> "Instead of writing Xi, they should really write X[i]; because Xi is ambiguous.
> "Instead of writing Xi, they should really write X[i]; because Xi is ambiguous. I find that dealing with all the ambiguity in syntax can be rather frustrating." This is a feature of math, not a bug. The potential for ambiguity is the cost that one pays to have a flexible and extensible notation which can be adapted to concepts yet undiscovered. This is generally not the case with code [1]. When you are exploring new ideas you want the ability to redefine your notation to match the nature and structure of the abstactions you are examining. There is a finite number of symbols in the set of all human languages, and thus far we know of no reason that there should be a finite set of concepts in mathematics. Enforcing a one-to-one mapping from a given sequence of symbols to a given concept forces you to either limit the space of concepts you can consider or to eventually deal with impractically large sequences of symbols for relatively simple concepts. [1] Yes, Lisp and DSLs are a thing, but you still have to define what a given sequence of symbols means. In an interpreted language, the interpreter computes the meaning using inputs and any necessary state. In math, the meaning is necessarily dependent on context as well.
Posted by john_b on Jun 30, 2015, 9:19 PM
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Here in Argentina we are in permanent summer time GMT-3 since a long time, but we should be in GMT-4.
NewYou should do some basic research yourself.
NewWell, actually not.
NewI have a 2022 mini that I use constantly.
NewTwo observation: 1.
NewCautiously optimistic for them.
NewI have two televisions - living room TV with an AppleTV and bedroom TV with some Roku device.
I hate that they claim the pricing like that.
> "Instead of writing Xi, they should really write X[i]; because Xi is ambiguous.
> "Instead of writing Xi, they should really write X[i]; because Xi is ambiguous. I find that dealing with all the ambiguity in syntax can be rather frustrating." This is a feature of math, not a bug. The potential for ambiguity is the cost that one pays to have a flexible and extensible notation which can be adapted to concepts yet undiscovered. This is generally not the case with code [1]. When you are exploring new ideas you want the ability to redefine your notation to match the nature and structure of the abstactions you are examining. There is a finite number of symbols in the set of all human languages, and thus far we know of no reason that there should be a finite set of concepts in mathematics. Enforcing a one-to-one mapping from a given sequence of symbols to a given concept forces you to either limit the space of concepts you can consider or to eventually deal with impractically large sequences of symbols for relatively simple concepts. [1] Yes, Lisp and DSLs are a thing, but you still have to define what a given sequence of symbols means. In an interpreted language, the interpreter computes the meaning using inputs and any necessary state. In math, the meaning is necessarily dependent on context as well.
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