, witnessed and lamented simultaneously for the first time in the destruction of war. Chicago Philharmonic and many other orchestras gained concert halls absolutely unrivalled for the next fifty years and equalled only occasionally today. My late cofounder was much better known for managing a important 20th century British classical composer whose preference for the aforementioned hall (and incumbent conductor) was almost as much of a thorn in the side of European musical nobility as receiving his Order of Merit* from HM the Queen in his Nike sneakers. Deutsche Grammafon and the listening public concurred voting with their wallets, driving classical music sales of records beyond all expectations, thanks to the work of BBN and the American people who gave such incredible support for post war music when Europe was stumbling from the beginning of one recovery to the next.
the rest of original comment in my profile simply too long
I've been going deeper into the mid-19th century to pre-WWI era. I keep thinking that the war eras of the 20th century and industrial consumerism lost the diversity of ideas and art that preceded it.
I've been diving into (or revisiting) Darwin, Thoreau, Ruskin, Tolstoi, to name a few. It was an incredibly rich era that could help us better navigate this one.
I get a sense that Orwell, Huxley, and Bradbury, had a better connection to it and could articulate warnings of where the mid-20th century might end up if it progresses on its path. I don't think we've ever been closer to realizing their warnings.
Could be a coincidence, but that was just before Heisenberg's uncertainty principle (1927) and Godel's incompleteness theorem (1931) dashed the dream of perfect knowledge.
Wittgenstein famously did not believe in Gödel's incompleteness theorem, as well as thinking Cantor's diagonalisation argument was bunk.
Can you say more of either of these? Especially the diagonalization argument which seems difficult to, er, argue with.
You can find what he had to say on Cantor's argument here: http://www.logicmuseum.com/cantor/wittgensteinquotes.htm
These are excerpts, some paragraphs are missing, but the gist is more or less there and you can find the full discussion in 'Remarks on the Foundations of Mathematics'.
Even the Remarks on the Foundations of Mathematics are only a selection of some of Wittgenstein's notebooks made by the editors of his posthumous publications. It is not a work by Wittgenstein in the same sense as the Tractatus or the Philosophical Investigations.
The Part II of the Remarks on the Foundations of Mathematics, which is the part on Cantor, is especially questionable. It is compiled from two documents of Wittgenstein's Nachlass, Ms-117 and Ms-121, but only about a third of the remarks in Ms-121 were included in the published book. There are also other notebooks were Wittgenstein discussed Cantor (most notably Ms-162a and Ms-126b) and which were not published at all. The editors made the decision to exclude some of these remarks because Wittgenstein's notebooks often contain merely drafts of remarks that were never fully developed, so it would be wrong to say that the published book is a deliberate misrepresentation of Wittgenstein's thoughts, but the situation is definitely quite nuanced and complex.
I personally think that the Remarks on the Foundations of Mathematics are very interesting, but that it's a disservice to Wittgenstein and any reader of his works to read his remarks on the philosophy of mathematics as a disconnected collection of aphorisms. The context really matters and his more mathematical remarks only make sense against the backdrop of the Philosophical Investigations and perhaps even his later writings such as On Certainty.
I'm not an expert on Wittgenstein, but I think the critique of Cantor's diagonal argument is more to do with its implication that an infinite set can be "bigger" than another. To say so is more of a semantics argument than a mathematical one as it takes for granted the meaning of "infinite". That is, if you define an infinite set as being inherently without size, it makes no sense to then assign it comparitive sizes via cardinality.
I think it has to do with Wittgenstein's constructivism. Since humans can never actually construct an infinite set, one cannot say that such a thing exists as a constructivist. As such, infinity would be a fuzzy without-size concept that Witty was suspicious of. But if one does think mathematical objects are real, then it's not a problem.
I'm guessing constructivists have found better ways to approach infinity than Witty, without conceding that infinity is real.
I don't get the sense that Wittenstein was suspicious of infinity as an idea / concept in itself, only of its treatment in mathematical logic. Otherwise much of his writings on it could've been far more terse.
Wittgenstein was not a constructivist, though. At least in his later years he explicitly argued against any -ism as a position and tried to avoid philosophical theses as a whole. (Whether he succeeded with this undogmatic approach is another question of course, but to say that he was a constructivist would commit him to a position that he did not advocate for, even if many of his remarks can certainly be read in such a way if they are read in isolation.)
Unless he published a formal demonstration of Gödel's 'error', Wittengenstein's belief is of mere biographical interest. History is littered with eminent people who had all sorts of erroneous beliefs about theories and ideas that we now see as having withstood the test of time.
It's a notable portion of 'Remarks on the Foundations of Mathematics'.
Wittgenstein never held the view that Gödel's theorem was wrong or erroneous, though. He "only" thought that the philosophical interpretations and the view of the theorem as astounding and incredibly deep were misleading.
In general, Wittgenstein wasn't exactly a mathematician...
This is unfortunately a widespread interpretation of Wittgenstien's philosophy of mathematics, but it is not a very charitable reading.
Wittgenstein emphasised on numerous occasions (for example directly at the beginning of his lectures on the foundations of mathematics in 1939) that his interest in these proofs was _philosophical_ and that he never intended to criticise any of them _on mathematical grounds_. He explicitly said that his aim was not to interfere with mathematicians, but to investigate the _philosophical conclusions_ drawn by these mathematicians from their proofs.
What exactly Wittgenstein found problematic is hard to describe in a short comment, because much of it depends on Wittgenstein's view of philosophy as a whole, but one example is the platonist bent of Gödel's theorem and his conviction that there are some mathematical "facts" that can never be discovered by mathematical reason. Wittgenstein wants to ask what it means to say that something is "intuitively true", but not provable in any consistent system, but he does not want to object to Gödel's results, merely its "standing".
In Cantor's case Wittgenstein is interested in the concept of the transfinite and of infinities "bigger" than other infinities. He does not object to Cantor's proof at all, but regards the philosophical conclusions drawn from it with suspicion.
(One good example of a philosophical abuse of Gödel's theorem is the argument that computers will never be able to think like humans, because Gödel's theorem demonstrates a limit to what any computer can do as a formal system, but we humans can nevertheless grasp the unprovable statements as intuitively true. This is basically the argument by J. R. Lucas. This is the kind of philosophical nonsense that Wittgenstein wanted to attack and his position on these matters is coincidentally quite similar to Turing's position, who was a student of Wittgenstein's lectures on the foundations of mathematics.)
It certainly did not help that the so-called Remarks on the Foundations of Mathematics are in some parts highly selective constructions by the editors of his posthumous writings.
tl;dr: it's complicated. Wittgenstein never objected to the mathematical results by Gödel and Cantor, but he thought that their results were often blown out of proportion by shoddy philosophical conclusions made on the basis of these perfectly fine mathematical arguments.
Also world events. WWI, The Great Depression, WWII, the Holocaust, the Atomic Bomb, and then the following Cold War where everyone lived in fear of nuclear annihilation dashed the dream the human intellect would inevitably lead to a utopia.
Maybe. On the other hand, that period saw incredible technological and societal progress. Thiel called it the period of "definite [technological] optimism." https://archive.org/details/ZeroToOneByPeterThiel/page/n47
And that period up to at least the 70s was highly productive in fields such as cybernetics and organisational psychology. Some of that way ahead of its time culturally, and some genius-level deep thinking behind it. The best of that work (Stafford Beer’s Viable System Model stands out for me) seems to represent some kind of golden age, work that would be hard to do today I suspect.
I agree with this impression. I often reflect on our times and wonder why there seems to be such a stark difference. Why do we lack such figures, pushing the boundaries in the same impressive way? Is it that not enough time has passed to fully realize the impact of the discoveries and works of our time, like there has been for the work of the early 1900's? Have the problems gotten harder that we are bumping up against a kind of soft boundary that's preventing the seemingly frequent revolutionary breakthroughs? Or is it a matter separate from the practice of science or art; a phenomenon of culture that is impacting the our capacity to discover? I think it's an interesting question to mull over.
Were the breakthroughs of history regarded as such during their formation, generally speaking? Maybe we will look back on this period as one rife with breakthroughs, but can’t make the historic judgment in real-time.
In the case of Wittgenstein and the Vienna Circle, there certainly was a perception that something radical was being done.
Wittgenstein was one of the richest heirs in Europe so at the least he had all the time in the world, and lived in a time with such little competition that they gave him a PhD for writing a non-academic book none of them understood.
Looking at his biography, you feel like people were just hanging out with him because he was rich, since his personality was so bad and he clearly hated everyone he ever met.
To say that "people were just hanging out with him because he was rich" is a very biased and uncharitable reading of his biography. He gave away all his inheritance pretty early in his life and later often had to depend on friends such as Keynes, Russell and Moore to support applications for grants so that he could continue his research at Cambridge. Of course it's true that he came from an extremely privileged background and was never in danger of starving to death, but he could spend as much time on his philosophy as he did because he lived a modest life and was lucky enough to be supported by Russell when he first came to Cambridge.
Wittgenstein would have a very impressive DOTA MMR today.
Thanks. I have whiskey is my nasal cavity now.
I don't drink anymore. I was still able to vividly imagine the sensation of whisky out the nose.
The same is true in literature. Who today compares with Elliot, Yeats, Huxley, Orwell or the war poets? Maybe that seriousness of purpose is only possible when civilisation is in the balance.
One figure hanging over Western poetry for the second half of the 20th century is Celan, and it is hard to claim he is inferior to Eliot or Yeats. And if you like this kind of serious poetry, I really recommend J.H. Prynne (start with The White Stones), who is still active even.
The problem with poetry today is not a lack of talent, it is an inability for that talent to get mass attention when 1) poetry has been marginalized in today's media landscape, and 2) cultural scenes are now so fractured that people can't reach agreement on who is great and therefore keep the list of great poets going.
Part of it is that there's just so many more people. Many more voices. And a louder speaker for them to yell into. And so much less reason to focus on any particular individual.
You could spend your whole life studying philosophy/economics/political science, etc, write an amazing thesis, many volumes long, have all sorts of insights. And in terms of the world's massive population: how would you stand out? Would you be famous? Would people read you? Considered canon / important? Unlikely. You might get some notoriety, but that notoriety is more likely to spread to rather mediocre or showmen pop-philosophers like a Jordan Peterson (or their equivalent on the "left").
And in some ways knowledge of many kinds has been democratized, and information and materials more broadly available to all. So we're building a broader knowledge base and things are applied in that way, rather than by "great men"... which is likely the sign of a mature civilization and a more democratic ethos.
Christopher Nupen has made an outstanding documentary about Viennese Radicalism portrayed in particular through Wittgenstein and Shoenberg. I can't recommend it enough.
https://www.youtube.com/watch?v=DRI_ZSh6iF4
I think those same people are spending their mental energy on deciphering law, writing code, and trying to predict the stock market now.
Also James Joyce, and others like him.
Things all work around that time. Physics aside even maths ...