It’s quite common for humans – especially those who work in manufacturing – to tie a knot, strip the casing off a cable, insert a pin in a hole or use a hand tool such as a drill. They may seem like simple tasks, but are really very complex and involve extremely fine finger and hand motions.

Though robots are getting more and more involved in factory work and in a wide range of other types of jobs – including in the service industry and health care – their dexterity is not nearly as impressive. Since people first brought them to work in automotive factories more than 50 years ago, we have built robots that can weld, paint and assemble parts quite well. Today’s best robotic hands can pick up familiar objects and move them to other places – such as taking products from warehouse bins and putting them in boxes.

But robots can’t orient a hand tool properly – say, lining up a Phillips head screwdriver with the grooves on a screw, or aiming a hammer at a nail. And they definitely can’t use two hands together in detailed ways, like replacing the batteries in a remote control.

Human hands are excellent at those tasks and much more. To even come close to rivaling what our hands are easily capable of, robot hands need better agility, reliability and strength – and they need to be able to sense more accurately and move even more finely than they do now, to figure out what they’re holding and how to grip it best. For robots to be able to work alongside humans, we’ll have to figure out how to make robots that can literally lend us a hand when our own two are not enough.

My research group at Northeastern University is working on doing just this, in particular for humanoid robots like NASA’s Valkyrie, which has three fingers and a thumb on each hand. Each digit has knuckle-like joints, and each hand has a wrist that can rotate easily. We’re working on creating motions – combinations of arm, wrist, finger and thumb movements that collectively accomplish a task, like moving a wrench in a circle to tighten a bolt, or pulling a cart from one place to another.

The importance of hands

Rather than making each robot a custom machine tailored for a very specific task, we need to design multi-use robots, or even such capable machines that they might be called “general purpose” – good for almost any task. One key to the success of these types of robots will be excellent hands.

Our work focuses on designing a new class of adaptable robot hands capable of precise fine movements and autonomous grasping. When robots are able to hammer in nails, change batteries and make other similar movements – basic for humans but very complex for robots – we’ll be well on our way to human-like dexterity in robotic hands.

Achieving this goal also involves inventing new designs that incorporate hard and soft elements – the way human bone gives strength to a grip, with skin spreading the pressure so a wine glass doesn’t shatter.

Faster development and testing

Modern technological improvements are making the development process easier. With 3D printing, we can make prototypes very quickly. We can even make low-cost disposable components to try different arrangements of mechanisms, like two- or three-fingered grippers for simple pick-and-place tasks or anthropomorphic robot hands for more delicate operations.

As electronic cameras and sensors get smaller, we’re able to incorporate them in new ways. For instance, if we put pressure sensors and cameras in a robotic hand, they can give feedback to the robot controller (whether human or automated) when a grip is secure, or if something starts to slip. One day they may be able to sense which direction the slipping object is moving, so the robot can catch it.

These abilities are already second nature to humans through vision and proprioception (the ability to sense the relative positions of body parts without looking or thinking about it). Once we’re able to achieve them in robots, they’ll be able to do things like detect if a grasp is too strong and is squeezing an object too hard.

Planning coordinated movements

Another milestone will be developing methods for robots to figure out what motions they need to make in real time, including sensing what’s going on in their hands at each moment. If a robot hand can detect changes in objects it is handling, or manipulate items while holding them, they could help with those common manual tasks like knot-tying and wire-stripping.

Working with two hands together is even farther into the future, though it would provide a significant boost, particularly for manufacturing. A robot that can operate a drill with two hands or pass machine parts from one hand to the other would be big improvements, allowing factories to automate even more steps in their processes.

We humans haven’t developed these systems yet. Achieving human-like autonomous robot dexterity will keep robotics researchers, technologists and innovators busy in the foreseeable future. It won’t slow down the ongoing robotics revolution in manufacturing, because current processes still have lots of room for automation to improve safety, speed and quality. But as we make robots even better, they’ll be able to give us a hand.

The April 4, 2017 chemical attack on the rebel-held town of Khan Sheikhoun in Syria led to at least 70 deaths and more than 100 people requiring medical attention, prompting an outcry from the international community. It led to the April 7 US bombing of the Shayrat air base.

It is alleged that sarin was used in the Khan Sheikhoun attack. This particular chemical became famous in 1995 with the Tokyo subway attack, launched by members of the cult movement Aum Shinrikyo.

Was it sarin?

Sarin is an organophosphorus compound and was first synthesised in 1938 in Germany as part of a pesticide research program.

Sarin is a moderately volatile substance – that is, it readily forms a gas – which can be taken up by inhalation or skin contact. It is an inhibitor of the enzyme acetylcholinesterase, which is critical in regulating nerve function.

When exposed to a low dose of a nerve agent such as sarin, people experience increased production of saliva, a running nose and a feeling of pressure on the chest. The pupils of the eye becomes contracted, so-called “pin-point” pupils.

Pin point pupils, which have been recorded in video footage of the Khan Sheikhoun attack, are a characteristic consequence of acetylcholinesterase inhibitors like sarin. This clinical sign is quite different from the irritating effects of chlorine and mustard gas.

Medium to higher dose exposure to sarin and other nerve agents can result in difficulty in breathing and coughing, abdominal cramps and vomiting, and sometimes involuntary discharge of urine and faeces. Increased saliva production, running eyes and sweating may occur, as well as muscular weakness, tremors or convulsions. Loss of consciousness, and death due to respiratory failure may be seen at higher doses.

Survivors of the Tokyo subway sarin attack recovered reasonably well but experienced some clinically detectable neurological effects, and some evidence of brain changes.

Although sarin use is suspected in Khan Sheikhoun, there are many organophosphorus insecticides that would exert the same effect (in sufficient quantity). It is possible that an organophosphate pesticide or a simple organophosphate (not normally classified as a chemical weapon) was used in this attack.

The production of sarin requires special facilities and is expensive, perhaps running into the tens of millions of dollars. Similar chemicals, such as tabun, are less expensive to make.

Will we ever know what was used?

In order to establish the identity of the substances used in Khan Sheikhoun, a combination of information needs to be gathered and assessed. In particular the results of chemical tests on wipe samples, soil and clothing samples must be determined and verified.

The Organisation for the Prohibition of Chemical Weapons (OPCW) Fact Finding Team would be the most authoritative source to reveal the nature of the chemical(s) used, and we will await their report. However, in the past these reports have been inconclusive owing to the time taken to gather chemical samples, limits of detection, specificity and the presence of mixtures.

The conflict in Syria involves the government military forces, the rebels, ISIS and the Kurds. It is sometimes hard to know where the chemicals might be coming from (for example, from neighbouring countries), or whether they have been produced or sourced locally.

Local history of chemical attacks

This experience in Syria may lead to improved medical responses in the case of future attacks. But in the absence of detailed knowledge of the substances involved, the treatment of casualties is unlikely to be optimal.

With so many individual chemical substances, and improvised mixtures, only generic decontamination and treatment procedures can be used. However, it may be feasible to have chemical specialists attached to hospitals collecting and storing specimens for subsequent analysis.

Sadly, the use of chemicals in Khan Sheikhoun is not an isolated incident. After all, a recent report of the OPCW Fact Finding Mission for the period December 2015 to November 20, 2016, recorded 65 potential incidents of the use of chemical weapons reported in open sources.

The use of chemical weapons has a long history in the region. On March 16, 1988, Iraq dropped bombs containing multiple toxic chemicals on the Kurdish city of Halabja, killing thousands.

It’s been the scientific equivalent of a never ending soap opera. The pygmy human species Homo floresiensis (aka ‘the Hobbit’), discovered in 2003 in a cave on the island of Flores, has been bogged down in a mire of controversy for almost 15 years.

Is it a new human species or just a diseased Homo sapiens? If it’s a new kind of human, where does it fit into the evolutionary tree? How old is it? How did it get to Flores in the first place? These are just a few of the questions that have befuddled anthropologists, and the reasons we’ve lacked satisfactory answers to them are three-fold.

First of all, we don’t yet have a lot of bones from the Hobbit’s kind, despite the valiant efforts of Indonesian, Australian and American archaeologists to find them. From Liang Bua 1 (LB1), the most complete individual found so far, there is a skull, shoulder, arm and forearm bones, wrist bones, close to half of its pelvis, and thigh, leg and foot bones.

Additional bones were found during excavations in 2004 from different individuals to LB1 and include an adult lower jaw and upper and lower limb bones, and even some limb bones from a Hobbit child.

Not a bad sample really, but there’s not nearly enough evidence to fully resolve its place in human evolution. And for many other species, like say Homo erectus from Indonesia, we don’t have many limb bones to compare with the Hobbit’s in the first place.

Bits of modern human here, pieces of Lucy’s kind there, chimpanzee resemblances everywhere! The Hobbit’s the weirdest looking human we’ve found so far, and its strange appearance is the second major reason why it’s been at the heart of one of the nastiest squabbles I’ve witnessed in anthropology.

The overall picture we get from the bones is of a creature that had a very small brain, large teeth and walked about on two-feet but in way very different to our own style of moving. Yet, strangely, it also had very short legs and long arms like a chimpanzee, and probably spent a lot of time living in the trees as well as toddling about on the ground.

Finally, the Hobbit was first believed to be just a mere 18,000 years old, though its age has now been revised to between 100,000 and 60,000 years old. This is way too young given the way the Hobbit looks! And while I don’t doubt it’s accuracy, it’s still shockingly young.

What we might expect to find at this time is something more akin to say a tropical Neanderthal. But instead, with the Hobbit, we have something much more primitive, more like Homo habilis or even Australopithecus afarensis, which both lived millions of years ago in Africa.

One researcher who has made it her life’s mission to resolve the Hobbit’s identity is Debbie Argue from the Australian National University. Argue has claimed to have finally solved the riddle of the Hobbit in a new study published in the Journal of Human Evolution.

According to Argue and her team’s findings the Hobbit is indeed a very primitive species and one closely related to Homo habilis. This fits with my own impressions of Homo floresiensis, but one must always keep an open mind and go where the data take you!

Now, if they’re right, then early humans must have migrated out of Africa more than 2 million years ago and spread right across Asia into the far reaches of oceanic Indonesia. Until the Hobbit came along we thought this region had only been settled by Homo sapiens perhaps 50,000 years ago. So this is a very big shift in our thinking!

Question is, are they right? Well, their work is detailed and undoubtedly well executed, and the results are pretty clear-cut. But there will always be uncertainty with these kinds of studies, and with the Hobbit in particular, for the reasons I’ve outlined.

Still, their broad findings are identical to another study published in 2015 by Mana Membo and her team which concluded the Hobbit to be one of the most primitive members of Homo found so far.

But I find it a little troubling that yet another study published only last year by Valeray Zeitoun and his team, using a similar method to both Argue and Membo, concluded the Hobbit could confidently be placed within Homo erectus.

Implication? The Hobbit isn’t a new species at all, but just a dwarfed version of Homo erectus. But I think it’s too soon to jettison the name Homo floresiensis just yet. For a start, only Argue’s study has accounted for the Hobbit’s weird limb bones, and these must surely weigh heavily on any decision we make about how to classify it?

For me, the Hobbit continues to be best understood as a very primitive member of Homo, with all of the implications this brings for us. And wow! What implications they are!

On a final note, despite the disagreement among these studies, they do mark a maturing of discussions surrounding the Hobbit. We seem to have finally said goodbye to the destructive personal attacks of the past and moved onto figuring out what the Hobbit really is.

Star-Lord Peter Quill and the gang are back as Guardians of the Galaxy, Volume 2 opens in cinemas from today in another outing of the galactic blockbuster.

It’s one of the most fun films I’ve seen in years, combining hilarity with characters you care about, and spectacular visuals that trump the first instalment, Guardians of the Galaxy in 2014.

With the awesome music of “Awesome Mixtape #2”, the team unravel the mystery parentage of Quill (played by Chris Pratt) and meet several new characters (watch the credits carefully). Old foes become new allies and there are treats in store for fans of the comics.

But what about the actual science in the film, how does that stack up?

I’m going to start by giving the film a very generous allowance for being a blockbuster made for entertainment, not an educational documentary. That being said, it’s always fun to get stuck into some of the maths- and science-filled scenarios in the film.

Be warned though, there are some mild spoilers ahead.

Maths fail as humour

It was fantastic to see the film uses explicit maths fails as an integral part of the humour.

Not surprisingly, some of the villain characters in the film aren’t particularly bright, and one memorable scene has them screwing up (in several different ways) elementary maths – basic fractions and percentages – when arguing about a juicy cash bounty.

Maths fails have been used as humour in other films and television shows; William Shatner’s tongue in cheek maths in Star Trek being one good example:

These were pretty simple maths fails though and there was a lot of other maths and science in the rest of the film.

Escaping a quantum asteroid field

In one of the many starship chase scenes in the film, the ships have to navigate through what is called a quantum asteroid field.

Asteroids come and go. 123rf.com/Tom De Spiegelaere/Michael Milford

Asteroids randomly appear and disappear as the ships navigate through the field, making it a very dangerous way to escape (a nice twist on traditional asteroid fields where you can see all the asteroids).

So what are the chances of a ship making it through the quantum asteroid field?

The field looks to be mostly empty space. So let’s say that each second the ship spends in the field, there’s a 1 in 100 chance that an asteroid will suddenly materialise on top of the ship, destroying it.

If a ship spends 3 minutes navigating the length of the field, we can calculate the chances of any one ship making it through:

= (survival chance per second)^{number of seconds}

= (1 – destruction chance per second)^{number of seconds}

= (1 – 0.01)^{3 × 60}

= (0.99)¹⁸⁰

= 16.38%

That’s pretty high actually, a 1 in 6 chance. From watching the film, it looks like not many make it through (apart from the heroes of course).

If we know how many of the ships actually make it through, we can work out the survival rate per second. Let’s say 1 (just the heroes’ ship) out of 100 ships make it through, then the chance of surviving the field per second becomes:

= (Chance of surviving field)^{1/number of seconds}

= (Chance of surviving field)^1/180

= (0.01)^1/180

= 0.9747

= 97.47%

Which would suggest a higher danger from the asteroids – a 2.53% chance of being destroyed by a quantum asteroid in any second.

Elevation grenades

Rocket Raccoon (again voiced somewhat unrecognisably by Bradley Cooper) gets to kick some butt in this film too.

Yet another unique weapon is some sort of electrical effect mine, which chucks aliens high up into the air only for them to fall back to earth again (see the trailer):

Elevating the aliens. 123rf.com/Beata Kraus, Chastity/Michael Milford

To chuck aliens so they reach the top of the pine trees (say 30m), we can work out the velocity of the blast:

2 × gravity × height-change = v-final² – v-initial²

At the top, the alien’s velocity (v-final) is zero, so:

2 × -9.81 × 30 = 0² – v-initial²

v-initial² = 2 × 9.81 × 30

v-initial = square root (2 × 9.81 × 30)

v-initial = 24.26 m/s

So to knock the aliens up to the treetops, the mine would have to propel them upwards at an initial speed of about 24m/s.

This is actually a very low blast velocity (possibly to reduce harm), compared to typical conventional explosives that can travel faster than the speed of sound (although objects hit by the blast don’t necessarily travel as fast).

Visiting every planet

One of the characters, the awesomely named Ego (Kurt Russell), has spent many years visiting many, if not all of the planets in the galaxy.

Visiting every planet. 123rf.com/Viktar Malyshchyts, Vadim Sadovski/Michael Milford

This, one can imagine, is not a trivial feat.

According to a recent study, there might be approximately 100 billion planets in our Milky Way galaxy.

To work out how long it normally takes to visit all these planets, you’d have to solve the infamous travelling salesman problem. This problem is about calculating the fastest way to visit a number of locations.

Luckily for us, this particular character regularly has to return to home base. We can simplify the calculation a little by assuming they only visit one planet per trip away from their base.

We also need to know how big the Milky Way is. Best estimates are that it’s between 100,000 and 180,000 light years in diameter. We can simplify this by saying it’s a circle of uniform diameter 140,000 light years.

We can also simplify matters by assuming that the home base is optimally positioned at the centre of the galaxy.

Our traveller is going to need to make 100 billion trips out to a planet and back.

Stars (and associated planets) are generally more densely distributed near the centre of the galaxy, and more sparse further out. A rough approximation we can use is that the average distance from home base to a planet is one quarter of the galaxy diameter – 35,000 light years. That’s a return trip of 70,000 light years, so the total trip distance is:

= average trip distance × number of trips

= 70,000 light years × 100,000,000,000

= 7,000,000,000,000,000 light years

That’s 7 quadrillion (7×10¹⁵) light years. The universe is estimated to be only about 14 billion years old, which is nowhere near enough time to visit all those planets one by one.

With some more calculations, it turns out even visiting all the planets in one go takes longer than the age of the universe.

So, even with speed of light transportation, this is stretching what might be possible for Ego.

Yondu kicks butt

Yondu Udonta (Michael Rooker) is the morally ambiguous rogue and leader of a group of outlaw mercenaries called the Ravagers. He kidnapped Peter as a boy in the original Guardians film, and raised him into adulthood, resulting in a complex relationship to say the least.

Yondu is armed with one of the most unique of weapons in recent film history, a lethal arrow that he can control by whistling. He uses it to great effect in the first film, but steps up his game even further in Volume 2.

Shooting the enemy, one arrow at a time. 123rf.com/mik38, Chastity/Michael Milford

In one scene, he clears out an entire ship of bad guys. It’s not clear how fast Yondu’s arrow can go, but let’s say it can go faster than a car but slower than a plane, say maybe 275kmh, like a conventional arrow.

A large spacecraft might have a couple of kilometres of corridors and various rooms spread out within it, so the time to clear out the baddies is:

= total distance / speed

= 2km / 275kmh

= 0.0073 hours

= 26.3 seconds

Most fight scenes involving Yondu don’t last more than a few seconds, so that sounds about right.

The verdict

Guardians of the Galaxy, Volume 2 is a lot of fun. Hats off to the scriptwriters and director for the explicit maths fail jokes, and for all the other science- and math-filled content.

Some of the fantastical situations in the film could happen mathematically, but at least one of them would be tough.

Still, films are made to be entertaining, and Guardians of the Galaxy, Volume 2 delivers in an epic way.

Humans are visual creatures. Objects we call “beautiful” or “aesthetic” are a crucial part of our humanity. Even the oldest known examples of rock and cave art served aesthetic rather than utilitarian roles. Although aesthetics is often regarded as an ill-defined vague quality, research groups like mine are using sophisticated techniques to quantify it – and its impact on the observer.

We’re finding that aesthetic images can induce staggering changes to the body, including radical reductions in the observer’s stress levels. Job stress alone is estimated to cost American businesses many billions of dollars annually, so studying aesthetics holds a huge potential benefit to society.

Researchers are untangling just what makes particular works of art or natural scenes visually appealing and stress-relieving – and one crucial factor is the presence of the repetitive patterns called fractals.

Pleasing patterns, in art and in nature

When it comes to aesthetics, who better to study than famous artists? They are, after all, the visual experts. My research group took this approach with Jackson Pollock, who rose to the peak of modern art in the late 1940s by pouring paint directly from a can onto horizontal canvases laid across his studio floor. Although battles raged among Pollock scholars regarding the meaning of his splattered patterns, many agreed they had an organic, natural feel to them.

My scientific curiosity was stirred when I learned that many of nature’s objects are fractal, featuring patterns that repeat at increasingly fine magnifications. For example, think of a tree. First you see the big branches growing out of the trunk. Then you see smaller versions growing out of each big branch. As you keep zooming in, finer and finer branches appear, all the way down to the smallest twigs. Other examples of nature’s fractals include clouds, rivers, coastlines and mountains.

In 1999, my group used computer pattern analysis techniques to show that Pollock’s paintings are as fractal as patterns found in natural scenery. Since then, more than 10 different groups have performed various forms of fractal analysis on his paintings. Pollock’s ability to express nature’s fractal aesthetics helps explain the enduring popularity of his work.

The impact of nature’s aesthetics is surprisingly powerful. In the 1980s, architects found that patients recovered more quickly from surgery when given hospital rooms with windows looking out on nature. Other studies since then have demonstrated that just looking at pictures of natural scenes can change the way a person’s autonomic nervous system responds to stress.

For me, this raises the same question I’d asked of Pollock: Are fractals responsible? Collaborating with psychologists and neuroscientists, we measured people’s responses to fractals found in nature (using photos of natural scenes), art (Pollock’s paintings) and mathematics (computer generated images) and discovered a universal effect we labeled “fractal fluency.”

Through exposure to nature’s fractal scenery, people’s visual systems have adapted to efficiently process fractals with ease. We found that this adaptation occurs at many stages of the visual system, from the way our eyes move to which regions of the brain get activated. This fluency puts us in a comfort zone and so we enjoy looking at fractals. Crucially, we used EEG to record the brain’s electrical activity and skin conductance techniques to show that this aesthetic experience is accompanied by stress reduction of 60 percent – a surprisingly large effect for a nonmedicinal treatment. This physiological change even accelerates post-surgical recovery rates.

Artists intuit the appeal of fractals

It’s therefore not surprising to learn that, as visual experts, artists have been embedding fractal patterns in their works through the centuries and across many cultures. Fractals can be found, for example, in Roman, Egyptian, Aztec, Incan and Mayan works. My favorite examples of fractal art from more recent times include da Vinci’s Turbulence (1500), Hokusai’s Great Wave (1830), M.C. Escher’s Circle Series (1950s) and, of course, Pollock’s poured paintings.

Although prevalent in art, the fractal repetition of patterns represents an artistic challenge. For instance, many people have attempted to fake Pollock’s fractals and failed. Indeed, our fractal analysis has helped identify fake Pollocks in high-profile cases. Recent studies by others show that fractal analysis can help distinguish real from fake Pollocks with a 93 percent success rate.

How artists create their fractals fuels the nature-versus-nurture debate in art: To what extent is aesthetics determined by automatic unconscious mechanisms inherent in the artist’s biology, as opposed to their intellectual and cultural concerns? In Pollock’s case, his fractal aesthetics resulted from an intriguing mixture of both. His fractal patterns originated from his body motions (specifically an automatic process related to balance known to be fractal). But he spent 10 years consciously refining his pouring technique to increase the visual complexity of these fractal patterns.

Fractal complexity

Pollock’s motivation for continually increasing the complexity of his fractal patterns became apparent recently when I studied the fractal properties of Rorschach inkblots. These abstract blots are famous because people see imaginary forms (figures and animals) in them. I explained this process in terms of the fractal fluency effect, which enhances people’s pattern recognition processes. The low complexity fractal inkblots made this process trigger-happy, fooling observers into seeing images that aren’t there.

Pollock disliked the idea that viewers of his paintings were distracted by such imaginary figures, which he called “extra cargo.” He intuitively increased the complexity of his works to prevent this phenomenon.

Pollock’s abstract expressionist colleague, Willem De Kooning, also painted fractals. When he was diagnosed with dementia, some art scholars called for his retirement amid concerns that that it would reduce the nurture component of his work. Yet, although they predicted a deterioration in his paintings, his later works conveyed a peacefulness missing from his earlier pieces. Recently, the fractal complexity of his paintings was shown to drop steadily as he slipped into dementia. The study focused on seven artists with different neurological conditions and highlighted the potential of using art works as a new tool for studying these diseases. To me, the most inspiring message is that, when fighting these diseases, artists can still create beautiful artworks.

My main research focuses on developing retinal implants to restore vision to victims of retinal diseases. At first glance, this goal seems a long way from Pollock’s art. Yet, it was his work that gave me the first clue to fractal fluency and the role nature’s fractals can play in keeping people’s stress levels in check. To make sure my bio-inspired implants induce the same stress reduction when looking at nature’s fractals as normal eyes do, they closely mimic the retina’s design.

When I started my Pollock research, I never imagined it would inform artificial eye designs. This, though, is the power of interdisciplinary endeavors – thinking “out of the box” leads to unexpected but potentially revolutionary ideas.

Our world view and resultant actions are often driven by a simple theorem, devised in secret more than 150 years ago by a quiet English mathematician and theologian, Thomas Bayes, and only published after his death.

Bayes’ Theorem was famously used to crack the Nazi Enigma code during World War II, and now manages uncertainty across science, technology, medicine and much more.

So how does it work?

Bayes’ Theorem explained

Thomas Bayes’ insight was remarkably simple. The probability of a hypothesis being true depends on two criteria:

1. how sensible it is, based on current knowledge (the “prior”)


2. how well it fits new evidence.

Yet, for 100 years after his death, scientists typically evaluated their hypotheses against only the new evidence. This is the traditional hypothesis-testing (or frequentist) approach that most of us are taught in science class.

The difference between the Bayesian and frequentist approaches is starkest when an implausible explanation perfectly fits a piece of new evidence.

Let me concoct the hypothesis: “The Moon is made of cheese.”

I look skywards and collect relevant new evidence, noting that the Moon is cheesy yellow in colour. In a traditional hypothesis-testing framework, I would conclude that the new evidence is consistent with my radical hypothesis, thus increasing my confidence in it.

But using Bayes’ Theorem, I’d be more circumspect. While my hypothesis fits the new evidence, the idea was ludicrous to begin with, violating everything we know about cosmology and mineralogy.

Thus, the overall probability of the Moon being cheese – which is a product of both terms – remains very low.

Admittedly, this is an extreme caricature. No respectable scientist would ever bother testing such a dumb hypothesis.

But scientists globally are always evaluating a huge number of hypotheses, and some of these are going to be rather far-fetched.

For example, a 2010 study initially suggested that people with moderate political views have eyes that can literally see more shades of grey.

This was later dismissed after further testing, conducted because the researchers recognised it was implausible to begin with. But it’s almost certain that other similar studies have been accepted uncritically.

The Bayesian approach in life

We use prior knowledge from our experiences and memories, and new evidence from our senses, to assign probabilities to everyday things and manage our lives.

Consider something as simple as answering your work mobile phone, which you usually keep on your office desk when at work, or on the charger when at home.

You are at home gardening and hear it ringing inside the house. Your new data is consistent with it being anywhere indoors, yet you go straight to the charger.

You have combined your prior knowledge of the phone (usually either on the office desk, or on the charger at home) with the new evidence (somewhere in the house) to pinpoint its location.

If the phone is not at the charger, then you use your prior knowledge of where you have sometimes previously left the phone to narrow down your search.

You ignore most places in the house (the fridge, the sock drawer) as highly unlikely a priori, and hone in on what you consider the most likely places until you eventually find the phone. You are using Bayes’ Theorem to find the phone.

Belief and evidence

A feature of Bayesian inference is that prior belief is most important when data are weak. We use this principle intuitively.

For example, if you are playing darts in a pub and a nearby stranger says that he or she is a professional darts player, you might initially assume the person is joking.

You know almost nothing about the person, but the chances of meeting a real professional darts player are small. DartPlayers Australia tells The Conversation there are only about 15 in Australia.

If the stranger throws a dart and hits the bullseye, it still mightn’t sway you. It could just be a lucky shot.

But if that person hits the bullseye ten times in a row, you would tend to accept their claim of being a professional. Your prior belief becomes overridden as evidence accumulates. Bayes’ Theorem at work again.

The one theory to rule them all

Bayesian reasoning now underpins vast areas of human enquiry, from cancer screening to global warming, genetics, monetary policy and artificial intelligence.

Risk assessment and insurance are areas where Bayesian reasoning is fundamental. Every time a cyclone or flood hits a region, insurance premiums skyrocket. Why?

Risk can be tremendously complex to quantify and current conditions might provide scant information about likely future disasters. Insurers therefore estimate risk based on both current conditions and what’s happened before.

Every time a natural disaster strikes, they update their prior information on that region into something less favourable. They foresee a greater probability of future claims, and so raise premiums.

Bayesian inference similarly plays an important role in medical diagnosis. A symptom (the new evidence) can be a consequence of various possible diseases (the hypotheses). But different diseases have different prior probabilities for different people.

A major problem with online medical tools such as webMD is that prior probabilities are not properly taken into account. They know very little about your personal history. A huge range of possible ailments can be thrown up.

A visit to a doctor who knows your prior medical records will result in a narrower and more sensible diagnosis. Bayes’ Theorem once again.

Alan Turing and Enigma

Bayesian approaches allow us to extract precise information from vague data, to find narrow solutions from a huge universe of possibilities.

They were central to how British mathematician Alan Turing cracked the German Engima code. This hastened the allied victory in World War II by at least two years and thus saved millions of lives.

To decipher a set of encrypted German messages, searching the near-infinite number of potential translations was impossible, especially as the code changed daily via different rotor settings on the tortuously complex Enigma encryption machine.

Turing’s crucial Bayesian insight was that certain messages were much more likely than other messages.

These likely solutions, or “cribs” as his team called them, were based on previous decrypted messages, as well as logical expectations.

For example, messages from U-boats were likely to contain phrases related to weather or allied shipping.

The strong prior information provided by these cribs greatly narrowed the number of possible translations that needed to be evaluated, allowing Turing’s codebreaking machine to decipher the Enigma code rapidly enough to outpace the daily changes.

Bayes and evolution

Why are we so interested in Bayesian methodology? In our own field of study, evolutionary biology, as in much of science, Bayesian methods are becoming increasingly central.

From predicting the effects of climate change to understanding the spread of infectious diseases, biologists are typically searching for a few plausible solutions from a vast array of possibilities.

In our research, which mainly involves reconstructing the history and evolution of life, these approaches can help us find the single correct evolutionary tree from literally billions of possible branching patterns.

In work – as in everyday life – Bayesian methods can help us to find small needles in huge haystacks.

The dark side of Bayesian inference

Of course, problems can arise in Bayesian inference when priors are incorrectly applied.

In law courts, this can lead to serious miscarriages of justice (see the prosecutor’s fallacy).

In a famous example from the UK, Sally Clark was wrongly convicted in 1999 of murdering her two children.

Prosecutors had argued that the probability of two babies dying of natural causes (the prior probability that she is innocent of both charges) was so low – one in 73 million – that she must have murdered them.

But they failed to take into account that the probability of a mother killing both of her children (the prior probability that she is guilty of both charges) was also incredibly low. So the relative prior probabilities that she was totally innocent or a double murderer were more similar than initially argued.

Clark was later cleared on appeal with the appeal court judges criticising the use of the statistic in the original trial.

This highlights how poor understanding of Bayes’ Theorem can have far-reaching consequences. But the flip side is that Bayesian methods with well justified, appropriate priors can provide insights that are otherwise unobtainable.

On April 6, 1917, the United States declared war against Germany and entered World War I. Since August 1914, the war between the Central and Entente Powers had devolved into a bloody stalemate, particularly on the Western Front. That was where the U.S. would enter the engagement.

How prepared was the country’s military to enter a modern conflict? The war was dominated by industrially made lethal technology, like no war had been before. That meant more death on European battlefields, making U.S. soldiers badly needed in the trenches. But America’s longstanding tradition of isolationism meant that in 1917 U.S. forces needed a lot of support from overseas allies to fight effectively.

In Europe, American combat troops would encounter new weapons systems, including sophisticated machine guns and the newly invented tank, both used widely during World War I. American forces had to learn to fight with these new technologies, even as they brought millions of men to bolster the decimated British and French armies.

Engaging with small arms

In certain areas of military technology, the United States was well-prepared. The basic infantrymen of the U.S. Army and Marine Corps were equipped with the Model 1903 Springfield rifle. Developed after American experience against German-made Mausers in the Spanish American War, it was an excellent firearm, equal or superior to any rifle in the world at the time.

The Springfield offered greater range and killing power than the U.S. Army’s older 30-40 Krag. It was also produced in such numbers that it was one of the few weapons the U.S. military could deploy with to Europe.

Machine guns were another matter. In 1912, American inventor Isaac Lewis had offered to give the U.S. Army his air-cooled machine gun design for free. When he was rejected, Lewis sold the design to Britain and Belgium, where it was mass-produced throughout the war.

With far more soldiers than supplies of modern machine guns, the U.S. Army had to adopt several systems of foreign design, including the less-than-desirable French Chauchat, which tended to jam in combat and proved difficult to maintain in the trenches.

Meeting tank warfare

American soldiers fared better with the Great War’s truly new innovation, the tank. Developed from the need to successfully cross “No Man’s Land” and clear enemy-held trenches, the tank had been used with limited success in 1917 by the British and the French. Both nations had combat-ready machines available for American troops.

After the U.S. entered the war, American industry began tooling up to produce the French-designed Renault FT light tank. But the American-built tanks, sometimes called the “six-ton tank,” never made it to the battlefields of Europe before the Armistice in November 1918.

Instead, U.S. ground forces used 239 of the French-built versions of the tank, as well as 47 British Mark V tanks. Though American soldiers had never used tanks before entering the war, they learned quickly. One of the first American tankers in World War I was then-Captain George S. Patton, who later gained international fame as a commander of Allied tanks during World War II.

Chemical weapons

Also new to Americans was poison gas, an early form of chemical warfare. By 1917 artillery batteries on both sides of the Western Front commonly fired gas shells, either on their own or in combination with other explosives. Before soldiers were routinely equipped with gas masks, thousands died in horrific ways, adding to the already significant British and French casualty totals.

Scientists on both sides of the war effort worked to make gas weapons as effective as possible, including by devising new chemical combinations to make mustard gas, chlorine gas, phosgene gas and tear gas. The American effort was substantial: According to historians Joel Vilensky and Pandy Sinish, “Eventually, more than 10 percent of all the chemists in the United States became directly involved with chemical warfare research during World War I.”

Naval power for combat and transport

All the manpower coming from the U.S. would not have meant much without safe transportation to Europe. That meant having a strong navy. The U.S. Navy was the best-prepared and best-equipped of all the country’s armed forces. For many years, it had been focusing much of its energy on preparing for a surface naval confrontation with Germany.

But a new threat had arisen: Germany had made significant progress in developing long-range submarines and devising attack tactics that could have posed severe threats to American shipping. German Navy U-boats had, in fact, devastated British merchant fleets so badly by 1917 that British defeat was imminent.

In May 1917, the British Royal Navy pioneered the convoy system, in which merchant ships carrying men and materiel across the Atlantic didn’t travel alone but in large groups. Collectively protected by America’s plentiful armed escort ships, convoys were the key to saving Britain from defeat and allowing American ground forces to arrive in Europe nearly unscathed. In fact, as military historian V.E. Tarrant wrote, “From March 1918 until the end of the war, two million U.S. troops were transported to France, for the loss of only 56 lives.”

Taking to the skies

Some of those Americans who made it to Europe climbed above the rest – right up into the air. The U.S. had pioneered military aviation. And in 1917, air power was coming into its own, showing its potential well beyond just intelligence gathering. Planes were becoming offensive weapons that could actively engage ground targets with sufficient force to make a difference on the battlefield below.

But with fewer than 250 planes, the U.S. was poorly prepared for an air war in Europe. As a result, American pilots had to learn to fly British and French planes those countries could not man.

Despite often lacking the weapons and technology required for success, it was ultimately the vast number of Americans – afloat, on the ground and in the air – and their ability to adapt and use foreign weapons on foreign soil that helped turn the tide of the war in favor of the Allies.

The discovery of massive galaxy that stopped making any new stars by the time the Universe was only 1.65 billion years old means we may have to rethink our theories on how galaxies formed.

The galaxy, known as ZF-COSMOS-20115, formed all of its stars (more than three times as many as our Milky Way has today) through an extreme starburst event.

But it stopped forming stars to become a “red and dead” galaxy not much more than a billion years after the Big Bang. Such galaxies are common in our Universe today but not expected to have existed at this ancient epoch. Galaxies turn red when they stop forming stars due to the resulting absence of hot, blue stars that have very short lifetimes.

This discovery by our team sets a new record for the earliest massive red galaxy, with details published in Nature this month.

It is an incredibly rare find that poses a new challenge to galaxy evolution models to accommodate the existence of such galaxies much earlier in the Universe.

An earlier discovery

To put this discovery in context, I’d like to give a short, personal history of research on early massive galaxies.

In 2004 I wrote an uncannily similar Nature paper about the existence of massive, old galaxies in the early Universe that were discovered in deep near-infrared surveys. At that time we were peering back across space to 3 billion years after the Big Bang.

These were a challenge for the models of galaxy formation that scientists were working with at the time, the start of a period where our pictures of how galaxies formed were rapidly being rewritten.

At the time, a picture of galaxies forming by lots of mergers in hierarchical assembly was in vogue. The problem was that this meant that today’s massive galaxies were in little bits billions of years ago.

But significant changes were made – driven in part by observations of the abundance of early massive galaxies, the observations of large gas-rich disk galaxies at these epochs and the discovery of “red nuggets” – extremely compact massive elliptical galaxies which stopped forming stars early on.

We moved to a picture where most galaxy growth and formation was driven by the formation of stars within the galaxy itself, from cosmic gas coming in to the galaxy.

This gas is fed into galaxies along the cosmic web by cold streams that are effective early on and allow us to grow massive galaxies more quickly in the computer modelling.

Many, many astronomers contributed to these developments and it was fun to play a minor role.

The new discovery

So what about this new discovery? This stems from the ZFOURGE survey, a deep near-infrared imaging survey we have been conducting on the Magellan telescopes in Chile, since 2010.

Back in 2013, one of our students, Caroline Straatman of Leiden University, discovered a population of pale red dots in the ZFOURGE survey.

These dots were bright in the near-infrared but very faint in the 35 other wavelength bands we observed. This peak suggested the presence of roughly 500 million year old stars but at a huge cosmic redshift.

In the local Universe this peak appears in blue light, so the redshift points to a time around 1.5 billion years after the Big Bang. The light suggested that no young stars were present, and the near-infrared brightness suggested these were massive objects (10¹¹ solar masses).

To put this in context, our Milky Way has been growing continuously for 12 billion years but is 3-5 times less massive.

Even more remarkably, the galaxies looked like ellipticals and were almost point sources, even with high-resolution Hubble Space Telescope observations. They were less than 5,000 light years across. Extremely dense red nuggets at an earlier time than anyone had suspected.

Lines in the spectrum

In 2012 a powerful new near-infrared spectrograph was commissioned on the W M Keck telescopes in Hawaii. Last year we used it to get a two-night exposure on some of these objects.

We were amazed when we got a spectrum of the brightest (and most massive). They showed the distinct signature of Balmer absorption lines of stars around 500 million years old. Importantly there was no sign of current star-formation.

This galaxy was already massive and between 500 million and 1 billion years old.

It must have formed extremely fast, and then its star formation died quickly. This extreme behaviour could require significant rewriting of our pictures of galaxy formation in the first billion years of cosmic history.

Why? Well, we think galaxies form in the centres of halos of cold dark matter. Dark matter particles is not made of ordinary atoms, and particle physicists are still trying to detect these in the laboratory.

These halos can form very early and act as seeds for galaxy formation giving it a kick start. Without dark matter it would be difficult to form any galaxy.

The problem is at this early time there are barely enough massive dark matter halos to accommodate such massive galaxies. As a consequence in simulated Universes we don’t find this population of non-star forming galaxies so early, nor do we find the massive ancestors with extreme star-formation rates a billion years earlier.

So, do we need two recipes for galaxy formation where some form extremely quickly and the rest take 12 billion years?

Time will tell. The history of this field has shown that the theoretical community has a very strong record of postdiction (as opposed to prediction), and I expect a slew of papers will turn up in the next few weeks to explain this object!

Teasing of theorists aside, galaxy formation is a very difficult field to work in; the astrophysics are complex and it is very much driven by new observations which is why it is so much fun to work in.

Meanwhile our groups are pursuing the quest for massive galaxies to even earlier times. We have designed new filters to identify these and hope to start a new survey using the Gemini telescopes this year. Theorists, get your predictions in now.

People have long been intrigued by figuring out the center of the places where we live.

You’re probably familiar with the concept of center of population. Imagine placing an equal weight at the residential location of each individual; the center of population would be the single point on a map that balances all those weighted spots. The U.S. Census Bureau, for example, produces a map each decade showing the location of the country’s center, summarizing the geographic distribution of the national population. The U.S. center has moved steadily west – it first crossed the Mississippi River in 1980 – and in recent decades has taken a turn to the south.

What about if you sweep all the people off the landscape? Where is the geographic center of a region? This simple question has both a clear answer and an interesting history. The geographic center is also a balance point – it’s analogous to a center of mass or a center of gravity. For a two-dimensional region, it is the point at which you could balance, say, a cardboard cutout of the region on the head of a pin.

And that, surprisingly, is exactly how the geographic center of the United States and its states were found by the U.S. Geological Survey in the 1920s. Spots in Piscataquis County, Maine, Twiggs County, Georgia, and McCulloch County, Texas, for instance, all got their claims to fame almost a century ago based on the head-of-a-pin method. The USGS’ findings at that time have since been perpetuated and sustained as lists you’d find in almanacs, statistical abstracts, various online sites and beyond.

Surely we can improve upon this cardboard cutout approach. I’ve come up with a new technique that can, in fact, find more accurate geographic centers.

What’s at stake

Who really cares about finding a geographic center, though? After all, it has no real-world correlation with how a landscape functions or the way an ecosystem works.

One motivating reason is that a geographic center is a location that provides maximum accessibility to all parts of the region. Historically, they were often used as the location for the seats of county government. Such locations ensured government offices would be equally accessible to all.

A second raison d’etre for geographic centers is that the concept has given places a way to claim something unique – a perhaps odd, but nevertheless definite, source of civic pride that simultaneously allows individual identification with place. It’s a way to tout the town and market it to tourists. Just as some people want to visit all state capitals or every state’s highest point, geographic centers offer yet another inventory for those compiling creative bucket lists. Other tourists simply find themselves close to the center and are drawn to it for a classic photo opp in front of a plaque or monument.

A third reason is more basic – as a fundamental summary measure for regions, we should make sure that we locate them accurately. Just as the center (or average, or mean) of a set of data provides a convenient summary measure, a geographic center summarizes succinctly the location of a region.

A more precise calculation

So, how do we find this point accurately? Most states have somewhat irregular shapes which make it harder to answer this question than if their borders described simple rectangles, for instance.

Some people have found the geographic center of two-dimensional polygons by taking a mathematical approach that uses the coordinates of the polygon’s corners. We know that the average of a set of numbers is the number which minimizes the sum of squared distances from all numbers in the set to itself. This is a characteristic of simple averages as well as centers of gravity. We can apply it to our region. We’re looking for the one spot in the region’s interior that has the smallest sum of squared distances from each point in the region.

While this two-dimensional solution might be adequate for finding the center of small geographical regions, for large regions we need to consider that they lie on the surface of what is close to a three-dimensional sphere – Earth.

Now the goal becomes one of finding the balance point as the location that minimizes the sum of squared great-circle distances from all points in the region to it. (The great-circle distance is the shortest distance between two points located on the surface of a sphere.)

To do this, the trick is to find an appropriate map projection. All map projections result in distortion of the Earth’s surface – the familiar Mercator projection, for example, is well known for its distortions of areas at high latitudes.

It turns out that another projection – the azimuthal equidistant projection – provides exactly what we want: It measures distance accurately from the center of the map. This is the version of our planet that you find on the United Nations’ emblem, where the map has been centered on the North Pole.

So, we can find the geographic center of a large region as follows, using a process of repeated refinement:

1. Map the region’s boundary using the azimuthal equidistant projection, initially guessing where the geographic center might be, and centering the map there.


2. Use the existing mathematical method for finding the center of a two-dimensional polygon to find the geographic center on this initial map.


3. Use the result from step 2 to create a new azimuthal equidistant map, this time centered on the new estimate of the center.


4. Repeat steps 2 and 3 until the location of the center does not change from one step to the next.

How much of an improvement is this over the old cardboard method? Road-trippers and tourist bureaus don’t need to panic, but there are 10 states where the geographic center, as determined by this method, moved by more than five miles from the old USGS centers. Discrepancies tend to be largest for the largest states and states with more complex shapes (including Alaska, Florida, Texas and New York). The geographic center for the entire contiguous U.S. lies near Agra, Kansas, 27.9 miles from the USGS’ long-designated center in Lebanon, Kansas. No word on whether a rivalry has emerged in the Sunflower State.

Many Americans are worried about their online privacy and security. And rightly so: Nearly half of Americans have encountered at least one serious problem with online safety.

There are a wide range of potential problems: Some people fall victim to criminally malicious attackers who steal personal information like Social Security or bank account numbers, compromise online accounts and conduct online scams stealing people’s money. Other people find friends or family members have shared private information without their consent. And still others lose jobs or other opportunities because prospective employers find unflattering information about them online. What all these situations have in common is simple: We do not have control over the information we believe to be private.

One key to staying safer online may be getting advice from the right places – people and sources with accurate, helpful information that can let you take control of your online privacy and security. My own research, in collaboration with Sean Kross and Michelle Mazurek, explores where people get their advice about online security, and how useful it actually is.

Those sources include librarians, government websites and co-workers. They offer a wide range of advice, such as customizing social media privacy settings and using password managers, which can make it easier to use strong, complex passwords without having to remember them.

We analyzed a survey of 3,000 internet users across the United States, and found that where people get advice has a lot to do with their online safety experiences. We found that no matter how wealthy or how poor a person is, no matter her education level, the speed of her internet service or whether she has a smartphone, a person’s online safety is closely related to where, and from whom, she gets advice about online security.

Finding good advice

Approximately 70 percent of Americans learn about online security behaviors as a result of advice shared by friends, family and co-workers, or on websites they visit. Often they get this advice in casual conversation or web browsing. The advice they get can influence their behavior, ideally making them better at protecting themselves in the future.

Many people get privacy and security advice from their friends and relatives: 38 percent of Americans received assistance from people close to them. But they may not get very good information: 49 percent of them reported at least one online safety incident, such as identity theft or falling victim to an online scam. Emotional closeness doesn’t necessarily mean someone has good information to share.

Twenty percent of Americans sought out advice from their co-workers. One in four of those who did so also reported an online safety incident – half as many as those who took advice from friends and family.

The 25 percent of Americans who take advice from websites report fewer incidents than those who took advice from friends and coworkers. Only 14 percent of people who took advice from a government website reported an online safety problem. And just more than one in five people who took advice from a nongovernmental website reported an online safety incident.

The 13 percent of Americans who get advice from teachers or librarians, however, report the lowest frequency of online negative experiences: 8 percent of them had an online safety problem.

Evaluate the source

With so much security advice available, of such varied quality, our research suggests people should not just follow their friends’ advice, or do something they read about online. Instead, when asking for advice from co-workers, friends and family, people should also ask how they learned this information. And they should think critically about the answers they get. Do those answers jibe with other advice from other sources? Seeking out people who work in internet or technology fields can also give useful perspectives, either about others’ advice or their own suggestions.

Our findings also suggest that librarians are underutilized but potentially very valuable sources of online safety information. We asked local librarians for a few suggestions of good resources for getting started with protecting your information. They recommended Get Started With Privacy, the Security Cheat Sheet and Security Starter Pack & Tutorials as good first steps to making an online security plan.

To help keep children safe online, the librarians also recommended the National Cybersecurity Alliance website, with security and privacy activities and information for kids and parents alike. Our research also suggests that teachers may be a good source of high quality online security advice.

Research suggests that people should keep their software updated, use a password manager to assist with having strong and unique passwords and use two-factor authentication to further secure their online accounts. With better advice from better sources, more people will stay safer online.

Learning how to drive is an ongoing process for we humans as we adapt to new situations, new road rules and new technology, and learn the lessons from when things go wrong.

But how does a driverless car learn how to drive, especially when something goes wrong?

That’s the question being asked of Uber after last month’s crash in Arizona. Two of its engineers were inside when one of its autonomous vehicles spun 180 degrees and flipped onto its side.

Uber pulled its test fleet off the road pending police enquiries, and a few days later the vehicles were back on the road.

Smack, spin, flip

The Tempe Police Department’s report on the investigation into the crash, obtained by the EE Times, details what happened.

The report says that the Uber Volvo (red in the graphic below) was moving south at 38mph (61kmh) in a 40mph (64kmh) zone when it collided with the Honda (blue in the graphic) turning west into a side street (point 1).

Knocked off course, the Uber Volvo hit the traffic light at the corner (point 2) and then spun and flipped, damaging two other vehicles (points 3 and 4) before sliding to a stop on its side (point 5).

Thankfully, no one was hurt. The police determined that the Honda driver “failed to yield” (give way) and issued a ticket. The Uber car was not at fault.

Questions, questions

But Mike Demler, an analyst with the Linley Group technology consultancy, told the EE Times that the Uber car could have done better:

It is totally careless and stupid to proceed at 38mph through a blind intersection.

Demler said that Uber needs to explain why its vehicle proceeded through the intersection at just under the speed limit when it could “see” that traffic had come to a stop in the middle and leftmost lanes.

The EE Times report said that Uber had “fallen silent” on the incident. But as Uber uses “deep learning” to control its autonomous cars, it’s not clear that Uber could answer Demler’s query even if it wanted to.

In deep learning, the actual code that would make the decision not to slow down would be a complex state in a neural network, not a line of code prescribing a simple rule like “if vision is obstructed at intersection, slow down”.

Debugging deep learning

The case raises a deep technical issue. How do you debug an autonomous vehicle control system that is based on deep learning? How do you reduce the risk of autonomous cars getting smashed and flipped when humans driving alongside them make bad judgements?

Demler’s point is that the Uber car had not “learned” to slow down as a prudent precautionary measure at an intersection with obstructed lines of sight. Most human drivers would naturally beware and slow down when approaching an intersection with obstructed vision due to stationary cars.

When it comes to deep reinforcement learning, this relies on “value functions” to evaluate states that result from the application of policies.

A value function is a number that evaluates a state. In chess, a strong opening move by white such as pawn e7 to e5 attracts a high value. A weak opening such as pawn a2 to a3 attracts a low one.

The value function can be like “ouch” for computers. Reinforcement learning gets its name from positive and negative reinforcement in psychology.

Until the Uber vehicle hits something and the value function of the deep learning records the digital equivalent of “following that policy led to a bad state – on side, smashed up and facing wrong way – ouch!” the Uber control system might not quantify the risk appropriately.

Having now hit something it will, hopefully, have learned its lesson at the school of hard knocks. In future, Uber cars should do better at similar intersections with similar traffic conditions.

Debugging formal logic

An alternative to deep learning is autonomous vehicles using explicitly stated rules expressed in formal logic.

This is being developed by nuTonomy, which is running an autonomous taxi pilot in cooperation with authorities in Singapore.

NuTonomy’s approach to controlling autonomous vehicles is based on a rules hierarchy. Top priority goes to rules such as “don’t hit pedestrians”, followed by “don’t hit other vehicles” and “don’t hit objects”.

Rules such as “maintain speed when safe” and “don’t cross the centreline” get a lower priority, while rules such as “give a comfortable ride” are the first to be broken when an emergency arises.

While NuTonomy does use machine learning for many things, it does not use it for normative control: deciding what a car ought to do.

In October last year, a NuTonomy test vehicle accident was involved in an accident: a low-speed tap resulting in a dent, not a spin and flip.

The company’s chief operating officer Doug Parker told IEEE Spectrum:

What you want is to be able to go back and say, “Did our car do the right thing in that situation, and if it didn’t, why didn’t it make the right decision?” With formal logic, it’s very easy.

Key advantages of formal logic are provable correctness and relative ease of debugging. Debugging machine learning is trickier. On the other hand, with machine learning, you do not need to code complex hierarchies of rules.

Time will tell which is the better approach to driving lessons for driverless cars. For now, both systems still have much to learn.