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Hi, I'm the author. Please keep in mind that I wrote this when I was 16. Thanks for your comments -- I agree with many of them. The only part of this that I st

by colah3 9y ago

Hi, I'm the author. Please keep in mind that I wrote this when I was 16. Thanks for your comments -- I agree with many of them. The only part of this that I still think is at all interesting is the section on quantifiers, and to a lesser extent the octal numbers. And I don't think they're that interesting. In general, while I do think there is interesting potential for improving notation -- Feynman diagrams come to mind as a somewhat modern example of notation impacting research -- I don't think this is what it looks like. > he proposes replacing well-known, well-distinguished symbols (alphabets and digits) with symbols that reflect a certain geometric interpretation. That's what most of it is, although the quantifiers are a more "grammatical" change. I think the best defense I can level of the symbol proposals is that the people most effected by low-level notational choices like symbols are probably young students learning them for the first time. It seems plausible there might be significant pedagogical gains in other symbols.

gizmo686 9y ago
Math major here. I too came out of your paper thinking that the quantifiers are the only interesting part of you paper; interesting enough, in fact, that I may start using them myself. One criticism is that there is no way to use them for variables that occur in more than one place. That is, you could not use them to right "for all x in R, x<x+1". I propose a simple addition of an optional subscript for the variable name in the quantifier. My other criticism is that it seems less natural to read that notation. With the standard notation, you can simply replace the symbol with English words and read it. While the transliteration in your notation is likely possible, it seems more complicated. In this sense, I would probably view this notation more as a shorthand. For pedagogical purposes, I feel like separating the qualifier from the usage of the variable is a good idea.
- giomasce 9y ago
  It is not the only problem, unfortunately. For example, there is no way to specify the order of quantifiers, which is very important (if you commute existiential and universal quantifiers, in general you change the meaning of a formula). So, for example, the definitions of pointwise and uniform continuity would we written identically, and that is not tolerable. Probably you could solve also this by adding another index to quantified quantities, but at that point are you really solving the problem of complexity? Complexity is not only measured in terms of verbosity (i.e., length of the expressions you produce); ability to quickly locate information and ease of manipulation are also important, and it seems to me that this formalism fails completely. In the "traditional" formalism you separate the "final fact" you want to assert from its "conditions", given by the quantifiers; usually, you want to process those pieces of information at different times. Also, you have rules for quantifier introduction and elimination, which seems to be a nightmare with the proposed formalism. That said, I do encourage new proposals and experimentation with notations, as with anything else in mathematics, even from young students. There have been cases in maths in which some good idea for a new notation made an entire field much easier (I am thinking for example to Einstein notation for tensor calculus).
jhanschoo 9y ago
Hi, thanks for replying! I'm sorry if I come off as overly critical. I did indeed think that this was the work of a very curious teenage mind who nevertheless still had insufficient experience with academic-level mathematics.

by colah3 9y ago

gizmo686 9y ago

Math major here. I too came out of your paper thinking that the quantifiers are the only interesting part of you paper; interesting enough, in fact, that I may start using them myself. One criticism is that there is no way to use them for variables that occur in more than one place. That is, you could not use them to right "for all x in R, x<x+1". I propose a simple addition of an optional subscript for the variable name in the quantifier. My other criticism is that it seems less natural to read that notation. With the standard notation, you can simply replace the symbol with English words and read it. While the transliteration in your notation is likely possible, it seems more complicated. In this sense, I would probably view this notation more as a shorthand. For pedagogical purposes, I feel like separating the qualifier from the usage of the variable is a good idea.

giomasce 9y ago
It is not the only problem, unfortunately. For example, there is no way to specify the order of quantifiers, which is very important (if you commute existiential and universal quantifiers, in general you change the meaning of a formula). So, for example, the definitions of pointwise and uniform continuity would we written identically, and that is not tolerable. Probably you could solve also this by adding another index to quantified quantities, but at that point are you really solving the problem of complexity? Complexity is not only measured in terms of verbosity (i.e., length of the expressions you produce); ability to quickly locate information and ease of manipulation are also important, and it seems to me that this formalism fails completely. In the "traditional" formalism you separate the "final fact" you want to assert from its "conditions", given by the quantifiers; usually, you want to process those pieces of information at different times. Also, you have rules for quantifier introduction and elimination, which seems to be a nightmare with the proposed formalism. That said, I do encourage new proposals and experimentation with notations, as with anything else in mathematics, even from young students. There have been cases in maths in which some good idea for a new notation made an entire field much easier (I am thinking for example to Einstein notation for tensor calculus).

jhanschoo 9y ago

Hi, thanks for replying! I'm sorry if I come off as overly critical. I did indeed think that this was the work of a very curious teenage mind who nevertheless still had insufficient experience with academic-level mathematics.