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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?"
Haha yes, of course people who are never exposed to equations are rubbish at reading them. It's a self-reinforcing feedback loop. I fear that the only way to get the general public to become more familiar with how to read equations would be to sneak them into sports coverage or something. Other than that my only other thought on the subject, is that surely anyone even a little bit interested in the Heisenberg uncertainty principle would be prepared to at least attempt equations and if not merely skim them and come back to them if needed?
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Should articles be written with intelligence and nuance when writing for a "general audience"?
It might be useful in some areas, but quantum mechanics... is one of the hardest places to start.
To put it another way, even if you introduce some equations for quantum mechanics, you are still going to look like an idiot compared to someone from the field... even someone from the field as it existed in the 1920s.
It might be better to go find experts in the field, and have them write short articles for the general public that are about established but not widely known things.
I agree with this. What I'd like to see is equations added in, where helpful, in the same way as small images in a body of text. Then you could put a caption below, just to say something informal but informative about the equation. I think that way it would be easy for people to decide whether they want to read it. Some people aren't going to want to, so it's important that it's not something you have to read through in the article itself.
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I think the parent referred to the fact that in Quantum Mechanics you can have the equations right and still talk nonsense. The point is that the equations alone don't say much. This is especially true for the uncertainty relation. For example, the position-momentum uncertainty equation and the energy-time uncertainty relation look quite the same, but their meaning is completely different (this is related to the fact that in quantum mechanics there is no such thing as a time operator).
Personally I think that part of the problem is the non-metric units that are still in use. By accepting that it is in any way sensible to use them, you've already given up on the logical, elegant approach to quantification. You've made it more likely that people resort to the "football fields" etc.
Betteridge's Law of Headlines says no.
And at least in this particular case, "no" is indeed the correct answer. Equations can never be a substitute for actual understanding. You can use equations to develop understanding by starting from an earlier point and transform the initial equation to establish a new fact. But where do you start with quantum mechanics? "Quantum states are being represented by rays in a complex Hilbert space"?
If anything, equations can be used to create an argumentum ad auctoritatem, and I'm not sure that this is a good thing.
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I would generally agree; but generally don't go beyond linear algebra; and in the wonderful modern age add a link or a QR on a printed article with links to improve understanding.
On these extra information sites have further links to more detailed information for those that are interested, further to this the same technique could be used with any technically dense subject matter...main artcle with basic scientific info ->link-> more in depth about original content ->link-> specific detail about relevant fields
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.
I would be opposed to any sort of calculus in an equation for popular press. But algebra? Yes. Algebra makes some things easier to understand.
And YES, it will require a little more mental effort for most people, but mental effort is a good gauge of how much someone is learning. In fact, put both the equation and a sentence explaining it. But algebra is sufficient for explaining the vast majority of physical concepts in a compact form.
Math equations are a language. A language we are all taught from middle school. We can and should use it, and use it clearly.
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.
I think you are confusing mathematicians with engineers. Any mathematician worth his/her salt should know that the Pythagorean Theorem comes straight from the 2-norm in a Euclidean space, which is what most people mean when they say "the distance between two things". You can of course get philosophical and say, "why the 2-norm"?, but this is easily answered by an application of d'Alembert's principle. Now, you see what I did there? Yet another thing to figure out "why is it so", and indeed, you have to work fairly hard to find out how deep the rabbit hole goes.
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I don't know. I think the best way to invest in education is to invest in good jobs for parents. When the downward pressure on the lowest 2/3 of the economic scale becomes so great that it breaks up families, causes young people to give up on society, it makes it impossible to have the kind of family structures that create the highest possibility of children entering school with their interests already raised.
By trying to treat the problem at the school-level, we're just medicating the symptom, not dealingi with the underlying disease. That's why I think the effort to pour money into pre-school education completely misses the point. Those kids have to go home sometime.
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Or, besides writing down the equation, EXPLAIN the equation. And not just write down what the equation says, but what it means.
Let's take a simple one - E=mc^2.
It says the amount of energy something contains is related to its mass (or the amount of "stuff") it contains. The relation is a big one - it's equal to the speed of light squared, so a tiny amount of mass (stuff) produces a LOT of energy. This equation is fundamental to nuclear physics, including peaceful uses such as nuclear power plants, to destructive uses such as nuclear weapons.
Thus the paragraph put close to the equation helps those who can't read the equation to still understand what it says, and it also explains where it's used and what it means.
But you're correct on the fundamental problem - it's because those in the sciences (and engineering) put little weight on the "arts" side of things (including things like writing) as they believe that stuff is a lot of fluff. (I can't generalize this, but if you ask a lot of people in IT, they seem to look down on studying anything that isn't related to their field - like why should a computer scientist or engineer take courses in philosophy or logic, or take classes in English or writing or even home economics).
Likewise, a lot of people take arts because they want to avoid the math and science.
Which is terrible - and it leads to this gulf of communications problems where journalists (or any writer, really) misinterprets some scientific or technical thing because the writer and the technical person are failing to communicate effectively (a problem on BOTH sides). Or how technical people look upon sales, marketing and PR people with disdain, because those people know how to relate to the public, but often fail to relate to the technical staff.
Perhaps instead of the token math or science class for an arts degree, or the token arts/business class for a technical/science degree, the two should be combined more tightly to produce a more well-rounded person who may be technical, but understands the other side.