8 ms·

Symbols are symbols, are symbols. Instead of trying to compress everything into a very limited set of "daily language" symbols we should be trying to expand ou

by redial 9y ago

Symbols are symbols, are symbols. Instead of trying to compress everything into a very limited set of "daily language" symbols we should be trying to expand our ideas, including our language(s).

adamnemecek 9y ago
Let's add Chinese, Amharic and Arabic characters. Why not, expanding is expanding.
- d8421l01vv4r 9y ago
  In some branches of engineering (traditional engineering, not software), there are sometimes too few symbols in the Latin and Greek alphabets, so they have to rely heavily on subscripts. Expanding the set of symbols would be useful here, but I guess it's hard to get people to accept change unless they absolutely have to.
  - Jtsummers 9y ago
    A part of the problem is character entry. If it were easy to enter in all these symbols APL may have taken off and we wouldn't have gotten ASCII variants of it like J. So it's somewhat easier to just take our latin alphabet and turn a single symbol into a pair of letters or a letter with a subscript. The symbols in math are great for writing by hand, but can become cumbersome when typing.
- bjl 9y ago
  Hebrew is already quite widely used in certain fields (specifically set theory).
- e12e 9y ago
  Arabic numerals are already widely used in mathematics...
dahart 9y ago
I'm not sure what that means. Are you saying the use of Greek letters is a good thing, and that we need more of them, not less? Or do you mean that all symbols are equally easy to learn for beginners, whether they're English or Greek or Chinese or abstract? Or do you mean that we should do away with symbols that don't mean anything and use real language to describe math instead? The symbols we use in math aren't to be confused with the ideas, they are shorthand. Ideas and symbols are independent, and we still have to explain what Greek letters do using English anyway. We use Greek letters for convenience, not for expressive power. Writing "∫ x ∂x" is only faster and more compact than writing "The integral of the equation x over x", it is not an improvement of the concept, right? Use of symbols is the act of trying to compress everything into a smaller set, not the other way around. For the modern audience, the use of Greek letters may hamper learning because the symbols are unfamiliar and foreign looking. It takes cognitive effort to learn the Greek letters in addition to the cognitive effort to learn the mathematical ideas. What if we could remove the cognitive effort on letters, and focus on the pure math ideas? What if the Greek letters are a speed bump to learning? That we use ∑ for sum and ∆ for change are arbitrary - canonical, but completely arbitrary. History could have decided that a circle was the integral symbol, or the capital letter I. Maybe math would be easier to learn if we switch to capital letter I.
- Jtsummers 9y ago
  > The symbols we use in math aren't to be confused with the ideas, they are shorthand. Ideas and symbols are independent, and we still have to explain what Greek letters do using English anyway. We use Greek letters for convenience, not for expressive power. Writing "∫ x ∂x" is only faster and more compact than writing "The integral of the equation x over x", it is not an improvement of the concept, right? It is not, strictly, an improvement on the concept. It's the same concept expressed two ways. But you cannot symbolically manipulate that prose text, where as you can stick that integral statement into an equation and manipulate it there along with the other expressions of the equation. The ability to perform those manipulations is an improvement.
  - dahart 9y ago
    Very true, good point, it's much easier and more convenient to do algebra on the symbolic expression. There is a reason math has evolved the way it has. Not using any symbols would suck, no question. But, nothing about writing math in text prevents manipulating the text, right? You can do it, it would just be laborious and exhausting for people who are familiar with the use of symbols.

by redial 9y ago

Symbols are symbols, are symbols. Instead of trying to compress everything into a very limited set of "daily language" symbols we should be trying to expand our ideas, including our language(s).

adamnemecek 9y ago

Let's add Chinese, Amharic and Arabic characters. Why not, expanding is expanding.

d8421l01vv4r 9y ago
In some branches of engineering (traditional engineering, not software), there are sometimes too few symbols in the Latin and Greek alphabets, so they have to rely heavily on subscripts. Expanding the set of symbols would be useful here, but I guess it's hard to get people to accept change unless they absolutely have to.
- Jtsummers 9y ago
  A part of the problem is character entry. If it were easy to enter in all these symbols APL may have taken off and we wouldn't have gotten ASCII variants of it like J. So it's somewhat easier to just take our latin alphabet and turn a single symbol into a pair of letters or a letter with a subscript. The symbols in math are great for writing by hand, but can become cumbersome when typing.
bjl 9y ago
Hebrew is already quite widely used in certain fields (specifically set theory).
e12e 9y ago
Arabic numerals are already widely used in mathematics...

dahart 9y ago

I'm not sure what that means. Are you saying the use of Greek letters is a good thing, and that we need more of them, not less? Or do you mean that all symbols are equally easy to learn for beginners, whether they're English or Greek or Chinese or abstract? Or do you mean that we should do away with symbols that don't mean anything and use real language to describe math instead? The symbols we use in math aren't to be confused with the ideas, they are shorthand. Ideas and symbols are independent, and we still have to explain what Greek letters do using English anyway. We use Greek letters for convenience, not for expressive power. Writing "∫ x ∂x" is only faster and more compact than writing "The integral of the equation x over x", it is not an improvement of the concept, right? Use of symbols is the act of trying to compress everything into a smaller set, not the other way around. For the modern audience, the use of Greek letters may hamper learning because the symbols are unfamiliar and foreign looking. It takes cognitive effort to learn the Greek letters in addition to the cognitive effort to learn the mathematical ideas. What if we could remove the cognitive effort on letters, and focus on the pure math ideas? What if the Greek letters are a speed bump to learning? That we use ∑ for sum and ∆ for change are arbitrary - canonical, but completely arbitrary. History could have decided that a circle was the integral symbol, or the capital letter I. Maybe math would be easier to learn if we switch to capital letter I.

Jtsummers 9y ago
> The symbols we use in math aren't to be confused with the ideas, they are shorthand. Ideas and symbols are independent, and we still have to explain what Greek letters do using English anyway. We use Greek letters for convenience, not for expressive power. Writing "∫ x ∂x" is only faster and more compact than writing "The integral of the equation x over x", it is not an improvement of the concept, right? It is not, strictly, an improvement on the concept. It's the same concept expressed two ways. But you cannot symbolically manipulate that prose text, where as you can stick that integral statement into an equation and manipulate it there along with the other expressions of the equation. The ability to perform those manipulations is an improvement.
- dahart 9y ago
  Very true, good point, it's much easier and more convenient to do algebra on the symbolic expression. There is a reason math has evolved the way it has. Not using any symbols would suck, no question. But, nothing about writing math in text prevents manipulating the text, right? You can do it, it would just be laborious and exhausting for people who are familiar with the use of symbols.