5 ms·

I'll disagree. I read many papers with mathematics in them, and I get a lot of the concepts but the symbology used doesn't make sense to me so its hard for me t

I'll disagree. I read many papers with mathematics in them, and I get a lot of the concepts but the symbology used doesn't make sense to me so its hard for me to understand what is exactly going on. The sentence after the equation that explains each symbol is necessary for me, and many others as well. Not everyone has taken 8 math classes to know each kroniger delta by heart.

wiz21c 5y ago
except that mathematicians like to use shortcuts notation everywhere, shortcuts that only them understand... For example P(A|B,C) ?= P(A|B;C). Moreover, mathematician seems driven by a frugal principle. They try to condense their though in the smallest number of symbols. To me it's like writing a Perl program with the shortest amount of text. Of course, the result is right, but it's super hard to understand.
- GDC7 5y ago
  Yeah, it's like there is something in their brain which differs from non-mathematicians. Non-mathematicians discover something and then want the largest number of people to understand that thing as well, and they want to be the ones explaining it and see the sparkle in the eyes of the ones receiving the information and "getting it" for the first time. Mathematicians want their peers to understand first and foremost in the quickest way possible, they then rely on 3rd parties to explain it to people who they consider "normies", they slap their name on the theorem or the demonstration and further use what they consider "subordinates" to explain it to the few "normies" who want to make an effort to understand it.
  - deleted 5y ago
    [deleted]
robomartin 5y ago
Well, musical notation looks like gibberish to someone who did not learn it. That said, I do agree with you 100% on scientific papers. Without an explanation of the formulas to cater to a wider audience a lot of papers fall into the "and then a miracle occurs" fallacy. Not because that's what they actually do. Not at all. I say this because to a large set of readers the impenetrable math has to be taken as a divine act that moves you from step n to n+1. I remember going to lunch with one of my math professors in college. He was working on his PhD and was about to publish his thesis. As we sat down to eat he was very excited as he pulled out a sheet of paper from his pocket. It had been folded 3 or 4 times. You could tell he had been carrying this thing around, folding and unfolding it, for a long time because the folds showed wear. This piece of paper was full of formulas, both sides, there was not a single blank area on the entire sheet. He unfolded it and proceeded to give me a quick talk about what he was working on. He was very excited about it and I was happy for him. And yet that entire piece of paper looked like a language from another galaxy to me. I was on my third Calculus course. I had no clue what he was talking about. Digressing a bit: To this day I remember this when helping my kids with math, science and coding. As a matter of fact, I am currently working on an explanation of exponentiation and logarithms. In both cases everything looks great if things are even multiples of the base. The minute you do something like 2*2.1 or log_base_3(35.53) you hit the "and then a miracle occurs" problem, where you have to explain a thing by using the thing ("A white horse is a horse that is white"). I've spent the last couple of days working on cleaning-up an explanation of these things that makes sense without using a miracle to get to the answer. One of the problems is that there are natural explanations for things like square and cube (area and volume), but, what do powers of 2.1 and 3.25 mean? It is interesting how things completely break down. I don't think I have found a single mathematics text that bridges this gap. If anyone has a sensible explanation of this I'd love to hear it!
- ectopod 5y ago
  You can start explaining fractional powers with roots, e.g. x^0.5
  - robomartin 5y ago
    Right, the problem is that you quickly run into the "miracle occurs" territory. The square root of a number takes us from an area to the length of the side of the square corresponding to that area. The cube root is the same for a cube. What is the 10th root of x? It's a number that, when multiplied by itself ten times equals x. OK. How do you compute this number? The best I can offer at this point is, for simplicity, a brute force search or, for faster results, a bisection search algorithm. In other words, the "and then a miracle occurs" moment is right there. The fact that I can key these numbers into a calculator and get the answer isn't the kind of explanation I want to use for my kid. I don't want to say "once you get here you pick-up your calculator", because the legitimate question then might be "If it's magic, why don't I just pick it up at the start of the problem?" To be clear, I don't mean "miracle" as anything other than "this shit is hard-to-impossible to explain or calculate by hand". That said, you could probably run through a quick bisection search by hand and likely converge on a low error answer in 2 to 5 cycles. The meaning of of the e root of b explained with exponentiation and the exponentiation is explained with the root.
    - hdctambien 5y ago
      I think the magic/miracle of math is that you can go from "real world" into "math world" then back into "real world". If a rule is true for c and n and n+1, and you can physically represent the idea when n=2 and n=3, then you can apply that representation theoretically to n>3 to understand ideas that are not easily understandable. The 10th root of x takes you from a measurement of an 10 dimensional object to the measurement of a 9 dimensional object. That's crazy, right? Without needing to "understand" what an 10 dimensional object is, you know something about it because you understand what roots mean with lower values... Of course, that doesn't help you actually calculate the 10th root of x. Is there a better way than basically guess, check, and refine? The calculator is just really fast at doing that (and only needs to calculate a relatively small number of significant digits). Sometimes that's just how math is. The only magic there is that computers are very fast at computation compared to people.
deleted 5y ago
[deleted]
Jensson 5y ago
> I read many papers with mathematics in them That is the problem, non-mathematicians usually doesn't fully understand the math they use in their papers and thus the math becomes opaque. Papers written by real mathematicians are usually much easier to read, although of course the math in them is much much harder.
I_AM_A_SMURF 5y ago
Most mathematics paper will define the symbols they use beyond the basics (and sometimes even the basics). If you are thinking about extremely common symbols then... it's like complaining that somebody not trained in music cannot read a music sheet.

wiz21c 5y ago

except that mathematicians like to use shortcuts notation everywhere, shortcuts that only them understand... For example P(A|B,C) ?= P(A|B;C). Moreover, mathematician seems driven by a frugal principle. They try to condense their though in the smallest number of symbols. To me it's like writing a Perl program with the shortest amount of text. Of course, the result is right, but it's super hard to understand.

GDC7 5y ago
Yeah, it's like there is something in their brain which differs from non-mathematicians. Non-mathematicians discover something and then want the largest number of people to understand that thing as well, and they want to be the ones explaining it and see the sparkle in the eyes of the ones receiving the information and "getting it" for the first time. Mathematicians want their peers to understand first and foremost in the quickest way possible, they then rely on 3rd parties to explain it to people who they consider "normies", they slap their name on the theorem or the demonstration and further use what they consider "subordinates" to explain it to the few "normies" who want to make an effort to understand it.
- deleted 5y ago
  [deleted]

robomartin 5y ago

Well, musical notation looks like gibberish to someone who did not learn it. That said, I do agree with you 100% on scientific papers. Without an explanation of the formulas to cater to a wider audience a lot of papers fall into the "and then a miracle occurs" fallacy. Not because that's what they actually do. Not at all. I say this because to a large set of readers the impenetrable math has to be taken as a divine act that moves you from step n to n+1. I remember going to lunch with one of my math professors in college. He was working on his PhD and was about to publish his thesis. As we sat down to eat he was very excited as he pulled out a sheet of paper from his pocket. It had been folded 3 or 4 times. You could tell he had been carrying this thing around, folding and unfolding it, for a long time because the folds showed wear. This piece of paper was full of formulas, both sides, there was not a single blank area on the entire sheet. He unfolded it and proceeded to give me a quick talk about what he was working on. He was very excited about it and I was happy for him. And yet that entire piece of paper looked like a language from another galaxy to me. I was on my third Calculus course. I had no clue what he was talking about. Digressing a bit: To this day I remember this when helping my kids with math, science and coding. As a matter of fact, I am currently working on an explanation of exponentiation and logarithms. In both cases everything looks great if things are even multiples of the base. The minute you do something like 2*2.1 or log_base_3(35.53) you hit the "and then a miracle occurs" problem, where you have to explain a thing by using the thing ("A white horse is a horse that is white"). I've spent the last couple of days working on cleaning-up an explanation of these things that makes sense without using a miracle to get to the answer. One of the problems is that there are natural explanations for things like square and cube (area and volume), but, what do powers of 2.1 and 3.25 mean? It is interesting how things completely break down. I don't think I have found a single mathematics text that bridges this gap. If anyone has a sensible explanation of this I'd love to hear it!

ectopod 5y ago
You can start explaining fractional powers with roots, e.g. x^0.5
- robomartin 5y ago
  Right, the problem is that you quickly run into the "miracle occurs" territory. The square root of a number takes us from an area to the length of the side of the square corresponding to that area. The cube root is the same for a cube. What is the 10th root of x? It's a number that, when multiplied by itself ten times equals x. OK. How do you compute this number? The best I can offer at this point is, for simplicity, a brute force search or, for faster results, a bisection search algorithm. In other words, the "and then a miracle occurs" moment is right there. The fact that I can key these numbers into a calculator and get the answer isn't the kind of explanation I want to use for my kid. I don't want to say "once you get here you pick-up your calculator", because the legitimate question then might be "If it's magic, why don't I just pick it up at the start of the problem?" To be clear, I don't mean "miracle" as anything other than "this shit is hard-to-impossible to explain or calculate by hand". That said, you could probably run through a quick bisection search by hand and likely converge on a low error answer in 2 to 5 cycles. The meaning of of the e root of b explained with exponentiation and the exponentiation is explained with the root.
  - hdctambien 5y ago
    I think the magic/miracle of math is that you can go from "real world" into "math world" then back into "real world". If a rule is true for c and n and n+1, and you can physically represent the idea when n=2 and n=3, then you can apply that representation theoretically to n>3 to understand ideas that are not easily understandable. The 10th root of x takes you from a measurement of an 10 dimensional object to the measurement of a 9 dimensional object. That's crazy, right? Without needing to "understand" what an 10 dimensional object is, you know something about it because you understand what roots mean with lower values... Of course, that doesn't help you actually calculate the 10th root of x. Is there a better way than basically guess, check, and refine? The calculator is just really fast at doing that (and only needs to calculate a relatively small number of significant digits). Sometimes that's just how math is. The only magic there is that computers are very fast at computation compared to people.

deleted 5y ago

[deleted]

Jensson 5y ago

> I read many papers with mathematics in them That is the problem, non-mathematicians usually doesn't fully understand the math they use in their papers and thus the math becomes opaque. Papers written by real mathematicians are usually much easier to read, although of course the math in them is much much harder.

I_AM_A_SMURF 5y ago

Most mathematics paper will define the symbols they use beyond the basics (and sometimes even the basics). If you are thinking about extremely common symbols then... it's like complaining that somebody not trained in music cannot read a music sheet.