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As much as we talk about math literacy here (compared to other platforms anyway), I can't help but feel like the incomprehensibility of high level math to layme

As much as we talk about math literacy here (compared to other platforms anyway), I can't help but feel like the incomprehensibility of high level math to laymen is a feature. It's not talked about outside of academia often, because why would it be, but for a long time philosophy resisted efforts to 'mathmatecize' (my own word) the field because of concern that it would become inscrutible to outsiders. As a result, academic philosophy is much more politically polarized than math. Where would we be if every step forward in mathematics was met with backlash for not paying adequate concern to some arbitrary set of external implications? Anyone can disagree of course but just looking at the political affiliation ratios of educators makes it clear that one aspect of the hard sciences historically has been an ability to stay focused on utility despite post-modernism. I'm probably being unfair though, the humanities continue to produce persuasive arguments (persuasive emphasis being one of the first things most lit and speech majors learn during critical thinking and writing courses in college) they've just dropped the pretense of being truth seeking persuits.

StandardFuture 6y ago
Obfuscation is a practice of the entirety of Academia for a long while now. The art of obfuscation is not new at all. A small anecdote, I remember a Taiwanese friend mentioning the history of the complexity of Chinese characters and how they were devised, in part, to ensure that the lower class(es) could not learn them. Obfuscation inherently guarantees a lot of things out of the box: you appear more enlightened, only a class of people can understand and thus judge your work, and all newcomers can only become "in the know" if and only if they are trained by someone who already is "in the know". This is very appealing to anyone with even minor insecurities (most people), and has been widely utilized throughout many areas of human society in time. Math is merely one example where this practice has presence. EDIT: I will admit that the more democratized the internet has made knowledge, and the more prevalent higher-degrees become in society, the more awareness people have of this issue and the more it gets called out. So, all in all, there is the positive side of things that this art of obfuscation is in decline of use for things where it should never be used (like education, science, etc.).
- augustt 6y ago
  I'd say this is generally not true, at least in math. There's definitely poor notation and misnomers that come from tradition, but it's hardly deliberate as "obfuscation" implies.
  - mkl 6y ago
    I'm not sure I agree (I have a PhD in maths). There are many maths papers and books I've tried to understand where that seems to have been deliberately made more difficult than it needs to be. Sure, you could argue that I didn't have the necessary prerequisite knowledge at that point, or that the authors simply weren't good at explaining things, but I do get the impression that it's sometimes more than that. Using specialised meanings for words without definition or reference (words that are used for other purposes elsewhere so they can't be searched for) is a key problem, as is the same with notation, and as is leaving out crucial steps. If you're already in the know, those things are probably clear.
    - memexy 6y ago
      But that sounds like bad exposition. What benefit would any author get from purposely obfuscating what they're trying to share?
      - mkl 6y ago
        Could well be, and I have no definitive evidence otherwise, but sometimes it's hard to imagine anyone being that bad at exposition. Some "benefits" might be seeming smarter and more knowledgeable than they are, making it harder to exactly replicate their methods (most relevant in applied areas), or citations by intimidation ("I don't understand this, but it seems impressive and relevant, so I better cite it.").
        elbear 6y ago
        They all sound plausible and likely. There are people obfuscating knowledge for all the reasons you mentioned. At the same time, it doesn't mean there's a concerted effort to obfuscate mathematics. Explaining things is hard, because you have to create a clear picture of the audience in your mind. Then, you have to draw the lines between what they know and what you want to introduce. The curse of knowledge is a big obstacle here.
memexy 6y ago
Many of the early mathematicians were mystics. So in a way the incomprehensibility is a feature and not a bug but for those that are well versed in the language it is a rich source of analogies and metaphors. > "Good mathematicians see analogies. Great mathematicians see analogies between analogies." To see analogies between analogies requires compressing concepts into symbols that at first glance are not as comprehensible as regular words and sentences but math is really just another language and people can learn it and apply it fruitfully. -- https://en.wikipedia.org/wiki/Stefan_Banach#Quotes#:~:text=Good%20mathematicians,analogies%20between%20analogies https://en.wikipedia.org/wiki/Stefan_Banach#Quotes#:~:text=G....
joe_the_user 6y ago
I might see it this way because I've been studying math for a long time (though not professionally most of it) but I don't think modern math is ever made more complicated or hard to understand just for the heck of it. That's because math is already felt as extremely hard for most people. I think anyone in professional math is working really hard to make the field more comprehensible to themselves and so to the world - and the reason for this is the more a mathematician understands and more compactly they can understand it, the further they can go. And certainly, the way a mathematician put things curtly makes it harder for the laymen, I think the biggest harm to the layman's understanding of math is a math education that gets people conditioned to not think abstractly and think of math as a series of dull exercises.
- j7ake 6y ago
  I agree. If some mathematicians purposeful obfuscated or made more complicated than necessary certain topics, it would create an arbitrage opportunity for others to clarify and simplify the topic. There are definitely tangible rewards for those who can clarify and simplify a topic, because it can lead to discoveries and insights. This gradual clarification of a topic hinges on the actual importance of the topic. If a topic is not important, I can see people getting away with obfuscating or complicating results.
  - bonoboTP 6y ago
    Respectable, pro mathematicians don't obfuscate. But there are definitely math professors in non-top universities who get kicks out of torturing students and think "this is supposed to be hard" etc. I'm definitely a math enthusiast but I have personally met people like that. Typically the exams are under strong time pressure and are more about rote learning of fixed types of exercises and remembering definitions. On the other hand, I had math profs who radiated curiosity and fun and the exams were just a few questions, but you had to think to solve them and you weren't under much time pressure. So while mathematicians aren't purposefully obscure, the math people (teachers) the average person interacts with are sometimes purposefully obscure.
- deleted 6y ago
  [deleted]
tsimionescu 6y ago
> As a result, academic philosophy is much more politically polarized than math. I don't think this is a clear conclusion at all. Philosophy is inherently very political (all political ideas ultimately come from philosophy, after all). Philosophy is also concerned with the real world and human affairs much more than abstract math is. It's also funny that you bring up post-modernism, a philosophical current famous and often ridiculed for being one of the most deliberately obfuscated. I also know that a lot of the efforts of brininging mathematical thinking and abstraction in the humanities end up exactly in obscurantism: most of the field can't understand it, but it has cultural clout so they can't admit that, and it becomes a source of empty prestige, with maths literally sprinkled on studies just to access that clout. Even in medicine, math-y papers are/were often accepted unconditionally, with peer review unable to check the actual maths, but unwilling to admit their lack of mathematical culture. For an example, there was a medical article published in 1993 [0], which is a re-discovery of the trapese method of integration. This got around 100 citations. Of course, that article is at least correct. In postmodern literary studies, there is a famous example of an intentionally meaningless, but very abstract and complex sounding article that was successfully published in one of the leading journals, despite ultimately being gibberish [1]. My utlimate point being, I don't think there is any link between obscurity of a field and its resistance to internal or external politics. [0] http://care.diabetesjournals.org/cgi/content/abstract/17/2/152 http://care.diabetesjournals.org/cgi/content/abstract/17/2/1... [1] https://en.m.wikipedia.org/wiki/Sokal_affair https://en.m.wikipedia.org/wiki/Sokal_affair
- singron 6y ago
  In philosophy 101, my professor said that philosophy was focused on controversial topics because once you could prove a side, it would become science. E.g. the heavens used to be a philosophic topic until we had the ability to prove heliocentrism. Math is much more focused on the realm of what can be proved. Unproven statements in math (e.g. conjectures or axioms) are the exceptions that prove the rule.
  - leereeves 6y ago
    Professional mathematicians spend their lives working on the unproven. It just seems like math is about what's already been proven because it takes so much education to reach the unproven ideas and unanswered questions.
ganzuul 6y ago
As an exclusive club, it's a feature. As pursuit for knowledge it's a tragedy. There are many highly intelligent people who are differently able to absorb mathematical literature. Consider, perhaps, if the gender imbalance is caused by the time needed to take care of children and a household. - Time which mathematics in its current state unfairly demands. Human brains are structurally not very different. If raw compute is about the same across individuals then the progress of academia relies on people with highly differing form of intelligence. An obvious example is people on the spectrum with seemingly absent emotional intelligence but vast capacity for abstract creativity. There should be many more types of intelligence available to us given a better communication protocol. Since I'm firmly in the camp of gaining knowledge for the benefit of mankind, I think the camp which instead of descriptive names gives names like "Hausdorff" or "Abelian" to important mathematical concepts are intellectual looters and a detriment to the field. As you seem to say we are in the same camp, I hope you see the conflict in gatekeeping.
- vertbhrtn 6y ago
  What descriptive alternative would you use for "abelian group"?
  - gizmo686 6y ago
    commutative group (which happens to be another name they often go by).
    - archgoon 6y ago
      Which is just a synonym for abelian. You're not about to guess what 'commutative group' is from it's name any more than you're going to guess what an 'abelian group' is, unless you have already learned what commutative or abelian means in the specific context of algebra. I'm always baffled that programmers, who freely adopt frameworks and languages with mostly meaningless names (which incidentally makes them easier to google for), continue to insist that names are the major stumbling block in learning math. It's utter nonsense. You pick up the names and terminology quickly enough (or look them up if you forget); the hard part is applying them.
vertbhrtn 6y ago
IMHO, people don't get philosophy. There's philosophy about the "inner side of things", that uses cryptic symbolism with ten layers of meanings, and philosophy for the public. Only the latter is taught in schools and discussed. All these famous philosophers of the past - Plato, Aristotle, and even the modern Kant - were known first for their contribution to that "inner" philosophy, and coincidentally they also left a few texts comprehensible by the public, and only those texts are discussed. There are famous philosophers that only cared about the "inner side of things", there are statues to honor them, their books are kept by some libraries and individuals who recognize significance of those books, but you wouldn't hear their names, unless you do some research. Modern science has the same dualism: some scientists bother to educate the public and simplify ideas for them, while some don't and only leave incomprehensible cryptic math. Einstein is a good example: GTR is what made him famous, but he got a public award (Nobel prize) for some side research.
- bonoboTP 6y ago
  Can you link some texts that are about the "inner side of things"? Not sure what you exactly mean by these words.
  - vertbhrtn 6y ago
    I'd recommend to start with Plato and do some research about who he really was. The Plato's wikipedia page is a good example of what I'm talking about: lots of attention to insignificant details and an attempt to present Plato as some kind of "inventor of dialogue techniques."
    - bonoboTP 6y ago
      To be honest, you are not writing clearly, and this raises my crank/quack alarms. If you have a concrete text that discusses this plainly, even if it's a full book, I'd be glad to hear it. Just saying that it's some mystery, some forbidden secret knowledge, which mere mortals don't understand, is not convincing. I have never heard of the phrase "the inner side of things". If this has a meaning, surely someone has written about it.
agumonkey 6y ago
so you're thinking being cryptic acts as a natural filter to keep the noise away ?
js8 6y ago
I think the incomprehensibility of high level mathematics is as much a planned feature as is incomprehensibility of Haskell to a common programmer. And yet, people who know Haskell find it actually more expressive than e.g. Java, precisely because it is more abstract, and neatly unifies some concepts. I think what I realized from being a programmer, just like in programming, there is no single language of mathematics. Different sub-fields invented different languages, and since everybody wants to remain productive, the effort to unify the languages is extremely difficult and unrewarding. Yet is much more accepted activity in mathematics than in programming. But it's not really intentional, it's just a side effect of natural tendency of various research groups to have somewhat different languages.
cannabis_sam 6y ago
Seriously, how intellectually compromised and paranoid do you have to be to ascribe these weird motivations onto the entire field of mathematicians??? They’re not a cabal, quite the opposite, they fight like schoolchildren (look up Leslie Lamport view on natural deduction, especially OR-elimination) The conflict between philosophy and mathematics that you describe, is generally understood as the debate around logical positivism, the adoption of which necessitates an extremely naive philosophy of scientific knowledge. You can even throw Gödel/Turing into this, which really finalizes any dumb debate about formalizing philosophy as math/logic, but at no point is there any proof of a conspiracy to keep mathematics off-limit for “normal people”. Like, it’s literally published in journals, and it is easily followed, as long as you actually spend the time to understand the fundamentals it’s built on.
claudiawerner 6y ago
>Anyone can disagree of course but just looking at the political affiliation ratios of educators makes it clear that one aspect of the hard sciences historically has been an ability to stay focused on utility despite post-modernism. Can you explain this further? How does political affiliation of educators have anything to do with the focus on "utility despite post-modernism"? Further, isn't there some utility in a discussion on the meaning, importance, and place of 'utility'? >they've just dropped the pretense of being truth seeking persuits. Is there any evidence or reasoning to persuade the reader of this statement? >but for a long time philosophy resisted efforts to 'mathmatecize' (my own word) the field because of concern that it would become inscrutible to outsiders This isn't the case in my experience, rather, philosophers were concerned about the implications in terms of the kinds of arguments they can make and their relevance if the field were 'mathematized' - you may not be aware, for instance, of 'analytical Marxism' which proposes that mathematical models are a superior way to continue Marx's project - but it is not without its critics on methodological grounds[0]. As you would expect, mathematicians and quantitative economists working within analytical Marxism share some 'politically polarized' views too. Where is there space for the 'utility' of a political-economic project within your schema? "The conception of mathematics as a mere language contains, however, the seeds of its own destruction. The notion of language as a simple medium through which ideas are communicated has been challenged from diverse perspectives; it has been reinterpreted as both constitutive of, and constituted by, the process of theorizing (e.g., by Williams 1977, 32). The use of mathematics in social theory, too, may be reconceptualized as a discursive condition of theories, which constrains and limits, and is partly determined by, those theories. Mathematical concepts, such as the equilibrium position associated with the solution to a set of simultaneous equations or the exogenous status of the rules of a game, partly determine the notions of relation and causality among the theoretical objects designated by the theories in which the means of mathematical formalization are utilized." [0] As Amariglio & Callari said, claims of rigor and clarity may just as well be used as rhetorical devices, in exactly the same way Descartes proceeded with rhetoric to 'prove' his own mind and God.

StandardFuture 6y ago

Obfuscation is a practice of the entirety of Academia for a long while now. The art of obfuscation is not new at all. A small anecdote, I remember a Taiwanese friend mentioning the history of the complexity of Chinese characters and how they were devised, in part, to ensure that the lower class(es) could not learn them. Obfuscation inherently guarantees a lot of things out of the box: you appear more enlightened, only a class of people can understand and thus judge your work, and all newcomers can only become "in the know" if and only if they are trained by someone who already is "in the know". This is very appealing to anyone with even minor insecurities (most people), and has been widely utilized throughout many areas of human society in time. Math is merely one example where this practice has presence. EDIT: I will admit that the more democratized the internet has made knowledge, and the more prevalent higher-degrees become in society, the more awareness people have of this issue and the more it gets called out. So, all in all, there is the positive side of things that this art of obfuscation is in decline of use for things where it should never be used (like education, science, etc.).

augustt 6y ago
I'd say this is generally not true, at least in math. There's definitely poor notation and misnomers that come from tradition, but it's hardly deliberate as "obfuscation" implies.
- mkl 6y ago
  I'm not sure I agree (I have a PhD in maths). There are many maths papers and books I've tried to understand where that seems to have been deliberately made more difficult than it needs to be. Sure, you could argue that I didn't have the necessary prerequisite knowledge at that point, or that the authors simply weren't good at explaining things, but I do get the impression that it's sometimes more than that. Using specialised meanings for words without definition or reference (words that are used for other purposes elsewhere so they can't be searched for) is a key problem, as is the same with notation, and as is leaving out crucial steps. If you're already in the know, those things are probably clear.
  - memexy 6y ago
    But that sounds like bad exposition. What benefit would any author get from purposely obfuscating what they're trying to share?
    - mkl 6y ago
      Could well be, and I have no definitive evidence otherwise, but sometimes it's hard to imagine anyone being that bad at exposition. Some "benefits" might be seeming smarter and more knowledgeable than they are, making it harder to exactly replicate their methods (most relevant in applied areas), or citations by intimidation ("I don't understand this, but it seems impressive and relevant, so I better cite it.").
      - elbear 6y ago
        They all sound plausible and likely. There are people obfuscating knowledge for all the reasons you mentioned. At the same time, it doesn't mean there's a concerted effort to obfuscate mathematics. Explaining things is hard, because you have to create a clear picture of the audience in your mind. Then, you have to draw the lines between what they know and what you want to introduce. The curse of knowledge is a big obstacle here.

memexy 6y ago

Many of the early mathematicians were mystics. So in a way the incomprehensibility is a feature and not a bug but for those that are well versed in the language it is a rich source of analogies and metaphors. > "Good mathematicians see analogies. Great mathematicians see analogies between analogies." To see analogies between analogies requires compressing concepts into symbols that at first glance are not as comprehensible as regular words and sentences but math is really just another language and people can learn it and apply it fruitfully. -- https://en.wikipedia.org/wiki/Stefan_Banach#Quotes#:~:text=Good%20mathematicians,analogies%20between%20analogies https://en.wikipedia.org/wiki/Stefan_Banach#Quotes#:~:text=G....

joe_the_user 6y ago

I might see it this way because I've been studying math for a long time (though not professionally most of it) but I don't think modern math is ever made more complicated or hard to understand just for the heck of it. That's because math is already felt as extremely hard for most people. I think anyone in professional math is working really hard to make the field more comprehensible to themselves and so to the world - and the reason for this is the more a mathematician understands and more compactly they can understand it, the further they can go. And certainly, the way a mathematician put things curtly makes it harder for the laymen, I think the biggest harm to the layman's understanding of math is a math education that gets people conditioned to not think abstractly and think of math as a series of dull exercises.

j7ake 6y ago
I agree. If some mathematicians purposeful obfuscated or made more complicated than necessary certain topics, it would create an arbitrage opportunity for others to clarify and simplify the topic. There are definitely tangible rewards for those who can clarify and simplify a topic, because it can lead to discoveries and insights. This gradual clarification of a topic hinges on the actual importance of the topic. If a topic is not important, I can see people getting away with obfuscating or complicating results.
- bonoboTP 6y ago
  Respectable, pro mathematicians don't obfuscate. But there are definitely math professors in non-top universities who get kicks out of torturing students and think "this is supposed to be hard" etc. I'm definitely a math enthusiast but I have personally met people like that. Typically the exams are under strong time pressure and are more about rote learning of fixed types of exercises and remembering definitions. On the other hand, I had math profs who radiated curiosity and fun and the exams were just a few questions, but you had to think to solve them and you weren't under much time pressure. So while mathematicians aren't purposefully obscure, the math people (teachers) the average person interacts with are sometimes purposefully obscure.
deleted 6y ago
[deleted]

tsimionescu 6y ago

> As a result, academic philosophy is much more politically polarized than math. I don't think this is a clear conclusion at all. Philosophy is inherently very political (all political ideas ultimately come from philosophy, after all). Philosophy is also concerned with the real world and human affairs much more than abstract math is. It's also funny that you bring up post-modernism, a philosophical current famous and often ridiculed for being one of the most deliberately obfuscated. I also know that a lot of the efforts of brininging mathematical thinking and abstraction in the humanities end up exactly in obscurantism: most of the field can't understand it, but it has cultural clout so they can't admit that, and it becomes a source of empty prestige, with maths literally sprinkled on studies just to access that clout. Even in medicine, math-y papers are/were often accepted unconditionally, with peer review unable to check the actual maths, but unwilling to admit their lack of mathematical culture. For an example, there was a medical article published in 1993 [0], which is a re-discovery of the trapese method of integration. This got around 100 citations. Of course, that article is at least correct. In postmodern literary studies, there is a famous example of an intentionally meaningless, but very abstract and complex sounding article that was successfully published in one of the leading journals, despite ultimately being gibberish [1]. My utlimate point being, I don't think there is any link between obscurity of a field and its resistance to internal or external politics. [0] http://care.diabetesjournals.org/cgi/content/abstract/17/2/152 http://care.diabetesjournals.org/cgi/content/abstract/17/2/1... [1] https://en.m.wikipedia.org/wiki/Sokal_affair https://en.m.wikipedia.org/wiki/Sokal_affair

singron 6y ago
In philosophy 101, my professor said that philosophy was focused on controversial topics because once you could prove a side, it would become science. E.g. the heavens used to be a philosophic topic until we had the ability to prove heliocentrism. Math is much more focused on the realm of what can be proved. Unproven statements in math (e.g. conjectures or axioms) are the exceptions that prove the rule.
- leereeves 6y ago
  Professional mathematicians spend their lives working on the unproven. It just seems like math is about what's already been proven because it takes so much education to reach the unproven ideas and unanswered questions.

ganzuul 6y ago

As an exclusive club, it's a feature. As pursuit for knowledge it's a tragedy. There are many highly intelligent people who are differently able to absorb mathematical literature. Consider, perhaps, if the gender imbalance is caused by the time needed to take care of children and a household. - Time which mathematics in its current state unfairly demands. Human brains are structurally not very different. If raw compute is about the same across individuals then the progress of academia relies on people with highly differing form of intelligence. An obvious example is people on the spectrum with seemingly absent emotional intelligence but vast capacity for abstract creativity. There should be many more types of intelligence available to us given a better communication protocol. Since I'm firmly in the camp of gaining knowledge for the benefit of mankind, I think the camp which instead of descriptive names gives names like "Hausdorff" or "Abelian" to important mathematical concepts are intellectual looters and a detriment to the field. As you seem to say we are in the same camp, I hope you see the conflict in gatekeeping.

vertbhrtn 6y ago
What descriptive alternative would you use for "abelian group"?
- gizmo686 6y ago
  commutative group (which happens to be another name they often go by).
  - archgoon 6y ago
    Which is just a synonym for abelian. You're not about to guess what 'commutative group' is from it's name any more than you're going to guess what an 'abelian group' is, unless you have already learned what commutative or abelian means in the specific context of algebra. I'm always baffled that programmers, who freely adopt frameworks and languages with mostly meaningless names (which incidentally makes them easier to google for), continue to insist that names are the major stumbling block in learning math. It's utter nonsense. You pick up the names and terminology quickly enough (or look them up if you forget); the hard part is applying them.

vertbhrtn 6y ago

IMHO, people don't get philosophy. There's philosophy about the "inner side of things", that uses cryptic symbolism with ten layers of meanings, and philosophy for the public. Only the latter is taught in schools and discussed. All these famous philosophers of the past - Plato, Aristotle, and even the modern Kant - were known first for their contribution to that "inner" philosophy, and coincidentally they also left a few texts comprehensible by the public, and only those texts are discussed. There are famous philosophers that only cared about the "inner side of things", there are statues to honor them, their books are kept by some libraries and individuals who recognize significance of those books, but you wouldn't hear their names, unless you do some research. Modern science has the same dualism: some scientists bother to educate the public and simplify ideas for them, while some don't and only leave incomprehensible cryptic math. Einstein is a good example: GTR is what made him famous, but he got a public award (Nobel prize) for some side research.

bonoboTP 6y ago
Can you link some texts that are about the "inner side of things"? Not sure what you exactly mean by these words.
- vertbhrtn 6y ago
  I'd recommend to start with Plato and do some research about who he really was. The Plato's wikipedia page is a good example of what I'm talking about: lots of attention to insignificant details and an attempt to present Plato as some kind of "inventor of dialogue techniques."
  - bonoboTP 6y ago
    To be honest, you are not writing clearly, and this raises my crank/quack alarms. If you have a concrete text that discusses this plainly, even if it's a full book, I'd be glad to hear it. Just saying that it's some mystery, some forbidden secret knowledge, which mere mortals don't understand, is not convincing. I have never heard of the phrase "the inner side of things". If this has a meaning, surely someone has written about it.

agumonkey 6y ago

so you're thinking being cryptic acts as a natural filter to keep the noise away ?

js8 6y ago

I think the incomprehensibility of high level mathematics is as much a planned feature as is incomprehensibility of Haskell to a common programmer. And yet, people who know Haskell find it actually more expressive than e.g. Java, precisely because it is more abstract, and neatly unifies some concepts. I think what I realized from being a programmer, just like in programming, there is no single language of mathematics. Different sub-fields invented different languages, and since everybody wants to remain productive, the effort to unify the languages is extremely difficult and unrewarding. Yet is much more accepted activity in mathematics than in programming. But it's not really intentional, it's just a side effect of natural tendency of various research groups to have somewhat different languages.

cannabis_sam 6y ago

Seriously, how intellectually compromised and paranoid do you have to be to ascribe these weird motivations onto the entire field of mathematicians??? They’re not a cabal, quite the opposite, they fight like schoolchildren (look up Leslie Lamport view on natural deduction, especially OR-elimination) The conflict between philosophy and mathematics that you describe, is generally understood as the debate around logical positivism, the adoption of which necessitates an extremely naive philosophy of scientific knowledge. You can even throw Gödel/Turing into this, which really finalizes any dumb debate about formalizing philosophy as math/logic, but at no point is there any proof of a conspiracy to keep mathematics off-limit for “normal people”. Like, it’s literally published in journals, and it is easily followed, as long as you actually spend the time to understand the fundamentals it’s built on.

claudiawerner 6y ago

>Anyone can disagree of course but just looking at the political affiliation ratios of educators makes it clear that one aspect of the hard sciences historically has been an ability to stay focused on utility despite post-modernism. Can you explain this further? How does political affiliation of educators have anything to do with the focus on "utility despite post-modernism"? Further, isn't there some utility in a discussion on the meaning, importance, and place of 'utility'? >they've just dropped the pretense of being truth seeking persuits. Is there any evidence or reasoning to persuade the reader of this statement? >but for a long time philosophy resisted efforts to 'mathmatecize' (my own word) the field because of concern that it would become inscrutible to outsiders This isn't the case in my experience, rather, philosophers were concerned about the implications in terms of the kinds of arguments they can make and their relevance if the field were 'mathematized' - you may not be aware, for instance, of 'analytical Marxism' which proposes that mathematical models are a superior way to continue Marx's project - but it is not without its critics on methodological grounds[0]. As you would expect, mathematicians and quantitative economists working within analytical Marxism share some 'politically polarized' views too. Where is there space for the 'utility' of a political-economic project within your schema? "The conception of mathematics as a mere language contains, however, the seeds of its own destruction. The notion of language as a simple medium through which ideas are communicated has been challenged from diverse perspectives; it has been reinterpreted as both constitutive of, and constituted by, the process of theorizing (e.g., by Williams 1977, 32). The use of mathematics in social theory, too, may be reconceptualized as a discursive condition of theories, which constrains and limits, and is partly determined by, those theories. Mathematical concepts, such as the equilibrium position associated with the solution to a set of simultaneous equations or the exogenous status of the rules of a game, partly determine the notions of relation and causality among the theoretical objects designated by the theories in which the means of mathematical formalization are utilized." [0] As Amariglio & Callari said, claims of rigor and clarity may just as well be used as rhetorical devices, in exactly the same way Descartes proceeded with rhetoric to 'prove' his own mind and God.