[…] most recently in January 2024, when physicists Arnab Priya Saha and Aninda Sinha of the Indian Institute of Science presented a completely new formula for calculating it, which they later published in Physical Review Letters.
Saha and Sinha are not mathematicians. They were not even looking for a novel pi equation. Rather, these two string theorists were working on a unifying theory of fundamental forces, one that could reconcile electromagnetism, gravity and the strong and weak nuclear forces
[…]
For millennia, mankind has been trying to determine the exact value of pi. […]
One famous example is Archimedes, who estimated pi with the help of polygons: by drawing an n-sided polygon inside and one outside a circle and calculating the perimeter of each, he was able to narrow down the value of pi.
A common method for determining pi geometrically involves drawing a bounding polygon inside and outside a circle and then comparing the two perimeters.
Fredrik/Leszek Krupinski/Wikimedia Commons
Teachers often present this method in school
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In the 15th century experts found infinite series as a new way to express pi. […]
For example, the Indian scholar Madhava, who lived from 1350 to 1425, found that pi equals 4 multiplied by a series that begins with 1 and then alternately subtracts or adds fractions in which 1 is placed over successively higher odd numbers (so 1/3, 1/5, and so on). One way to express this would be:
This formula makes it possible to determine pi as precisely as you like in a very simple way.
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As Saha and Sinha discovered more than 600 years later, Madhava’s formula is only a special case of a much more general equation for calculating pi. In their work, the string theorists discovered the following formula:
This formula produces an infinitely long sum. What is striking is that it depends on the factor λ , a freely selectable parameter. No matter what value λ has, the formula will always result in pi. And because there are infinitely many numbers that can correspond to λ, Saha and Sinha have found an infinite number of pi formulas.
If λ is infinitely large, the equation corresponds to Madhava’s formula. That is, because λ only ever appears in the denominator of fractions, the corresponding fractions for λ = ∞ become zero (because fractions with large denominators are very small). For λ = ∞, the equation of Saha and Sinha therefore takes the following form:
The first part of the equation is already similar to Madhava’s formula: you sum fractions with odd denominators.
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As the two string theorists report, however, pi can be calculated much faster for smaller values of λ. While Madhava’s result requires 100 terms to get within 0.01 of pi, Saha and Sinha’s formula for λ = 3 only requires the first four summands. “While [Madhava’s] series takes 5 billion terms to converge to 10 decimal places, the new representation with λ between 10 [and] 100 takes 30 terms,” the authors write in their paper.Saha and Sinha did not find the most efficient method for calculating pi, though. Other series have been known for several decades that provide an astonishingly accurate value much more quickly. What is truly surprising in this case is that the physicists came up with a new pi formula when their paper aimed to describe the interaction of strings.
Researchers at Cornell University tapped into fungal mycelia to power a pair of proof-of-concept robots. Mycelia, the underground fungal network that can sprout mushrooms as its above-ground fruit, can sense light and chemical reactions and communicate through electrical signals. This makes it a novel component in hybrid robotics that could someday detect crop conditions otherwise invisible to humans.
The Cornell researchers created two robots: a soft, spider-like one and a four-wheeled buggy. The researchers used mycelia’s light-sensing abilities to control the machines using ultraviolet light. The project required experts in mycology (the study of fungi), neurobiology, mechanical engineering, electronics and signal processing.
“If you think about a synthetic system — let’s say, any passive sensor — we just use it for one purpose,” lead author Anand Mishra said. “But living systems respond to touch, they respond to light, they respond to heat, they respond to even some unknowns, like signals. That’s why we think, OK, if you wanted to build future robots, how can they work in an unexpected environment? We can leverage these living systems, and any unknown input comes in, the robot will respond to that.”
The fungal robot uses an electrical interface that (after blocking out interference from vibrations and electromagnetic signals) records and processes the mycelia’s electrophysical activity in real time. A controller, mimicking a portion of animals’ central nervous systems, acted as “a kind of neural circuit.” The team designed the controller to read the fungi’s raw electrical signal, process it and translate it into digital controls. These were then sent to the machine’s actuators.
Cornell University / Science Robotics
The pair of shroom-bots successfully completed three experiments, including walking and rolling in response to the mycelia’s signals and changing their gaits in response to UV light. The researchers also successfully overrode the mycelia’s signals to control the robots manually, a crucial component if later versions were to be deployed in the wild.
So this is a pin a bit larger than an AA battery which does one thing: it transcribes your musings and makes notes. Where does the AI come in? Speech and speaker recognition, audio trimming, summarisation and mind-maps.
You see a lot of doubtful reviews on this thing out there, mostly on the basis of how badly the Rabbit and the Humane did. The writers don’t seem to understand that generalistic AI is still a long way off from being perfect whereas task specific AI is incredibly useful and accurate.
Unfortunately it does offload the work to the cloud, which absolutely has very very many limits (not least of which being privacy = security – and notes tend to be extremely private, not to mention accessibility).
All in all a good idea, let’s see if they pull it off.
Lobbying groups across most of the device manufacturing industry—from tractor manufacturers to companies that make fridges, consumer devices, motorcycles, and medical equipment—are lobbying against legislation that would require military contractors to make it easier for the U.S. military to fix the equipment they buy, according to a document obtained by 404 Media.
The anti-repair lobbying shows that manufacturers are still doing everything they can to retain lucrative service contracts and to kill any legislation that would threaten the repair monopolies many companies have been building for years.
In a May hearing, Sen. Elizabeth Warren explained that “contractors often place restrictions on these deals [with the military] that prevent service members from maintaining or repairing the equipment, or even let them write a training manual without going back to the contractor.”
“These right to repair restrictions usually translate into much higher costs for DOD [Department of Defense], which has no choice but to shovel money out to big contractors whenever DOD needs to have something fixed,” she added. Warren gave the example of the Littoral combat ship, a U.S. Navy vessel that costs hundreds of millions of dollars per ship.
“General Dynamics and Lockheed Martin consider much of the data on the ship to be proprietary, so the Navy had to delay missions and spend millions of dollars on travel costs just so that contractor-affiliated repairmen could fly in, rather than doing this ourselves,” she said.
To solve this problem, Warren and other lawmakers introduced something called Section 828 of the Defense Reauthorization Act, a must-pass bill that funds the military. Section 828 is called “Requirement for Contractors to Provide Reasonable Access to Repair Materials,” and seeks to solve an absurd situation in which the U.S. military cannot always get repair parts, tools, information, and software for everything from fighter jets to Navy battleships, because the companies want to make money by selling their customers repair contracts.
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The fact that groups who represent companies that have nothing to do with the military have lined up to oppose this suggests that device manufacturers more broadly are worried about a national right to repair law, and that the entire sector is trying to kill repair legislation even if it would not affect them.
