Month: July 2016

Debunking One Of The Biggest Stereotypes About Women In The Gaming Community

Although women now make up almost half of all video game players, the gaming community remains, in some ways, hostile toward women.

For example, the GamerGate controversy, which began in 2014 and involved a harassment campaign against prominent female gamers, journalists and designers, reflected a longstanding undercurrent of misogyny and sexism in the community. In some cases, those who challenged the sexism found themselves threatened with rape or death.

Theres also the long-held stereotype that men are simply better gamers than women. Women gamers are often perceived as incompetent players who arent genuinely interested in the games but rather sign up to get attention. If a female gamer does play well, shes often derided as a hacker someone who cheats to gain an advantage because there is no way a girl can be that good.

In a recent study, we set out to examine whether men really make better gamers than women and, if so, what drove the gender performance gap. Specifically, we wanted to compare how quickly men and women leveled up in Massively Multiplayer Online (MMO) games, which are online worlds where thousands of players develop characters, make friends, join groups, complete quests and slay dragons together.

If men are actually better gamers than women, they should advance to higher levels within the same amount of play time. But if they dont progress any faster, this finding would help refute one of the most pervasive stereotypes that continue to exist in the gaming community.

The Conversation

Getting to the next level

Our research used anonymous server data from over 10,000 men and women in two MMOs, EverQuest II in the United States and Chevaliers’ Romance III in China. We knew each players actual gender through their account registration information.

When players finish quests and kill monsters in MMOs, they earn experience points. When experience points reach a threshold, the player ascends to the next level, which unlocks new abilities, skills and access to new content. As in most video games, levels indicate a players progress.

Naturally, players spending a lot of time in the game are likely to reach high levels. That is why the speed of leveling up, rather than the level itself, measures performance in our study.


A still from EverQuest II, one of the two MMO games analyzed in the study. Phil… Just Phil/flickr, CC BY-ND

Before getting to our findings, we want to point out a couple of things we took into consideration. First, players who had reached the top level in the games were excluded in our analyses. Because top-level players couldnt advance any further, their rate of leveling up was essentially zero. We removed these players to avoid confounding our analyses, but this also meant that we were not able to measure gender differences between the most advanced players.

Second, our analysis recognized that the rate of leveling up slows down as players progress. For example, it would take a lot more time and effort for a level 60 player to level up than a level 30 player. Therefore, our analysis compared apples to apples by evaluating players’ performance only against others who were at the same level.

Contrary to the stereotype, we found that player gender itself does not cause performance differences. Instead, the perception of women as poor gamers is fueled by other factors. For example, we found that women spent less time playing overall than men and chose more assistive character classes, such as Priests, who fare better healing group members than fighting on their own. When we took such factors into account by statistically controlling them in the analyses, the gender performance gap disappeared; women advanced at least as fast as men did in both games.

We also realized that different players are interested in different aspects of MMOs, and a few of those differences may correlate with gender. Theres some empirical evidence that men tend to focus more on achievement in video games leveling up rapidly, gaining in-game status and competing against others while women are drawn to social interactions, whether its helping other players or forming long-term relationships.

This suggests that men should advance faster than women. However, we found the opposite: Women advanced at least as fast as men did. So taking into account different play motivations (which we were unable to do in this studys analysis) likely only strengthens our conclusions.

Beyond video games

The stereotype that women are inferior gamers is not only false, but could also make women more easily discouraged and less likely to play in the first place. Of course, this gender performance stereotype exists in a number of other contexts. In the software development community GitHub, for example, women are perceived as worse coders than men.

Our research has notable implications for this important social issue. Studies have shown that video games can be an important gateway to science, technology, engineering and mathematics (STEM) fields. If stereotypes about girls and women are preventing them from playing, then it could potentially contribute to preexisting gender inequality and stereotyping in these fields.

One approach to dealing with this issue is to promote stereotype-free gaming experiences for women and girls through female-supportive gaming communities, such as the PMS Clan, one of the oldest and most renowned female-oriented gaming communities in the world. Scholars such as Gabriela Richard at Pennsylvania State University have found that members of these communities are more confident and perceive themselves as better gamers.

Game designers can also help. They have the ability to construct the games to make them less hostile and more welcoming to female players. For example, Riot Games established the Tribunal, a system that allows the player community to review reported bad behaviors from fellow players, and then vote on whether to punish the offender. Banned players also get a reform card with the details of the offense, as well as judgments from the Tribunal. So far, the Tribunal has significantly reduced online harassment.

While programs like Tribunal are a starting point in the larger battle to end gender stereotypes, our findings will hopefully allow female gamers to realize that, when it comes to inherent skill, theyre on a level playing field.

The ConversationCuihua Shen, Professor of Communication, University of California, Davis and Rabindra Ratan, Assistant Professor of Communication, Michigan State University

This article was originally published on The Conversation. Read the original article.

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This Proposed Lego Set Honors Women In NASA

More than 40 American women have flown in space, and many others have worked at NASA as cosmonauts, analysts, researchers and engineers. Yet when most people think about the U.S. space program, it’s the names of men that tend to first come to mind: Buzz and Neil, Carl and Alan, Gus and Jim.

But one female science writer is trying to change that with the help of a handful of figurines.

Maia Weinstock, deputy editor of MIT News and a self-described “Lego tinkerer,” has proposed a new Lego set celebrating the women of NASA.

The set would come with five figurines representing five notable NASA pioneers: Margaret Hamilton, Katherine Johnson, Nancy Grace Roman, Mae Jemison and Sally Ride. 

Maia Weinstock
A science writer has proposed this new Lego set celebrating the women of NASA.

Hamilton was a computer scientist who developed onboard flight software for the Apollo mission, and Johnson was a mathematician who worked on the Mercury and Apollo programs. According to NASA, Johnson’s calculations were “critical” to the success of the Apollo moon landing program.  

Maia Weinstock
Katherine Johnson, mathematician and space scientist.

Maia Weinstock
Computer scientist Margaret Hamilton.

Roman was an astronomer and one of the first female executives at NASA. Known as the “Mother of Hubble,” she was one of the masterminds behind the Hubble Space Telescope. 

Ride and Jemison were both astronauts. Ride became the first American woman in space in 1983. About a decade later, Jemison became the first African-American woman in space.

“I think it’s so vitally important that all people in this world are involved in the process of discovery,” Jemison once said.

Maia Weinstock
Lego versions ofSally Ride (left) and Mae Jemison.

“Women have played critical roles throughout the history of the U.S. space program … yet in many cases, their contributions are unknown or under-appreciated — especially as women have historically struggled to gain acceptance in the fields of science, technology, engineering, and mathematics (STEM),” Weinstock wrote in her Lego Ideas proposal.

Lego Ideas encourages people to suggest new Lego sets to the company. If a project hits 10,000 supporters, the proposed set is sent for official review.

Weinstock’s proposal had garnered about 3,000 supporters as of Monday morning. NASA itself has shown its support:

In recent years, Lego has been adding more female characters in scientific fields to its collection. In 2013, for instance, it released its first female lab scientist minifigure. Last year, new spaceport sets included female aerospace engineers and female astronauts. 

Still, based on Lego Ideas proposals, it seems consumer interest in female STEM figurines remains high. In addition to the Women in NASA set, there are currently also proposals for an Amelia Earhart set, a Girls in STEM set and a number of other science-related sets featuring female characters.

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Jason Day leads big hitters hoping to follow Henrik Stensons example

The US PGA Championship is the second of two quickfire majors and it could define the season for some of golfs more illustrious names

The confirmation Tiger Woods will not participate in the US PGA Championship represented little more than an exercise in administration with 2016s final major lending itself to a multitude of more fascinating storylines. With each medical bulletin, Woods career is consigned further into the past. Chief among more pressing matters is the sudden possibility of Jason Day, Jordan Spieth and Rory McIlroy concluding the year without a major success.

An Oxford graduate in mathematics is hardly required to point out that at least two of the illustrious trio will suffer such a fate. In this, the second major in three weeks, fast conclusions are inevitable. Seasons will suddenly be defined.

One wonders what golf has left aside for its latest trick. The majors of 2016 have proved epic for such different reasons: Spieths collapse at Augusta, the rules fiasco and ending of Dustin Johnsons drought at Oakmont. A week ago, Henrik Stenson emerged triumphant from one of the most sensational days of championship golf in memory. The Masters, US Open and Open Championship have all seen first-time major champions.

The curious scheduling of this season, owing primarily to the return of golf to the Olympic Games, means Stenson would be entitled still to be in celebratory mode when the US PGA gets underway at Baltusrol from Thursday. The rest of us are still catching breath from super Sunday in Ayrshire. If it is unfortunate Stenson will not have the down time he unquestionably earned, golf fans should relish the return to a stage that has produced such fireworks. Even 2015s majors, the Open perhaps aside, threw up special narratives as befitting their status.

Baltusrols lower course can stretch to 7,400 yards, a matter that will disappoint the traditionalists. Yet there is endearing history at the New Jersey venue: Jack Nicklaus won two of his US Opens there with Phil Mickelsons solitary success in the final major of the year coming at Baltusrol in 2005. Mickelson prevailed on a Monday finish, owing to weather delays, having shot rounds of 67, 65, 72 and 72. Four under par was rather typical of winning Baltusrol aggregates, in a nod to how fierce this course can be. Stenson made the cut 11 years ago, finishing in a share of 47th. Then aged 29, this marked only the second time Stenson had survived for a major weekend.

Mickelson was therefore worthy of sufficient spotlight this time around even before the part he played in Stensons Royal Troon triumph. Mickelson did next to nothing wrong on the closing day but still found himself signing for a 65 in the painful knowledge that, at 46, he will not have many major opportunities left.

This timing doesnt give me a chance to take time off, Mickelson said. It forces me to keep my game sharp. Ive got a lot of special memories going back to Baltusrol and probably that we dont have a month to wait between majors is a good thing for me. Ill try to look at the positives and take that into Baltusrol and keep my game sharp, as opposed to going home and taking some time off.

Im very excited with the work Ive put in with how [Mickelsons coach] Andrew Getson has helped me with my swing. The way I was able to hit fairways with ease coming down the stretch at Troon and hit my iron shots right on line, draws and fades and so forth, basically that comes from getting my swing back on plane.

Its been a little work in progress to get it on plane and then capture the field and the face awareness throughout the swing. Four days at the Open was pretty stress-free golf. So it tells me that weve done good work. Im excited where my game is at and where its headed.

That said, surely an element of mental scarring is inevitable. Mickelson could barely believe the lengths to which Stenson reached to claim the Claret Jug. In what represents further bad news for Mickelson, and despite a couple of exceptions, the US PGA has proved a young mans game in recent times. Twelve months ago, Day lifted the Wanamaker Trophy when in the midst of a run of four wins from late July to the same juncture of September.

Its been a crazy last 12 months, said Day this week in Ontario, where he is also the defending champion at the Canadian Open.

I cant get too complacent with where Im at. I know that Im currently ranked the best player in the world but I need to work hard. I need to work harder than I ever have before to keep that spot. I need to work harder than I ever have before to win tournaments, because its only getting tougher.

I guess the way that I look at myself is a little bit different, too. Coming into this event last year, I felt confident about my game. But knowing this event would springboard me to six wins, a major championship, getting to No1, Id be very surprised by that.

Its coming into the crunch time for me pressure-wise, because being kind of the favourite going into each tournament and expectation levels are high and then all that amounts to pressure you put on yourself and stress you put on yourself. Youve got to somehow manage yourself, manage your ego; then somehow execute the shot, execute the gameplan, and go out there and try to win.

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How A Little Mathematics Can Help Create Some Beautiful Music

The ConversationSince the time of Pythagoras around 500 BCE, music and mathematics have had an intimate and mutually supportive relationship.

Mathematics has been used to tune musical scales, to design musical instruments, to understand musical form and to generate novel music. But what can mathematics say about one of the most common features of contemporary music rhythmic loops?

Repeated rhythmic loops are an essential component of most electronic dance music and hip-hop, and also play an important role in rock, jazz, Latin and non-Western music.

Now, two mathematical models of rhythmic loops made in a free software application called XronoMorph can be used to generate exciting new musical structures that would otherwise be hard to compose or perform.

XronoMorph: An Introduction

Rhythmic Loops: Circles And Polygons

A natural geometrical characterisation of a periodic structure, such as a rhythmic loop, is as a circular arrangement of points. You can travel clockwise around a circle but inevitably you come back to where you started.

A common feature of rhythmic loops is that they are multilevel. For example, in Latin percussion, different instruments play different interlocking patterns that may or may not coincide. Such rhythms can be depicted by multiple polygons on the same circle.

A simple geometrical representation is to draw lines that make each of these independent levels into an independent polygon. In this way, a multilevel rhythm becomes a collection of inscribed polygons.

Clave (top) + Conga (bottom) rhythm in score notation. Andrew Milne, Author provided Clave (red) + Conga (blue) rhythm as polygons. Andrew Milne, Author provided

But Which Polygons?

There are more than 17 trillion different rhythms, and that is only counting rhythms with three levels where every beat occurs at one of 16 distinct time locations (16 being a very common temporal subdivision in music).

But, realistically, only a small proportion of these are of musical interest. The trick is to find them.

Two mathematical principles well-formedness and perfect balance allow us to easily navigate two distinct rhythmic sub-spaces that are of musical interest, but hard to explore with traditional computational tools or notation.

Well-Formed Polygons

Well-formedness elegantly generalises three properties commonly found in real-world multilevel rhythms:

  • each rhythmic level comprises only a small number of distinct beat lengths, often only one or two;

  • each levels beats are fairly evenly spaced in time there arent sudden clusters of events followed by long gaps; and

  • the rhythmic levels are hierarchical there is a slow and metrically dominant level; above this is a faster and weaker level that splits the previous levels beats; above this is an even faster and weaker level that splits the previous levels beats; and so on.

Every level of a well-formed rhythm has two beat lengths: a long beat and a short beat. The length of a given beat is the time between its onset and the onset of the following beat.

A multilevel well-formed rhythm can then be fully defined by three numerical parameters: the numbers of long and short beats in the lowest level rhythm, and the ratio of the sizes of its long and short beats.

From these three numbers, an entire rhythmic hierarchy can be calculated, such that each level has no more than two beat lengths, each level arranges these beat lengths to make them as evenly spaced as possible and each successive level in the hierarchy is created by splitting the long beats of the level below.

Using XronoMorph, the above three parameters can be freely manipulated. The rhythmic hierarchy emerging from them often has great aesthetic appeal. Every level is related to every other level and is also intrinsically well-formed. Together, they create a somewhat self-similar and interwoven structure reminiscent of fractals.

A demonstration of how a well-formed hierarchy is built, and the effect of the lowest levels beat-size ratio.

Perfectly Balanced Polygons

Perfect balance is a mathematical principle that can generalise polyrhythms, a type of rhythm commonly used in sub-Saharan African music.

Unlike well-formed rhythms and most Western rhythms, polyrhythms are not hierarchical. They are more like an alliance of different rhythmic levels, each of equal status.

In a polyrhythm, two or more levels, each comprising evenly spaced beats, are superimposed.

Geometrically, they are combinations of regular polygons like equilateral triangles, squares, regular pentagons, and so forth. In real-world polyrhythms, beats from all levels typically coincide at a single location in the period.

A standard 2:3:6 polyrhythm. For clarity, the hexagonal level is not shown.

A standard 3:4:12 polyrhythm. For clarity, the 12-gon level is not shown.

A standard 3:5:15 polyrhythm. For clarity, the 15-gon level is not shown.

A notable feature of these polyrhythms is that the average position, or centre of gravity, of the circularly arranged beats is precisely at the centre of the circle. This property is defined as perfect balance.

All regular polygons are perfectly balanced, so any combination of regular polygons is also perfectly balanced, and this is true regardless of the individual rotations of the polygons.

This allows an immediate generalisation of standard polyrhythms. The regular polygons can be independently rotated (time-shifted) so they never coincide. This is a musical feature that is, as far as we know, rarely exploited but which produces exciting rhythmic grooves.

Perfectly balanced music constructed with independently rotated regular polygons: 2 digons, 3 squares, 1 heptagon. The polygons have been independently rotated so unlike a standard polyrhythm there is no single location at which they all coincide.

But perfect balance opens up yet another fascinating generalisation of standard polyrhythms. There are certain perfectly balanced shapes irregular elemental polygons that are not produced by a simple combination of regular polygons.

An irregular elemental polygon: 1 triangle + 1 pentagon – 1 digon. Only the labelled vertices are sounded. Andrew Milne, Author provided An irregular elemental polygon: 2 digons + 3 pentagons – 3 digons – 2 triangles. Only the labelled vertices are sounded. Andrew Milne, Author provided

Intriguingly, such polygons are constructed by summing differently rotated positively-weighted and negatively-weighted regular polygons. When a positively-weighted vertex and a negatively-weighted vertex coincide they cancel out.

Legal patterns are produced when no negative weights are left behind. So, although we never hear these negative beats directly, they have a ghostly impact by cancelling out some of the positive beats.

In XronoMorph, a wide choice of regular and irregular elemental polygons can be combined and independently rotated, creating a fascinating subspace of generalised polyrhythms.


We developed the rhythmic loop generator XronoMorph to demonstrate these principles, hoping it might inspire musicians and music enthusiasts to create novel and interesting rhythms that would be hard to play manually or to otherwise compose.

Simple and attractive software interfaces can also transform a need for expert knowledge into a willingness to intuitively interrogate the interface. In this way, we also hope it will encourage musical engagement, with potential application in music education by allowing visual exploration of complex rhythmic patterns.

Early reaction from musicians and composers has been highly enthusiastic with comments such as This is an inspired design truly musical, the most interesting and inventive new app around and this really helps me better understand and create beats.

This lends support to the long-held notion that there is a profound connection between mathematics and music, and that a little mathematics can help create some beautiful music.

XronoMorph screenshot. Andrew Milne, Author provided

Andrew J. Milne, Postdoctoral Research Fellow in Music Cognition and Computation, Western Sydney University and Steffen A. Herff, PhD candidate, Memory and Music Perception, Western Sydney University

This article was originally published on The Conversation. Read the original article.

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Mastery Over Mindset: The Cost Of Rolling Out A Chinese Way Of Teaching Maths

The ConversationHalf of primary schools in England will receive 41m over four years to teach mathematics using a method called the mastery approach that is used in Chinese schools. Yet during the last ten years many primary schools in England have started embracing another method, called the mindset approach, which is supported by 30 years of psychological research in the US and more recently in the UK.

While the mastery model breaks down learning into small goals which have to be achieved before moving on, the mindset maths model aims to get pupils to develop an intuitive understanding of mathematical concepts before learning formal procedures such as addition or multiplication. Can the two work together in schools to help young children learn maths?

Mindset Is About Motivation

Mindset theory has established that each person has ingrained beliefs regarding each subject, which pre-determine whether learning the subject will be successful. Carol Dweck, the most prominent researcher in this field, has demonstrated spectacularly that a wrong kind of environment can destroy a learners motivation, possibly with long-lasting effects.

Learning environments impact how well people learn.Syda Productions/Shutterstock

Vice versa, it is possible to build learning environments which nurture a learners motivation and so make learning possible. Mathematics, a subject which is often portrayed as difficult in the media, has immediately attracted the attention of researchers, and a number of principles have evolved for developing classroom environments which are conducive to learning mathematics.

One thing that proponents of both the mastery and mindset theory agree with is avoiding the idea that a child can have a gift for maths so that high expectations are set for all pupils. According to mindset theory, a learners belief that they are or are not talented is a dangerous illusion, which damages their progress.

Some of the suggestions for organising in-class activities are similar in the mastery and mindset approaches. For example, all pupils spend the same period of time working on the same problem, rather than some pupils racing forward to the next problem. This may involve some pupils starting work, perhaps unsuccessfully, on some deeper or more general versions of the problem.

A Shortcut To Maths Concepts

While on the surface the mastery approach talks of a curriculum designed to enable deep conceptual, as well as procedural, knowledge, a look at its principles and sample lessons reveals undue concentration on numerous rigid objectives, achieved in a strict linear order.

In one implementation of the mastery approach, the process of adding two numbers is split into 23 consecutive learning objectives, which all need to be mastered separately, and may be tested separately by the teacher.

The goal: avoid maths anxiety. J2R/

Mindset approach is completely different. It aims to be more exploratory, and tends to start from the complicated concepts, rather than reaching them by a long path. This stems from the belief that most ideas of mathematics are not abstract, but directly correspond to what can be demonstrated by real-world models. For example, a mindset-approach teacher can introduce addition via joining two heaps of cardboard counters (or other props) together, explore properties of addition via activities, and only then break the process of adding numbers into procedural steps.

Developing Number Sense

Mindset approach advocates that pupils develop what is called number sense: an ability to choose (or invent) those methods of working with numbers which are more convenient and efficient in a particular situation.

As a simple example, a person possessing number sense will never calculate 5×3 as 3+3+3+3+3, because the process of adding threes is slower, less convenient and more prone to error than adding fives, that is, 5+5+5.

Too Fast, Too Soon?

What is concerning at this stage is that unlike the mindset approach there is, as yet, no indication that the mastery approach is being systematically and empirically tested. Only one preliminary study in the UK has been published, and it expresses only cautious optimism regarding the mastery model.

There are striking differences between mindset-approach and mastery-approach classroom activities, and we are not sure that in the long term, the mastery approach is better. The new government focus on the mastery method may also be confusing for teachers, after they have been encouraged to teach with the mindset approach.

What’s the best method to learn complicated concepts?Triff/Shutterstock

We are left with some worrying unanswered questions particularly as half of UK schools are now being encouraged to move to a mastery approach before any empirical evaluation of its impact on learning has taken place.

Alexei Vernitski, Senior Lecturer in Mathematics, University of Essex and Sherria Hoskins, Head of Psychology, University of Portsmouth

This article was originally published on The Conversation. Read the original article.

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An “Emotional AI” Is Being Developed By A Team Of Russian Researchers

Artificial intelligence (AI) has made a few spectacular-sounding headlines this year, with various organizations showing off their own digital creations cognitive capabilities. These tend to relate to logical intelligence, dealing with mathematics, rationality, and decision-making.

However, just this month, a team of researchers from the National Research Nuclear University Moscow Engineering Physics Institute (NRNU MEPhI) has announced that they are developing an AI that is able to have both narrative and emotional intellect. If this so-called Virtual Actor (VA) is able to understand human emotions, it will buck the trend in the types of AIs emerging from other research teams across the world.

Googles DeepDream, for example, is a truly surreal convoluted neural network that can think of hallucinogenic images. AlphaGo is able to trounce human masters in the mathematically complex game of Go, and the unrelated ALPHA AI can best very experienced fighter pilots in aerial combat simulations. As impressive as these are, human emotions a notoriously abstract subject at times do not enter into their decision-making processes.

Although it is unlikely to be ready no earlier than 18 months from now, its developers have given some insights as to how it may operate. VA will be able to understand the context of what is happening around it, as well as predicting the outcomes of unfolding scenarios involving human participants.

One of its roles is as an actor in the most literal sense of the word taking on roles of various people in group discussions. Instead of being programmed to understand people, it would set itself questions and seek out the answers for itself.

The first form the VA would take would be one embodied in a simplified videogame. Every action in this game has an emotional connection, with the objective of the VA to gain rapport with its human participants. The team notes that if a human player cannot tell the difference between the VA and another human essentially the Turing test then their AI would have succeeded in its objectives.

Biological solutions are in many respects superior to artificial solutions in terms of their adaptability, learning ability, resistance to unexpected interventions, and so on, and we would like to model these principles on the computer, Alexei Samsonovich, VA project member and professor of the cybernetics department at MEPhI, told Sputnik News.

Image in text: Google’s DeepDream looks for patterns in images and enhances them after “thinking” about what the patterns look like, much to the consternation of Albert, IFLS’s office dog. Google

This is easier said than done, of course. Neuroscientists still have a long way to go to understand the complexities of human emotions, so developing an AI that can understand them will be a gargantuan task.

The team notes that there are several approaches to this. The bottom-up approach involves the reproduction of the human brain, or parts of it, from scratch, which means that a series of artificial neural networks are required. The team wishes to take another approach, which they describe as bottom-up and top-down at the same time, combining neural network construction and higher level cognitive modeling and psychology.

If this seems quite unclear, then its probably because it is supposed to be. MEPhI has received a grant to study biologically substantiated cognitive system models, and VA will be the outcome, but as noted by Samsonovich, there is a huge gap in our understanding of thought processes, particularly when it comes to replicating them.

Essentially then, the team isnt entirely sure what they will do to achieve their goal, but they are open to trying a number of approaches simultaneously. One key point, however, is that they feel current computing power is enough to replicate humanoid intelligence, and that biologically realistic artificial neural networks arent necessary.

Only time will tell if theyre right.

Artificial, emotional intelligence is just 18 months away? That’s probably somewhat optimistic. Christian Lagerek/Shutterstock

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Did you solve it? Where’s the best place to tie your shoe in an airport?

The solution to todays travel teaser.

Earlier today I asked you the following questions:

You are in an airport, and you are walking from security to your gate. The distance includes stretches of travelator, or moving walkway, and stretches of floor. You have a constant walking speed, u, and the travelators also have constant speed, v. So, when you are on the travelator you are traveling at u + v.

1. You need to stop to tie your shoe. If tying your shoe always takes the same time, will you get to the gate quicker if you tie your shoe on the travelator, off the travelator or does it make no difference?

2. You have enough energy to walk at faster speed, w, for a fixed time. In order to get to the gate quicker, do you increase your speed when you are on the travelator, off the travelator or does it make no difference?

The answers:

  1. Tie your shoelace on the travelator.
  2. Speed up off the travelator.

The explanations (simple):

Lets simplify the details and suppose that there is a single stretch of floor followed by a single stretch of travelator. Theres a lovely intuitive explanation of why it is better to tie your laces on the travelator.

Imagine two people, say, Angela and Beatrice, start walking from security at the same time. Angela stops to tie her shoe immediately before the travelator, but Beatrice ties her shoe as soon as she steps on the travelator. By the time Angela has finished tying her shoe and steps on the travelator, Beatrice will now be way ahead of her and Angela will never make up the distance.

There is a similar intuitive explanation of why it is better to fast-walk before you get to the travelator. Imagine again that Angela and Beatrice start together. Say, to keep it simple, that Angela fast-walks straight away, which puts her at a distance D in front of Beatrice. When Angela steps on the travelator she is D ahead, but while she is on the travelator, and Beatrice is not, Angela increases her distance from Beatrice to more than D. When Beatrice reaches the travelator, she can start fast-walking, but so long as both her and Angela remain on the travelator she will never make up more than D.

The history

The shoelace puzzle was first posed by Terence Toe, I mean Terence Tao. (Couldnt resist, sorry). He is one of the most celebrated mathematicians alive. He featured this problem on his blog in 2008, two years after winning the Fields Medal.

How well did you do?

About 15,000 of you submitted answers. The majority – just – got the first one correct. For the second question, however, the correct answer was the one chosen by the fewest people. Interesting.

Q1: where do you tie your shoe?

on the travelator: 47.3%

off the travelator: 11.4%

doesnt matter: 41.3%

Q2: where do you speed up?

on the travelator: 28.7%

off the travelator: 17.2%

doesnt matter: 54.1%

The explanations (trickier)

Here is a more thorough explanation of the answers using some algebra. Again lets assume there is a single stretch of floor and a single stretch of travelator. Lets start by defining the terms.

T = time it takes to tie laces.

u:human speed

v: travelator speed

Df: Floor distance

Dtr: travelator distance

The relevant equation:

Speed = distance/time, and so, time = distance/speed

Question 1: Total time = time on floor + time on travelator + time tying laces = (distance on floor/speed on floor) + (distance on travelator/speed on travelator) + T = Df/u + Dtr/(u + v) + T

If laces tied on floor, the total time: Df/u + T + Dtr/(u + v)

If laces tied on the travelator, the total time: (Df/u) + T + (Dtr Tv)/(u + v)

Since Dtr > Dtr Tv, the total time if laces tied on floor is greater, so you get there quicker if you tie laces on the travelator.

Question 2: Now let T = time spent at higher speed w.

Total time if speeding on floor: T + (Df Tw)/u + Dtr/(u + v)

Total time is speeding on travelator: (Df/u) + T + (Dtr T(w+ v))/(u + v)

Since w > u then w/u > (w + v)/(u + v) and (I promise) this shows that total time is less when you walk fast on the floor.

Because of the time and space constraints of this blog I havent been able to explain each step in detail. Im sure some commentators will be able to help out below the line if you are still confused. Thanks all!

I post a puzzle here on a Monday every two weeks. If you are reading this on the Guardian app, click where it says Follow Alex Bellos and youll get an alert when I publish the next puzzle. If you want to propose a puzzle for this column, please email me Id love to hear it.

Im the author of three popular maths books including Alexs Adventures in Numberland and the maths colouring book Snowflake Seashell Star. You can check me out on Twitter, Facebook, Google+, my personal website or my Guardian maths blog.

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Our nine-point guide to spotting a dodgy statistic

Brexit is just the latest instance of politicians bending figures to match their agenda

I love numbers. They allow us to get a sense of magnitude, to measure change, to put claims in context. But despite their bold and confident exterior, numbers are delicate things and thats why it upsets me when they are abused. And since theres been a fair amount of number abuse going on recently, it seems a good time to have a look at the classic ways in which politicians and spin doctors meddle with statistics.

Every statistician is familiar with the tedious Lies, damned lies, and statistics gibe, but the economist, writer and presenter of Radio4s More or Less, Tim Harford, has identified the habit of some politicians as not so much lying to lie means having some knowledge of the truth as bullshitting: a carefree disregard of whether the number is appropriate ornot.

So here, with some help from the UK fact-checking organisation Full Fact, is a nine-point guide to whats really going on.

Use a real number, but change its meaning

Theres almost always some basis for numbers that get quoted, but its often rather different from what is claimed. Take, for example, the famous 350m, as in the We send the EU 350m a week claim plastered over the big red Brexit campaign bus. This is a true National Statistic (see Table 9.9 of the ONS Pink Book 2015), but, in the words of Sir Andrew Dilnot, chair of the UK Statistics Authority watchdog, it is not an amount of money that the UK pays to the EU. In fact, the UKs net contribution is more like 250m a week when Britains rebate is taken into account and much of that is returned in the form of agricultural subsidies and grants to poorer UK regions, reducing the figure to 136m. Sir Andrew expressed disappointment that this misleading claim was being made by Brexit campaigners but this ticking-off still did not get the busrepainted.

George Osborne quoted the Treasurys projection of 4,300 as the cost per household of leaving the EU. Photograph: Matt Cardy/Getty Images

Make the number look big (but not too big)

Why did the Leave campaign frame the amount of money as 350m per week, rather than the equivalent 19bn a year? They probably realised that, once numbers get large, say above 10m, they all start seeming the same all those extra zeros have diminishing emotional impact. Billions, schmillions, its just a Big Number.

Of course they could have gone the other way and said 50m a day, but then people might have realised that this is equivalent to around a packet of crisps each, which does not sound soimpressive.

George Osborne, on the other hand, preferred to quote the Treasurys projection of the potential cost of leaving the EU as 4,300 per household per year, rather than as the equivalent 120bn for the whole country. Presumably he was trying to make the numbers seem relevant, but perhaps he would have been better off framing the projected cost as 2.5bn a week so as to provide a direct comparison with the Leave campaigns 350m. It probably would not have made any difference: the weighty 200-page Treasury report is on course to become a classic example of ignoredstatistics.

Recent studies confirmed higher death rates at weekends, but showed no relationship to weekend staffing levels. Photograph: Peter Byrne/PA

Casually imply causation from correlation

In July 2015 Jeremy Hunt said: Around 6,000 people lose their lives every year because we do not have a proper seven-day service in hospitals. and by February 2016 this had increased to 11,000 excess deaths because we do not staff our hospitals properly at weekends. These categorical claims that weekend staffing was responsible for increased weekend death rates were widely criticised at the time, particularly by the people who had done the actual research. Recent studies have confirmed higher death rates at weekends, but these showed norelationship to weekend staffinglevels.

Tom Blenkinsop and David Cameron on nurse numbers at PMQs, December 2014

Choose your definitions carefully

On 17 December 2014, Tom Blenkinsop MP said, Today, there are 2,500 fewer nurses in our NHS than in May 2010, while on the same day David Cameron claimed Today, actually, there are new figures out on the NHS there are 3,000 more nurses under this government. Surely one must bewrong?

But Mr Blenkinsop compared the number of people working as nurses between September 2010 and September 2014, while Cameron used the full-time-equivalent number of nurses, health visitors and midwives between the start of the government in May 2010 and September 2014. So they were both, in their own particular way,right.

Indicator hopper: Health secretary Jeremy Hunt. Photograph: PA

Use total numbers rather than proportions (or whichever way suits your argument)

In the final three months of 2014, less than 93% ofattendances at Accident and Emergency units were seen within four hours, the lowest proportion for 10 years. And yet Jeremy Hunt managed to tweet that More patients than ever being seen in less than four hours. Which, strictly speaking, was correct, but only because more people were attending A&E than ever before. Similarly, when it comes to employment, an increasing population means that the number of employed can go up even when the employment rate goes down. Full Fact has shown how the political parties play indicator hop, picking whichever measure currently supports their argument.

Is crime going up or down? Dont ask Andy Burnham. Photograph: PA

Dont provide any relevant context

Last September shadow home secretary Andy Burnham declared that crime is going up, and when pressed pointed to the police recording more violent and sexual offences than the previous year. But police-recorded crime data were de-designated as official statistics by the UK Statistics Authority in 2014 as they were so unreliable: they depend strongly on what the public choose to report, and how the police choose to recordit.

Instead the Crime Survey for England and Wales is the official source of data, as it records crimes that are not reported to the police. And the Crime Survey shows a steady reduction in crime for more than 20 years, and no evidence of an increase in violent and sexual offences lastyear.

Exaggerate the importance of a possibly illusory change

Next time you hear a politician boasting that unemployment has dropped by 30,000 over the previous quarter, just remember that this is an estimate based on a survey. And that estimate has a margin of error of +/- 80,000, meaning that unemployment may well have gone down, but it may have gone up the best we can say is that it hasnt changed very much, but that hardly makes a speech. And to be fair, the politician probably has no idea that this is an estimate and not a headcount.

Serious youth crime has actually declined, but thats not because of TKAP. Photograph: Action Press / Rex Features

Prematurely announce the success of a policy initiative using unofficial selected data

In June 2008, just a year after the start of the Tackling Knives Action Programme (TKAP), No 10 got the Home Office to issue a press release saying the number of teenagers admitted to hospital for knife or sharp instrumentwounding in nine police force areas fell by 27% according to new figures published today. But this used unchecked unofficial data, and was against the explicit advice of officialstatisticians. They got publicity, but also a serious telling-off from the UK Statistics Authority which accused No 10 of making an announcement that was corrosive of public trust in officialstatistics. The final conclusionabout the TKAP was that serious youth violence had declined in the country, but no more in TKAP areas thanelsewhere.

Donald Trump: Am I going to check every statistic?
Photograph: Robert F. Bukaty/AP

If all else fails, just make the numbers up

Last November, Donald Trump tweeted a recycled image that included the claim that Whites killed by blacks 81%, citing Crime Statistics Bureau San Francisco. The US fact-checking site Politifact identified this as completely fabricated the Bureau did not exist, and the true figure is around 15%. When confronted with this, Trump shrugged and said, Am I going to check every statistic?

Not all politicians are so cavalier with statistics, and of course its completely reasonable for them to appeal to our feelings and values. But there are some serial offenders who conscript innocent numbers, purely to provide rhetorical flourish to theirarguments.

We deserve to have statistical evidence presented in a fair and balanced way, and its only by public scrutiny and exposure that anything will ever change. There are noble efforts to dam the flood of naughty numbers. The BBCs More or Lessteam take apart dodgy data, organisations such as Full Fact and Channel 4s FactCheck expose flagrant abuses, the UK Statistics Authority write admonishing letters. The Royal Statistical Society offers statistical training for MPs, and the House of Commons library publishes a Statistical Literacy Guide: how to spot spin and inappropriate use ofstatistics.

They are all doing great work, but the shabby statistics keep on coming. Maybe these nine points can provide a checklist, or even the basis for a competition how many points can your favourite minister score? In my angrier moments I feel that number abuse should bemade a criminal offence. But thats a law unlikely to be passed bypoliticians.

David Spiegelhalter is the Winton Professor of the Public Understanding of Risk at the University of Cambridge and president elect of the Royal StatisticalSociety

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Does This Image Freak You Out? If It Does, This Is What It Means

Phobias are weird. Irrationally fearing something that you perhaps shouldn’t can really get in the way of normal day-to-day life. I know someone so scared of heights that he can’t even drive over a bridge. I also know someone who’s physically repulsed by the sight of seeing milk being poured. Weird.

I’ve not looked it up but I’m pretty sure the latter fear doesn’t have a name. That means it’s easier to laugh at her for having such an odd phobia. And I do. This was the same for “the fear of holes” but, after someone first wrote about it on the internet in 2005, it’s been given a name – Trypophobia.

By “the fear of holes”, I don’t mean the book OR the film adaptation starring ShiaLabeouf – I mean things like a lotus seed pod.

If that makes you feel queasy, there’s a chance you suffer from trypophobia.

Knowing the triggers of trypophobia is all well and good but knowing what actually causes it is a whole new challenge and is largely disputed. As most phobias are boil down to a fear of one’s own safety, that’s where trypophobia differs.

One of the leading theories is all maths-y. It suggests that the mathematical properties of the trigger images require more brain power to translate and subsequently cause visual discomfort, headache or eye strain.

Like this for example…

If you’re anything like me, that doesn’t make you shudder because of the hole placement or anything, it’s simply because it’s repulsive.

Anyway, do you fear holes? Maybe you have trypophobia… Let us know in the comments!

H/T: IFLScience

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Genius by numbers: why Hollywood maths movies don’t add up

From A Beautiful Mind to The Theory of Everything and The Man Who Knew Infinity, Hollywood loves a mathematician. So why cant it get beyond the fevered prodigy scribbling equations on windows?

In the Tina Fey sitcom Unbreakable Kimmy Schmidt, wealthy Manhattanite Jacqueline Vorhees wails to her assistant that she cant afford to get divorced. Even though shed get $1m for every year of her marriage.

I spend 100 grand a month. Ill be broke in 10 years, she wails. No, thats wrong, counters Kimmy (Ellie Kemper), who scribbles some sums with a marker on Mrs Vorheess window. So $100,000 times 12 months. Thats $1.2m a year. Divide that into $12m, and yes, youd be broke in 10 years. But if you invest some of it, assuming a 7% rate of return, using the compound interest formula, your money would almost double.

Kimmy turns round triumphantly: Mrs Voorhees, I mathed, and you can get divorced! Mrs Vorhees eyes Kimmy narrowly. Those are not, she complains, erasable markers. What she doesnt mention is that math isnt a verb. Not yet.

The scene is, among other things, Feys satire of the Hollywood cliche of genius squiggling on glass. In A Beautiful Mind (2001), for instance, Russell Crowe, playing troubled maths star John Forbes Nash Jr, writes formulae on his dorm window. This scene is echoed in The Social Network (2010), where Andrew Garfield sets out the equations for Facebooks business model on a Harvard window while Jesse Eisenbergs Mark Zuckerberg looks on. In the opening scene of Good Will Hunting (1997), janitor prodigy Matt Damon writes equations on a bathroom mirror.

Why do so many Hollywood maths whizzes forego paper? Stanford mathematician Keith Devlin explains. Depicting a mathematician scribbling formulas on a sheet of paper might be more accurate, but it certainly doesnt convey the image of a person passionately involved in mathematics, as does seeing someone write those formulas in steam on a mirror or in wax on a window, nor is it as cinematographically dramatic.

Good point. When we watch A Beautiful Mind and look through the window at our Russ, Hollywoods most built mathematician (counterexamples on postcards, please show your workings), we pass beyond incomprehensible equations and convince ourselves were seeing Genius at Work. Even if, as some critics have complained uncharitably, Russs pi glyphs, greater-than and less-than symbols and such dont make sense.

But theres another way maths movies can confound the Boredom Equation, namely by leaving a black hole where the maths should be. The Man Who Knew Infinity, the new film starring Dev Patel and Jeremy Irons about the great Indian mathematician Srinivasa Ramanujan, is intriguing in this respect. Although we see Ramanujan doing maths, mostly the film is interested in other things how he falls in love with his wife, the pain of separation when he travels from Madras to study at Cambridge, the racism he suffers in England and, most stirringly, the narrative arc from lowly clerk to globally recognised mathematician.

Hollywoods most built mathematician Russell Crowe in A Beautiful Mind. Photograph: Universal Studios

That said, the film has its charming moments. When Hardy visits Ramanujan in a nursing home, he complains about the boring number of the cab that brought him there. Ramanujan begs to differ: 1,729 is the smallest that is expressible as the sum of two cubes in two different ways. Today 1,729 is known as the Hardy-Ramanujan number. How does that work, you may be wondering? Like this: 1729 = 13 + 123 = 93 + 103.

Ramanujans mentor GH Hardy (Irons) is an atheist and rationalist, exasperated that this Indian prodigy cannot produce proofs for his work and, worse, is doubtful that proofs can explain the inexplicable. You wanted to know how I get my ideas, says Ramanujan. God speaks to me. But while the film may sketch two different mathematical philosophies, we leave the cinema with a warm glow that comes from anything but hard thinking.

If you want to learn some more about Ramanujans contribution to mathematics, rent High School Musical. Freeze-frame it at the moment brainy Gabriella Montez challenges her teacher. On the board are two of the equations of the inverse of the constant pi (1/) that Ramanujan offered in his first paper published in England. Shouldnt the second equation read 16 over pi? asks Gabriella. Of course it should.

Cinema often struggles with dramatising difficult ideas, particularly if they are abstract. One way of overcoming that problem is by metaphorical explanation. For instance, in Nicholas Roegs Insignificance (1985), a Marilyn Monroe-like character demonstrates relativity using toy trains and flashing lights. In The Theory of Everything, Jane Hawking uses a pea and a potato to explain the difference between quantum theory and general relativity, while her husbands friends explain Hawking Radiation with beers and crisps.

Movie explanations of difficult stuff, though, may obscure rather than enlighten. Whats more, some directors know this and have fun pointing out the shortcomings of their medium and those of their audiences. In Adam McKays The Big Short (2016), for instance, Margot Robbie sits in a tub sipping champagne and describing how sub-prime loans work. Her explanation is doubtless coherent, but when Im looking at a beautiful woman in a bubble bath, Im not thinking about credit default swaps. So sue me. Later in the film, chef Anthony Bourdain chops fish in his kitchen while describing how collateralised debt obligations work. Finally, Selena Gomez plays roulette to illustrate the idea of gambling on other peoples gambles.

Each scene serves as a parody of explanation. They are part of a film that mocks you, you poor jerk, and your intellectual aspirations. You are never ever going to understand how difficult stuff works from watching movies, however much youd like to.

Sometimes, though, cinema can give a real insight into the intellectual process. In Agora (2009), Rachel Weisz as ancient philosopher Hypatia does an experiment on a ship to test relative motion. If, she hypothesises, you drop a heavy sack from the mast while the ship is moving forward, it will fall on the deck several feet behind the mast. The sack is dropped and falls much closer to the mast than she predicted. Hypatia claps her hands in delight. But you were wrong! says the ships captain. Yes, but it is definitive proof! The sack behaves as if the boat were stationary.

What does that mean?

I dont know. But the same principle could be applied to the Earth. It could be moving around the sun without us realising.

Hypatia, that is to say, infers a revolutionary heliocentric cosmology from her falsified hypothesis. The film thus generously gives us what we are effectively denied in Good Will Hunting or A Beautiful Mind the inside track on how someone clever is thinking about a problem. Whats more, its an antidote to Hollywoods vision of genius. It suggests that getting stuff wrong is at least as important in the story of human intellectual progress as being right all the time.

Maths is often reduced to nothing more than a MacGuffin. In Rushmore (1998), for instance, Max Fischer (Jason Schwartzman) is reading the newspaper while his teacher tells his class that on the blackboard is the hardest geometry equation in the world. What credits would anyone solving it get, asks one student. Well, considering Ive never seen anyone get it right, including my mentor Dr Leaky at MIT, I guess if anyone here can solve that problem, Id see to it that none of you ever have to open another math book again for the rest of your lives.

Thus tempted, Fischer folds his paper and goes to the blackboard, and squiggles his solution while nonchalantly sipping espresso. The film at this point has nothing to declare but Fischers genius. Do we really believe Jason Schwartzmann can compute the area of an ellipse? Sure. Whatever.

Genius squiggling is there once again merely to help Hollywood tell the sentimental story it never tires of: namely the story of someone usually borderline demented and by definition insufficiently recognised sticking it to the establishment.

Genius squiggling Rushmore

None of this should suggest we cant learn maths from movies. In Tina Feys Mean Girls (2004), for example, Lindsay Lohan plays a finalist in the Illinois high school mathletes state championship. Will her North Shore High team stick it to those prep school toffs opposite? Heres the first question: Twice the larger of two numbers is three more than five times the smaller, and the sum of four times the larger and three times the smaller is 71. What are the numbers? Got it yet? 14 and 5. In the end, Lohans team become the new state champs because she wins the sudden death tie-break. What does the scene prove? That those of you who thought Lindsay Lohan cant do maths should really have a word with yourselves.

Perhaps the most resonant maths scene in Hollywood cinema, though, comes in a very old comedy. In the Abbott and Costello movie In the Navy (1941), Lou is a ships cook. Hes baked 28 doughnuts, which he reckons is just enough to give 13 to each of his seven officers. But seven goes into 28 four times, objects Lous straight man. Not so, says Lou, who goes on to prove it on the blackboard in a masterclass of cheating and illusion. The scene demonstrates a general truth, namely that when Hollywood does maths, it doesnt necessarily add up.

The Man Who Knew Infinity is released on 8 April.

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