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I've always liked the idea of math as a type of language. When you learn quantum computing, for example, you go beyond the limits of our informal language (Engl

I've always liked the idea of math as a type of language. When you learn quantum computing, for example, you go beyond the limits of our informal language (English, etc.) which developed in a purely classical world. This is why pop science articles on quantum phenomena never really make any sense. They try to use metaphors to explain concepts, but there is no existing concept in our informal language to use as a referent. Many quantum phenomena belong to an ontological category that is entirely new to most adults. For example, superposition: you try to explain it as something being in two places at once, but this doesn't make sense nor is it very helpful for understanding how objects in superposition behave. In order to understand quantum concepts you have to learn a new language - that of mathematics. Then it becomes easy! Superposition is just linear combination. Done. Also if you enjoy thinking about this topic I recommend Neal Stephenson's book Anathem, which I just finished. It is a complete slog at the start, with endless boring architectural descriptions. I listened to it in audiobook form which made that section much more pleasant.

dfischer 6y ago
In my understanding, that’s exactly what math is, a language. And various modes of thought have utilized the language of mathematics to communicate ideas that were otherwise not possible or not consistently able to arrive at same conclusions. This is very interesting. What is language? When does language evolve? Is language itself consciousness? Whenever there’s a leap in language is it because something had to be constructed to help assign an abstraction to a coordinate in space where thoughts exist? It appears we’re languages all the way down. Or analogicalmachines? Lol. Lots to unpack here - some with what many would call not nice Consequences. What happens when a minority elite (unsure how else to describe it?) disciplines require a language that the majority lack the finesse to use? Example: math used in physics, or programming in computation. If the languages being used introduce more complexity without the ability to reduce net complexity then it damages the communication of the specie using it. I’ve been thinking about this quite a bit on our trajectory as a species. Complexity in language leads to information silos which leads to various existential risks based on information and miscommunication. Also interesting coercion / authoritarian emergence comes out of those creating a new language to reason about an abstraction which leads to a success that negatively impacts those which do not know the language and if the space to understand said language is sufficiently far enough you have much room for manipulation. Also, who gets to say which language is the right one? What happens when a new language is created that is more advanced and the majority disallow it preventing an evolution? Interesting dynamics.
- ahelwer 6y ago
  We don't have to stumble around blind here. Philosophy has long pondered the nature of language. A more recent idea is that a language as we think of it - English, French, etc. - does not exist per se; rather we engage in "games" with each other which are languages in themselves. For example, when I buy something from a shop I am playing the "purchase an item at the cashier stand" game. Both the cashier and myself know all the valid moves in the game - they say the price, I provide a method of payment, etc. Some of these moves involve use of a limited subset of English words, but even if I'm in a foreign country where the cashier doesn't speak English we can usually make it work. This interaction is a language in itself. If I were to walk up to the cashier and try to play the "negotiate salary for a full-time position" game, only confusion would result - I would be speaking the wrong language, even though I'm emitting sounds which we both find familiar. Much confusion and anguish in the world results from people playing the wrong language game with each other - for example, one person playing the "venting frustrations" game while another plays the "provide advice" game. In this analysis, the "explain quantum phenomena" game is just a language where the rules are especially strange and prone to pitfalls. Deploying vocabulary from mathematics, a system with very well-defined and mutually-understood rules, enables us to navigate this space.
  - dfischer 6y ago
    Yes, I see humanity engaging in games and LARPing as an interaction between those who are aware of the game being defined by arbitrary rules, and those who don’t. Most don’t realize it’s arbitrary. I’ve thought about what you said recently and it comes down to “well-defined” being relative. Usually to those that are defining it. It’s not objective. Additionally that’s enforcing or coercing a game unto others that they may not wish to engage with or may not be able to conceptualize it. Some people prefer characteristics over others. Have predispositions to likings and not likings. Using a language is in of itself agreeing to a game. If a thing requires consent of will to proceed as a rule, it’s a game. Language, or any system of rules would be part of agreeing to a confined space of possibilities and “game-space” Interesting to ponder nonetheless at a different abstraction. I keep trying to go “deeper” behind the language itself, I arrive at signal and then we’re in a puddle of discrete and non discrete values. Fun.
username90 6y ago
Math isn't a language, it has a language. You can easily invent your own language to describe different aspects of maths. Saying that it is a language is like saying that computer science is a language since people write C etc.
- ahelwer 6y ago
  Does not follow. You can use a thesaurus to find many different ways to say the same thing in informal languages.
  - username90 6y ago
    When you do math you invent new language, ie you add notation and describe what they mean. The math is the actual concepts, not the language you create, an other person could have structured his language for this problem very differently yet ultimately describing the same thing. Edit: To clarify better, the way you solve math is that first you solve the problem, then you figure out how to communicate the solution. This can either use language people created before or you create new language, you can just use English or you can just draw pictures and have no words at all. Either way you are doing maths.
    - ahelwer 6y ago
      Sounds identical to articulating a concept in any informal language.
      - srtjstjsj 6y ago
        Yes. And concepts (math) aren't language.
        dfischer 6y ago
        All concepts are language.
      - beagle3 6y ago
boxfire 6y ago
Even in your own comment, equating Superposition and linear combination, you are almost there but not quite. A spanning set of linear combinations is not the same thing as reference to the concept of linear combinations. One might argue small difference, but we are talking about the precision of language here.
7thaccount 6y ago
I've tried the audiobook, but could never make it past the descriptions of the monastery that take up endless minutes which slow to an eternity.
- ahelwer 6y ago
  It really is worth it if you get past that part, which I completely agree is a total slog. The audiobook is very well done. Things pick up considerably once you get to Apert.
mensetmanusman 6y ago
Can you form abstractions without language?
- beagle3 6y ago
  I'm not sure I understand the issue. It's clear that every animal has the abstraction "food", which applies to groups of molecules and atoms, and does not require anything like a language.
- dfischer 6y ago
  It’s a great question. That depends on if an emotion and image would be language. Given we had no language and communicated telepathically I’ve imagined that: 1. Using a feeling 2. Using a mental image May be enough to form abstractions but that may in of itself be within the set of languages. Said another way though, does language require symbols? It’s certainly possible to imagine language without words and we live in a time where symbols are abstractions for entire concepts within the noosphere. Language is fundamentally based on abstractions. Abstractions are fundamentally based on mind. If the mind conjures abstractions then is it fundamentally a language no matter what? Probably. What are the ways that we may use language to communicate? Far more than we think of today. Every time we extend the abstraction we are essentially evolving as a species. Almost to the point where our evolution is entirely dependent on our ability to abstract novelty continuously.
  - andrewjl 6y ago
    > 2. Using a mental image https://en.wikipedia.org/wiki/Aphantasia https://en.wikipedia.org/wiki/Aphantasia There are many who are unable to form images in their mind. Aphantasia isn't rare. But it's also not universal and people with aphantasia somehow manage to communicate to those without well enough most of the time. Perhaps then language isn't just visual images or purely mathematical abstractions. I think the view of Wilfrid Sellars, basically language as a collectively-authored set of referents to a non-visual conceptual "picture" of reality, matches well with what you're saying here.
    - 6y ago

dfischer 6y ago

In my understanding, that’s exactly what math is, a language. And various modes of thought have utilized the language of mathematics to communicate ideas that were otherwise not possible or not consistently able to arrive at same conclusions. This is very interesting. What is language? When does language evolve? Is language itself consciousness? Whenever there’s a leap in language is it because something had to be constructed to help assign an abstraction to a coordinate in space where thoughts exist? It appears we’re languages all the way down. Or analogicalmachines? Lol. Lots to unpack here - some with what many would call not nice Consequences. What happens when a minority elite (unsure how else to describe it?) disciplines require a language that the majority lack the finesse to use? Example: math used in physics, or programming in computation. If the languages being used introduce more complexity without the ability to reduce net complexity then it damages the communication of the specie using it. I’ve been thinking about this quite a bit on our trajectory as a species. Complexity in language leads to information silos which leads to various existential risks based on information and miscommunication. Also interesting coercion / authoritarian emergence comes out of those creating a new language to reason about an abstraction which leads to a success that negatively impacts those which do not know the language and if the space to understand said language is sufficiently far enough you have much room for manipulation. Also, who gets to say which language is the right one? What happens when a new language is created that is more advanced and the majority disallow it preventing an evolution? Interesting dynamics.

ahelwer 6y ago
We don't have to stumble around blind here. Philosophy has long pondered the nature of language. A more recent idea is that a language as we think of it - English, French, etc. - does not exist per se; rather we engage in "games" with each other which are languages in themselves. For example, when I buy something from a shop I am playing the "purchase an item at the cashier stand" game. Both the cashier and myself know all the valid moves in the game - they say the price, I provide a method of payment, etc. Some of these moves involve use of a limited subset of English words, but even if I'm in a foreign country where the cashier doesn't speak English we can usually make it work. This interaction is a language in itself. If I were to walk up to the cashier and try to play the "negotiate salary for a full-time position" game, only confusion would result - I would be speaking the wrong language, even though I'm emitting sounds which we both find familiar. Much confusion and anguish in the world results from people playing the wrong language game with each other - for example, one person playing the "venting frustrations" game while another plays the "provide advice" game. In this analysis, the "explain quantum phenomena" game is just a language where the rules are especially strange and prone to pitfalls. Deploying vocabulary from mathematics, a system with very well-defined and mutually-understood rules, enables us to navigate this space.
- dfischer 6y ago
  Yes, I see humanity engaging in games and LARPing as an interaction between those who are aware of the game being defined by arbitrary rules, and those who don’t. Most don’t realize it’s arbitrary. I’ve thought about what you said recently and it comes down to “well-defined” being relative. Usually to those that are defining it. It’s not objective. Additionally that’s enforcing or coercing a game unto others that they may not wish to engage with or may not be able to conceptualize it. Some people prefer characteristics over others. Have predispositions to likings and not likings. Using a language is in of itself agreeing to a game. If a thing requires consent of will to proceed as a rule, it’s a game. Language, or any system of rules would be part of agreeing to a confined space of possibilities and “game-space” Interesting to ponder nonetheless at a different abstraction. I keep trying to go “deeper” behind the language itself, I arrive at signal and then we’re in a puddle of discrete and non discrete values. Fun.

username90 6y ago

Math isn't a language, it has a language. You can easily invent your own language to describe different aspects of maths. Saying that it is a language is like saying that computer science is a language since people write C etc.

ahelwer 6y ago
Does not follow. You can use a thesaurus to find many different ways to say the same thing in informal languages.
- username90 6y ago
  When you do math you invent new language, ie you add notation and describe what they mean. The math is the actual concepts, not the language you create, an other person could have structured his language for this problem very differently yet ultimately describing the same thing. Edit: To clarify better, the way you solve math is that first you solve the problem, then you figure out how to communicate the solution. This can either use language people created before or you create new language, you can just use English or you can just draw pictures and have no words at all. Either way you are doing maths.
  - ahelwer 6y ago
    Sounds identical to articulating a concept in any informal language.
    - srtjstjsj 6y ago
      Yes. And concepts (math) aren't language.
      - dfischer 6y ago
        All concepts are language.
    - beagle3 6y ago

boxfire 6y ago

Even in your own comment, equating Superposition and linear combination, you are almost there but not quite. A spanning set of linear combinations is not the same thing as reference to the concept of linear combinations. One might argue small difference, but we are talking about the precision of language here.

7thaccount 6y ago

I've tried the audiobook, but could never make it past the descriptions of the monastery that take up endless minutes which slow to an eternity.

ahelwer 6y ago
It really is worth it if you get past that part, which I completely agree is a total slog. The audiobook is very well done. Things pick up considerably once you get to Apert.

mensetmanusman 6y ago

Can you form abstractions without language?

beagle3 6y ago
I'm not sure I understand the issue. It's clear that every animal has the abstraction "food", which applies to groups of molecules and atoms, and does not require anything like a language.
dfischer 6y ago
It’s a great question. That depends on if an emotion and image would be language. Given we had no language and communicated telepathically I’ve imagined that: 1. Using a feeling 2. Using a mental image May be enough to form abstractions but that may in of itself be within the set of languages. Said another way though, does language require symbols? It’s certainly possible to imagine language without words and we live in a time where symbols are abstractions for entire concepts within the noosphere. Language is fundamentally based on abstractions. Abstractions are fundamentally based on mind. If the mind conjures abstractions then is it fundamentally a language no matter what? Probably. What are the ways that we may use language to communicate? Far more than we think of today. Every time we extend the abstraction we are essentially evolving as a species. Almost to the point where our evolution is entirely dependent on our ability to abstract novelty continuously.
- andrewjl 6y ago
  > 2. Using a mental image https://en.wikipedia.org/wiki/Aphantasia https://en.wikipedia.org/wiki/Aphantasia There are many who are unable to form images in their mind. Aphantasia isn't rare. But it's also not universal and people with aphantasia somehow manage to communicate to those without well enough most of the time. Perhaps then language isn't just visual images or purely mathematical abstractions. I think the view of Wilfrid Sellars, basically language as a collectively-authored set of referents to a non-visual conceptual "picture" of reality, matches well with what you're saying here.
  - 6y ago