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Physicists avoid highly mathematical work despite being trained in advanced mathematics, new research suggests. The study, published in the New Journal of Physics, shows that physicists pay less attention to theories that are crammed with mathematical details. This suggests there are real and widespread barriers to communicating mathematical work, and that this is not because of poor training in mathematical skills, or because there is a social stigma about doing well in mathematics.
Dr Tim Fawcett and Dr Andrew Higginson, from the University of Exeter, found, using statistical analysis of the number of citations to 2000 articles in a leading physics journal, that articles are less likely to be referenced by other physicists if they have lots of mathematical equations on each page. [...] Dr Higginson said: "We have already showed that biologists are put off by equations but we were surprised by these findings, as physicists are generally skilled in mathematics.
"This is an important issue because it shows there could be a disconnection between mathematical theory and experimental work. This presents a potentially enormous barrier to all kinds of scientific progress."
http://phys.org/news/2016-11-physicists-mathematics.html
[Abstract]: Statistical Analysis of the Effect of Equations on Citations
(Score: 3, Insightful) by khallow on Sunday November 13 2016, @05:40PM
So one of the things that "lots of mathematical equations on each page" may be selecting for is poorly written physics papers.
(Score: 2) by opinionated_science on Sunday November 13 2016, @06:01PM
agreed. And for those of us with fluid maths reading skill, finding mistakes first is the usual way of reading - Does the logical derivation fit "the rules". Then "do the assumptions apply".
But it depends on the mathematics - derivations of number theory proofs take some concentration. Differential equations are fun ;-) Especially numerically, with BLAS...
But if you're going to hide bad answers, this is where things get lost on the non-technically trained public.
The general lack of numeracy , allows politicians to be hoodwinked by unknown statistics...
(Score: 3, Informative) by mcgrew on Sunday November 13 2016, @08:26PM
The general lack of numeracy , allows politicians to be hoodwinked by unknown statistics...
On the contrary, they rely on the general public's innumeracy. Example: Illinois Governor Bruce Rauner's charge that "the average state worker makes $60,000 per year" whenhe was running for office. Accurate, but meaningless. The meaningful number is the median, not the mean. The average is WAY above the median. Don't forget, mathematicians have to eat, too, and it's as easy for a politician to hire one.
Before I retired, my boss held a PhD in statistics, and I worked for Illinois. As tRUMP said, "I love uneducated voters." He would not have been elected without them, and neither would Rauner have.
We have a president who posted a fake video of himself shitting on America
(Score: 0) by Anonymous Coward on Sunday November 13 2016, @06:36PM
(Score: 1, Insightful) by Anonymous Coward on Sunday November 13 2016, @06:40PM
Well, programmers who write code similar to how math is usually written are called shitty programmers for producing nigh unreadable, difficult-to-maintain code. It's possible to understand it, but it's an unnecessary waste of time. It's laziness at its finest, but the tradition would be too hard to break.
(Score: 2) by EvilSS on Sunday November 13 2016, @06:54PM
thanks for clearing that up.
(Score: 1) by khallow on Sunday November 13 2016, @09:42PM
So using math in a math-heavy field is lazy. Man, there are a ton of lazy fucks in the field of pure mathematics then.
It can be actually. If I copy my math work directly from my notes into the computer with little to no explanation, that's going to be pretty lazy right there. The laziness here is not the using of math, it's not doing the work to make the math more understandable to the reader.
(Score: 2) by EvilSS on Monday November 14 2016, @06:53PM
(Score: 1) by khallow on Monday November 14 2016, @11:51PM
Ah, and you can state, as fact, that this is the case with every paper that the study in question evaluated then?
No. But it would be a fact that your demand would be irrelevant to my earlier observation since I wasn't characterizing papers but rather a common and lazy technique for slamming out papers which just happens to result in high math content.
(Score: 2) by EvilSS on Tuesday November 15 2016, @02:27PM
(Score: 1) by khallow on Tuesday November 15 2016, @03:48PM
OK, then you have experience in publishing scientific papers?
I even have experience in publishing scientific papers where I copied the math from my notes into the paper in said lazy way that I just described. In my defense, I was a lot younger then and didn't realize what a mess I was making or the enormous patience of my advisors. It takes a lot of learning and experience to write decent math IMHO.
Have anything to back up that argument?
Here's the abstract [projecteuclid.org] and paper [projecteuclid.org] in all their shining glory. Tell me I'm wrong. Even worse, a year earlier I had made up overheads of that work and presented those in public. That was even worse since I learned a bit about writing and presentation of math afterward.
And LaTex is a life saver here. I can't imagine how this paper would look written in Word, but it would be even uglier.
(Score: 1) by Ethanol-fueled on Sunday November 13 2016, @10:29PM
If you worked for ID and you asked Carmack to explain his fast inverse square root [wikipedia.org] in his code comments, the whole shop would have laughed your ass right out the door.
(Score: 2) by LoRdTAW on Monday November 14 2016, @05:33PM
Not too hard to grok this. The evil floating point bit level hack accesses the float memory as a long int and stores it to i. Then it's shifted right by one and subtracted from the magic number 0x5f3759df. It's then converted back to a float and stored to y. Then its off to a bit of math to take the original number (divided by two), multiplied by the square of y, subtracted from 1.5 and multiplied once again by y all as float. An optional second iteration perhaps further refines the answer. Then the result is returned. The magic number is probably a constant and easily conveyed in hex form that allows the result to properly align to the IEEE float format to avoid NaN errors.
(Score: 1) by khallow on Sunday November 13 2016, @08:35PM
So what you are saying is that the majority of physicists lack the math skills to understand their own field. Got it.
Well, you could try reading my post to see what I actual said. Got it?
(Score: 2) by JoeMerchant on Sunday November 13 2016, @08:46PM
So, in school, I spent about 10-20% of my time in math and math heavy coursework, learned some cool stuff, then graduated and went to work in bio-informatics analysis software development, which is more or less where I've been since 1990. In this relatively math-heavy line of work, I break out the heavy math tools about once every 5 years - I'd say, honestly, less than 0.2% of my work involves any kind of math more complex than a column sum on a spreadsheet. My younger colleagues shy away from the "heavy stuff," preferring to go shop for a library package that has already worked it out for them (which may sometimes be an efficient alternative to "roll and validate your own".)
Occasionally I run up against intractable math problems (care to simulate the heating at the tip of an arbitrarily bent coil of wire placed in an MRI receiving 64 or 128MHz RF excitation pulses?... nope, and neither does anyone else as far as we can tell.) Sometimes it's just hard, maybe a dozen lines of algebra - once I had to fill a sheet of paper with the equation solution (taking the better part of a full day, plus another day to find the mistake and verify the final solution was correct.) In between, literal years go by with no reason to do anything more than a summation, or possibly run a signal through somebody else's FFT library.
For all the study of math, it doesn't appear to be "where the work is at" in real life. Maybe 0.2% of the working population does heavy math >20 hours a week, the rest of us just have meetings where we talk about how to rate something 1-5 for a decision making table, even if half the people in the room don't understand the math behind the table, that doesn't stop them from voicing their opinion, at length, about how the topic du jour deserves to be a 3 instead of a 4.
🌻🌻🌻 [google.com]
(Score: 1, Touché) by Anonymous Coward on Sunday November 13 2016, @09:36PM
I reject your claim; it is usually the mathematics that clarifies the blathering prose.
(Score: 1) by khallow on Sunday November 13 2016, @09:46PM
(Score: 0, Flamebait) by Francis on Sunday November 13 2016, @10:01PM
That's really not true. Mathematics is much more precise when it comes to describing things than English is. What's more, since many people in physics are not native English speakers, using math is preferable as that's something that they've all got in common. If you want to describe the motion of particles, or forces, the natural way of doing that is via some form of mathematical notation. Doing so with English leads to a huge loss in both precision and readability.
Having lots of mathematical equations on each page for a field like physics isn't really a problem. It would be a problem for a field like sociology where there's a less precise level of understanding available.
(Score: 0) by Anonymous Coward on Sunday November 13 2016, @11:28PM
It would be a problem for a field like sociology where there's a less precise level of understanding available.
What exactly are you saying? Are you implying that sociology is not a precise science? Do you not realize that social sciences deal with actual data, facts from the real world, and statistics, not the imaginary mumbo-jumbo world where theorists posit things like "particles" and "dark matter" and then use "numbers" to say stringy theoretical things about them!
Doing so with English leads to a huge loss in both precision and readability.
This is completely wrong! The only reason that English does this is that the majority of people who speak English are idiots, idiots and Americans. But I repeat myself. Perhaps you should speak auf Deutsch, for great science! Who do you think invented sociology?
(Score: 1, Interesting) by Francis on Monday November 14 2016, @04:26AM
It's not completely wrong, you'd run into the exact same problem in German, French, Mandarin or Swahili in terms of trying to describe things in a language that's designed for communicating other things. We chose English as the standard because that was the dominant language at the time when it was standardized. It had been French, Latin, Greek and various other languages depending upon the era, but English was spread widely enough that it was standardized to. The same way that if you're a pilot, then you'd better know how to speak English.
As for sociology, no it's not a precise science and the whole idea that it is is rather ridiculous. Apart from age and a few extremely rudimentary indicators, none of it is quantitative data, it's qualitative data which gets interpreted as best as possible, but lacks a uniform measure. It's not like a mile or a KG which are defined units that can be used as such, most of the data you find cropping up in the social sciences is heavily dependent upon the conditions for replication and as such, much of the time fails because of the lack of reliability in the measures.
(Score: 1) by khallow on Sunday November 13 2016, @11:48PM
That's really not true. Mathematics is much more precise when it comes to describing things than English is. What's more, since many people in physics are not native English speakers, using math is preferable as that's something that they've all got in common. If you want to describe the motion of particles, or forces, the natural way of doing that is via some form of mathematical notation. Doing so with English leads to a huge loss in both precision and readability.
Sure, you have to keep in mind that your paper may be read by someone who can barely read English. But it's still better than solid math. Sorry.
I might add that I speak from experience here. My first math paper was utter crap. It was an interesting though relatively simple result on shoehorning the fractional part (the remainder after you subtract off the integer part) of geometric like sequences (the sequence increases in each term by a factor that is bounded from below) into a narrow slot (say between 0 and some epsilon greater than 0). I wrote it as part of a master's thesis on such things. The problem though was that it was a poorly written wall of math and had a lot of extraneous detail as well.
Sure, the person who doesn't understand English could eventually puzzle out what was in the paper, but it would have taken a while. I could do a lot better, such as taking one or two pages to describe what earlier took me half a dozen. So seriously, I believe even for people who have trouble with written English, an approach which is more sparing of math formulas would be better.
(Score: 0, Troll) by Francis on Monday November 14 2016, @04:42AM
I don't agree with that at all and decades of trying to read as various authors try to convey in English what should be conveyed in math just reinforce the notion that it's sheer madness to try and use language designed for people to communicate such ideas.
The point is, that if the math is written in a way that requires people to puzzle their way through it, then either the math was improperly written or was targeted at the wrong audience. It's not the fault of the math as a language anymore than it would be using Shakespearean prose to communicate the rules on the customs and immigration forms. One shouldn't blame English for that, they should blame it on the idiot that thought it was a good idea to use archaic words and grammar to express something that requires a lower level of English.
Same thing here. If you're going to comment on the equations, that's fine, but you're going to lose a ton of precision in doing so and if you don't, that suggest that you probably fucked up the math in some way. Either you reduced it too far, or you didn't use sensible notation during the process. Either way, that's not the fault of the math, it's an indication that the people using it didn't know what they were talking about.
Day after day, I run into books written by learned morons where they removed information by simplifying things that shouldn't be simplified. They're still mathematically valid equations, but they've removed so much of the information, that you can no longer understand it, you just have to memorize it. And that's a shame.
In this case, why on earth would anybody in their right mind throw out all the information by trying to shoehorn things into English that make much more sense being expressed using math? Right now I'm reading an engineering textbook and the author has done a heroic job of making the English comprehensible and relevant, but it's still not as good as just using the appropriate math to communicate most of the ideas he's looking to communicate.
Anybody wishing to get into a field like physics are engineering ought to be prepared for the relevant abstract thought, both in terms of reading and writing. Blaming the math for operator error is rather immature and isn't to be encouraged.
(Score: 1) by khallow on Monday November 14 2016, @09:38AM
I don't agree with that at all and decades of trying to read as various authors try to convey in English what should be conveyed in math just reinforce the notion that it's sheer madness to try and use language designed for people to communicate such ideas.
Well, I didn't say avoid math altogether. But a lot can be and should be communicated by normal written language because it's a better tool for the task than math is.
(Score: 2) by driven on Monday November 14 2016, @03:54AM
In software development, programmers use comments to clarify what a section of code does.
Then there's the school of thought that if you break your code into well-named functions and use well-named variables, comments are often not needed.
With mathematicians using single letter 'variable' names (often not even stating their purpose) and strange symbols, mathematical formulas look more like poorly written Perl code than something that is meant to be picked up and used by someone other than the author or someone trying to learn about math.
Formulas aren't even that long - why not expend a few extra letters to clarify meaning? Hard for me to believe that today's mathematical representations can't be improved upon and made more tractable to more people (including myself).
(Score: 2, Insightful) by khallow on Monday November 14 2016, @08:50AM
Formulas aren't even that long - why not expend a few extra letters to clarify meaning?
Because it means a lot more work and overhead for the researcher. In mathematical work, these symbols are used far more often than in computer programs. The researcher is trying to construct a variety of certificates demonstrating certain things and there is plenty of backtracking, dead ends, etc that aren't present in computer programs. I think it would be more like requiring computer programs to make their computations human-readable. That would introduce a fair amount of overhead.
Similarly, it generates work and overhead for any readers confirming the results of the paper. And if the researcher uses one set of symbols for research efficiency and other for discussion of the work, that's more work for everyone.
Finally, what actually is worth communicating in this way? Math is notorious for being a place where meaning creates problems rather than solves them.
A common source of new math is abstraction of a math description of some physical system. The variables and concepts to the physical system lose a lot of their meaning when so abstracted. But often phrases and variables are retained, such as with Lagrangian [wikipedia.org] and Hamiltonian [wikipedia.org] mechanics, where the labels that originally corresponded to physical parameters such as "action" get reused even in contexts where they don't make sense. Compatibility with related material turned out to be more important than a paper that was somewhat more self-contained. (I guess that's another problem with math, its concepts and variables tends to have an overly broad scope compared to programming.)
Alternately, one might wish to strip away meaning. A classic example of this is the Lorenz system [wikipedia.org], something I'm studying at the moment. Edward N. Lorenz, a mathematician and meteorologist was studying chaotic behavior of a model of weather systems he had constructed, and attempted to abstract out what was causing the chaotic behavior. The result is expressed in terms of three completely abstract functions x, y, and z of a single independent variable t (which managed to retain its meaning of "time"). Presumably, the three variables originally meant things like wind speed, temperature, or moisture content, but that has been completely stripped away.
When one assigns a meaning to variables, the reader will usually do so as well. That usually aids in understanding, but it can hinder it as well. Math is patterns promiscuously applied. If a pattern appears or is represented in a system, then the consequences of that pattern appear as well, even if no one is aware of the existence of the pattern in the system!