The governing body, World Athletics, allows several slightly different shapes for a 400-metre track. The simplest lay-out consists of two semi-circles joined by straight lines. The radius of the semi-circles, measured to the inside edge of the track, is 36.5m. The straights are 84.39m long. We can easily check that these curves add up to a length of 400m, by computing \[ 2 \cdot \pi \cdot 36.5 + 2 \cdot 84.39 = 398.116\ldots \] Hang on… This is no mistake! The official distance is measured 30cm away from the inside edge of the track. If we take this into account, the radius of the semicircles increases to 36.8m, and we find \[ 2 \cdot \pi \cdot 36.8 + 2 \cdot 84.39 = 400.001\ldots \] Close enough, I suppose… I’ll just round everything to two decimal places from now on. Still, this means that if a runner manages to stay close to the inside edge, they may be able to complete a lap in less than 400m!

Where are the start lines?

The lanes on an athletics track are numbered 1 to 8 (or however many lanes there are), starting from the inside. To make a race fair to those running further from the inside of the bend, the starting positions in different lanes are staggered.

The width of a lane is 1.22m, or 4 feet. So while a bend in lane 1 is $36.80 \pi \approx 115.61$ metres long, the same bend in lane 2 has a length of $38.02 \pi \approx 119.44$ metres. Each time we move one lane further out, the bend gets longer by $1.22 \pi \approx 3.83$ metres. (I’m ignoring some weird technicalities here, concerning where exactly the official distance is measured in each lane.)

In a 200m race, where the athletes run one bend and one straight, the runner in lane 2 starts 3.83m ahead of the one in lane 1. In each lane further out, the start line is again 3.83m ahead of the start line in the previous lane. In the 400m, runners navigate both bends to complete one lap of the track, so the starts are staggered by twice the distance, 7.67m per lane.

In the 800m, the situation is a bit more complicated, because athletes are allowed to break out of their lane after the first bend. Their staggered start is similar to that of the 200m, but needs to be corrected to account for the distance from where the runners leave their lane to the inside of the next bend.

Why do laps get longer?

To compute that a lap gets longer by 7.67m each time we move a lane further out, we assumed that the track consists of straight lines and semi-circles. This is true for one of the standard track layouts, but World Athletics allows slightly different shapes as well. Luckily, the answer doesn’t change if the track is a different shape. As long as over the course of a lap we turn a total of $360^\circ$, then moving some distance $d$ outwards increases the length of lap by $2 \pi d$. However, if the track were a figure of eight, then we would turn just as much to the left as to the right, so there the net turning angle would be zero. This means that every lane would be exactly the same length, avoiding the need for a staggered start.

For some reason, this track layout is frowned upon by World Athletics

Curved start lines

In the longer distances (such as the 1500m, 5000m and 10,000m), runners are not bound to any specific lane. Does that mean that the start line should be a straight line perpendicular to the lanes? No! Because that would still put runners on the outside at a disadvantage: they would have to cover more distance in order to reach the inside edge of the track. To obtain the actual shape of the start line, first imagine winding a rope (shown in blue) around the inside edge of the bend.

Wind the bobbin up

Next, pull the end of the rope to the outside of the track, so that the rope starts unwinding, but remains taut. The curve traced by the endpoint of the rope is the start line (shown in orange). Since the length of the rope does not change, this guarantees that each runner will have exactly the same distance to cover.

Wind it the other way

The curve obtained this way is called the involute of the curve the rope was wrapped around. Because the start lines for the 5000m and 10,000m are positioned at the start of a semi-circular bend, their shape is that of the involute of a circle. If we continue drawing the involute of a circle beyond the width of the track, we get a spiral. If we draw several involutes on the same circle they have the satisfying property that the strips between them are of constant width.

Involutes of a circular running track

Some other curves have aesthetically pleasing involutes. My favourite is the cardioid, whose involute is a cardioid that is three times as large and rotated by $180^\circ$. Here too, we could think of the involute as a start line. If you have to run from the blue cardioid to the cusp of the green shaded cardioid, without going into the shaded area, the distance you have to travel is independent of where on the blue cardioid you start!

Pretty and mathematical: the involute of a cardioid is a cardioid

Involute gears

As a sports fan I hate to admit it, but the most interesting application of the involute of a circle has nothing to do with athletics. It occurs in mechanical transmission. The teeth of gears are often made such that their sides are involutes of a circle. This leads to a smooth transmission of force between the two gears, which is not the case with other tooth shapes!

For example, consider a gear with angular teeth (shown in orange):

A gear with angular teeth…

When two such gears engage, there will almost always be a a corner of one tooth driving the other gear (pink circles). This causes several issues. One issue is that the corners would wear down very quickly. Another is that there would be vibrations in the transmission, because the point of contact jumps all over the place as the gears rotate against each other:

… will lead to a bumpy ride as the corners of the teeth jump around.

In an involute gear (shown in blue), the sides of the teeth are involutes of a circle called the base circle (black):

Gears with involute teeth…

The base circle is larger than the physical disk the teeth are mounted on. A few of its involutes are shown in red, matching the profile of the teeth. The force between two involute gears is always transmitted along the same line (pink), tangent to the base circles of both gears. The contact point (circled in pink) moves steadily along this line as the gears rotate.

… have a smooth ride as the contact point glides smoothly along the pink line

You can imagine that the two gears are connected by a piece of string that is unwinding from one gear while winding onto the other gear. The relative motion of the string and one of the gears is exactly the same as the relative motion of the rope and the athletics track when we were marking out the 10,000m start line. But now we are in a frame of reference where, instead of moving the rope/string sideways to unwind it, we are rotating the track/gear and pulling the rope/string.

By imagining this string, we see that the torque is transmitted as if the two wheels were connected by a drive belt instead of having interlocking teeth. This implies that the gear ratio (the ratio of the angular velocities of both gears) stays exactly the same throughout the motion. In particular, there is no sudden jolt when the next corner of a tooth catches. Theoretically, the transmission is perfectly smooth.

The shape of the teeth of an involute gear depends on the size of the base circle of that gear, but not on the size of the gear we pair it with. The only things that need to be standardised are the ‘pitch’ (how far apart consecutive teeth are) and the ‘pressure angle’ (which relates to the distance between the base circles of two engaged gears). If we have a set of involute gears in various sizes, each with the same pitch and pressure angle, we can pair any two to build a smooth transmission.

With these benefits, it should come as no surprise that many of the gears you’ll find in real-world machines (or in a Lego set) are involute gears.

I wonder if somewhere in the world there is a big machine containing a gear with a base circle radius of 36.5m. Then you could bring this giant gear to an athletics track and perfectly align one of its teeth with the start line. Sadly, the largest gear I could find any concrete information about, though it weighs a whopping 73.5 tonnes, has a radius of less than 7m. So, if you manage to find a 36.5-metre gear to bring to your local running track, please remember to lift with your legs, not your back!

The post Gearing up for the track appeared first on Chalkdust.

The teaching profession is one of the most female-dominated in the United States. Among elementary school teachers, 89 percent are women, and in kindergarten, that number is almost 97 percent.

Many sociologists, writers and parents have questioned whether this imbalance hinders young boys at the start of their education. Are female teachers less understanding of boys’ need to horse around? Or would male role models inspire boys to learn their letters and times tables? Some advocates point to research that lays out why boys ought to do better with male teachers.

But a new national analysis finds no evidence that boys perform or behave better with male teachers in elementary school. This challenges a widespread belief that boys thrive more when taught by men, and it raises questions about efforts, such as one in New York City, to spend extra to recruit them.

“I was surprised,” said Paul Morgan, a professor at the University at Albany and a co-author of the study. “I’ve raised two boys, and my assumption would be that having male teachers is beneficial because boys tend to be more rambunctious, more active, a little less easy to direct in academic tasks.”

Related: Our free weekly newsletter alerts you to what research says about schools and classrooms.

“We’re not saying gender matching doesn’t work,” Morgan added. “We’re saying we’re not observing it in K through fifth grade.”

Middle and high school students might see more benefits. Earlier research is mixed and inconclusive. A 2007 analysis by Stanford professor Thomas Dee found academic benefits for eighth-grade boys and girls when taught by teachers of their same gender. And studies where researchers observe and interview a small number of students often show how students feel more supported by same-gender teachers. Yet many quantitative studies, like this newest one, have failed to detect measurable benefits for boys. At least 10 since 2014 have found zero or minimal effects. Benefits for girls are more consistent.

This latest study, “Fixed Effect Estimates of Teacher-Student Gender Matching During Elementary School,” is a working paper not yet peer reviewed. Morgan and co-author Eric Hu, a research scientist at Albany, shared a draft with me.

Morgan and Hu analyzed a U.S. Education Department dataset that followed a nationally representative group of 8,000 students from kindergarten in 2010 through fifth grade in 2017. Half were boys and half were girls. 

More than two-thirds — 68 percent — of the 4,000 boys never had a male teacher in those years while 32 percent had at least one. (The study focused only on main classroom teachers, not extras like gym or music.)

Among the 1,300 boys who had both male and female teachers, the researchers compared each boy’s performance and behavior across those years. For instance, if Jacob had female teachers in kindergarten, first, second and fifth grades, but male teachers in third and fourth, his average scores and behavior were compared between the teachers of different genders.

Related: Plenty of Black college students want to be teachers, but something keeps derailing them

The researchers found no differences in reading, math or science achievement — or in behavioral and social measures. Teachers rated students on traits like impulsiveness, cooperation, anxiety, empathy and self-control. The children also took annual executive function tests. The results did not vary by the teacher’s gender.

Most studies on male teachers focus on older students. The authors noted one other elementary-level study, in Florida, that also found no academic benefit for boys. This new research confirms that finding and adds that there seems to be no behavioral or social benefits either.

For students at these young ages, 11 and under, the researchers also didn’t find academic benefits for girls with female teachers. But there were two non-academic ones: Girls taught by women showed stronger interpersonal skills (getting along, helping others, caring about feelings) and a greater eagerness to learn (represented by skills such as keeping organized and following rules).

When the researchers combined race and gender, the results grew more complex. Black girls taught by Black women scored higher on an executive function test but lower in science. Asian boys taught by Asian men scored higher on executive function but had lower ratings on interpersonal skills. Black boys showed no measurable differences when taught by Black male teachers. (Previous research has sometimes found benefits for Black students and sometimes hasn’t.)

Related: Bright black students taught by black teachers are more likely to get into gifted-and-talented classrooms

Even if data show no academic or behavioral benefits for students, there may still be compelling reasons to diversify the teaching workforce, just as in other professions. But we shouldn’t expect these efforts to move the needle on student outcomes.

“If you had scarce resources and were trying to place your bets,” Morgan said, “then based on this study, maybe elementary school isn’t where you should focus your recruitment efforts” to hire more men.

To paraphrase Boyz II Men, it’s so hard to say goodbye — to the idea that young boys need male teachers.

Contact staff writer Jill Barshay at 212-678-3595, jillbarshay.35 on Signal, or barshay@hechingerreport.org.

This story about male teachers was produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for Proof Points and other Hechinger newsletters.

The post Do male teachers make a difference? Not as much as some think appeared first on The Hechinger Report.

The most intriguing robots aren’t built to work, but to make us imagine other worlds.

A few months ago, I visited the Futurism retrospective organized to mark the 80th anniversary of Filippo Tommaso Marinetti’s death at the National Gallery in Rome. The rooms were filled with archives of an ultra-modernist machinic dream: posters, paintings, and sculptures coexisted alongside engines, telegraphs, cars, and airplanes. It was impossible to ignore the voice of the visionary ideologue of Futurism echoing through the sober neoclassical halls of the museum: “We affirm that the magnificence of the world has been enriched by a new beauty: the beauty of speed.”

For the Futurists, every machine was, essentially, a time-machine: more than tools designed to perform a specific task, technological objects were the historical embodiment of humanity’s universal drive toward progress. Looking beyond the notoriously controversial implications of its political affiliations, the genius of the Futurist avant-garde was its intuition that the evolution of machines could capture cultural transformations better than any other human practice. And thus, even the arts and letters — the highest expressions of humanism — had to listen to the roar of engines.

In October 2021, visitors to London’s Tate Modern entered a space populated by visions of a very different future. Floating, semi-transparent organisms hovered slowly in the air like seraphic creatures from the ocean’s depths. These aerobes, as they were baptized by Korean-American artist Anicka Yi, who conceived them, are pachydermic, calm, and silent. These flying automata respond to human presence, changing altitude and behavior based on the proximity of people in the space. “When you look at these aerobes, it gives you a feeling almost opposite to the uncanny valley”, Yi explains. “You know that they’re mechanical, yet they feel palpably alive.” Unlike anthropomorphic robots, whose imperfect resemblance to humans often generates a sense of subtle unease (or “uncanniness”), Yi’s automata are neither disturbing nor reassuring, but designed to evoke a sense of sublime otherness, like swimming alongside a whale in the sea. Their scale is imposing, but their presence invites attention rather than fear. These artistic-technological objects are difficult to define: they are man-made artifacts but serve no instrumental function. They move around their environment guided by their perceptions, interacting with each other and the world around them. Yi describes them, borrowing a term from Donna Haraway, as “a new kind of companion species.” In Haraway’s terms, a “companion species” is not a familiar reflection of the human but a meaningful otherness, whose distance from us enables us to inhabit new forms of relation and coexistence.

Robots are strange objects of inquiry. Whenever I encounter them in my research, I catch myself pondering the contrast between their negligible impact on my daily life and their imposing presence in my cultural imagination. Of course, industrial robots already serve significant purposes, but their usefulness does not entirely justify the appeal they hold towards us. Beyond their intended use, each robot, in its synthetic and self-contained individuality, seems to embody something like the quintessence of the technological object. There is something paradigmatic and powerful about these beings that dominates our imagination of the future. And while for a long time the word “robot” has corresponded to a very specific image (an anthropomorphic, mechanical, rigid artifact), Anicka Yi’s flying automata signal a broader change in how these technological objects are imagined and constructed.

Over the past 20 years, robotics has undergone a significant transition. A field once dominated by anthropomorphic bodies and rigid materials has begun to embrace a much wider range of possible incarnations, starting with the use of plastic and flexible materials to replace steel and hard polymers. Cecilia Laschi, one of the most authoritative figures in the field of robotics, has frequently emphasized how this transition from “rigid” to “soft” robots goes far beyond a simple change in the choice of materials, reflecting instead a broader transition in the entire anatomy of the automata, in the strategies used to control them, and in the philosophy that drives their construction. The most notable engineering achievement by Laschi and her colleagues at the Sant’Anna Institute in Pisa is a robotic arm originally designed in 2011 and inspired by the muscular hydrostatics of the octopus. In octopuses, limbs are capable of complex behaviors such as swimming and manipulating objects through coordinated deformations of muscle tissue, without any need for rigid components. In the robot designed by Laschi and her colleagues, the robotic limb’s movement is achieved similarly through deformable smart materials known as “shape memory alloys.”

RelatedI Bought a Robot Cat for My Rabbit — and Fell Into the Weird World of Animal-Robot Research

Unlike a conventional robot, these movements are not pre-programmed, but emerge from the material’s response to external forces. This new engineering logic is part of what Laschi describes as embodied intelligence, an approach in which the robot’s behavior emerges from integrating its physical structure and interaction with the world. The concept of “embodiment” challenges the hierarchical separation between body and mind, representation and experience. Rather than conceiving of intelligence as the product of an active mind controlling a passive body, embodiment emphasizes the relationship between cognition and corporeality. Originating in philosophy, over the last 20 years, this concept has begun to spread and establish itself in the field of engineering, opening up new avenues for the design of versatile and adaptive robots. “The octopus is a biological demonstration of how effective behavior in the real world is closely linked to body morphology,” Laschi and her co-workers explain, “a good example of embodied intelligence, whose principles derive from the observation in nature that adaptive behavior emerges from the complex and dynamic interaction between body morphology, sensorimotor control, and the environment.”

Back in Shanghai, some time after visiting the National Gallery, I visited a retrospective on Hajime Sorayama, a Japanese artist famous for having crystallized the image of the 20th-century robot into a simultaneously futuristic and nostalgic icon. Since the 1980s, Sorayama has reproduced the same sculpture endlessly with minimal variations: a slender, curvy female figure covered in chrome-plated armor, halfway between erotic fetish and deity of a long-lost future. These works, laconically branded “Sexy Robot” followed by a serial number, seem to both celebrate and poke fun at the modernist stereotype of the automaton as a triumph of control and mechanical efficiency, replicating the seductive mirage of glittering, endless progress. While Yi’s creatures project us into an alien and still nascent technological future, Sorayama’s figures are captivating precisely because they perfectly reflect our expectations. If Yi’s aerobes are soft, sensitive, and radically non-human, Sorayama’s sexy robots are superhuman, dazzling, and wonderfully unfeeling.

Despite their radical aesthetic and philosophical distance, Sorayama’s and Yi’s robots have at least one thing in common — their uselessness. More specifically, they are both instruments of aesthetic contemplation rather than functional tools. Robots, for that matter, are often described in terms of what they can do: as artifacts designed to facilitate work, if not carry it out in our place. This conception, already spelled out in the familiar etymology of the word “robot” (from the Czech robota, “forced labor,” a term popularized by science fiction writer Karel Čapek), is deeply entrenched in twentieth-century industrial culture. Still, even before being called by that name, robots weren’t always just tools in the service of human productivity.

In a 1964 article entitled Automata and the Origins of Mechanism and Mechanistic Philosophy, historian of technology Derek de Solla Price traced the history of automata from antiquity, challenging the notion that such machines were created primarily to serve human labor. Mechanisms, he observed, long functioned as epistemic devices before they became useful tools: they acted as microcosmic mirrors to the greater order of the world. For centuries, automata accompanied the human imagination, helping thinkers to conceive of a rational universe governed by regular mechanisms (well before such mechanisms could be practically put to work). This historical lineage complicates the view of the machine as a purely instrumental tool: its material utility was often secondary to its epistemic power. This non-utilitarian interest in robots has been emerging time and time again in art practices.

In “After Care,” an installation recently exhibited at Copenhagen Contemporary, artists Rhoda Ting and Mikkel Bojesen set fully soft, pneumatically activated robots to wriggle and burrow inside a large pit of rocks and dirt. Visitors were invited to handle the robots as if in a “petting zoo” — engaging with them not as instruments but as alien “companion species,” valued more for their strangeness and presence than for any practical use.

The work of Cecilia Laschi and many other pioneers in robotics is already demonstrating that new soft robots can significantly expand the functionality, sustainability, and resilience of technologies from past centuries. However, beyond the still limited applications of these artifacts, the soft machines of the 21st century seem to signal a more complex transition, primarily epistemic and cultural, in our understanding of and relationship with the world.

Yi’s fluttering creatures and Ting and Bojesen’s wriggling mollusks exist in continuity with a long history in which technological artifacts were philosophical and cosmological devices before being tools programmed to perform a task. And if the automata of past centuries spoke of celestial spheres and universes orchestrated like clockwork, what worlds do the soft machines of the 21st century evoke? Even contemporary robots, whether swimming in engineering laboratories or floating in art galleries, are first and foremost cosmological mirrors, and the worlds they evoke are very different from those of their ancestors. The new automata, it seems, speak to us of ecological continuity, profound otherness, and possible coexistences with that which is most distant from us.

Laura Tripaldi is a writer and researcher at the Center for AI Culture of NYU Shanghai. She is the author of “Parallel Minds” (Urbanomic Press).

This article first appeared on Laura’s Substack, Soft Futures.

One of my favorite things in all of professional sports is the unofficial holiday referred to as “Bobby Bonilla Day.” The short version of it is that Bonilla played for the New York Mets decades ago and eventually bought out his contract in 2000 when they decided they were done with him. Rather than pay the $5.9 million buyout of the contract up front, the team instead made the bonkers decision to negotiate a deferred payment schedule for that amount with 8% interest over the course of 25 years. The result is that the Mets will be paying Bonilla $1.2 million per year every July 1st, starting in 2011 and ending in 2035. And if you can’t make sense of the math on that one, it’s because you aren’t aware that the Mets ownership was one of Bernie Madoff’s many victims, which is why they had to defer the payments.

November 10th is not Bobby Bonilla Day. But it should be named “Let Us Play No One Lives Forever, You Assholes Day.” The classic spy-shooter turned 25 on that date and, for the exact same reasons we’ve detailed for a god damned decade now, you still can’t buy the game.

Here’s the short of it. Due to a series of mergers, closures, and rights purchases, the IP rights for No One Lives Forever and its sequel have been potentially split into three pieces between Warner Bros., Activision, and 20th Century Fox, like it was some kind of fucking horcrux. I say potentially because nobody really knows who owns what, if anything, when it comes to these games. When one company, Nightdive Studios, attempted to remaster and re-release the game as they’ve done with other titles, along with securing trademark rights to the game which hasn’t been sold in over a decade, all three companies complained that they may have rights to it and may sue over it.

All of those qualifiers are, again, because even these companies themselves don’t know what rights they actually have. And why is that? Well, because the gaming rights deals were inked before digital storage was widely used for this sort of thing and, well, nobody seems to be able to locate the actual paperwork denoting who owns what. Here’s an example of an exchange Nightdive had with Activision.

“So we went back to Activision and, [after] numerous correspondence going back and forth, they replied that they thought they might have some rights, but that any records predated digital storage. So we’re talking about a contract in a box someplace.” Kuperman laughed. “The image I get is the end of Indiana Jones… somewhere in a box, maybe in the bowels of Activision, maybe it was shipped off to Iron Mountain or somewhere. And they confessed, they didn’t have [their] hands on it. And they weren’t sure that they even had any of those rights.”

Which didn’t keep Activision from warning Nightdive that it might totally sue if it moved forward with remastering the game. The other companies made similar noises.

So what’s a person to do if they want to play this game? You can’t buy it legitimately currently. It’s not even for sale anywhere. And a situation like that, which I’ve stated before, completely breaks the copyright bargain. The only option is, as Kotaku of all places notes, to download it for free from somewhere.

Downloading games that are available for sale is piracy. It’s illegal, and it’s not supportive of developers and their art. But when companies have gone out of their way to refuse to take your money for a game for the better part of two decades, it’s a very different situation. Look, I’m not your real mom and dad, and I can’t tell you what to do. But if you were to click on this link (link removed by Techdirt due to us not knowing where it takes you) and download both games (as well as spin-off Contract Jack), you’d end up with modernized versions of these classic games, with mods that allow them to work on Windows 10 and 11, and in widescreen. And what better time to do (or not do) this than on the first game’s 25th anniversary?

At this point (as indeed it was over eight years ago, the last time I suggested just downloading it, to no negative response at all) we have to consider No One Lives Forever to be abandonware. No one is willing to take ownership of it, although those that could do so sometimes mindlessly threaten to intervene should anyone else try to rebuild it for sale. Nightdive were scared off a decade ago, and it’s been sitting on GOG’s Dreamlist since that launched earlier this year (with 87,171 people saying they’d pay for it if they could). It’s far too small of a concern for any of the megacorps who might own it to spend the time and money to work out if they do, but it’s far too big of a concern within gaming history to be allowed to just disappear. Thank goodness for the anonymous heroes running NOLF Revival. I thank them for their service.

It’s the only option the public has to play this game and enjoy this small piece of our collective culture. The real answer here is some sort of copyright reform that makes this situation not a thing. If a company, or group of companies, won’t offer a piece of work for sale, can’t be bothered to understand what they own of it, if anything, and have no plans to figure any of that out… then how can this be copyright infringement?

So happy “Let Us Play No One Lives Forever, You Assholes” Day. Maybe we’ll be able to play this game legitimately by the time Bobby Bonilla stops making his million and change per year.