Why boredom is anything but boring

Implicated in everything from traumatic brain injury to learning ability, boredom has become extremely interesting to scientists.

Can Economics Change Your Mind?

Economics is sometimes dismissed as more art than science. In this skeptical view, economists and those who read economics are locked into ideologically motivated beliefs—liberals versus conservatives, for example—and just pick whatever empirical evidence supports those pre-conceived positions. I say this is wrong and solid empirical evidence, even of the complicated econometric sort, changes plenty of minds.

Can economics change your mind?

Where to start? I could write a whole ongoing blog on this question (wait…). In any case, here are just a few examples of where I have changed my mind due to economic evidence:

Iran's blogfather: Facebook, Instagram and Twitter are killing the web

Hossein Derakhshan was imprisoned by the regime for his blogging. On his release, he found the internet stripped of its power to change the world and instead serving up a stream of pointless social trivia

Game Theory (Open Access textbook with 165 solved exercises) by Giacomo Bonanno.

Why too much evidence can be a bad thing

(Phys.org)—Under ancient Jewish law, if a suspect on trial was unanimously found guilty by all judges, then the suspect was acquitted. This reasoning sounds counterintuitive, but the legislators of the time had noticed that unanimous agreement often indicates the presence of systemic error in the judicial process, even if the exact nature of the error is yet to be discovered. They intuitively reasoned that when something seems too good to be true, most likely a mistake was made.

In a new paper to be published in The Proceedings of The Royal Society A, a team of researchers, Lachlan J. Gunn, et al., from Australia and France has further investigated this idea, which they call the "paradox of unanimity."

"If many independent witnesses unanimously testify to the identity of a suspect of a crime, we assume they cannot all be wrong," coauthor Derek Abbott, a physicist and electronic engineer at The University of Adelaide, Australia, told Phys.org. "Unanimity is often assumed to be reliable. However, it turns out that the probability of a large number of people all agreeing is small, so our confidence in unanimity is ill-founded. This 'paradox of unanimity' shows that often we are far less certain than we think."

The researchers demonstrated the paradox in the case of a modern-day police line-up, in which witnesses try to identify the suspect out of a line-up of several people. The researchers showed that, as the group of unanimously agreeing witnesses increases, the chance of them being correct decreases until it is no better than a random guess.

In police line-ups, the systemic error may be any kind of bias, such as how the line-up is presented to the witnesses or a personal bias held by the witnesses themselves. Importantly, the researchers showed that even a tiny bit of bias can have a very large impact on the results overall. Specifically, they show that when only 1% of the line-ups exhibit a bias toward a particular suspect, the probability that the witnesses are correct begins to decrease after only three unanimous identifications. Counterintuitively, if one of the many witnesses were to identify a different suspect, then the probability that the other witnesses were correct would substantially increase.

The mathematical reason for why this happens is found using Bayesian analysis, which can be understood in a simplistic way by looking at a biased coin. If a biased coin is designed to land on heads 55% of the time, then you would be able to tell after recording enough coin tosses that heads comes up more often than tails. The results would not indicate that the laws of probability for a binary system have changed, but that this particular system has failed. In a similar way, getting a large group of unanimous witnesses is so unlikely, according to the laws of probability, that it's more likely that the system is unreliable.

The science myths that will not die

False beliefs and wishful thinking about the human experience are common. They are hurting people — and holding back science.

The Strangest, Most Spectacular Bridge Collapse (And How We Got It Wrong)

Bridge building has been bedeviling humans for a long time, probably since the 1st century. That may explain why, even when they can't carry lots of people or things, bridges are particularly good at carrying lots of meaning: breaking, burning, going too far, going nowhere; the bridges between cultures, across generations, the ones we’ll cross when we come to them. To this day, however, the meanings of Gertie's collapse and that unforgettable footage—"among the most dramatic and widely known images in science and engineering," wrote one engineer—remain murky.

For physics teachers, the footage of Gertie has proved irresistible as a lesson in wave motion—and, specifically, a textbook example of the power of forced resonance. The image of the undulating bridge left its mark on scores of students (including me) as a demonstration of what one canonical version of the film calls “resonance vibrations." Since then, scores of books and articles, from Encyclopedia Britannica to a Harvard course website, have reported that the Tacoma Narrows was destroyed by resonance.

But it turns out it wasn't. And yet, while science has known that for years, lots of people (including me) apparently didn't get the memo.

Guess the correlation

The aim of the game is simple. try to guess how correlated the two variables in a scatter plot are. The closer your guess is to the true correlation, the better.

Paradox at the heart of mathematics makes physics problem unanswerable

Gödel’s incompleteness theorems are connected to unsolvable calculations in quantum physics.

Undecidability of the Spectral Gap (full version) by Toby Cubitt, David Perez-Garcia, Michael M. Wolf

We show that the spectral gap problem is undecidable. Specifically, we construct families of translationally-invariant, nearest-neighbour Hamiltonians on a 2D square lattice of d-level quantum systems (d constant), for which determining whether the system is gapped or gapless is an undecidable problem. This is true even with the promise that each Hamiltonian is either gapped or gapless in the strongest sense: it is promised to either have continuous spectrum above the ground state in the thermodynamic limit, or its spectral gap is lower-bounded by a constant in the thermodynamic limit. Moreover, this constant can be taken equal to the local interaction strength of the Hamiltonian. This implies that it is logically impossible to say in general whether a quantum many-body model is gapped or gapless. Our results imply that for any consistent, recursive axiomatisation of mathematics, there exist specific Hamiltonians for which the presence or absence of a spectral gap is independent of the axioms. These results have a number of important implications for condensed matter and many-body quantum theory.

Notes on the Oxford IUT workshop by Brian Conrad

Since he was asked by a variety of people for his thoughts about the workshop, Brian wrote the following summary. He hopes that a non-specialist may also learn something from these notes concerning the present situation. Forthcoming articles in Nature and Quanta on the workshop will be addressed at the general public. This writeup has the following structure:

Background

What has delayed wider understanding of the ideas?

What is Inter-universal Teichmuller Theory (IUTT = IUT)?

What happened at the conference?

Audience frustration

Concluding thoughts

Technical appendix