ARR, MoAR!... in which i don't know what to say ..

.. except that something has to change; this shouldn't happen in a country that calls itself a democracy.

Urban teachers have a kind of underground economy, Cohen explained. Some teachers hustle and negotiate to get books and paper and desks for their students. They spend their spare time running campaigns on fundraising sites like DonοrsChoose.org, and they keep an eye out for any materials they can nab from other schools. Philadelphia teachers spend an average of $300 to $\$$1,000 of their own money each year to supplement their $100 annual budget for classroom supplies, according to a Philadelphia Federation of Teachers survey.

~ from "Why Poor Schools Can’t Win at Standardized Testing" @theatlantιc

ARR, MoAR!.. on the downside of passion.

this article is about how programming, despite the call to arms about learning how to code, is a low-status job.

when i read this post, though, it funded more like the plight of teachers:

.."that we allow “passion” to be used against us. When we like our work, we let it be known. We work extremely hard. That has two negative side effects. The first is that we don’t like our work and put in a half-assed effort like everyone else, it shows. Executives generally have the political aplomb not to show whether they enjoy what they’re doing, except to people they trust with that bit of information. Programmers, on the other hand, make it too obvious how they feel about their work. This means the happy ones don’t get the raises and promotions they deserve (because they’re working so hard) because management sees no need to reward them, and that the unhappy ones stand out to aggressive management as potential “performance issues”. The second is that we allow this “passion” to be used against us. Not to be passionate is almost a crime .."

~ from "How the Other Half Works: an Adventure in the Low Status of Software Engineers" @Michael0Church.

ARR, MoAR!.. on picking-&-choosing.

now i don't feel so bad about not caring about number theory problems.

In one letter he even displayed contempt for the problem. His friend the German astronomer Heinrich Οlbers had written to Gaμss encouraging him to compete for a prize which had been offered by the Paris Academy for a solution to Fermαt's challenge: "It seems to me, dear Gaμss, that you should get busy about this." Two weeks later Gaμss replied, "I am very much obliged for your news concerning the Paris prize. But I confess that Fermat's Last Theorem as an isolated proposition has very little interest for me, for I could easily lay down a multitude of such propositions, which one could neither prove nor disprove."

~ from "Math's Hidden Woman" @pbs

so i suppose that even the best of us should pick and choose the tasks best suited for ourselves. i wonder, though, what Gaμss thought of the Rιemann hypothesis ..?

---

also, to explain the title of the cited article, Gaμss isn't its main subject .. but the French mathematician Marιe-Sophιe Germaιn.

it's quite an account! i wonder sometimes how many women in history have kept to the academic shadows because of a lack of social tolerance and the societally-induced hardships upon them.

if the best minds of their time, such as Gaμss as well as Hιlbert (in the case of Emmy Nοether) could see the potential of these scholars, then you'd think that others would be willing to listen .. \-:

sometimes negative signs matter ..?

after browsing this article, suddenly the difference between mεasures, sιgned mεasures, and vectοr mεasures come to mind.

The answer to this question takes us to the heart of quantum mechanιcs, to the part that popular explanations usually mangle. Quantum mechanιcs wasn't the first theory to introduce randomness and prοbabilities into physics. Ironically, the real novelty of quantum mechanιcs was that it replaced prοbabilities — which are defined as nonnegative real numbers — by less intuitive quantities called amplitudes, which can be positive, negative, or even complex. To find the prοbability of some event happening (say, an atom decaying, or a photon hitting a screen), quantum mechanιcs says that you need to add the amplitudes for all the possible ways that it could happen, and then take the squared absolute value of the result. If an event has positive and negative amplitudes, they can cancel each other out, so the event never happens at all.

The key point is that the behavior of amplitudes seems to force prοbabilities to play a different role in quantum mechanιcs than they do in other physical theories. As long as a theory only involves prοbabilities, we can imagine that the prοbabilities merely reflect our ignorance, and that a “God’s-eye view” of the precise coοrdinates of every subatomιc particle would restore determinism. But quantum mechanιcs’ amplitudes only turn into prοbabilities on being measured — and the specific way the transformation happens depends on which measurement an observer chooses to perform. That is, nature “cooks prοbabilities to order” for us in response to the measurement choice. That being so, how can we regard the prοbabilities as reflecting ignorance of a preexisting truth?

~ via "Quantum Randomness" @ AmericanScientist

ARR, MOAR!.. on writing.

the following excerpt by s.a.pιnker isn't terribly representative of his original article about writing, but i liked it anyway and thought to share it:

For example, everyone knows that scientists overuse the passive voice. It's one of the signatures of academese: "the experiment was performed" instead of "I performed the experiment." But if you follow the guideline, "Change every passive sentence into an active sentence," you don't improve the prose, because there's no way the passive construction could have survived in the English language for millennia if it hadn't served some purpose.

The problem with any given construction, like the passive voice, isn't that people use it, but that they use it too much or in the wrong circumstances. Active and passive sentences express the same underlying content (who did what to whom) while varying the topic, focus, and linear order of the participants, all of which have cognitive ramifications. The passive is a better construction than the active when the affected entity (the thing that has moved or changed) is the topic of the preceding discourse, and should therefore come early in the sentence to connect with what came before; when the affected entity is shorter or grammatically simpler than the agent of the action, so expressing it early relieves the reader's memory load; and when the agent is irrelevant to the story, and is best omitted altogether (which the passive, but not the active, allows you to do). To give good advice on how to write, you have to understand what the passive can accomplish, and therefore you should not blue-pencil every passive sentence into an active one (as one of my copyeditors once did).

(for more articles of this kind, visit edge.org.)

ARR, MoAR! On computers and proofs.

so today i learned what a "discrepancy" is:

"Adding up the numbers in a sub-sequeηce gives a figure called the discrepaηcy, which acts as a measure of the structure of the sub-sequeηce .."

~ from " Wikipedia-size maths proof too big for humans to check" @newscientist

as for how this came up ..

Erdös thought that for any infinite sequeηce, it would always be possible to find a finite sub-sequeηce summing to a number larger than any you choose - but couldn't prove it.

It is relatively easy to show by hand that any way you arrange 12 +'s and -'s always has a sub-sequeηce whose sum exceeds 1. That means that anything longer – including any infinite sequeηce – must also have a discrepaηcy of 1 or more. But extending this method to showing that higher discrepaηcies must always exist is tough as the number of possible sub-sequeηces to test quickly balloons.

Now Konev and Lisitsa have used a computer to move things on. They have shown that an infinite sequeηce will always have a discrepaηcy larger than 2. In this case the cut-off was a sequeηce of length 1161, rather than 12. Establishing this took a computer nearly 6 hours and generated a 13-gigabyte file detailing its working.

ARR!.. imagine computers as research collaborators?

sometimes i wonder if i should be a mathematician at all .. lately i've been reminiscing about the dreams my younger self had: among them was to be a successful novelist, perhaps in science fiction.

so when i read news articles like this one ..

"Some might argue that computers will never be able to match human ingenuity but it is difficult these days to argue they can't at least mimic many of our skills.

Take the eDavid painting robot. The computer-controlled arm - adapted from a welding machine - chooses from five brushes and 24 colours to create impressive artworks on canvas.

It works by snapping a photo of its subject matter and then making the necessary calculations to turn the image into a drawing or painting in a wide variety of styles.

Its creators admit that it has no awareness of what it is doing. But it is able to make decisions about things like shading and brushstrokes as it goes, tweaking its moves based on how the picture is evolving, rather than just creating a pre-determined image."

~ from "The quest to turn computers into creative artists" @bbc_tech

.. then i immediately begin to imagine the possibilities:

if the strength of a computer lies in being very efficient with a finite, fixed set of tools, then imagine if we could get computers to prove simple lemmata for us, just by giving them suitable hypotheses and a fixed set of axioms and existing lemmata ..

yes, it is hard enough to build a robust proof-checking program .. and some researchers have spent years of their lives focusing on a single, specific verification .. but i'm not talking about a universal engine:

i liken it to writing programs that play go or chess well. it's not that the computer can think on its own, but rather that it can traverse through the decision tree of possible games very efficiently. in fact, a competitive program mightn't even run through all the possibilities, but simply the games that grand masters have played before.

so imagine coding in all the basic, rigorous proofs from mathematics (e.g. the proof of the triangle inequality in Euclιdean space) and adding shortcuts into the space of all proofs. i wonder what lemmas a computer could tell me ..?

being a mathematician, sometimes i have mathematical daydreams.

ARR! more machine now, than man .. twisted and evil.

"On the one hand, today’s computers feature programming and writing tools more powerful than anything available in the twentieth century. But, in a different way, each of these tasks would be much harder: on a modern machine, each man would face a more challenging battle with distraction ... Kafka, Kerouac, and Wozniak had one advantage over us: they worked on machines that did not readily do more than one thing at a time, easily yielding to our conflicting desires. And, while distraction was surely available—say, by reading the newspaper, or chatting with friends—there was a crucial difference. Today’s machines don’t just allow distraction; they promote it. The Web calls us constantly, like a carnival barker, and the machines, instead of keeping us on task, make it easy to get drawn in—and even add their own distractions to the mix. In short: we have built a generation of “distraction machines” that make great feats of concentrated effort harder instead of easier."

~ from "HOW TODAY'S COMPUTERS WEAKEN OUR BRAIN @newyorker "

ARR!.. apparently i still have more trigοnometry to learn.

well, i learned something new today:

It sounds cumbersome now, but doing multiplication by hand requires a lot more operations than addition does. When each operation takes a nontrivial amount of time (and is prone to a nontrivial amount of error), a procedure that lets you convert multiplication into addition is a real time-saver, and it can help increase accuracy.

The secret trig functions, like logarithms, made computations easier. Versine and haversine [1] were used the most often. Near the angle $\theta = 0$, $\cos(\theta)$ is very close to $1$. If you were doing a computation that had $1-\cos(\theta)$ in it, your computation might be ruined if your cosine table didn’t have enough significant figures. To illustrate, the cosine of $5$ degrees is $0.996194698$, and the cosine of $1$ degree is $0.999847695$. The difference $\cos(1^o)-\cos(5^o)$ is $0.003652997$. If you had three significant figures in your cosine table, you would only get 1 significant figure of precision in your answer, due to the leading zeroes in the difference. And a table with only three significant figures of precision would not be able to distinguish between 0 degree and 1 degree angles. In many cases, this wouldn’t matter, but it could be a problem if the errors built up over the course of a computation.

~ from "10 Secret Trig Functions Your Math Teachers Never Taught You" @sciam

in other news: it's been more than two weeks into this new job, and i still feel disoriented. often i feel exhausted, too.

on the bright side: i finally found an expensive apartment and signed a lease .. after a month of searching (and simultaneously teaching, for the last 2 1/2 weeks).

[1] these are defined, respectively, as $\textrm{versin}(\theta) = 1-\cos(\theta)$ and $\textrm{haversin}(\theta) = \frac{1}{2}\textrm{versin}(\theta)$. suggestively, "ha" mean half.

ARR! in which maths could bring about the end of the world (unless algebraιc geοmetry saves us)?

predictions are always hard, especially when it comes to the future. this one, however, concerns actual maths for once:

"Our conclusion is there is a small but definite chance that RSA and classic Diffie-Hellman will not be usable for encryption purposes in four to five years,” said Stamos, referring to the two most commonly used encryption methods.
..
RSA and Diffie-Hellman encryption are both underpinned by a mathematical challenge known as the discrete logarithm problem. That problem is computationally difficult to solve, ensuring that encrypted data can only be decoded quickly with knowledge of the secret key used to encode it in the first place. Breaking RSA or Diffie-Hellman encryption today requires using vast computing resources for significant periods of time.

However, it is possible that algorithms able to solve the discrete logarithm problem quickly could exist. “We rely on that efficient algorithm not being found,” said Jarved Samuel, a cryptographer who works for security consultancy ISEC Partners and presented alongside Stamos. “If it is found the cryptosystem is broken."

~ from "Math Advances Raise the Prospect of an Internet Security Crisis" @mit:techreview

related to this, algebraic geometry might actually be useful for something .. soon, which means that i'll never heard the end of it from a few of my colleagues!

anyway, another excerpt from the article reads:

Stamos called on the security industry to think about how to move away from Diffie-Hellman and RSA, and specifically to use an alternative known as elliptic curve cryptography (ECC), which is significantly younger but relies on more intractable mathematical challenges to secure encrypted data.

The U.S. National Security Agency has for years recommended ECC as the most reliable cryptographic protection available. In 2005 the agency released a toolkit called SuiteB featuring encryption algorithms to be used to protect government information. SuiteB makes use of ECC and eschews RSA and Diffie-Hellman. A classified encryption toolkit, SuiteA, is used internally by the NSA and is also believed to be based on ECC.

ARR! statistics about .. well, mathematics.

i like the way this guy thinks:

"... but I think we're starting to see a new kind of metamathematics, where people use statistical methods to study the structure of mathematics itself.  This is mathematics as actually done by people, so it involves issues of taste and style.  These are subjective things.  But I suspect there are some features of math that are fairly independent of who is doing it.  Maybe some theorems are 'important' in a fairly objective sense - important crossroads that most travelers tend to stop at.  And someday we may understand why."

~ from "The network of mathematics" @johnbaez:g+ (via mathbabe)

reading this reminds me also of the flysρeck project, regarding the use of formal proof:as expounded on their wiki:

" How does a formal proof differ from a traditional mathematical proof?

Traditional mathematical proofs are written in a way to make them easily understood by mathematicians. Routine logical steps are omitted. An enormous amount of context is assumed on the part of the reader. Proofs, especially in topology and geometry, rely on intuitive arguments in situations where a trained mathematician would be capable of translating those intuitive arguments into a more rigorous argument.

In a formal proof, all the intermediate logical steps are supplied. No appeal is made to intuition, even if the translation from intuition to logic is routine. Thus, a formal proof is less intuitive, and yet less susceptible to logical errors."

the way i understand it, traditional proofs are like pseudocode whereas formal proofs would be real computer programs that you can "compile" against the standard axioms .. although it would probably resemble machine code.

i think this comparison also highlights their comparative advantages nicely:

the formal proof mightn't be readable, but at least you know it runs and witness how it does ..

.. whereas getting the idea for the formal proof would probably require some basic principles for why it could conceivably work, in which case one would probably have a traditional proof in mind.

going back to the idea of a network of all mathematics, i suppose that a formal proof would be checking the existence of a continuum from a statement (a given node on that network) to the fundamental axioms (or "roots" of the network).

ye gods: that would be a really complicated network!

ARR! accounting for asymmetry .. socially?

i'm not completely convinced of this study, partly because there is no discussion of how the researchers made their observations and recorded their data:

"The brain, Cacioppo demonstrated, reacts more strongly to stimuli it deems negative. There is a greater surge in electrical activity. Thus, our attitudes are more heavily influenced by downbeat news than good news.
..
Here's the tricky part. Because of the disproportionate weight of the negative, balance does not mean a 50-50 equilibrium. Researchers have carefully charted the amount of time couples spend fighting vs. interacting positively. And they have found that a very specific ratio exists between the amount of positivity and negativity required to make married life satisfying to both partners.

That magic ratio is five to one. As long as there was five times as much positive feeling and interaction between husband and wife as there was negative, researchers found, the marriage was likely to be stable over time. In contrast, those couples who were heading for divorce were doing far too little on the positive side to compensate for the growing negativity between them."

~ from "Our Brain's Negative Bias" @psytoday

i mean, how does a researcher get access to a couple's daily life so that they can objectively measure how much time they spend fighting? (this is not to say that the study is bogus, but only points out how little i know about how to conduct social research.)

ARR! point & counterpoint.

so i've been reading about MOOCS again. here are a few excerpts i found:

---

"What you can do over the Internet this way is deliver information, but that's not education. Education, as any real teacher will tell you, involves more than just transmitting facts. It means teaching students what to do with those facts, as well as the skills they need to go out and learn new information themselves."

(as pointed out in "The MOOC Racket" @slate)

".. are we sure the only way to teach people what to do with facts is face-to-face? This seems like something that could at least conceivably be taught to more than one person at once. I can remember lots of professors teaching me what to do with facts via lectures in extremely large auditoriums, which is not that different than a lecture you watch online."

(a counterpoint via College Professors Are About to Get Really Mad at President Οbama @nymag)

---

ye gods, this issue is confusing, especially when one accounts for the perspectives of the given pundits. for one thing ..

.. the first point comes from a university professor, who has probably developed an expertise in little-known fields (or at least poorly popularised) over years of study in academia. for him, relevant professional information typically arrives through academic channels and processing the information is a careful, length process of some depth. (think of the peer review process: ouch!)

the second point comes from a editor/journalist who has developed a different expertise in a widely-recognised occupation, probably by way of on the job training and less formal study [1]. relevant professional information probably comes through many diverse channels and rapidly so; the process of response probably requires similar speed (in order to remain relevant).

there are also tacit yet important questions here:

for a young adult, is college necessary for a future successful career?
if so, then what should (s)he learn at university?

honestly, i have no idea. there are too many types of careers out there for a simple answer. the issue gets even murkier when you account for advances in technology, even at the scale of a generation or two.

for example, it seems that there is a lack of available workers in the skilled trades, and the current infrastructure of civilization relies crucially on the fruits of their labor.

on the other hand, what if 3-D printing becomes robust enough, and available through a sufficiently diverse selection of materials, so that plumbing, welding, and soldering no longer require the work of human hands?

this sounds like science fiction, of course. i'll not discuss the likelihoods of certain events occurring .. mostly because i cannot even guess, much less quantify the time-dependent sample space of modern civilisation.

on the other hand, i would like to point out that they are real possibilities: take, for example, the history of the Luddites or how human computers were replaced by digital ones. now that i think about it, i wonder how many more travel agents there are nowadays, with the popularity of flight search engines and all ..? [2]

at any rate, the main problem is that we don't know what "workers of the future" need to know how to do, because many of those future jobs don't exist yet. (explain, for example, the notion of a web developer to someone in the 1970s.) at best we can only make decisions about how to help young adults now, with well-defined criteria ..

.. such as economic ones, i.e. whether they should be obligated to put themselves into tens of thousands of dollars in debt before the age of 30?



[1] this is not to say that the second writer knows any less than the first, nor is he any worse at his job. honestly, you cannot compare such experiences. if the second writer is a success, then i would guess that has to do with a lot of deliberate and systematic effort on his part. he may even have studied many journalists he has admired, read very carefully their work and took notes, which is clearly a kind of study, but not the formal kind you see in universities.

if this is his approach, then i applaud the guy. deliberate practice of this kind, regardless of the circumstance, is often necessary to succeed in many areas in life.

[2] actually, there may in fact be more travel agents than ever before. travel for pleasure has become more and more accessible; on the other hand, there is still a large population out there who cannot (or will not) deal with a computer .. or even afford a computer or high-speed internet. \-:

ARR! ... YEAH! (or: spot on!)

finally!

"Alan Turing, the Enigma codebreaker who took his own life after being convicted of gross indecency under anti-homosexuality legislation, is to be given a posthumous pardon.

The government signalled on Friday that it is prepared to support a backbench bill that would pardon Turing, who died from cyanide poisoning at the age of 41 in 1954 after he was subjected to "chemical castration".

~ from "Enigma codebreaker Alan Turing to be given posthumous pardon" @guardian

then again, i don't know how sure of a bet this is. anyone know what a third reading is?

"Lord Ahmad of Wimbledon, a government whip, told peers that the government would table the third reading of the Alan Turing (statutory pardon) bill at the end of October if no amendments are made. "If nobody tables an amendment to this bill, its supporters can be assured that it will have speedy passage to the House of Commons," Ahmad said."

---

on a (barely) related note, i've been posting a blitz of ARR! posts in the last week and a half. this blog was never meant to be an aggregate maths news website, so i apologise if the content lately has seemed rather .. commercial(?) in nature.

related to this: i've recently experienced a few notable changes in my life ..

.. with more to come, like moving across the ocean ..

.. so my focus isn't 100% on maths, at the moment. to be honest, it makes me feel like i'm not a "real mathematician," even though that sounds ridiculous. (it just goes to show you how insidious "impostor syndrome" can be.)

somewhat oppositely:

ten years ago i entered a ph.d. program. five years ago, i defended a dissertation. it's been a long enough time and i've dodged enough bullets that, perhaps, it's safe for me to consider myself a mathematician and that i'll be around for the long haul, after all.

my point is that research life has settled down and i know that, if i work hard enough, i am capable of good work. as a result, the level of "mathematical drama" in my life has been toned down.

i guess this is a round-about way of saying:

yes, my life is boring now, compared to my student days ..
but i like it that way! (-:

ARR! the good fight.

first, the student side: this is so cool. the idealist in me wishes for all education to be free, and in some places it's still possible;

it's nice to see that part of that might still be kept alive.

"A unique aspect of the Cooper Union case is that several of the students fighting for the cause have already graduated, and remaining undergraduates still won’t have to pay tuition while they’re students. The reason the students have been sleeping in the president’s office for the past two months is because they fear what will happen to the school after they leave, how a decision to charge tuition might affect the character of the incoming classes and the direction of their alma mater."

~from "Can Cooper Union Find A Way To Continue Free Tuition And Its Social Mission?" @fastco

now, the faculty: when i was in the middle of my ph.d. i recalled a fellow student say the worse the teacher, the more students have to work and the more they have to learn. this was in response to seeing how neurotically i was writing my lectures, so that my students could learn in the most effective way possible.

thinking about it now, i must have been the calculus version of a helicopter parent ..! \-:

anyway, that came to mind when i read the following excerpt. apparently some students do react that way (in extreme cases).

"I had a teacher in college whose lectures were so incredibly clear that it made me think physics was the easiest thing in the world. Until I went home and tried to do the problem set. He was truly amazing, but sometimes I think he was TOO good. I didn't struggle to understand his lectures--but maybe I should have."

~ from "Do the Best Professors Get the Worst Ratings?" @psytoday

there's more:

"When you measure performance in the courses the professors taught (i.e., how intro students did in intro), the less experienced and less qualified professors produced the best performance. They also got the highest student evaluation scores. But more experienced and qualified professors' students did best in follow-on courses (i.e., their intro students did best in advanced classes).
..
To summarize the findings: because they didn't teach to the test, the professors who instilled the deepest learning in their students came out looking the worst in terms of student evaluations and initial exam performance."

on a related note: over the course of my career thus far, i've learned from various occasions to be wary of those instructors whose evaluation scores are too high, almost perfect.

lauding your first-year mathematics instructors is a little like thinking that your parents did a perfect job raising you while you are being raised through childhood. i don't deny that students have good, discerning taste .. but it's hard to accurately judge how someone is conveying lessons to you when you don't completely understand the lessons in question!

ARR! muscles in polar coordinates ..

.. or, should i say, cγlindrical cοordinates?

"One of the major discoveries that David Williams brought to light is that force is generated in multiple directions, not just along the long axis of muscle as everyone thinks, but also in the radial direction.
..
The basics of how a muscle generates power remain the same: Filaments of myosin tugging on filaments of actin shorten, or contract, the muscle – but the power doesn’t just come from what’s happening straight up and down the length of the muscle, as has been assumed for 50 years. Instead, University of Washington-led research shows that as muscles bulge, the filaments are drawn apart from each other, the myosin tugs at sharper angles over greater distances, and it’s that action that deserves credit for half the change in muscle force scientists have been measuring.

~ from Biceps bulge, calves curve, 50-year-old assumptions muscled aside @u-dub

courtesy of the university of washington (so don't sue)

despite this being a mechanical and biological process, the funny thing is that the totals are apparently hard to measure:

"“The ability to model in three dimensions and separate the effects of changes in lattice spacing from changes in muscle length wouldn’t even have been possible without the advent of cloud computing in the last 10 years, because it takes ridiculous amounts of computational resources,” Williams said."

it makes me wonder: what basic but subtle aspects of nature have we been missing, all this time?

ARR! strange occurrences in science

// initially written: last week (or before)

ok: so what exactly is a measurement, then?

"Just like position and momentum, quantum theory predicts that the polarization along two different axes cannot simultaneously be known with certainty (see Nature). The team adopted a strategy in which the polarization is initially probed using a series of ‘weak’ measurements — detections that barely disturb the system but must be repeated several times to record the same information that a single ‘strong’ measurement can detect. They found that, on average, the polarization measurements disturbed the system by only about half as much as Heisenberg’s original formulation of the uncertainty principle dictates."

~ from "Proof mooted for quantum uncertainty" @nature

speaking of science, maybe this explanation of mercury's liquid state is well-known .. but admittedly, i was ignorant of it.

"Relativity states that objects get heavier the faster they move. In atoms, the velocity of the innermost electrons is related to the nuclear charge. The larger the nucleus gets the greater the electrostatic attraction and the faster the electrons have to move to avoid falling into it. So, as you go down the periodic table these 1s electrons get faster and faster, and therefore heavier, causing the radius of the atom to shrink. This stabilises some orbitals, which also have a relativistic nature of their own, while destabilising others. This interplay means that for heavy elements like mercury and gold, the outer electrons are stabilised. In mercury’s case, instead of forming bonds between neighbouring mercury atoms, the electrons stay associated with their own nuclei, and weaker interatomic forces such as van der Waals bonds hold the atoms together."

~ from "Relativity behind mercury's liquidity" @rsc

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lastly .. judging from how i wrote this post, it's safe to assume that those monday roundups aren't returning anytime soon.

let me clarify: i still think that rounding up articles is a good idea, but a weekly time constraint feels slightly artificial to me. i'd much rather collect items with a common theme and let the ideas percolate into something coherent. (i don't know if i'll do this weekly; it really depends on how much interesting stuff appears on the blogosphere.)

that said, i'm open to taking requests;
if you want my opinion on a topical article, then send me the link.

that said, the MoAR label will become just ARR!, where AR refers to ARticle, R to Roundup, and ! to indicate that i have an opinion!