Additions to Chad Orzel’s article on physicists and philosophers

Chad Orzel wrote a column on his blog last week about James Blachowicz’s opinion piece in the New York Times titled “There is no scientific methods”. The Times article talks about how methods in science and those in, say, the humanities, are similar and then tries to make some point out of it regarding the validity of any thought.

Orzel uses an apt emoji (or is it kaomoji?) to describe the lack of a conclusion in Blachowicz’s article: ¯\_(ツ)_/¯. This is particularly representative of a lot of research in the social sciences. There are two things Orzel’s article misses out on, in my opinion: firstly, it does not talk about the fact that such a practice of abrupt endings — that feel as if a closing inverted comma is missing — are a manifestation of a deeper problem in the humanities, and one that particularly disturbs physicists: vagueness. Somehow, most social scientists I have come across are perfectly satisfied with an answer that appears to point them in some meaningful direction, and they seem oblivious to the fact that the same argument is being understood by different people differently as a direct result of its being vague. The open-ended state of arguments (or the lack of a conclusion altogether) catalyses this.

Consider this sentence which Orzel also quotes, albeit for a different purpose: “If scientific method is only one form of a general method employed in all human inquiry, how is it that the results of science are more reliable than what is provided by these other forms?” The argument begins by stating that the scientific method is only one form of inquiry. The only logical next step is to state that any other discipline which uses the same scientific method must also be similarly reliable. However, the sentence itself seems to assume without any base that if the scientific method is reliable, then any form of it is also reliable. This may be true, but is still certainly not a valid assumption without some sort of context.

The second argument that I think Orzel should have made is once again aimed at the three paragraphs he quotes from the Times article, where Blachowicz says that that the reliability of the scientific method stems from the fact that “science deals with highly quantified variables and that it is the precision of its results that supplies this reliability.” And then helpfully warns that “quantified precision is not to be confused with a superior method of thinking.” Except this is only part of the picture.

The reliability of science — I can only speak for physics anyway — does not come from sheer precision of so-called “highly quantifiable variables”1 but rather from mathematics. This language (or tool, depending on how you wish to look at it) that physicists employ has an inherent logic to it in that the validity of every step is ensured by the previously established validity of each of its preceding steps. For instance, having proved beyond doubt that 1+1=2, 1+1+1=3 and so on, to show that 2+2=4 with similar “reliability” means one only need show that 1+1=2, so 2+2=1+1+1+1=4. Now this is a dull example compared with the concreteness and logic that maths is really capable of, but it was meant to explain a point to people of the humanities.

I particularly like this paragraph in Orzel’s post that quite sums up how we all feel:

As a scientist, I often find myself nodding along with the steps of the process to work something out, only to be left waiting for some sort of concrete conclusion about what comes next. There’s a comprehensive failure to build on prior results, or even suggest how someone else might build on them in the future, and as a physicist I find this maddening.

It is this idea of a logical building block where the stability of each block depends on that of the blocks that came before it is what physics and mathematics have that gives our results solidity. It is precisely this habit of using building blocks that prompts us to take a step back and look at the entire structure as a “therefore” as Orzel points out. To build an argument without some form of conclusion is to have a fanfare that awkwardly fizzles out halfway through.

This is all no different from asking a question and not getting an answer. The lack of a conclusion can be particularly frustrating. It is also why those of us in physics are often accused of over-thinking things while

On bad metals

On Condensed Concepts yesterday, Ross Mckenzie talked about bad metals and the unitary limit. There were a couple of ideas I was unfamiliar with, and I note some points here for anyone similarly interested in this area. Dr Mckenzie’s own writing followed the paper “Breakdown of the universality of the Kadowaki-Woods Ratio in multi-band metals” by D.C. Cavanagh et al.

Generally, we consider a material to be a metal when its resistivity increases with increase in temperature, and its electron excitation spectrum has no gaps. Its classical picture is given by the Drude model in which electrons move some average distance between two collision-scattering events. This is called the “mean free path”. In its quantum mechanical picture given by Sommerfeld’s later model (which was built on Drude’s), like everywhere else in quantum mechanics, we consider plane-wave states with corresponding wavelengths.

To define a good metal we need to mash these two models together (which is not something I like) and state the following: when an electron propagates a distance longer than one wavelength, it may be considered a good metal. Further, the electron-electron collision that occurs is proportional to the number of excited electrons and the number of vacancies, both of which are proportional to the temperature, making the resistivity — afforded by such electron-electron collisions — proportional to the square of temperature.

When none of these (or even some of these) are violated, the material is considered a “bad metal”. In physics we have a lot of such boring names, and we hardly spend any time naming things elaborately like chemists or biologists may. Another interesting value at this point is that when the mean free path is lesser than the interatomic distance in a lattice, there occurs a violation of the Ioff-Mott-Regel limit (or Mott-Ioff-Regel limit, depending on whom you ask), which demands that the mean free path be equal to the interatomic distance.

“In reality, it is not clear whether the MIR limit exists in any known material.” As Dr Mckenzie points out. “Bad metals, be definition, violate it.” More information is available in the form of slides from a presentation by Sean Hartnoll at Stanford.

Additionally, the first property stated above is actually related to an interesting phenomenon known as the Kondo effect which describes how magnetic properties affect electronic scattering to give a typical resistivity-temperature variation wherein the resistivity has a minimum. The effect is actually too complex to describe accurately (here and now) but there are always sources to read on this. Try Andrzej Nowojewski’s write-up at Harvard, or Alexander Hewson’s book from Cambridge.

On simplification in popular science

Albert Einstein’s famous book, “Relativity” begins with a quote by Ludwig Boltzmann: “Elegance should be left to shoemakers and tailors.” Over the course of one’s study, nearly every physicist can attest to this. For a subject that is praised as the epitome of elegance, developing physics can be uncharacteristically ugly and raw. Not every equation is as beautiful as that pop star, E=mc^2, or Euler’s lesser known but similarly elegant e^{i\pi}+1=0. Like a lot of other things in life, the road to the final, elegant equation happens to be hard and turbulent. And one of the biggest components of such an elegant solution happens to be simplicity.

Being passionate about popular science writing, one of the arguments I am confronted with is about simplicity. By necessity, popular science writing has to be diluted to make sense considering the layperson’s somewhat limited understanding of physics — in my case, or more generally any science for that matter. This dilution has two key problems, but first let us put aside the probability that it is not required at all. I cannot attest to every scientific field, but like most disciplines, physics uses “shorthand” (for lack of a better term), or words and phrases that have a deep meaning and which are used to make the understanding of one idea concise, based on the assumption that the more basic idea underlined by the “shorthand” phrase is already known and its validity already agreed upon. Between physicists this is rarely a problem; with non-physicists it is the biggest obstacle.

To explain a simple idea, therefore, is simple as always. To explain a more complex idea, however, sentences or paragraphs will have to be used in place of individual jargon. This makes the text long-drawn, which can quickly be a turn-off — which is what popular science tries to avoid being. (If not, you could just read pre-print servers.) In other words, simplifying is unquestionably a need. The only issue left, then, is what are the effects of such simplification, whether good or bad.

The only good effect I can think of is that it aids in understanding an idea. Nearly everything else that comes to mind is negative. Back in May, the magazine Dream 2047, published monthly by India’s Department of Science and Technology, carried an editorial titled, “We should not oversimplify science communication”, which was really all about simplifying it in the first place. This actually followed up from two editorials in March and April (both of which are freely accessible) prompted by Baruch Fischhoff’s talk at the American Psychological Association’s Public Interest Leadership Conference. I will refrain from spoiling the talk itself for you, especially because it has been made freely available to watch online (video 4 in the playlist).

Dream 2047’s commentary on simplifying science dates as far back as Einstein (“Everything Should Be Made as Simple as Possible, But Not Simpler”, which has several interpretations of which popular science writing could be an instance) but the idea, in all possibility, predates him. More recently an article in Popular Science details Stanford epidemiologist Kristin Sainani’s attempt to teach scientists to write without using jargon or other technical bend. Most tips are incredibly basic — such as using the active voice, avoiding sesquipedalian verbiage (yes, that is one trip to the dictionary right there), or even “Paragraphs should have a focused structure, centring on a big idea.” — so basic they belong in beginner english writing classes. But one look at science writing will tell you how a lot of papers tend to get complicated more because of the language than the science itself, which is something that can (and should) be avoided simply because it serves no purpose. In other words, the simplicity in writing ought to be in its structure rather than the dumbing down of more technical ideas.

However we still have all the jargon to deal with. This is undoubtedly the hard part: when a reader cannot appreciate the nuances of a discipline and when everything has to be brought down to accommodate the layperson’s breadth of knowledge, the reader soon comes under the impression that their existing knowledge is all they need to fully understand a particular idea. Nothing could be farther from the truth. While it is true that such a condensation gives a fair idea of the topic at hand, it should also be noted that any condensation does one of two things:

  1. It approximates the idea in a bid to simplify it, without treating the exceptions and special cases with the same weight.
  2. The approximation carefully (and rather intelligently) limits itself to the information necessary under the scope of the text, without mentioning the ways in which it transforms under other circumstances.

In either case, the approximation — or simplification if you will — paints an incomplete picture. This is unavoidable; this is, in fact, the reason why physicists speak in the language of mathematics. Mathematics is concise and contains a vast amount of information within itself that can be extracted as necessary without making things messy; these inherent data often becomes apparent to a physicist as and when necessary, without the need for a hundred footnotes and tables. The only problem with this is that if such wonderfully succinct popular science writing does appear, most readers will have to learn a whole new language. Suddenly, simplifying looks like a brilliant idea after all. And it is, because there is a pattern here — perception. The fault lies not in simplifying but in how readers (mis)interpret simplified text as the complete explanation.

When we started Physics Capsule, my co-founder, Roshan Sawhil, and I had considerable discussions on how simple we should make our articles. While I insisted on having mathematics included in all writing so as to reduce miscommunication, Roshan leaned towards first publishing articles in a simplified format — in english, not in maths — and then writing companion articles which carried the necessary mathematics. Suffice it to say we were both right to some extent: the mathematics was necessary to fully appreciate the physics involved, and maths-heavy articles would turn off readers and work against us and even, at times, make articles unreadable to the layperson. We therefore came up with what we believe was a more elegant solution that we use now. We write the article in simple english and include boxed, optional mathematics sections in the article — reading the mathematics gives a better understanding while skipping the optional sections does not trip the reader’s continuity or understanding.

The initial big piece of advice my agent gave me was to start blogging. I wasn’t convinced that this was important, but I did what I was told. At first it was out on my lonesome and a year later, well, here we are at Scientific American. Best investment of time ever.

Not all popular science can be written this way. In his book, “A brief history of time”, Stephen Hawking famously states that “… each equation I included in the book would halve the sales”. Coming from a world of precise, technical terminology and a large bank of fundamental knowledge that is taken for granted as known and understood by everyone, most scientists seem to find it incredibly hard to even begin to write popular science, as an old article in The Scientist pointed out — “Popular science writing requires inspiration, perspiration” — while also carrying some interesting thoughts by Edward O. Wilson and Jay Gould. And then there is astrobiologist Caleb Schraf, also a blogger on SciAm, who wrote three years ago about his experience, and included some ideas and advice on, writing and publishing a popular science book. Almost everything he talks about extends to online or offline single articles too. And blogs — especially because publishing his first book was what made him start blogging and he describes it as the “best investment of time ever”.

Ultimately the onus is on the writer and the reader alike to use simplification responsibly. The writer will have to ensure that simplified texts do not distort the meaning they convey, and the reader will have to understand that almost everything they read is an approximation tailored to help understand ideas within the scope of the text and that such an approximation hides vast, complex concepts that often can only be grasped following — at least — a thorough formal introductory course in the subject. To me, at the end of the day, simplification, like writing proposals for research grants, is necessary evil.

On self-studying physics

All through my formal education in Physics I have seen a lot of people, including myself at one point, embarking on a mission to self-study physics. It is indeed a mission and a strenuous one at that. Physics is one of the fastest developing fields today, and because it is the oldest and has been the fastest developing field all through history, the amount of knowledge a student of physics has to learn to be able to justifiably comprehend the frontiers of research is greater than in any other field. This, on the one hand makes learning physics quite an enjoyment and accomplishment, and on the other it makes the task daunting and, almost certainly at some point down the road, discouraging.

Longtime Physics Forums member, micromass, about a week ago, wrote an “insight” article on the forum about self-studying physics/mathematics. Since I am about to begin rigorous self-studying sessions myself for the rest of this year, I decided to compile everything of note mentioned in the article as well as the ensuing discussion elsewhere on the Forum for future reference and ease for everyone who finds themselves in this position. By the time I compiled the discussions, I had poked around the rest of the Forum as well as leafed through older resources I had saved years ago and here they are in one tidy package.

1. Pick a topic, learn the maths

Funnily enough the first point comes from a Physics Stack Exchange question and mentions, briefly, the barebones approach that every other tip or suggestion is an altered form of. There are five steps: cover the absolute basics, find something advanced that interests you, become competent in it, learn the mathematics associated with it, and solve problems.

2. Study in bits and pause to recall

An old pamphlet written around 1955 for physics students mentions, among several other useful pieces of advice, that it helps greatly to “finish a paragraph, think out its main idea… finish the page, ask yourself what was on the page”. This simple method of recalling what is studied in small chunks can prove to be helpful both understanding and remembering over the long term. Remembering, not memorising.

3. Do not just read it

Also from the same pamphlet: “… don’t just read it. Underline important points, put your own comments in the margin, etc.” This is true and I have experienced it. It can be easy to get carried away by lucid texts (think David Griffith’s Classical Electrodynamics) and read on and on for tens of pages before realising that all the progress you made was for nought because you thought you “understood” it all but in ernest you never really absorbed any of it well enough to really know the physics.

4. Work out problems

Physics is problem solving. “The best of the texts come with exercises.” Gerard ’t Hooft says in his guide to become a good theoretical physicist. “Do them. find out that you can understand everything.” But solving problems means actually solving them. Reading a question and looking up the answer may leave you with a great taste of the subject, but reading a solved answer unfortunately hides the thought process behind arriving at the solution. This is something that only comes of actually solving problems.

5. Slow down and persevere

In the “insight” article published on Physics Forums writes micromass — “In studying mathematics, it is very important to take it slow. Reading a fiction book of 1000 pages will be much quicker than reading an abstract math book of 50 pages.” I would put this alongside point 3 above. Reading physics or mathematics is not recommended; slow down, follow, bits of the topic being covered, take a moment to recall and work out problems. Do not read through the text like it is an English language course book or popular science writing. This slow pace may take its toll on your patience, and the slow to seemingly absent increase in your proficiency inn the subject can drive you away from it, but stay and persevere.

6. Standard texts are standard for a reason

Besides avoiding popular science (books that shy away from equations for a good reason — you are often not their target audience) picking standard text books is usually your best bet. They do not have to suit you, but they did suit a lot of people and the probability of you gravitating towards one of these texts is greater than if you picked stuff by poking around in the dark; this also ensures you can start learning soon instead of wasting time checking and warming up to book after book.

7. Pick an area of focus

Instead of trying to chomp an entire text, which can often be a Herculean task, Andrew Kirk recommends focusing on one major theorem or portion of the text as opposed to the whole thing, so as to make studying physics (and the textbook itself) less daunting. Unlike aiming to finish entire books, which can be tiresome and off-putting, going from theorem to theorem gives you more reasonable goals that can be accomplished in a day or two and which will in turn fuel your enthusiasm for studying further.

I can keep going on and on, but it is important to realise that one has to start somewhere and following these seven tips should take you a long way in self-studying (or, now that I look back, even in academically studying) physics. They are a condensation of my own experiences corroborate and supported by several other, more experienced physicists or students around the world. I will be putting these to the test myself, starting tomorrow, with a lengthy bout of self-study and will write a follow up article if possible by early next year.

The physics behind Interstellar — Christopher Nolan’s space drama

As a man of physics, Interstellar is a film I would not miss for the world; if not for the physics, for the images — and director Chris Nolan’s images have always been powerful. Interstellar does not fall short on that. However, it helps for the layperson to learn a thing or two about physics before watching the film, which is why I wrote this article — and made sure there are no spoilers.

The film is really very small, but dressed as an operatic journey through space and time. The use of physics is interesting, almost exciting, and what holds the audience’s attention is (surprisingly) as much the science as the story of a parent-child relationship.

And yet, like so many films before it, Interstellar falls short merely because it was hyped far too much and it set itself an unrealistically high barrier.

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