Spiders' web secrets unraveled

Johns Hopkins University researchers discovered precisely how spiders build webs by using night vision and artificial intelligence to track and record every movement of all eight legs as spiders worked in the dark.

Their creation of a web-building playbook or algorithm brings new understanding of how creatures with brains a fraction of the size of a human's are able to create structures of such elegance, complexity and geometric precision. The findings, now available online, are set to publish in the November issue of Current Biology.

"I first got interested in this topic while I was out birding with my son. After seeing a spectacular web I thought, 'if you went to a zoo and saw a chimpanzee building this you'd think that's one amazing and impressive chimpanzee.' Well this is even more amazing because a spider's brain is so tiny and I was frustrated that we didn't know more about how this remarkable behavior occurs," said senior author Andrew Gordus, a Johns Hopkins behavioral biologist. "Now we've defined the entire choreography for web building, which has never been done for any animal architecture at this fine of a resolution."

Web-weaving spiders that build blindly using only the sense of touch, have fascinated humans for centuries. Not all spiders build webs but those that do are among a subset of animal species known for their architectural creations, like nest-building birds and puffer fish that create elaborate sand circles when mating.

The first step to understanding how the relatively small brains of these animal architects support their high-level construction projects, is to systematically document and analyze the behaviors and motor skills involved, which until now has never been done, mainly because of the challenges of capturing and recording the actions, Gordus said.

Here his team studied a hackled orb weaver, a spider native to the western United States that's small enough to sit comfortably on a fingertip. To observe the spiders during their nighttime web-building work, the lab designed an arena with infrared cameras and infrared lights. With that set-up they monitored and recorded six spiders every night as they constructed webs. They tracked the millions of individual leg actions with machine vision software designed specifically to detect limb movement.

"Even if you video record it, that's a lot of legs to track, over a long time, across many individuals," said lead author Abel Corver, a graduate student studying web-making and neurophysiology. "It's just too much to go through every frame and annotate the leg points by hand so we trained machine vision software to detect the posture of the spider, frame by frame, so we could document everything the legs do to build an entire web."

They found that web-making behaviors are quite similar across spiders, so much so that the researchers were able to predict the part of a web a spider was working on just from seeing the position of a leg.

"Even if the final structure is a little different, the rules they use to build the web are the same," Gordus said. "They're all using the same rules, which confirms the rules are encoded in their brains. Now we want to know how those rules are encoded at the level of neurons."

Future work for the lab includes experiments with mind-altering drugs to determine which circuits in the spider's brain are responsible for the various stages of web-building.

"The spider is fascinating," Corver said, "because here you have an animal with a brain built on the same fundamental building blocks as our own, and this work could give us hints on how we can understand larger brain systems, including humans, and I think that's very exciting.

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Mathematician reveals world’s oldest example of applied geometry

A UNSW mathematician has revealed the origins of applied geometry on a 3700-year-old clay tablet that has been hiding in plain sight in a museum in Istanbul for over a century.

The tablet -- known as Si.427 -- was discovered in the late 19th century in what is now central Iraq, but its significance was unknown until the UNSW scientist's detective work was revealed today.

Most excitingly, Si.427 is thought to be the oldest known example of applied geometry -- and in the study released today in Foundations of Science, the research also reveals a compelling human story of land surveying.

"Si.427 dates from the Old Babylonian (OB) period -- 1900 to 1600 BCE," says lead researcher Dr Daniel Mansfield from UNSW Science's School of Mathematics and Statistics.

"It's the only known example of a cadastral document from the OB period, which is a plan used by surveyors define land boundaries. In this case, it tells us legal and geometric details about a field that's split after some of it was sold off."

This is a significant object because the surveyor uses what are now known as "Pythagorean triples" to make accurate right angles.

"The discovery and analysis of the tablet have important implications for the history of mathematics," Dr Mansfield says. "For instance, this is over a thousand years before Pythagoras was born."

Hot on the heels of another world-first find

In 2017, Dr Mansfield conjectured that another fascinating artefact from the same period, known as Plimpton 322, was a unique kind of trigonometric table.

"It is generally accepted that trigonometry -- the branch of maths that is concerned with the study of triangles -- was developed by the ancient Greeks studying the night sky in the second century BCE," says Dr Mansfield.

"But the Babylonians developed their own alternative 'proto-trigonometry' to solve problems related to measuring the ground, not the sky."

The tablet revealed today is thought to have existed even before Plimpton 322 -- in fact, surveying problems likely inspired Plimpton 322.

"There is a whole zoo of right triangles with different shapes. But only a very small handful can be used by Babylonian surveyors. Plimpton 322 is a systematic study of this zoo to discover the useful shapes," says Dr Mansfield.

Tablet purpose revealed: surveying land

Back in 2017, the team speculated about the purpose of the Plimpton 322, hypothesizing that it was likely to have had some practical purpose, possibly used to construct palaces and temples, build canals or survey fields.

"With this new tablet, we can actually see for the first time why they were interested in geometry: to lay down precise land boundaries," Dr Mansfield says.

"This is from a period where land is starting to become private -- people started thinking about land in terms of 'my land and your land', wanting to establish a proper boundary to have positive neighbourly relationships. And this is what this tablet immediately says. It's a field being split, and new boundaries are made."

There are even clues hidden on other tablets from that time period about the stories behind these boundaries.

"Another tablet refers to a dispute between Sin-bel-apli -- a prominent individual mentioned on many tablets including Si.427 -- and a wealthy female landowner," Dr Mansfield says.

"The dispute is over valuable date palms on the border between their two properties. The local administrator agrees to send out a surveyor to resolve the dispute. It is easy to see how accuracy was important in resolving disputes between such powerful individuals."

Dr Mansfield says the way these boundaries are made reveals real geometric understanding.

"Nobody expected that the Babylonians were using Pythagorean triples in this way," Dr Mansfield says. "It is more akin to pure mathematics, inspired by the practical problems of the time."

Creating right angles -- easier said than done

One simple way to make an accurate right angle is to make a rectangle with sides 3 and 4, and diagonal 5. These special numbers form the 3-4-5 "Pythagorean triple" and a rectangle with these measurements has mathematically perfect right angles. This is important to ancient surveyors and still used today.

"The ancient surveyors who made Si.427 did something even better: they used a variety of different Pythagorean triples, both as rectangles and right triangles, to construct accurate right angles," Dr Mansfield says.

However, it is difficult to work with prime numbers bigger than 5 in the base 60 Babylonian number system.

"This raises a very particular issue -- their unique base 60 number system means that only some Pythagorean shapes can be used," Dr Mansfield says.

"It seems that the author of Plimpton 322 went through all these Pythagorean shapes to find these useful ones.

"This deep and highly numerical understanding of the practical use of rectangles earns the name 'proto-trigonometry' but it is completely different to our modern trigonometry involving sin, cos, and tan."

Hunting down Si.427

Dr Mansfield first learned about Si.427 when reading about it in excavation records -- the tablet was dug up during the Sippar expedition of 1894, in what's the Baghdad province in Iraq today.

"It was a real challenge to trace the tablet from these records and physically find it -- the report said that the tablet had gone to the Imperial Museum of Constantinople, a place that obviously doesn't exist anymore.

"Using that piece of information, I went on a quest to track it down, speaking to many people at Turkish government ministries and museums, until one day in mid 2018 a photo of Si.427 finally landed in my inbox.

"That's when I learned that it was actually on display at the museum. Even after locating the object it still took months to fully understand just how significant it is, and so it's really satisfying to finally be able to share that story."

Next, Dr Mansfield hopes to find what other applications the Babylonians had for their proto-trigonometry.

There's just one mystery left that Dr Mansfield hasn't unlocked: on the back of the tablet, at the very bottom, it lists the sexagesimal number '25:29' in big font -- think of it as 25 minutes and 29 seconds.

Read more at Science Daily

Geometry of an electron determined for the first time

Quantum computing concept.

Physicists at the University of Basel are able to show for the first time how a single electron looks in an artificial atom. A newly developed method enables them to show the probability of an electron being present in a space. This allows improved control of electron spins, which could serve as the smallest information unit in a future quantum computer. The experiments were published in Physical Review Letters and the related theory in Physical Review B.

The spin of an electron is a promising candidate for use as the smallest information unit (qubit) of a quantum computer. Controlling and switching this spin or coupling it with other spins is a challenge on which numerous research groups worldwide are working. The stability of a single spin and the entanglement of various spins depends, among other things, on the geometry of the electrons -- which previously had been impossible to determine experimentally.

Only possible in artificial atoms

Scientists in the teams headed by professors Dominik Zumbühl and Daniel Loss from the Department of Physics and the Swiss Nanoscience Institute at the University of Basel have now developed a method by which they can spatially determine the geometry of electrons in quantum dots.

A quantum dot is a potential trap which allows to confine free electrons in an area which is about 1000 times larger than a natural atom. Because the trapped electrons behave similar to electrons bound to an atom, quantum dots are also known as "artificial atoms."

The electron is held in the quantum dot by electric fields. However, it moves within the space and, with different probabilities corresponding to a wave function, remains in certain locations within its confinement.

Charge distribution sheds light

The scientists use spectroscopic measurements to determine the energy levels in the quantum dot and study the behavior of these levels in magnetic fields of varying strength and orientation. Based on their theoretical model, it is possible to determine the electron's probability density and thus its wave function with a precision on the sub-nanometer scale.

"To put it simply, we can use this method to show what an electron looks like for the first time," explains Loss.

Better understanding and optimization

The researchers, who work closely with colleagues in Japan, Slovakia and the US, thus gain a better understanding of the correlation between the geometry of electrons and the electron spin, which should be stable for as long as possible and quickly switchable for use as a qubit.

"We are able to not only map the shape and orientation of the electron, but also control the wave function according to the configuration of the applied electric fields. This gives us the opportunity to optimize control of the spins in a very targeted manner," says Zumbühl.

The spatial orientation of the electrons also plays a role in the entanglement of several spins. Similarly to the binding of two atoms to a molecule, the wave functions of two electrons must lie on one plane for successful entanglement.

Read more at Science Daily