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Your comment shows a common misunderstanding of what mathematicians are trying to do. Modern mathematical notation is not obfuscated, it is in fact making the o

by mirosam 10y ago

Your comment shows a common misunderstanding of what mathematicians are trying to do. Modern mathematical notation is not obfuscated, it is in fact making the object being described much easier to perceive for humans. Explaining the equation you see in English words is what every physics book does, however the equation itself represents a concept that is not human. It comes from an alien universe of symmetries and relations and we have spent centuries to arrive at the current way of writing these down in a way which makes them easy to work with. You can formulate the solution to a quadratic equation as: The negative linear term, added and subtracted from the square root of the quantity which is the difference between the square of the linear term and the product of four times the constant term and the quadratic term, all divided by twice the quadratic term. Modern mathematicians write: x = (-b +- sqrt(b^2 - 4ac)) / 2a The difference is night and day. You cannot remove the essential complexity from a problem. You can only try to get close to its representation.

niftich 10y ago
Though I can't speak for the parent post's author, applying that post's spirit to your example would instead yield, for the quadratic formula: 'The negative linear term, added and subtracted from the square root of the discriminant, all divided by twice the quadratic term'; then before or after this you'd define the discriminant, as it's an illuminating concept in its own right. I see the target of this wishful thinking a sort-of middle-ground between a formula's derivation/proof and its compact form.
terryf 10y ago
While this might not be the OP's point, but for me the main problem are the one-character variable names. Generally computer code that just operates on cryptic one-letter variable names, is considered bad code. Yet equations almost always have one letter variables and the worst part of all, their meaning is almost never explained anywhere Case in point, what are b, a and c? what is their meaning if I have to measure them, what is the device for measuring them or what quantity do they represent?
- orbifold 10y ago
  The point is that variables are evil and arbitrary. So you give them short names to signal that you could replace them with anything else, what matters is how they appear together. Additionally different subfields of mathematics and physics usually adopt naming conventions.
  - agumonkey 10y ago
    Took me years before thinking of variables that way and mathematical expressions are constraints over sets, formulas expressing relations of interests that way.
- jasode 10y ago
  >Case in point, what are b, a and c? what is their _meaning_ The "b, a, and c" in the quadratic equation are abstractions. They are placeholders for any number. That math equation is purposely designed to not have any concrete meaning for a,b,c. Therefore, asking for their meaning does't make any sense. I'll try an analogy. We can give provide analogous "computer equation" for taking the last four characters of a string: s2 = Right(s1, 4); If someone were to ask "what is the _meaning_ of s1?", it would be a nonsensical question. The s1 is a placeholder for any string. The s1 could be a domain name and you want to extract the TLD (".com", ".org", ".edu"). Or the s1 could be a date "mm-dd-yyyy" and you want to extract the "2016" from ""10-31-2016". The s1 could be a placeholder for a thousand unrelated applications. If you further generalize the "computer equation" to be take the rightmost "x" amount of characters, you'd replace the "4" with "x" like this: s2 = Right(s1, x); ... it could trigger confusion as to "what does x _mean_? And what measuring device does it come from?" The "x" is an abstraction/parameter/argument of any number. That number could be 4, or 40000. (You might be tempted to say, "but I know 'x' stands for the number of characters I want from the string!" If so, by analogy you can also say that "c" in the quadratic equation stands for the number that satisfies the equation when you know "x", "a", and "b" ... which just circles back to each 1-character variable not having a concrete "meaning." The concrete meaning of "a,b,c" in the quadratic equation depends on whether the equation was modeling something in physics, or engineering, or finance.[1][2] The concrete meaning of "s1" and "x" in the "computer equation" depends on whether you're parsing logs, decomposing dates, verifying credit card numbers, etc. The analogy above could have been demonstrated with regex such as "(.+)(.{4})" ... which would trigger questions, *"why do programmers use 1-character symbols such as '.' and '+' instead of "anycharacterm_oneormoretimes_consideredasagroup_then_anycharacters_fourtimes_consideredasagroup" ... etc tldr: computer programmers also deal with weird-looking "equations" but since they are used to them, they have the background knowledge to decipher them. [1]https://www.mathsisfun.com/algebra/quadratic-equation-real-world.html https://www.mathsisfun.com/algebra/quadratic-equation-real-w... [2]https://www.boundless.com/algebra/textbooks/boundless-algebra-textbook/quadratic-functions-and-factoring-6/applications-of-quadratic-functions-46/financial-applications-of-quadratic-functions-135-6111/ https://www.boundless.com/algebra/textbooks/boundless-algebr...
digookdigook 10y ago
This is rather poetic. There is no difference, mathematical notation is a natural language and initiated mathematicians will read it in sentence form. Reading is a process of form recognition disconnect from vocalization. On the other hand, language seems to be mostly perceived as vocalisation, because that's the form it's learned from. As anecdotal evidence, tongue is an idiom for language and people have to make an actual effort to read without vocalizatio in order to increase reading-speed. Note that your literal example does contain a lot more information about context. IE, you even omitted the quadratic equation itself. That shows exactly the problem that I thought the Parent would mean: I prefer source code in a given language, that's actually compiled and maybe even proven correct, over terse mathematical notation that leaves a lot to context, intuition and shared information. Computability Theory gave rise to Computers, not the other way around.

by mirosam 10y ago

niftich 10y ago

Though I can't speak for the parent post's author, applying that post's spirit to your example would instead yield, for the quadratic formula: 'The negative linear term, added and subtracted from the square root of the discriminant, all divided by twice the quadratic term'; then before or after this you'd define the discriminant, as it's an illuminating concept in its own right. I see the target of this wishful thinking a sort-of middle-ground between a formula's derivation/proof and its compact form.

terryf 10y ago

While this might not be the OP's point, but for me the main problem are the one-character variable names. Generally computer code that just operates on cryptic one-letter variable names, is considered bad code. Yet equations almost always have one letter variables and the worst part of all, their meaning is almost never explained anywhere Case in point, what are b, a and c? what is their meaning if I have to measure them, what is the device for measuring them or what quantity do they represent?

orbifold 10y ago
The point is that variables are evil and arbitrary. So you give them short names to signal that you could replace them with anything else, what matters is how they appear together. Additionally different subfields of mathematics and physics usually adopt naming conventions.
- agumonkey 10y ago
  Took me years before thinking of variables that way and mathematical expressions are constraints over sets, formulas expressing relations of interests that way.
jasode 10y ago
>Case in point, what are b, a and c? what is their _meaning_ The "b, a, and c" in the quadratic equation are abstractions. They are placeholders for any number. That math equation is purposely designed to not have any concrete meaning for a,b,c. Therefore, asking for their meaning does't make any sense. I'll try an analogy. We can give provide analogous "computer equation" for taking the last four characters of a string: s2 = Right(s1, 4); If someone were to ask "what is the _meaning_ of s1?", it would be a nonsensical question. The s1 is a placeholder for any string. The s1 could be a domain name and you want to extract the TLD (".com", ".org", ".edu"). Or the s1 could be a date "mm-dd-yyyy" and you want to extract the "2016" from ""10-31-2016". The s1 could be a placeholder for a thousand unrelated applications. If you further generalize the "computer equation" to be take the rightmost "x" amount of characters, you'd replace the "4" with "x" like this: s2 = Right(s1, x); ... it could trigger confusion as to "what does x _mean_? And what measuring device does it come from?" The "x" is an abstraction/parameter/argument of any number. That number could be 4, or 40000. (You might be tempted to say, "but I know 'x' stands for the number of characters I want from the string!" If so, by analogy you can also say that "c" in the quadratic equation stands for the number that satisfies the equation when you know "x", "a", and "b" ... which just circles back to each 1-character variable not having a concrete "meaning." The concrete meaning of "a,b,c" in the quadratic equation depends on whether the equation was modeling something in physics, or engineering, or finance.[1][2] The concrete meaning of "s1" and "x" in the "computer equation" depends on whether you're parsing logs, decomposing dates, verifying credit card numbers, etc. The analogy above could have been demonstrated with regex such as "(.+)(.{4})" ... which would trigger questions, *"why do programmers use 1-character symbols such as '.' and '+' instead of "anycharacterm_oneormoretimes_consideredasagroup_then_anycharacters_fourtimes_consideredasagroup" ... etc tldr: computer programmers also deal with weird-looking "equations" but since they are used to them, they have the background knowledge to decipher them. [1]https://www.mathsisfun.com/algebra/quadratic-equation-real-world.html https://www.mathsisfun.com/algebra/quadratic-equation-real-w... [2]https://www.boundless.com/algebra/textbooks/boundless-algebra-textbook/quadratic-functions-and-factoring-6/applications-of-quadratic-functions-46/financial-applications-of-quadratic-functions-135-6111/ https://www.boundless.com/algebra/textbooks/boundless-algebr...

digookdigook 10y ago

This is rather poetic. There is no difference, mathematical notation is a natural language and initiated mathematicians will read it in sentence form. Reading is a process of form recognition disconnect from vocalization. On the other hand, language seems to be mostly perceived as vocalisation, because that's the form it's learned from. As anecdotal evidence, tongue is an idiom for language and people have to make an actual effort to read without vocalizatio in order to increase reading-speed. Note that your literal example does contain a lot more information about context. IE, you even omitted the quadratic equation itself. That shows exactly the problem that I thought the Parent would mean: I prefer source code in a given language, that's actually compiled and maybe even proven correct, over terse mathematical notation that leaves a lot to context, intuition and shared information. Computability Theory gave rise to Computers, not the other way around.