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Ask Slashdot: Should More Math and Equations Be Used In the Popular Press?
raque writes "The NY Times recently published two op-eds in their Philosophy section, The Stone, discussing how Heisenberg's Uncertainty principle is abused. The second is a followup to the first. The author struggled to make clear his point and left the impression he was creating a strawman argument. In his followup he said he was avoiding equations because he was writing for a general audience. I replied to both articles, asking whether showing some basic equations would have worked better, allowing math to illustrate where metaphors struggled. Now I'm asking the same question to everyone on Slashdot. Would Dr. Callendar have been better off just diving in and dealing with Heisenberg and quantum mechanics using the tools that were developed for it?"
Probability that more maths equations should be used > 0
Betteridge's Law of Headlines says no.
Newspapers intentionally and consistently use language that does not require a master degree in English language to understand. So where is the point in writing an article that requires a PhD in physics for understanding?
Just point out the conclusions of the scientists.
You should insert just easy equations
You'll make people smarter and able to understand the subject if you explain what's going on in the example you want to discuss. That's a pretty basic idea in writing popular science.
No kidding!!! What do you say at this point?
Without math, it's impossible to convey what you're trying to convey. The press is way too dumbed down already, and many times I've read science stories that are just plain misleading as they try to simplify the message.
Putting equations into news stories means that some people won't understand them, but most importantly it will encourage some of those people to investigate further, and learn how to read equations. If there's no math in the popular press in the first place, then there's no incentive for people to improve themselves.
char*f="char*f=%c%s%c;main(){printf(f,34,f,34);}";main(){printf(f,34,f,34);}
The first article linked is a fairly good layman's explanation. It doesn't need to delve into maths. It explains it better than you did in your comment.
In contrast, your comment has an ungrammatical first sentence, fails to explain the terms well at all, and leaves the reader scratching his head even if he knows the maths already. "the sums of all of the uncertainties - or differences - in a huge pile of measurements of the position and velocity of some particle we're measuring" - what the hell does that mean to a layperson? Now you need to define what the hell all those words and concepts mean, and you reintroduced measurement when the original article took pains to point out it's not about measurement. This is a classic "explanation that only makes sense to someone who already understands it".
Also, your use of 'x' as multiply is entirely non-standard at this level, but hey.
Professional Journalism 1, Rtbinc 0
Should articles be written with intelligence and nuance when writing for a "general audience"?
But they should start with adding footnotes with references first. Most popular science articles don't even mention their sources properly, which sometimes makes it really hard to follow up on them even if you are a scientist.
Everybody not willing to understand simple mathematics (with explanations) is being willfully ignorant. There is no way to reach such people, they would not comprehend the text either...
Most ACs are not even worth the keystrokes to insult them. Be generically insulted by this and ignored otherwise.
"The author notes that an editor warned him that for every equation in the book the readership would be halved, hence it includes only a single equation: E = mc2. Early in 1983, Hawking approached Simon Mitton, the editor in charge of astronomy books at Cambridge University Press, with his ideas for a popular book on cosmology. Mitton was doubtful about all the equations in the draft manuscript, which he felt would put off the buyers in airport bookshops that Hawking wished to reach. It was with some difficulty that he persuaded Hawking to drop all but one equation.[4] In addition to Hawking's notable abstention from presenting equations, the book also simplifies matters by means of illustrations throughout the text, depicting complex models and diagrams." https://en.wikipedia.org/wiki/A_Brief_History_of_Time it may not be true as after all the book sold rather well.
You can write about the results - which is important - but you can't write about the mechanics without at least describing the mathematical concepts and their relations with physical reality. This is why it's such a problem, because everyone deduces from the results written up in the newspapers how they think the mechanics work, and of course they get it wrong because it's profoundly unintuitive.
No kidding!!! What do you say at this point?
Come to think of it, if the tendency for PR firms to arrange for an "equation for the best sandwich" etc. suggests that an equation is actually quite an easy way of getting the public's attention.
No kidding!!! What do you say at this point?
They should start by using proper units. I know the USA is not metric, so they can use feet, miles and pounds, but football fields, states of delaware and volkswagens are not proper units. (and especially Library of Comgresses)
Equations are a great way of explaining something to someone who is familiar with equations. Someone who has done first year undergraduate maths and done reasonably well at it will appreciate having an equation to explain something.
Someone who did fairly poorly at high school maths will look at an equation and say, "What???"
Take Newton's second law. You can explain it in two ways. The first:
The second:
To someone familiar with mathematical models, the second is intuitive; if you increase the force, the acceleration increases. If you increase the mass but keep the force constant, the acceleration will have to decrease to satisfy the equation. But you have to already have that intuitive grasp of what an equation means, or the first explanation is always going to be easier to handle.
Slashdot - News for Nerds, Stuff that Matters, in ISO-8859-1 Has just realised that beta makes this signature redundant
I've written lots of reports with math formulas (in Latex) where they are needed. Most, if not all, the intended readers have a Ph.D. in experimental physics or optics but I noticed that unless the math is really trivial, they will not follow. Even the slightest math supported reasoning will throw them off. That experience tells me that math for the general audience is probably not a good idea. It is simply pointless the be correct if you are not coming across. Who hears the tree falling in the forest.
The general rule regarding the depth of detail in publications should be that they need to be understandable by the target audience. If you write for the general public, then the base text should be layman style, with some pointers where to get more in-depth information for those, who are above the average and more knowledgeable in the specific field. If the target audience is academic and/or scientific community of a specific field, then that's a totally different matter, and the text should be as to-the-point and in-depth as possible, since anyone from the audience would be able to produce superficial treatment of a topic in their field, even if they are not utmost experts of the specific topic, and they'll require exact and deep elaboration of the subject to be able to judge the subtleties, novelties, benefits, etc. I'd say that's all, and it's really not 'rocket science', just spend some time getting to know who'll you'll address with your writing.
I am putting myself to the fullest possible use, which is all I can think that any conscious entity can ever hope to do.
The innumeracy of the public is at a lower level than that. This is like arguing about whether kids should be taught calculus in school when they're struggling with basic arithmetic.
What we need is not more equations in the press, but more graphs, tables, and diagrams. I can't count the number of times I've seen a journalist try to explain, say, changing poll results or the interplay between mortgage rates and foreclosures using text, plus a quote from an expert which they clearly don't understand, when all they need is a quick line chart.
I'm a college professor, and in my classes that require essays I insist that the students incorporate graphical charts, maps, and diagrams. Generally speaking, they're awful at it, but it gets them thinking about data.
Science articles, one would presume, are written for persons interested in science. The idea that there is some broad swath of persons who wish to understand quantum mechanics but stand to be chased off by a simple formula strikes me as unlikely.
If it is a problem, then the logic is the kind of the logic that will perpetuate the problem: the reason math is not as digestible to a public audience is because they're not accustomed to it, and they're not accustomed to it because the media is choosing not to present it to them.
When things get complex, multiply by the complex conjugate.
Most of those who have studied advanced math have heard of the Heisenberg's Uncertainty Principle, but not every single one of them understand it
Putting the same Heisenberg's Unvertainty Principle to the "average Joe on the street" and you would most probably get a blank stare
This has nothing to do with elitism, this is about reality
Most people simply do not have the mental capacity to comprehend the meaning of 1 + 1 = 2, and if you do not believe me, go ask the people around you, why 1 + 1 = 2, and not 1 + 1 = 3 ?
Give me a break. In the 1920s Einstein wrote a popular book about special relativity (with formulas) and general relativity for the layman. And we're talking about 2 theories which at the time were at the frontier of physics research. In the last 90 years we haven't suddenly become idiots, so if popular science books talking about special/general relativity and quantum theory (a theory 90 years old !!!!) don't use equations it is because of stupid preconceptions. I've said it before people are not idiots, they may not be specialists in physics research but you can certainly explain them the basics of 2 theories which are almost 1 century old using carefully selected formulas. Nobody goes apeshit if you write Newton's formula of gravitation, why would you go crazy for Heisenberg's uncertaintly principle ?
Why reawaken the horrible and traumatic memories of school? Well, unless you were like me who was always good at math. In my case, I would object to news stories containing more references to bullying and teasing. But I've forgiven my childhood bullies of all that. It was easy to do and I've since and I've forgotten most of it. Forgetting it was just as easy as forgetting where I buried their bodies after I took my revenge. *muahahahaha* Ok, I'll take my pills now.
It's really quite a simple choice: Life, Death, or Los Angeles.
He wrote a book. How many people bought it? How many people read it? How many people understood it? How many people skipped the math?
Absolutely not.
Wikipedia has already fallen prey to this. Articles on all these things are just dense reference manuals iseful only to graduates in their subjects rather than enlightening explanations.
They failed when those same people got full of themselves taking over the subject matter. They are as useless as a "man page" on regular expressions.
(-1: Post disagrees with my already-settled worldview) is not a valid mod option.
Equations are short hand and full of a form of jargon specific to a field, in terms of the arcane symbols used to represent a property or constant, with the explanation of what each symbol means buried in the text. They are great at condensing meaning, and allowing somebody familiar with them to manipulate them easily. But they are actually terrible at conveying meaning to someone not familiar with the field it is describing.
Often diagrams are the best way to explain mathematical concepts where possible. In the end, most scientist presents with a set of equations or concept to understand, will inevitably spend some time plotting out or trying to pictorially described what it means, to help understand it. So why not short circuit that?
Would Dr. Callendar have been better off just diving in and dealing with Heisenberg
Maybe, but I can't wait to see how Hank Schrader is going to deal with Heisenberg.
Also if he was diving wouldn't that mean that his position on this wouldn't be clear?
M = h - c
I get the point - equations are meaningless without surrounding context
Most of those who have studied advanced math have heard of the Heisenberg's Uncertainty Principle, but not every single one of them understand it
Putting the same Heisenberg's Unvertainty Principle to the "average Joe on the street" and you would most probably get a blank stare
This has nothing to do with elitism, this is about reality
Most people simply do not have the mental capacity to comprehend the meaning of 1 + 1 = 2, and if you do not believe me, go ask the people around you, why 1 + 1 = 2, and not 1 + 1 = 3 ?
Give me a break. In the 1920s Einstein wrote a popular book about special relativity (with formulas) and general relativity for the layman. And we're talking about 2 theories which at the time were at the frontier of physics research. In the last 90 years we haven't suddenly become idiots, so if popular science books talking about special/general relativity and quantum theory (a theory 90 years old !!!!) don't use equations it is because of stupid preconceptions. I've said it before people are not idiots, they may not be specialists in physics research but you can certainly explain them the basics of 2 theories which are almost 1 century old using carefully selected formulas. Nobody goes apeshit if you write Newton's formula of gravitation, why would you go crazy for Heisenberg's uncertaintly principle ?
The cynic in me observes that in this country, every issue is expected to divide into 2 diametrically-opposed sides. Such as, for example, the party that eats their own babies which is the exact opposite of the party that eats everyone else's babies (yes, those are exact opposites and you can only chose one. Snarf).
Furthermore, in adherence to this post-Einstein Weltanschaung that everything should be as simple as possible, then made simpler, everything must be expressed in short sound-bytes suitable for framing on bumper stickers.
So shouldn't E=mc**2 be short enough? No, because statements like this require context. If you don't know what E, m, and c represent, it's just another math equation. And context won't fit on the bumper sticker.
I've actually had people tell me that no one but Einstein is smart enough to understand Einstein. The Gods themselves...
He wrote a book. How many people bought it? How many people read it? How many people understood it? How many people skipped the math?
Considering it has been in print ever since, I'd say it sold and continues to sell pretty well.
You can't write about quantum mechanics without equations - it is NOT an intuitive field.
The cat wants to know if he can come out of the box now.
Are you suggesting that we hide maths entirely? Look, there are some things I maybe understand a little, many things I don't understand, and probably an infinite amount of things I don't know about. Just because I don't understand something doesn't mean you should hide the problem from me. If maths is the best way to understand something then it should be used. If an article refers to data or a paper then it should be referenced. If you hide things from me (lies to children?) then I have to repeat the work of others to come to the same result. That is called a waste of time.
You, and I, (if you and I exist) are in a situation where the supposed greatest minds of our race understand maybe 2% of the rules. Probably far less. Although it is far more comfortable to sit in frount of media, dealing in made up social structures, assuming that what I can see is real, pretending I know it all and living in a fantasy land. I would quite like to have an inkling of what I don't know. It makes me humble, and it makes me careful.
The map is not the terrain. The rules are not the reality. Shine me a torch to see. And if it is dark, tell me of the possibilty of light.
I reserve the write to mangle english.
I think that graphs are often quite misleading. Especially when they are used to show statistical information. You can make very different graphs from same base data. One chooses the graph trying to get best propaganda value.
That is why we have the phrase "Lies, damned lies, and statistics"
My (48-year old Thai) girlfriend starts work at 6am and gets off at 6pm. She insists that means she works thirteen hours a day. It is amazing how incredibly dumb the average person is.
The Internet was invented at CERN to share research data among atomic scientists. Today the biggest use of the Internet seems to be Facebook.
The average IQ is supposed to be 100; until I moved to Thailand I had probably never even MET a person with an IQ below 110. Theory? Equations? Try "Unable to subtract 6am from 6pm". Science has all along been faced with the necessity of publishing conclusions, because the average person cannot comprehend the data or the formulas. Atomic science was ignored until Hiroshima; since then it is observed but rarely undrestood.
...but /. doesn't support math markup.
In most contexts this is too true, and quite sad. However, if you aren't allowed to tell a story "according to quantum mechanics", you have no chance of explaining the functioning of the ordinary objects all around us, like lasers, LEDs, microwave ovens, fucking magnets, superconductors, sunshine, and many others. The real problem is that "according to quantum mechanics" has been so abused that people reflexively glaze over when they hear it. That abuse has made the world stupider and sadder, and undoing the damage is a valuable endeavor.
Graphs are very helpful in really conveying what is going on. What we need more in discussions of politics is facts and many facts are about numbers. When discussing who has the right model of the US economy you really need to think of it scientifically. Each model is a hypothesis that needs to be tested. Economics is about aggregate behavior and so it's really a statistical statement. Yes the models are equations and those are nice to show too. But you need to show graphs. Folks who are not innumerate often prefer for example what Nate Silver put on fivethirtyeight.com to talking heads on TV who use neither equations or graphs. Many folks I know prefer Krugman's blog http://krugman.blogs.nytimes.com/ to what makes it into his columns in the Times.
If you can't show pictures of aggregate behavior you can only tell stories. Those stories can tug at heart strings and motivate people to feel strongly about an issue without really understanding the whole picture. That's one of the problems with our political discourse.
to the name "quantum mechanics" and probably figure that it is a guy who uses a wrench to do something on a car. "Heisenberg" is a guy who cooks blue meth on TV using methyl amine instead of the usual Nazi method.
You want to put math in newspaper articles? That would first require that journalists and editors understand the math. Journalists in the US generally can't differentiate between news and the crap they report on as if it were news (who won on American Idol, etc.).
One should bother because pandering to the lowest denominator will ensure that most will meet that expectation.
There is a range of happy media between a wall of mathematical formulae and proofs and an awkwardly written, purely textual interpretation. Not everyone will have a full (or even good) comprehension of the meaning, but those willing to be challenged will have something on which to proceed.
Those who don't care or who like pap can just move on to the latest on Kate and William (who, I believe, just had a baby or something).
Great minds think alike; fools seldom differ.
Didn't Arthur C Clarke have this argument with his publishers? Every equation resulted in a 80% reduction in audience?
Something to that effect.
.
To certain groups of people. I also doubt that many people truly understood it.
Filthy, filthy copyrapists!
Most people simply do not have the mental capacity to comprehend the meaning of 1 + 1 = 2
I work with integers modulo 2, you insensitive clod!
SJW n. One who posts facts.
And of course, once you get back to hardcore dynamical systems, qualitative reasoning tends to resurface due to the inability to analytically solve things.
John_Chalisque
Indeed. It's also interesting to note that Einstein's original papers are eminently readable to the Layman, compared to the kind of papers we see in journals today. Perhaps that's due to the complexity of the mathematics now advanced at the bleeding edge, or perhaps it's because journals try to be even more economical with space than they used to be. I don't know.
In my experience, the concept of entropy gets abused a hell of a lot more than the Heisenburg uncertainty principle.
+1 for making good use of the word Weltanschaung.
I do not think the original article was a success for various reasons. It is not easy to explain quantum mechanics convincingly, and I don't think the lack of equations was a main weakness. Those of us who are happy with equations with Hamiltonian operators and eigensolutions probably understand the uncertainty principle too. Those of us who have not touched serious maths, or have done it too long ago will be made to feel stupid rather than being helped.
I think what the article needs was good pictures. How about...
A picture of the Young's slit experiment. A light wave goes through two slits, and interferes with itself. You get fringe patterns. You can calculate the fringe patterns using classical physics.
A picture of the Stern-Gerlach experiment. An electron beam is split into two and interferes with itself. You get similar fringe patterns. What, what? This works with electrons? Yes, it even works with substantial molecules such as buckyballs. In fact, if you did your Young's Slit experiment with a very dim light source and a long integration time, you would be passing photons, one at a time, through the apparatus.
So, when a particle interferes with itself, does it go through the left slit or the right one? Some people say it goes through both, but it doesn't, really. The wave function, which we can calculate but we can't measure, may go through both slits in some senses, and determine the fringe pattern. If we install a detector that can tell us the electron is going through the left slit, or going through the right slit, then the electron goes through one slit, and we do not get the interference pattern. We can know which slit the electron goes through, or we can predict the interference pattern, but we can't do both.
A picture of a wave packet plotted in ordinary space, and in frequency space.
There is nothing magical about the observation, itself. The idea that being observed changes the states dates back to an old and rather unhelpful thing called the Copenhagen model. A better approach is to say that we can measure some property of a particle wavefunction such as the position, or the momentum of the particle; but in measuring the position we lose the ability to also measure the momentum, and vice-versa. In this case, the width of the wave packet determines how accurately we know where the particle is at the time of measurement, while the width in frequency space determines how accurately we know the momentum. Our measurement will tell us what the wavefunction was like at the point of the experiment, but nothing else. This is one form of the Uncertainty principle, but it can be applied to other measurements too.
See, it can be done. If you don't get it, don't worry: small things and quantum stuff are pretty weird.
Most literate people could probably handle arithmetic, fractions, simple exponents, some basic geometry, and linear equations.
However, I would not expect a general-audience article to feature calculus, statistics (beyond references to the mean and median), complex algebra, differentials, etc. As in, everything past pre-algebra class is sketchy, at best.
But algebra beyond linear equations, any kind of complex geometry (beyond rote formulas), calculus, just about anything with a sigma symbol in it, etc. I'm a Computer Engineer, and I don't remember how to do any of that stuff. Format of an equation describing a parabola? Method for computing integrals? How to calculate Standard Deviation? I've forgotten it all; it was 15+ years ago, and has no relevance to my day-to-day life. I could probably pick it up again relatively quickly if I needed to (okay, except for calculus and linear/diffEq; I sucked at it even at the time), but yeah, my eyes would start glazing over any article that relied on my understanding of even moderately complex math.
Nothing is hidden from you. You have Google. When I wanted to understand what Yang-Mills theory was, I went to Wikipedia. Finding that impossible to understand without knowing what a Gauge Theory was I hit another link. This continued on for some time and now I'm Rouse Ball Professor of Mathematics at Cambridge University.
But some learned wondrous things. And used that to go even deeper. Isn't that what education and learning is all about?
If it appeals to enough groups to stay in print, that's a fair number.;
I read the OP's letter, and while it was a great explanation of the actual details of the uncertainty principle by going over what the different variables meant, it didn't enhance my understanding at all. (Not least of all because it left out units.)
It stated the principle, and gave it's exact formula, but didn't tell me why it was true; it said it just was, and that was final. The NYTimes article explained WHY you can't measure both location and velocity simultaneously, and how this does and does not have application in our day-to-day world. The detail that minimum uncertainty is confined to the value of the Plank constant (especially when no units are given) is utterly irrelevant to somebody reading a general-interest science article.
Because if he doesn't cite the math not even the people that know the subject will know if he's right or wrong.
A big problem with "expert opinion" in the press is that they never have to substaniate their opinions. They instead make very vague arguments and say they would get into it further but not in the laypress. Then they fail to follow that up with any further publication in the specialized expert press where all readers could be assumed to understand the subject.
That needs to stop. Either cite your opinion with enough information to know whether your argument is false... OR don't do it.
I've decided to stop wasting my time responding to AC trolls/sockpuppets... so if you want a response from me... login.
Equations are just a way of expressing logic. Well thought through and logically written science articles aren't particularly common in the mainstream media, with their love scare stories, etc. I think a vital first step would be to improve on the quality of the in general articles and guide the reader through the scientific process. Once they've nailed that (if they every do) the presence or otherwise of equations is hardly worth worrying about.
soylentnews.org
If someone has an axe to grind, it's easy to make graphs lie. Lying with inferential statistics is a bit more involved, so that gets held off until third year. (No joke, I had a research methods assignment that required me to formulate conclusions then generate a dataset to support them.) But when you legitimately want to understand what's in data, or explain it honestly to someone else, the right visualisation beats statistics every time. Humans are pattern detectors, graphs contain patterns, statistics are just numbers. If you can't see a finding in the visualisation, and you have to rely on a statistical test to demonstrate it, there's a high risk that it's not really there.
In the last 90 years we haven't suddenly become idiots
Umm...Look around you.
When Fascism comes to America, it will call itself Anti-Fascism, and tell you to give up your guns.
The problem with the original article was that the writer asserted effect for cause: ..."
"....Why exactly is the uncertainty principle so misused? No doubt our sensationalist and mystery-mongering culture is partly responsible.
No, we have a sensationalist and mystery-mongering culture for the same reason we have superstition: fundamental human ignorance, and a failure of the educational system.
It's part of (I believe) a basic function of the human brain to try to organize and explain the environment around them. Lacking a known understanding, this drops to the default state of 'make shit up that reasonably fits the observations'.
Of course, whether one 'gets' the uncertainty principle may or may not be considered fundamental science education; I'd rather argue not. Nevertheless, the point is that with a firm grounding in basic sciences, EXPLAINING the uncertainty principle should be reasonably possible.
To the point of the poster, I don't believe 'equations' would have really made a difference in the presentation. I agree with the article's author that "measurement" is not intrinsic to the uncertainty principle, and in a sense it confuses it by getting 'down in the weeds'.
In my experience - and I'm hardly science-illiterate - equations 'lock in' relationships and are absolutely necessary for understanding, but equations are rarely useful in EXPLAINING something in general principles. In the same sense: explaining a game is usually is easier than throwing a rulebook at someone and telling them to "figure it out"
-Styopa
We don't expect journalists to write articles only in Basic English. If someone were to profess that they had never heard of Shakespeare, or didn't know what a metaphor was, we would rightly judge them as being ignorant, or at the least, highly under-educated. Yet, apparently, balking at the simplest of equations is perfectly acceptable.
It's no wonder that we have such shallow thinking, such an abysmal and superficial political discourse, such a disengagement with the notions of science and society, when everyone is given a free pass when it comes to mathematics and logic. Put equations in your writing. Judge those who complain about 'math'. People who are unwilling to think can barely be counted as citizens, having abrogated a fundamental and necessary duty.
Regular ignorance can be cured. Wilful ignorance is a blight. We need to demand better of our peers.
If I were to stand outside the universe and observe it then 1+1=2 would prove to be false being that matter is equal to energy. Therefore there is no two of anything--if you really want to be pedantic. It is only a *fact* in our current context of observation.
I object to power without constructive purpose. --Spock
But I want to be in the party that eats any baby.
"Lack of speed can be overcome. In the worst case by patience." --Znork
The author struggled to make clear his point and left the impression he was creating a strawman argument
Strange - I found his arguments (in the first article, didn't read the second) quite straight forward, and I feel that adding equations would only have obfuscated matters. Most people don't understand equations and inequalities or their specific significance, and that goes for a lot of well-educated people too. The significance of Heisenberg's inequality is that you can use it in quantitative calculations when you test your theory, but it does not in itself add much to your intuitive understanding of the principle.
The problem with the article IMO, is that the subject really does require a reasonably strong background in experimental physics. You need to know something about how experiments in particle physics are conducted, how the results are calculated, etc, before his arguments fall into place.
Indeed. It's also interesting to note that Einstein's original papers are eminently readable to the Layman, compared to the kind of papers we see in journals today. Perhaps that's due to the complexity of the mathematics now advanced at the bleeding edge, or perhaps it's because journals try to be even more economical with space than they used to be. I don't know.
Be careful, they seem readable but they're full of subtilities (and in some places even contain errors) especially his 1905 article on the Electrodynamics of Moving Bodies.
And furthermore while they "are" readable to today's audiences because we have almost a century dealing with special relativistic phenomena (it has even entered popular culture) it was not so at the time.
Take that into account.
More equations would certainly be a good thing but the general populous simply doesn't understand them. There's a quote from Hawking concerning 'A Brief History of Time':
"Someone told me that each equation I included in the book would halve the sales. I therefore
resolved not to have any equations at all. In the
end, however, I did put in one equation, Einstein's famous equation E=mc^2. I hope that this will not scare off half of my potential readers."
My suggestion for online publication is to include Starship Troopers style "would you like to know more" links as sidebars seldom work on phone-level hardware. In a print article you could include an 'in depth' url.
Ever notice that Cobra Commander sounds an awful lot like Star scream?
The first time I saw some advanced mathematical equations, I said "what the f*ck is that jibberish?" I knew at least that it was a type of math I never saw before, and quickly became obsessed to find out what it was. I proceeded to copy a whole bunch of it onto my notebook cover. My Vo-Tech Electronics instructor informed me that it was "calculus," and gave me an introductory text. After struggling a bit to get it, I finally began to understand derivatives, and proceeded to obsessively hand differentiate pages and pages of expressions the hard way, by taking the limit after algebraically manipulating the expression substituted into the fundamental definition of derivative. Then I proceeded to work through all the standard derivative form proofs. This was while being a stoner, and coming darn near dropping out of high school. Finally, my maturity caught up to my inherent potential after age 21, and I was able to succeed at college after the 3rd try, and land a respectable career as first a Chemist, then a Laser-Optical Technologist, then finally an Electronics Engineer.
The ability to learn calculus on my own planted a crucial seed of confidence in a person who had little self-esteem. This seed would later blossom into a strong autodidactic tendency which was a major factor in helping me get my act together.
Point being, you can never predict what will inspire people to discover something good about themselves which may ultimately lead to a contribution to society. So it is better to just let them have the truth.
Also, ignorance is not knowing that you don't know. At least if they are shown the equations, they will realize that they don't know what the heck it means. If that disturbs the egos of 0.0001% into wanting to learn something, then that is good.
Finally, raising a child has taught me that people behave according to the expectations placed on them. Within the constraints of their inherent ability, of course. But even that is somewhat plastic! I'm convinced a large element of our societal troubles stems from attempting to absolve people of responsibility for themselves.
1) You use no math. This conveys no information to those who might actually take something away from an article, while giving the masses a fluff piece which at best make them think they know something about the topic.
2) You use math. Now you can convey something meaningful to some part of the audience. You'll turn off some people too, but at least they'll realize they don't actually understand it.
One is better for sales, Two is better for humanity.
A good book to read on this topic is David Bodanis's E=mc^2,
"A biography of the world's most famous equation"
It's not just another Einstein book. It's actually about just the equation and its life.
The author gives examples of how printing houses using different equation notation were like Microsoft, driving out the competition for the standard.
All manner of symbols were used for math, some examples:
e================== mc^2 .aequs. mc^2
e || mc^2
e -----------> mc^2
e
e ][ mc^2
Anyway, yes equations "can" be nice too look at in mainstream media. :P
Only to show a simple proof or to inspire a reader into further learning.
Of course, if it looks like spaghetti to the masses, then maybe the publisher went too far
Regardless, wasn't Einstein known for explaining complex concepts in terms that even the non-scholastic could understand?
Don't think he used any equations to describe relativity to them.
In fact, Einstein was not even a good Mathematician, iirc.
Many people not particularly interested in science have some passing interest in what scientists have found, which is what the popular press is often going for. Less "how does quantum mechanics work?" and more "how did humans evolve?", "does [X] give me cancer?" and "what is anthropogenic global warming?".
10 PRINT CHR$(205.5+RND(1)); : GOTO 10
An introduction to Calculus from an MIT video series.
The first video requires so much previous knowledge to follow. The average person would have no idea what they were saying. And this is "Introductory" to the basics for what is being discussed in the article.
I only look human.
My mother is a halfling and my dad is an ogre, so that makes me an Ogreling
-- Stephen Hawking, "A Brief History of Time"
No, 1+1=2 has absolutely nothing to do with observation (other than that the concept of numbers originally was invented to capture the observed behaviour of things). Numbers are abstract concepts which stand for themselves and are independent of anything you may or may not observe. Even if we find out that there's no physically existing thing which exactly corresponds to the numbers, the numbers still obey the same laws. For example, I'm pretty sure that we will never find anything in the universe with the cardinality aleph_omega, but that doesn't change any mathematical insights we have about that cardinality.
Can we do something like "Holy shift! Look at that asymptote on that mother function!"
Its kept me from buying Penros's "Road to Reality" and Susskind's newest pop physics books. And I have a PhD in a physical science.
The exceptions seem to be books about mathematical philosophy or tricks.
Math is a language of its own. putting the equation in an article is fine as long as its something that would be understood. We use words from other languages all the time in English,
First, Einstein wrote a larger equation in his original 1905 paper including a momentum term.
Second, the derivation of the equation is as fascinating as the what the equation implies. It is derived computing energry with Lorentz contractions. Only high school algebra and physics needed - no calculus. But adding very deep physics intuition which eluded two centuries of previous mathematical physicists. The intution is that holding the universe to a speed limit says rest mass equals energy.
99% of the people reading the news won't understand it, so you are not benefiting anyone. It's no like you are going to educate people simply by showing them more math in news reporting. Its not like showing eco Alarmists the math of how the sun is outputting more energy at its peak in a 1000 year cycle is going to convince them that the sky isn't falling.
BTW, Dumageddon has already started and will not be saved by putting more truth into news reporting. The Roman Empire fell because the weak, lazy and stupid overpopulated and grossly outnumbered the philosophers and scientists who could not save them.
When in Rome...
I haven't thought of anything clever to put here, but then again most of you haven't either.
"This rock somehow finds the ideal path to roll down to the bottom of the hill, out of all possible paths! It must be using quantum superposition!"
Indeed - addition was the foundation of mathematics and was established as a general solution to the a priori knowledge gained from counting - I count pile A as having 3 things and pile B having 5 things, and if I count them together I always get 8 things. Eventually we abstracted that knowledge away from the particular things we were counting, and later came up with shorthand notation for long repetitive sequences of addition (multiplication and exponents), but that knowledge comes from the basis of mathematics as a model for the physical universe, not from any sort of provable theory. Okay, there are proofs that 1+1=2, but they're typically either comedic exercises in circular reasoning or part of a proof that Axiom Set B is a superset of Axiom Set A (which along with proof that A is a superset of B will prove that your alternate set of seemingly ridiculous axioms is logically equivalent to one of the broadly accepted sets)
Your apple example is fundamentally flawed though - you can't separate an apple into zero parts - it starts as one part and that number can only increase as you divide it. To separate it into zero parts you would have to remove everything *else* in the cosmos so that the apple is no longer a thing separate from cosmos but instead defines it, which is about as close to infinity as you're going to get.
--- Most topics have many sides worth arguing, allow me to take one opposite you.
Even standard mathematical notation is ambiguous. You can take the same math describing the same relationship, and publications from different fields will use entirely different notation and conventions. For that reason I prefer to convey mathematical relationships using code, whether it is matlab, c, c#, or what have you, all of them can be unambiguously interpreted by a machine. Even the best math paper cannot be parsed by a machine. I sometimes use math notation as a quick sketch on a whiteboard or an IM to someone to say "do something kinda like this but think it out", but if I have already thought it out, I put it in code so it is absolutely clear what I mean. I think hard math, even abstract math would benefit from using a computer language instead of math notation, its old and flawed and not as universal as people like to think. Even if the code isn't in a language you know, the syntax is clearly defined somewhere. If I read a paper in the journal of applied dendromorphology and they re-derive stokes theorem (and try to patent it) and have little tick marks everywhere, how am I supposed to know that "everyone uses those for time derivatives here! what else would you use"? You laugh, but I have seen stranger stuff, much stranger.
refactor the law, its bloated, confusing and unmaintainable.
But I want to be in the party that eats any baby.
doubleplusungood. There are only TWO parties. They are 100% opposite of each other. There can be nothing else. There is nothing in between. There is no outside position.
You are obviously mentally deranged. Stay where you are. MiniLuv will be along for you shortly.
But, in practice the press is quite happy using the dumbed down mass-appeal approach mixed with sensationalized and outright false representations of the truth. An equation would just get in the way.
I swear to God...I swear to God! That is NOT how you treat your human!
The universe has a limited resolution and the collision detection sux at small scales. As usual, bugfixes are not forthcoming and there will be no refunds.
The level of math in "general" media is a measure of the anti-intellectualism of a culture. In a highly anti-intellectual culture, more equations are a waste. Don't try to teach a pig to sing. It wastes your time and annoys the pig.
The only thing worse than leaving out an equation that will help make your point is including one where it does not. With the latter you either waste time explaining what the equations mean (which takes you away from the thrust of the argument) or lose your audience who stop trying to follow the rest of your argument.
Here the main point of his article is that the subjective nature of collapse that is inherit in the Coppenhagen interpretation is not the only game in town, so people are incorrect when they present this as a necessary consequence of QM. How would talking about equations help make his case?
Happy people make bad consumers.
Come on, it is just a off-by-one error, which is common even in software written by above-average-smarts-persons.
And it is definitely smarter to write a bill for one hour of work when you worked from 6am to 6am than to go for no compensation.
Hey don't blame me, IANAB
Sorry, was meant as a reply to:
"My (48-year old Thai) girlfriend starts work at 6am and gets off at 6pm. She insists that means she works thirteen hours a day. It is amazing how incredibly dumb the average person is. "
Evidently I'm too dumb to follow a thread on slashdot.
Hey don't blame me, IANAB
> This is like arguing about whether kids should be taught calculus in school when they're struggling with basic arithmetic.
It's funny that people who struggle with basic math in school have no problems doing calculations with money or baseball statistics.
It really says to me that the approach is just wrong.
Just show any only mildly complex equation with big Sigmas and function symbols and even just one derivation... To an alien. Now, imagine how much they're going to have to learn just to understand that bullshit -- even if they've already mastered all the verbal and written languages of Earth!
If only there were a more verbose system whereby more friendly names could be given to the symbols,
like, "let a equal 10. loop while( a is not equal to zero ){ doThingListedElsewhere() }". Oh if only we had solved this damn problem ages ago with almost EVERY computer programming language in existence.
The answer is to teach a simple (possibly scripting) language like JavaScript, or C, etc. in elementary school IN MATH CLASS. Though not the optimal choice I would vote for JavaScript because its a language every person has the ability to use on the data they most frequently interact with -- The web / HTML.
When I was a pre-teen child, like many others, I taught myself computer programming. I was making games, and spreadsheet software, and even selling them on Compuserve before highschool. Over one summer I independently invented trigonometry. The online help didn't say what SIN and COS functions were used for, and I was trying to find the angle between two points relative to the pixel grid, to turn an enemy ship towards a player -- I needed an angle to pass into the ROTATE( angle ) function before drawing the ship's lines so I made a "slopeRatio(x1, y1, x2, y2)" function that performed better than the built in SIN function because of wasted RAM with my extensive lookup table, and limited required precision, and I returned angles that didn't require multiplying by Pi... That opened the door for many other mathematical discoveries, like distance between points, 3D transforms and rotations, etc.
At the start of the 7th grade when they were trying to re-teach inequalities and order of operations (which I had mastered in 3rd grade in front of an amber screen), I proudly showed my 3D distance formulas to my teacher. She was dismissive and said, "That's nice, we'll cover Pythagoras in another grade, did you do your homework?" NO. THAT was my home work, not some worthless list of add/subtract/multiply/divide to perform by hand -- I INVENTED Trig by myself. She had nothing to teach a child!? I am not gloating, I am pointing out how trivial these revered mathematic discoveries are, and you'd know this too if you ever had to invent any of it yourself. The "amazing" discovery of ratios of the sides of triangles was OBVIOUS to a 12 year old child... There is no such thing as genius, given necessity humans invent, or re-invent as the case may be -- It's not hard, we all do it all the time; Aside: that's why no one searches software patents to use in the PTO database: It's faster to re-invent and yields a more tailored result!
With the revelation that there was a world of mathematics I had mastered parts of myself, I tried not to re-invent the wheels... ...", or ... }", etc. then as a middle schooler I could have picked up any mathematics book and applied its knowledge. Indeed, once I forced myself to absorb the symbols meanings and map them to C or BASIC I tackled Calculus... Instead of being awestruck at the "elegant genius" I thought, "That's It?! That's what everyone jokes about being so advanced?! I've turned curve equations into
I could have saved over a week of summer if I'd have known about c*c = a*a + b*b; instead of deriving it myself. So, I tried cracking open a mathematics book to learn more of the math that I was discovering myself already. However, in place of a For Loop, there was a Sigma Symbol... I didn't understand what I was looking at. Had the equation been verbosely explained in English I would have grokked it immediately since I was already using all of the principals myself. Had there been some simple pseudo-code saying "Do this N times:
"var a = 10; while( a != 0 ){ a = a - 1; someFunction();
its fine (eg. provide equations outside the main text in a separate background/proof box), generally a little more facts and less blabla would be very healthy to many articles (esp. in philosophy). At least I personally always aim for most clarity in fewest words (as fewer words reduce the possibility of making mistakes or the appearance of making mistakes because of bad and ambiguous phrasing eg. in two different parts of the text).
The simplest way to explain the uncertainty principle is this: if you have a wave train of finite length L, then the uncertainty in the wavenumber is at least 2*Pi/L. To see this imagine (or draw) a wave packet which attenuates to zero at either end (like an infinite wave convolved with a Gaussian). Now count the number of waves in the interval L - not so easy, is it?
Mathematically, one would Fourier transform the wave to obtain its frequency (the FT of the wave is a delta function, one point exactly at the frequency of the wave). But the FT of the wave packet has the delta function of the wave, convolved with the FT of the Gaussian - which is also a Gaussian. This leads to a Guassian in frequency space, and thus an uncertainty in the frequency of the wave packet. This type of uncertainty is a property of all wave-type phenomena, from sound waves to probability amplitudes.
Indeed, this is how Feynman treats the principle in Vol III, Ch. 2 of his mighty lecture series.
.: Semper Absurda
After the revolution, the moderates like you will be first against the wall.
Is this a serious question? Would you post Egyptian Hieroglyphic to illustrate some important fact about Egypt 3000 years ago? There are very few Math equations that people understand intuitively and they usually go something like this 5 + 3 = 8. Mathematicians will eat this stuff up. Physicists will appreciate it. Maybe some other math nerds might like it but in the end what will happen is the collective mass of humans will not even bother to shrug their shoulders before they move on.
I love big math formulae and I love equations in stuff but I realize that I am kind of a big nerd that way and the Gods honest truth is that I don't understand most of what I see. I guarantee that not only will most NY Times readers not understand what they are seeing, they will stop reading at that point ant move onto the next article.
Beware the wood elf!!!
It was a long sequence of people standing on the shoulders of the midgets who came before them. Honey Boo Boo could not appear on the Discovery channel until society was ready for it.
I'm an equal opportunity consumer. I HAVE NO SHAME.
"Lack of speed can be overcome. In the worst case by patience." --Znork
The paper on special relativity is fairly readable. The general relativity paper is practically illegible to the layman, requiring tensor mathematics that are usually not taught until the later stages of a physics degree.
He did, however, try to make it more generally accessible, at least to the determined student. This paper is pretty amazing:
http://en.wikisource.org/wiki/The_Foundation_of_the_Generalised_Theory_of_Relativity
One of the prime edicts of journalism is that you write for your audience, at a level your audience can understand; if you put math in it, less than 1% of the people reading the article, even in the NYT, are going to take anything useful from it besides whatever claim the headline or opening paragraph asserts.
In general, this means that for reporting intended to be consumed by the masses - as opposed to that published in specialized industry journals where certain assumptions can be made about the reader's education level - we write at a 9th to 10th grade reading level. There was even a small amount of noise a while back about one of Obama's speeches that was written even further down at about an 8th grade level.
In effect, this means no, you don't publish articles in the NYT or even WSJ that rely on what is, even for most college-educated readers, NP-hard mathematics that will make no sense to most readers and do absolutely nothing but confuse everyone else, thus failing to communicate the ideas the story is trying to convey in the first place and defeating the purpose of having published it outside of academic journals. You publish in the NYT or the like to reach and spread your message to the widest possible readership, not to reach the handful of specialists in your field who understand the math in question. He's trying to educate people and get them to think, sure, but that doesn't mean that he realistically expect any non-trivial percentage of the intended audience to possess the education or background to be able to make use of anything but generalities and concepts, as opposed to the fine mathematical mechanics underlying his assertion.
I'm better educated than most of my peers - in general, anyway - and quite literate in scientific theories and principles, but I'm also not an engineer, physicist or mathematician, and if you write an article that relies high-order maths to explain its premise, not even I am going to get anything but the gist: I most certainly am not going to grok it any better for the inclusion of math. Of my group of friends, peers and co-workers, only a very small portion of even that bright group of people would benefit from it, at which point you're talking about a readership that is significantly less than 0.25% of the population.
Q.E.D., no, articles written for general or popular consumption that are not inherently targeted at a narrow readership with relevant expertise should not be founded or premised upon the use of math to explain or convey concepts.
"Inveniemus Viam Aut Faciemus" 'We will find a way... Or we will make one!' --Hannibal of Carthage
But -1 for misspelling "Weltanschauung".
The Tao of math: The numbers you can count are not the real numbers.
When I said "geometry" I meant basic area and volume for 3 and 4 sided polygons, rectangular prisms, plus circles and spheres, along with remembering what a right triangle is. Not anything dealing with trig, proofs, more complicated polygons, etc. I went over this stuff in 6th grade anyway...
My upper limit would probably be 8th-grade algebra, along with a smattering of trig. Conic sections, geometric proofs, most of trig, calculus, stats more complicated than "calculate a mean and median", Linear/DiffEq... fuggedaboutit.
I disagree. Some math concepts are deep, but not Pythagoras. Probably the top 5% of high school graduates understand it, and the only reason the majority of the other 95% don't is that they haven't really tried enough. You really can't understand this animated GIF?
You're talking about mathematicians, who have decided that they will be devoted working with math more than any other field, and you think they don't understand? I can't imagine a single mathematician who can't understand Pythagoras.
And long division -- you don't understand why the numbers line up? How it works? I certainly look down on you for not understanding at this moment, but even then I bet if you thought about it for a bit, you'd understand. It's the decimal system -- meaning that the four digits ABCD represent Ax1000 + Bx100 + Cx10 + D -- and the distributive property of multiplication/division over addition/subtraction.
I can't imagine anyone STARTING to learn to become a mathematician without understanding long division (yes, I mean really grasping it, not just how to write the numbers), much less having become a mathematician.
404555974007725459910684486621289147856453481154 in hex is "You sank my Battleship?"
[GPG key in journal]
Copy/paste gets me every time.
As far as I know, she, like most people in Thailand, get paid by the day, not the hour.
Americans are repulsed and terrified by arithmetic. Forget about math. Won't happen. Readership would be lost. As far as science or math goes, most people in this country would rather be titillated by the mind-boggling physics explanations on shows like "Fringe" ("Time travel should be relatively easy to understand, Olivia. It's just like lassoing a calf, where the cowboy is a particle accelerator, the calf is a magnetic bottle of entangled positrosn, and the lariat operates in a way analogous to the Arrow of Time. Look at it that way, and there's no question that you could kill your grandfather before you were born.")
Idiot 1 + 1 == 10
Over and over in the press, it is statistical inference that is botched. In the area of medical developments, stories are given coverage that this or that breakthrough has been made when about half way through the story you find that the sample size of a study is very small. Or politicians make some well-known slight of hand with charts that present statistics that support their claims, with a bigger dataset or a different presentation might not support their claims at all.
It doesn't take equations or complex math to get people to recognize flaws in reasoning based on biased or incomplete data. Would people trust the FDA as much as if they were made aware that most of the applications for approvals are made from research studies the developers paid for themselves? The FDA is not funded well enough by Congress to be able to do independent research to support such clams. So it depends on biased research. That is why so many drugs and proceedures have to be pulled from the market after they have been approved by the FDA.
I don't know that I would be as concerned that the press have some math smarts, although that is not a bad thing, but it might be more important that they show some reasoning and inference skills to uncover bias and distortion of the facts. That might require some math skills, but the uncritical passing on of claims is a far more serious problem.
Yes, the main-stream media should use equations, and words, and diagrams, and graphs/charts, and pictures, and videos.
Quantum mechanics, OTOH, can get nasty. Look at Pauling and Wilson's book. They couldn't bring themselves to choose one style of mathematical notation and stick with it... instead, silently slipping from one to another every few pages, with absolutely no bridging.
Here: E^2 = p^2 c^2 + m_0^2 c^4
So, when p (momentum) is zero, E^2 = m_0^2 c^4
=> E = +/- m_0 c^2
Linky: http://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relation
To be, or not to be: isn't that quite logical, Slashdot Beta?