I know a bunch about formal languages (PhD in programming languages), so I did a spot check on the “grammar” described on page 45. It’s described as a “generative grammar”, though instead of words (sequences of symbols) it produces “L_O spacial relationships”. Since he uses these phrases to describe his “grammar”, and they have their standard meaning because he listed their standard definition earlier in the section, he is pretty clearly claiming to be making something akin to a formal grammar.
My spot check is then: is the thing defined here more-or-less a grammar, in the following sense?
There’s a clearly defined thing called a grammar, and there can be more than one of them.
Each grammar can be used to generate something (apparently an L_O) according to clearly defined derivation rules that depend only on the grammar itself.
If you don’t have a thing plus a way to derive stuff from that thing, you don’t have anything resembling a grammar.
My spot check says:
There’s certainly a thing called a grammar. It’s a four-tuple, whose parts closely mimic that of a standard grammar, but using his constructs for all the basic parts.
There’s no definition of how to derive an “L_O spacial relationship” given a grammar. Just some vague references to using “telic recursion”.
I’d categorize this section as “not even wrong”; it isn’t doing anything formal enough to have a mistake in it.
Another fishy aspect of this section is how he makes a point of various things coinciding, and how that’s very different from the standard definitions. But it’s compatible with the standard definitions! E.g. the alphabet of a language is typically a finite set of symbols that have no additional structure, but there’s no reason you couldn’t define a language whose symbols were e.g. grammars over that very language. The definition of a language just says that its symbols form a set. (Perhaps you’d run into issues with making the sets well-ordered, but if so he’s running headlong into the same issues.)
I’m really not seeing any value in this guy’s writing. Could someone who got something out of it share a couple specific insights that got from it?
I’d categorize this section as “not even wrong”; it isn’t doing anything formal enough to have a mistake in it.
I think it’s an attempt to gesture at something formal within the framework of the CTMU that I think you can only really understand if you grok enough of Chris’s preliminary setup. (See also the first part of my comment here.)
(Perhaps you’d run into issues with making the sets well-ordered, but if so he’s running headlong into the same issues.)
A big part of Chris’s preliminary setup is around how to sidestep the issues around making the sets well-ordered. What I’ve picked up in my conversations with Chris is that part of his solution involves mutually recursively defining objects, relations, and processes, in such a way that they all end up being “bottomless fractals” that cannot be fully understood from the perspective of any existing formal frameworks, like set theory. (Insofar as it’s valid for me to make analogies between the CTMU and ZFC, I would say that these “bottomless fractals” violate the axiom of foundation, because they have downward infinite membership chains.)
I’m really not seeing any value in this guy’s writing. Could someone who got something out of it share a couple specific insights that got from it?
I think Chris’s work is most valuable to engage with for people who have independently explored philosophical directions similar to the ones Chris has explored; I don’t recommend for most people to attempt to decipher Chris’s work.
I’m confused why you’re asking about specific insights people have gotten when Jessica has included a number of insights she’s gotten in her post (e.g. “He presents a number of concepts, such as syndiffeonesis, that are useful in themselves.”).
“gesture at something formal”—not in the way of the “grammar” it isn’t. I’ve seen rough mathematics and proof sketches, especially around formal grammars. This isn’t that, and it isn’t trying to be. There isn’t even an attempt at a rough definition for which things the grammar derives.
I think Chris’s work is most valuable to engage with for people who have independently explored philosophical directions similar to the ones Chris has explored
A big part of Chris’s preliminary setup is around how to sidestep the issues around making the sets well-ordered.
Nonsense! If Chris has an alternative to well-ordering, that’s of general mathematical interest! He would make a splash simply writing that up formally on its own, without dragging the rest of his framework along with it.
Except, I can already predict you’re going to say that no piece of his framework can be understood without the whole. Not even by making a different smaller framework that exists just to showcase the well-ordering alternative. It’s a little suspicious.
because someone else I’d funded to review Chris’s work
If you’re going to fund someone to do something, it should be to formalize Chris’s work. That would not only serve as a BS check, it would make it vastly more approachable.
I’m confused why you’re asking about specific insights people have gotten when Jessica has included a number of insights she’s gotten in her post
I was hoping people other than Jessica would share some specific curated insights they got. Syndiffeonesis is in fact a good insight.
Except, I can already predict you’re going to say that no piece of his framework can be understood without the whole. Not even by making a different smaller framework that exists just to showcase the well-ordering alternative. It’s a little suspicious.
False! :P I think no part of his framework can be completely understood without the whole, but I think the big pictures of some core ideas can be understood in relative isolation. (Like syndiffeonesis, for example.) I think this is plausibly true for his alternatives to well-ordering as well.
If you’re going to fund someone to do something, it should be to formalize Chris’s work. That would not only serve as a BS check, it would make it vastly more approachable.
I’m very on board with formalizing Chris’s work, both to serve as a BS check and to make it more approachable. I think formalizing it in full will be a pretty nontrivial undertaking, but formalizing isolated components feels tractable, and is in fact where I’m currently directing a lot of my time and funding.
“gesture at something formal”—not in the way of the “grammar” it isn’t. I’ve seen rough mathematics and proof sketches, especially around formal grammars. This isn’t that, and it isn’t trying to be.
[...]
Nonsense! If Chris has an alternative to well-ordering, that’s of general mathematical interest! He would make a splash simply writing that up formally on its own, without dragging the rest of his framework along with it.
My claim was specifically around whether it would be worth people’s time to attempt to decipher Chris’s written work, not whether there’s value in Chris’s work that’s of general mathematical interest. If I succeed at producing formal artifacts inspired by Chris’s work, written in a language that is far more approachable for general academic audiences, I would recommend for people to check those out.
That said, I am very sympathetic to the question “If Chris has such good ideas that he claims he’s formalized, why hasn’t he written them down formally—or at least gestured at them formally—in a way that most modern mathematicians or scientists can recognize? Wouldn’t that clearly be in his self-interest? Isn’t it pretty suspicious that he hasn’t done that?”
My current understanding is that he believes that his current written work should be sufficient for modern mathematicians and scientists to understand his core ideas, and insofar as they reject his ideas, it’s because of some combination of them not being intelligent and open-minded enough, which he can’t do much about. I think his model is… not exactly false, but is also definitely not how I would choose to characterize most smart people who are skeptical of Chris.
To understand why Chris thinks this way, it’s important to remember that he had never been acculturated into the norms of the modern intellectual elite—he grew up in the midwest, without much affluence; he had a physically abusive stepfather he kicked out of his home by lifting weights; he was expelled from college for bureaucratic reasons, which pretty much ended his relationship with academia (IIRC); he mostly worked blue-collar jobs throughout his adult life; AND he may actually have been smarter than almost anybody he’d ever met or heard of. (Try picturing what von Neumann may have been like if he’d had the opposite of a prestigious and affluent background, and had gotten spurned by most of the intellectuals he’d talked to.) Among other things, Chris hasn’t had very many intellectual peers who could gently inform him that many portions of his written work that he considers totally obvious and straightforward are actually not at all obvious for a majority of his intended audience.
On the flip side, I think this means there’s a lot of low-hanging fruit in translating Chris’s work into something more digestible by the modern intelletual elite.
I was hoping people other than Jessica would share some specific curated insights they got. Syndiffeonesis is in fact a good insight.
Gotcha! I’m happy to do that in a followup comment.
I think formalizing it in full will be a pretty nontrivial undertaking, but formalizing isolated components feels tractable, and is in fact where I’m currently directing a lot of my time and funding.
Great. Yes, I think that’s the thing to do. Start small! I (and presumably others) would update a lot from a new piece of actual formal mathematics from Chris’s work. Even if that work was, by itself, not very impressive.
(I would also want to check that that math had something to do with his earlier writings.)
My current understanding is that he believes that his current written work should be sufficient for modern mathematicians and scientists to understand his core ideas
Uh oh. The “formal grammar” that I checked used formal language, but was not even close to giving a precise definition. So Chris either (i) doesn’t realize that you need to be precise to communicate with mathematicians, or (ii) doesn’t understand how to be precise.
Please be prepared for the possibility that Chris is very smart and creative, and that he’s had some interesting ideas (e.g. Syndiffeonesis), but that his framework is more of a interlocked collection of ideas than anything mathematical (despite using terms from mathematics). Litany of Tarsky and all that.
Great. Yes, I think that’s the thing to do. Start small! I (and presumably others) would update a lot from a new piece of actual formal mathematics from Chris’s work. Even if that work was, by itself, not very impressive.
(I would also want to check that that math had something to do with his earlier writings.)
I think we’re on exactly the same page here.
Please be prepared for the possibility that Chris is very smart and creative, and that he’s had some interesting ideas (e.g. Syndiffeonesis), but that his framework is more of a interlocked collection of ideas than anything mathematical (despite using terms from mathematics). Litany of Tarsky and all that.
That’s certainly been a live hypothesis in my mind as well, that I don’t think can be ruled out before I personally see (or produce) a piece of formal math (that most mathematicians would consider formal, lol) that captures the core ideas of the CTMU.
So Chris either (i) doesn’t realize that you need to be precise to communicate with mathematicians, or (ii) doesn’t understand how to be precise.
While I agree that there isn’t very much explicit and precise mathematical formalism in the CTMU papers themselves, my best guess is that (iii) Chris does unambiguously gesture at a precise structure he has in mind, assuming a sufficiently thorough understanding of the background assumptions in his document (which I think is a false assumption for most mathematicians reading this document). By analogy, it seems plausible to me that Hegel was gesturing at something quite precise in some of his philosophical works, that only got mathematized nearly 200 years later by category theorists. (I don’t understand any Hegel myself, so take this with a grain of salt.)
tldr; a spot check calls bullshit on this.
I know a bunch about formal languages (PhD in programming languages), so I did a spot check on the “grammar” described on page 45. It’s described as a “generative grammar”, though instead of words (sequences of symbols) it produces “L_O spacial relationships”. Since he uses these phrases to describe his “grammar”, and they have their standard meaning because he listed their standard definition earlier in the section, he is pretty clearly claiming to be making something akin to a formal grammar.
My spot check is then: is the thing defined here more-or-less a grammar, in the following sense?
There’s a clearly defined thing called a grammar, and there can be more than one of them.
Each grammar can be used to generate something (apparently an L_O) according to clearly defined derivation rules that depend only on the grammar itself.
If you don’t have a thing plus a way to derive stuff from that thing, you don’t have anything resembling a grammar.
My spot check says:
There’s certainly a thing called a grammar. It’s a four-tuple, whose parts closely mimic that of a standard grammar, but using his constructs for all the basic parts.
There’s no definition of how to derive an “L_O spacial relationship” given a grammar. Just some vague references to using “telic recursion”.
I’d categorize this section as “not even wrong”; it isn’t doing anything formal enough to have a mistake in it.
Another fishy aspect of this section is how he makes a point of various things coinciding, and how that’s very different from the standard definitions. But it’s compatible with the standard definitions! E.g. the alphabet of a language is typically a finite set of symbols that have no additional structure, but there’s no reason you couldn’t define a language whose symbols were e.g. grammars over that very language. The definition of a language just says that its symbols form a set. (Perhaps you’d run into issues with making the sets well-ordered, but if so he’s running headlong into the same issues.)
I’m really not seeing any value in this guy’s writing. Could someone who got something out of it share a couple specific insights that got from it?
I think it’s an attempt to gesture at something formal within the framework of the CTMU that I think you can only really understand if you grok enough of Chris’s preliminary setup. (See also the first part of my comment here.)
A big part of Chris’s preliminary setup is around how to sidestep the issues around making the sets well-ordered. What I’ve picked up in my conversations with Chris is that part of his solution involves mutually recursively defining objects, relations, and processes, in such a way that they all end up being “bottomless fractals” that cannot be fully understood from the perspective of any existing formal frameworks, like set theory. (Insofar as it’s valid for me to make analogies between the CTMU and ZFC, I would say that these “bottomless fractals” violate the axiom of foundation, because they have downward infinite membership chains.)
I think Chris’s work is most valuable to engage with for people who have independently explored philosophical directions similar to the ones Chris has explored; I don’t recommend for most people to attempt to decipher Chris’s work.
I’m confused why you’re asking about specific insights people have gotten when Jessica has included a number of insights she’s gotten in her post (e.g. “He presents a number of concepts, such as syndiffeonesis, that are useful in themselves.”).
“gesture at something formal”—not in the way of the “grammar” it isn’t. I’ve seen rough mathematics and proof sketches, especially around formal grammars. This isn’t that, and it isn’t trying to be. There isn’t even an attempt at a rough definition for which things the grammar derives.
Nonsense! If Chris has an alternative to well-ordering, that’s of general mathematical interest! He would make a splash simply writing that up formally on its own, without dragging the rest of his framework along with it.
Except, I can already predict you’re going to say that no piece of his framework can be understood without the whole. Not even by making a different smaller framework that exists just to showcase the well-ordering alternative. It’s a little suspicious.
If you’re going to fund someone to do something, it should be to formalize Chris’s work. That would not only serve as a BS check, it would make it vastly more approachable.
I was hoping people other than Jessica would share some specific curated insights they got. Syndiffeonesis is in fact a good insight.
False! :P I think no part of his framework can be completely understood without the whole, but I think the big pictures of some core ideas can be understood in relative isolation. (Like syndiffeonesis, for example.) I think this is plausibly true for his alternatives to well-ordering as well.
I’m very on board with formalizing Chris’s work, both to serve as a BS check and to make it more approachable. I think formalizing it in full will be a pretty nontrivial undertaking, but formalizing isolated components feels tractable, and is in fact where I’m currently directing a lot of my time and funding.
My claim was specifically around whether it would be worth people’s time to attempt to decipher Chris’s written work, not whether there’s value in Chris’s work that’s of general mathematical interest. If I succeed at producing formal artifacts inspired by Chris’s work, written in a language that is far more approachable for general academic audiences, I would recommend for people to check those out.
That said, I am very sympathetic to the question “If Chris has such good ideas that he claims he’s formalized, why hasn’t he written them down formally—or at least gestured at them formally—in a way that most modern mathematicians or scientists can recognize? Wouldn’t that clearly be in his self-interest? Isn’t it pretty suspicious that he hasn’t done that?”
My current understanding is that he believes that his current written work should be sufficient for modern mathematicians and scientists to understand his core ideas, and insofar as they reject his ideas, it’s because of some combination of them not being intelligent and open-minded enough, which he can’t do much about. I think his model is… not exactly false, but is also definitely not how I would choose to characterize most smart people who are skeptical of Chris.
To understand why Chris thinks this way, it’s important to remember that he had never been acculturated into the norms of the modern intellectual elite—he grew up in the midwest, without much affluence; he had a physically abusive stepfather he kicked out of his home by lifting weights; he was expelled from college for bureaucratic reasons, which pretty much ended his relationship with academia (IIRC); he mostly worked blue-collar jobs throughout his adult life; AND he may actually have been smarter than almost anybody he’d ever met or heard of. (Try picturing what von Neumann may have been like if he’d had the opposite of a prestigious and affluent background, and had gotten spurned by most of the intellectuals he’d talked to.) Among other things, Chris hasn’t had very many intellectual peers who could gently inform him that many portions of his written work that he considers totally obvious and straightforward are actually not at all obvious for a majority of his intended audience.
On the flip side, I think this means there’s a lot of low-hanging fruit in translating Chris’s work into something more digestible by the modern intelletual elite.
Gotcha! I’m happy to do that in a followup comment.
Great. Yes, I think that’s the thing to do. Start small! I (and presumably others) would update a lot from a new piece of actual formal mathematics from Chris’s work. Even if that work was, by itself, not very impressive.
(I would also want to check that that math had something to do with his earlier writings.)
Uh oh. The “formal grammar” that I checked used formal language, but was not even close to giving a precise definition. So Chris either (i) doesn’t realize that you need to be precise to communicate with mathematicians, or (ii) doesn’t understand how to be precise.
Please be prepared for the possibility that Chris is very smart and creative, and that he’s had some interesting ideas (e.g. Syndiffeonesis), but that his framework is more of a interlocked collection of ideas than anything mathematical (despite using terms from mathematics). Litany of Tarsky and all that.
I think we’re on exactly the same page here.
That’s certainly been a live hypothesis in my mind as well, that I don’t think can be ruled out before I personally see (or produce) a piece of formal math (that most mathematicians would consider formal, lol) that captures the core ideas of the CTMU.
While I agree that there isn’t very much explicit and precise mathematical formalism in the CTMU papers themselves, my best guess is that (iii) Chris does unambiguously gesture at a precise structure he has in mind, assuming a sufficiently thorough understanding of the background assumptions in his document (which I think is a false assumption for most mathematicians reading this document). By analogy, it seems plausible to me that Hegel was gesturing at something quite precise in some of his philosophical works, that only got mathematized nearly 200 years later by category theorists. (I don’t understand any Hegel myself, so take this with a grain of salt.)
I finally wrote one up! It ballooned into a whole LessWrong post.