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> With all due respect, you have no idea what you're talking about, you aren't making any sense, and you're clueless about what mathematics is about when you c

> With all due respect, you have no idea what you're talking about, you aren't making any sense, and you're clueless about what mathematics is about when you call for ideas to be abstracted into "functions", and complain about naming conventions and so on. In your eagerness to apply what you've learned about software development to a completely different field you are grossly and misunderstanding what it is all about. You're right, I don't know much about the fields of mathematics and physics. > posts reveal a fundamental misunderstanding of what mathematics (and physics) is about. Tip: it's not about algorithms. So don't presume you can apply techniques from software development to mathematics, just as it doesn't make sense to apply tools from physics to computer programming. Actually quite the opposite. I do expect programming principles and tools to be able to aid in expressing ideas that can be thought about as a language. This is just visible with problems like unstandardized common variables. The only physics heavy book I've read some of recently is Kenneth Davies Ionosphereic Radio Propagation because it relates to my work. In it, there is a few pages dedicated to just defining what all of these funny greek symbols mean because they are used in pretty much every math heavy disiplin but each field takes them to mean their own thing. Even still with this quick referense there are large portions of the book that remain a mystery because they simply require understanding of this single field of physics common variable names and meanings to read. The chapter on VLF propegation (just after the diagram of these waves being propegated by the Earth's field lines) refers to X sub something (it's been a few days) and it relates that approximately to the plasma frequency at a region of space but it means something different. I have no idea what that variable is without finding a plasma physicist and asking them directly what that specific niche variable name means for this specific field under this specific topic relating to this one type of equation. Even with this simple example, I can show that it would be better to have a discriptive variable name rather then "X sub something". This is just one example from this week where this trend has bit me in the ass. If it's so easy to talk about this single situation where it's the case that a programming idea of descriptive variable names, then why don't other programming concepts fit in math? Can you prove why this is the case?

yorwba 10y ago
Since the book you are complaining about is available online (https://archive.org/details/IonosphericRadioPropagation https://archive.org/details/IonosphericRadioPropagation), I had a look to see for myself. Interestingly, the same paragraph that uses X without explanation also uses ν, which was just as mysterious to me. However, from your comment I gather that it denotes the plasma frequency. So it seems that the second variable was introduced correctly for you to understand it, while the first one was not. To use a programming metaphor, the documentation was lacking. I found an example of notation introduced right (in my opinion) on page 405: In order to take into account the double refraction in the ionosphere, it is convenient to use the two reflection coefficients ∥R∥ and ⟂R⟂ together with two conversion coefficients ∥R⟂ and ⟂R∥ - The first subscript denotes whether the electric field of the incident wave is parallel (∥) to or perpendicular (⟂) to the plane of incidence and the second subscript refers to the same characteristic in the reflected wave. The variables are mnemonic (_R_eflection), vary systematically and use pictographic symbols standardized in another field, and most importantly all of this is explained. Now you might object that all of this explanation wouldn't even be necessary if a more descriptive variable name had been used. But in programming, we frequently have to put a comment next to our variable declarations anyway, to give more context than a single word can provide. Using single-word variable names might still be a step up for readability when writing equations. But consider that when using the equation, you will end up writing those variables over and over again, with just slight modifications in parts of the formula. And when using some equations, e.g. the matrix inversion lemma, you end up blowing up your expressions to truly gigantic size. In programming, we would just factor the expressions into more manageable chunks. But when you need the expanded form of the expression to apply some simplification, you can't really do that, short of simply not writing down the step. Mathematical notation is really better suited for this kind of frequent manipulation and rewriting. Nonetheless, I think some of the lessons learned in programming concerning the use of dense formal languages might transfer to mathematics. One example is explicit declaration before use, which would probably have helped your problem with X just as well as a descriptive variable name. Another is the IDE experience, where hovering over a symbol gives you the contextual information you need to understand it.
- gravypod 10y ago
  I'm sorry but I failed to mention that this book has two revisions, one of which represents a HUGE change to the book. It was entierly rewritten, every diagram redone, all information re-sourced. The paragraph I'm speaking of does not appear in the original book. Our understanding of propegation of VLF hadn't changed much but the way it is explained, and our understanding of different extremely important phenomena, are not described in the first edition. (One of the most noticable cases of this is the only mentioning of Whistlers in the first book is in relation to Exospehric events which is definetly not the case). I'll recomment on this when I get into work and take a photo of the specific paragraph. I'll show it to you and maybe you can better describe what it is. If you've got an email in your description I'll shoot one off when I add it. > The variables are mnemonic (_R_eflection), vary systematically and use pictographic symbols standardized in another field, and most importantly all of this is explained. What's the mnemonic of "X"? > Using single-word variable names might still be a step up for readability when writing equations. But consider that when using the equation, you will end up writing those variables over and over again, with just slight modifications in parts of the formula And? I'm fine with that. If anything, as a programmer we can write IDEs for math majors. Maybe we might actually kill of LaTeX and get something that makes some sense to fill it's place. > But when you need the expanded form of the expression to apply some simplification, you can't really do that, short of simply not writing down the step. Mathematical notation is really better suited for this kind of frequent manipulation and rewriting. My MathIDE can with one click transform your reduced equation into an expanded form. It would also definetly possible to turn an expanded form into a reduced form. > Nonetheless, I think some of the lessons learned in programming concerning the use of dense formal languages might transfer to mathematics. One example is explicit declaration before use, which would probably have helped your problem with X just as well as a descriptive variable name. Another is the IDE experience, where hovering over a symbol gives you the contextual information you need to understand it. Yep I totally agree.
andrepd 10y ago
So your qualm is about notation? That it is confusing and too terse? It is so for good reason: you couldn't write complex expressions if you used single-word identifiers instead of letters. For example, try writing this relatively simple expression, Noether's theorem, using one-word identifiers: http://quicklatex.com/cache3/8a/ql_eb3c64b518d0f2b54ceada1f881bc38a_l3.png http://quicklatex.com/cache3/8a/ql_eb3c64b518d0f2b54ceada1f8... . It gets unwieldy. Imagine manipulating more complicated expressions and writing words instead of a simple symbol. Any effort it takes to memorize a convention is recouped several times over in ease of use. At any rate, I fail to see how else can concepts from software development apply to mathematics and physics, besides the superficial issue of identifiers.

yorwba 10y ago

Since the book you are complaining about is available online (https://archive.org/details/IonosphericRadioPropagation https://archive.org/details/IonosphericRadioPropagation), I had a look to see for myself. Interestingly, the same paragraph that uses X without explanation also uses ν, which was just as mysterious to me. However, from your comment I gather that it denotes the plasma frequency. So it seems that the second variable was introduced correctly for you to understand it, while the first one was not. To use a programming metaphor, the documentation was lacking. I found an example of notation introduced right (in my opinion) on page 405: In order to take into account the double refraction in the ionosphere, it is convenient to use the two reflection coefficients ∥R∥ and ⟂R⟂ together with two conversion coefficients ∥R⟂ and ⟂R∥ - The first subscript denotes whether the electric field of the incident wave is parallel (∥) to or perpendicular (⟂) to the plane of incidence and the second subscript refers to the same characteristic in the reflected wave. The variables are mnemonic (_R_eflection), vary systematically and use pictographic symbols standardized in another field, and most importantly all of this is explained. Now you might object that all of this explanation wouldn't even be necessary if a more descriptive variable name had been used. But in programming, we frequently have to put a comment next to our variable declarations anyway, to give more context than a single word can provide. Using single-word variable names might still be a step up for readability when writing equations. But consider that when using the equation, you will end up writing those variables over and over again, with just slight modifications in parts of the formula. And when using some equations, e.g. the matrix inversion lemma, you end up blowing up your expressions to truly gigantic size. In programming, we would just factor the expressions into more manageable chunks. But when you need the expanded form of the expression to apply some simplification, you can't really do that, short of simply not writing down the step. Mathematical notation is really better suited for this kind of frequent manipulation and rewriting. Nonetheless, I think some of the lessons learned in programming concerning the use of dense formal languages might transfer to mathematics. One example is explicit declaration before use, which would probably have helped your problem with X just as well as a descriptive variable name. Another is the IDE experience, where hovering over a symbol gives you the contextual information you need to understand it.

gravypod 10y ago
I'm sorry but I failed to mention that this book has two revisions, one of which represents a HUGE change to the book. It was entierly rewritten, every diagram redone, all information re-sourced. The paragraph I'm speaking of does not appear in the original book. Our understanding of propegation of VLF hadn't changed much but the way it is explained, and our understanding of different extremely important phenomena, are not described in the first edition. (One of the most noticable cases of this is the only mentioning of Whistlers in the first book is in relation to Exospehric events which is definetly not the case). I'll recomment on this when I get into work and take a photo of the specific paragraph. I'll show it to you and maybe you can better describe what it is. If you've got an email in your description I'll shoot one off when I add it. > The variables are mnemonic (_R_eflection), vary systematically and use pictographic symbols standardized in another field, and most importantly all of this is explained. What's the mnemonic of "X"? > Using single-word variable names might still be a step up for readability when writing equations. But consider that when using the equation, you will end up writing those variables over and over again, with just slight modifications in parts of the formula And? I'm fine with that. If anything, as a programmer we can write IDEs for math majors. Maybe we might actually kill of LaTeX and get something that makes some sense to fill it's place. > But when you need the expanded form of the expression to apply some simplification, you can't really do that, short of simply not writing down the step. Mathematical notation is really better suited for this kind of frequent manipulation and rewriting. My MathIDE can with one click transform your reduced equation into an expanded form. It would also definetly possible to turn an expanded form into a reduced form. > Nonetheless, I think some of the lessons learned in programming concerning the use of dense formal languages might transfer to mathematics. One example is explicit declaration before use, which would probably have helped your problem with X just as well as a descriptive variable name. Another is the IDE experience, where hovering over a symbol gives you the contextual information you need to understand it. Yep I totally agree.

andrepd 10y ago

So your qualm is about notation? That it is confusing and too terse? It is so for good reason: you couldn't write complex expressions if you used single-word identifiers instead of letters. For example, try writing this relatively simple expression, Noether's theorem, using one-word identifiers: http://quicklatex.com/cache3/8a/ql_eb3c64b518d0f2b54ceada1f881bc38a_l3.png http://quicklatex.com/cache3/8a/ql_eb3c64b518d0f2b54ceada1f8... . It gets unwieldy. Imagine manipulating more complicated expressions and writing words instead of a simple symbol. Any effort it takes to memorize a convention is recouped several times over in ease of use. At any rate, I fail to see how else can concepts from software development apply to mathematics and physics, besides the superficial issue of identifiers.