• Mathematik ist die Wissenschaft von dem, was an sich klar. — Carl Jacobi (1804-51).
• “Mathematics is the science of that which is clear by itself.” — Carl Jacobi.
• Mathematik ist die Wissenschaft von dem, was an sich klar. — Carl Jacobi (1804-51).
• “Mathematics is the science of that which is clear by itself.” — Carl Jacobi.
Overlord In Terms of Core Issues Around Maximal Engagement with Key Notions of the Über-Feral 
Which isn’t the same as mathematics being simple, of course
Hofstadter once wrote about how simple-looking things can sometimes be very hard, because their meaning is tied to complicated things elsewhere. He gave the example of music. Bach’s canons are very intricate. John Cage’s 4’33 is very simple (it’s just silence). Yet 4’33 is far harder to understand than a Bach canon.
To understand a Bach canon, you just listen to it. It speaks for itself. But for 4’33 to make sense, you need to understand Western art theory, modernism, postmodernism, negative space, pop art, irony, and various other things.
Bach’s “complicated” composition requires that you understand almost nothing. Cage’s “simple” composition requires that you understand almost everything. An alien would be far more confused by the latter than the former. There’s probably many other parallels. To me it seems that math is at the Bach end of the spectrum, while art is fundamentally Cagelike – it only makes sense in reference to the whole. A lot of ideas from the humanities only seem simple because the heavy lifting is done elsewhere.
Mathematics is the science of that which is clear by itself
Which isn’t the same as mathematics being simple, of course
Well, it’s a keyly core theme of the Overlord community that physics demands much more intelligence than sociology because physics is a much simpler subject. A novel is much more complex than a star, but that doesn’t make EngLit the intellectual equal or superior of astronomy.
Hofstadter once wrote about how simple-looking things can sometimes be very hard, because their meaning is tied to complicated things elsewhere. He gave the example of music. Bach’s canons are very intricate. John Cage’s 4’33 is very simple (it’s just silence). Yet 4’33 is far harder to understand than a Bach canon.
No, I disagree. Bach’s work is in the foreground and occupies your attention. So you don’t think of what lies beneath it and of all the questions it raises. It’s like a plinth with a golden nightingale on it. Cage’s 4’33” is like a plinth with nothing on it. When the nightingale is there, you don’t worry about the plinth.
To understand a Bach canon, you just listen to it. It speaks for itself.
Well, it speaks from Bach’s brain to your brain as an arrangement of notes in time. Nothing there is simple. Bach’s mastery is a good example of the Latin saying ars est celare artem: “the art is to conceal the art.” A good meal might make you think of the skill of the chef, but it shouldn’t make you think of the farm.
But for 4’33 to make sense, you need to understand Western art theory, modernism, postmodernism, negative space, pop art, irony, and various other things.
For a pun to make sense, you have to understand the language and context the pun is made in. That doesn’t make puns more complicated than humour and language in general. 4’33” is a kind of musical pun.
Bach’s “complicated” composition requires that you understand almost nothing.
No, as I said, I think it occupies your attention and so you don’t think about what lies beneath it.
Cage’s “simple” composition requires that you understand almost everything. An alien would be far more confused by the latter than the former.
Only if the alien’s culture didn’t include trivia or decadence. A child could enjoy Bach while being baffled by Cage, but that doesn’t make Bach childish. It’s important, tho’, that there are child prodigies in maths and music, but not in literature or humour.
There’s probably many other parallels. To me it seems that math is at the Bach end of the spectrum, while art is fundamentally Cagelike – it only makes sense in reference to the whole. A lot of ideas from the humanities only seem simple because the heavy lifting is done elsewhere.
Art is designed to change consciousness, which is what makes it complicated. But 4’33” doesn’t change consciousness in a very profound or important way compared to Bach’s music. Maths’ purpose to arrive at the truth, which constrains it and, in a way, simplifies it. Aesthetic appeal is incidental. The role of consciousness in maths is an interesting question. As is the role of maths in consciousness.
But do you think there’s any kind of difference between a plinth with nothing on it, and a plinth that should have something on it but doesn’t? Incidental nothingness vs deliberate nothingness, in other words? “4’33” is the latter.
Maybe you answer “no, an empty plinth is an empty plinth”. Which is true on a physical level, but I think in a discussion of art, authorial intent matters.
Bach has some “empty plinth” moments in his works – little pauses and rests where there’s no music. But this isn’t pointless silence, it’s given context and meaning by the music that comes before and after. You could argue that 4’33 is this same concept at the n+1 level: an entire piece of silence that’s given context and meaning by other things in Western culture.
Yes, but it’s a complexity that a child can appreciate. “Complexity” now seems like the wrong word, maybe there’s a better one.
If you gave an alien a record with “4’33” on it (and no other explanation), it would find it both meaningless and indistinguishable from any other blank vinyl record in the universe.
Maybe it would eventually guess that the record is a joke, but a joke about what? In Cage’s case it’s something quite specific (shallow Western “muzak”, the title’s in reference to how radio deejays won’t play anything longer than 4 minutes or so, etc), none of which an alien would know.
Could an alien understand Bach? I think so, although it probably wouldn’t appreciate it the same way a human would. Even if it had no concept of music or art, it could at least notice the grooves on the record, notice that they approximate a wave, and theorize that the wave could be propagated through a medium. An intelligent alien would at least get SOMEWHERE with a Bach record.
This isn’t just a hypothetical conversation. On the Voyager spacecraft a golden record was included, containing samples of terrestrial music. Bach, Mozart, Beethoven, even Chuck Berry. 4’33 isn’t on there, though. Or maybe it is. Maybe all music everywhere is 4’33, and just some of it happens to have other music playing over the top. How would we know?
But do you think there’s any kind of difference between a plinth with nothing on it, and a plinth that should have something on it but doesn’t? Incidental nothingness vs deliberate nothingness, in other words? “4’33” is the latter.
Yes, that’s what I meant: it was a deliberately empty plinth.
Maybe you answer “no, an empty plinth is an empty plinth”. Which is true on a physical level, but I think in a discussion of art, authorial intent matters.
It does, but I think my point still stands. If the plinth represents musical history, the plinth had to be there for both Bach and Cage to work with. But what Bach did fills your attention with something other than the plinth.
Bach has some “empty plinth” moments in his works – little pauses and rests where there’s no music. But this isn’t pointless silence, it’s given context and meaning by the music that comes before and after.
But pauses don’t make the plinth empty. They’re part of standard music.
You could argue that 4’33 is this same concept at the n+1 level: an entire piece of silence that’s given context and meaning by other things in Western culture.
I agree, but 4’33” is decadent. It’s a sign that musical culture is running out of ideas. The concept had appeared before in visual art, e.g. in Alphonse Allais’s work in the nineteenth century.
Well, it speaks from Bach’s brain to your brain as an arrangement of notes in time. Nothing there is simple.
Yes, but it’s a complexity that a child can appreciate. “Complexity” now seems like the wrong word, maybe there’s a better one.
Complexity is ok as a term I think. The ability of a child to appreciate Bach is an example of what you said about the heavy lifting being done elsewhere. We don’t need to make a conscious effort to see or hear.
Only if the alien’s culture didn’t include trivia or decadence.
If you gave an alien a record with “4’33” on it (and no other explanation), it would find it both meaningless and indistinguishable from any other blank vinyl record in the universe.
Not if the alien understood that it was intentionally blank: a frame without an image. The record of 4’33” comes with a title and a composer’s name and presents itself as a conventional record. So you step for a stair that isn’t there. It’s easily possible to imagine the same thing being done in alien cultures.
Maybe it would eventually guess that the record is a joke, but a joke about what? In Cage’s case it’s something quite specific (shallow Western “muzak”, the title’s in reference to how radio deejays won’t play anything longer than 4 minutes or so, etc), none of which an alien would know.
Why not? I don’t see why aliens couldn’t have shallowness and short attention spans in their own cultures.
Could an alien understand Bach? I think so, although it probably wouldn’t appreciate it the same way a human would.
Non-Westerners don’t appreciate it in the same way as Westerners, and Westerners now don’t appreciate it in the same way as Bach’s contemporaries did.
Even if it had no concept of music or art, it could at least notice the grooves on the record, notice that they approximate a wave, and theorize that the wave could be propagated through a medium. An intelligent alien would at least get SOMEWHERE with a Bach record.
Yes, and there are mathematical patterns in Bach and in music as a whole. Human and non-human: birdsong is evidence that music might well exist among aliens. It’s hard to imagine intelligent aliens not having language too, but language isn’t as clearly mathematical as music. Poetry comes closest, but language usually has utilitarian functions that get in the way of aesthetics, rhythm, etc.
This isn’t just a hypothetical conversation. On the Voyager spacecraft a golden record was included, containing samples of terrestrial music. Bach, Mozart, Beethoven, even Chuck Berry. 4’33 isn’t on there, though. Or maybe it is. Maybe all music everywhere is 4’33, and just some of it happens to have other music playing over the top. How would we know?
In the same way as we know whether a blank space in an art gallery is the work of an artist. Is there a frame? Is there a label? Cage didn’t create silence as a concept or a reality and 4’33” is silence in a particular context. It has a label, 4’33”, and it’s framed by the waiting audience, the pianist opening the lid of the piano, sitting there un-performing, closing the lid, then receiving the applause of the audience.
Similarly, an artist who paints a canvas in a single undifferentiated colour isn’t usually claiming that every instance of that colour is part of the art. If they do, then they’re expanding the usual sense of an art-work’s label. As far as I know, Cage meant his label to apply only to specific, deliberately created instances of silence.