Posted on 06/26/2024 5:44:58 AM PDT by Red Badger
String theory scientists studying the behavior of high energy particles say they have stumbled upon a mathematical “hack” that revealed a whole new way to represent the irrational number Pi. While the research is purely theoretical, the duo behind the Pi hack says this kind of theoretical work holds rewarding potential.
The researchers also believe their work could lead to a number of potential breakthroughs in the future, similar to how theoretical breakthroughs made by physicists nearly a hundred years ago resulted in technological advancements decades later.
AFTER 4,000 YEARS, PI IS STILL A MYSTERY
Defined as the ratio of a circle’s circumference to its diameter and often represented with the symbol π, the earliest written representations of Pi date back to around 1,900 BC and 1,50 BC in Babylon and Egypt, respectively. Still, although the concept of Pi itself is rather straightforward, mathematicians have struggled for centuries to calculate the number accurately, leading to Pi being classified as irrational.
Unfortunately for modern scientists, Pi is often needed when performing calculations related to a wide range of scientific inquiries, including disciplines as disparate as chemical engineering and aerospace design. In these cases, scientists often use a mathematical “series” to represent Pi instead of a rounded-off approximation like the 3.14 most people are familiar with. According to the researchers behind this latest discovery, “if pi is the “dish” then the series is the “recipe.”
Still, those representations have limitations, leaving researchers continually searching for a more accurate and efficient way to represent this irrational number. Now, Arnab Saha, a postdoc, and Aninda Sinha, a Professor at the Centre for High Energy Physics at the Indian Institute of Science (IISc), say they have stumbled upon a whole new way to represent Pi. If proven, it may offer scientists a whole new method for using the number in complex calculations.
ACCIDENTAL DISCOVERY OCCURRED DURING HIGH-ENERGY PHYSICS RESEARCH
Surprisingly, the team behind the potentially historic discovery says they weren’t even searching for a new representation of Pi. Instead, they were working on an aspect of String Theory that involved calculating the interactions of high-energy particles.
“Our efforts, initially, were never to find a way to look at pi,” Sinha explained. “All we were doing was studying high-energy physics in quantum theory and trying to develop a model with fewer and more accurate parameters to understand how particles interact.”
According to Sinha, it was during this process that he and Saha stumbled upon a whole new way to represent Pi, with the researcher noting, “We were excited when we got a new way to look at Pi.”
While the mathematics of the discovery are rather complex, the team says they are not the first to glimpse this new representation of Pi. Instead, they say that their representation “closely reaches” a representation made in the 15th century by Indian mathematician Sangamagrama Madhav. The team also says that 20th-century researchers also got close to their discovery but simply lacked the tools necessary to take their solution to the finish line.
“Physicists (and mathematicians) have missed this so far since they did not have the right tools, which were only found through work we have been doing with collaborators over the last three years or so,” Sinha explains. “In the early 1970s, scientists briefly examined this line of research but quickly abandoned it since it was too complicated.”
To make their historic discovery, Sinha and Saha say they “clubbed together” two firmly established mathematical tools known as Euler-Beta Functions and the Feynman Diagram. According to the press release announcing the discovery, “Euler-Beta functions are mathematical functions used to solve problems in diverse areas of physics and engineering, including machine learning, [while] The Feynman Diagram is a mathematical representation that explains the energy exchange that happens while two particles interact and scatter.”
As hoped, combining these tools resulted in an efficient model to help explain the particle interactions the team was studying. However, when confirming their calculations, they noted that the combination also netted something completely unexpected: a whole new way to represent Pi.
“The series that Sinha and Saha have stumbled upon combines specific parameters in such a way that scientists can rapidly arrive at the value of pi,” the press release explains, “which can then be incorporated in calculations, like those involved in deciphering scattering of high-energy particles.”
PURELY THEORETICAL DISCOVERY COULD OFFER UNSEEN BENEFITS IN THE FUTURE
While the work, published in the journal Physical Review Letters, is still purely theoretical, the team believes its new representation of Pi could help scientists across a wide range of disciplines, if not immediately.
For example, Sinha noted that 20th-century researcher Paul Dirac began his work on the mathematics of the motion and existence of electrons way back in 1928. However, Dirac didn’t live to see how his findings ultimately provided clues to the discovery of the positron and then to the design of Positron Emission Tomography (PET), which lets doctors scan the human body for diseases and abnormalities.
The team also points out that scientists can still enjoy the pure aspects of theory. As far as Sinha is concerned, that can be its own type of reward.
“Doing this kind of work, although it may not see an immediate application in daily life, gives the pure pleasure of doing theory for the sake of doing it,” the researcher said.
Christopher Plain is a Science Fiction and Fantasy novelist and Head Science Writer at The Debrief. Follow and connect with him on X, learn about his books at plainfiction.com, or email him directly at christopher@thedebrief.org.
Thanks Sheldon.
NASA would be full of idiots if they thought Pi was rational in any base. Or perhaps the source you heard it from is the idiot.
constant pi = 4*atan(1);
Lol. String pseudoscientists pretending to have relevancy.
It's an equation consisting of an infinite series, given in the next to last page of the Phys.Rev.Lett. article.
My favorites are apple and pecan…
When and if proof comes for string theory or some derivation of it, it will almost certainly be first stated as ideas and mathematics that explain otherwise puzzling observations and experimental results. That is how Einstein got his Nobel Prize for the photoelectric effect, not by lab work, but by mathematically describing light as composed of particles emitted with quanta of energy expressed by their frequency.
For physicists, Einstein suddenly made sense of light emission stimulated by electrons. He adopted Planck's proposal that light consisted of particles (photons), with Einstein further explaining their frequency as quanta of kinetic energy imparted by electrons. The warm glow from Edison's marvelous light bulb (and much else) was thereby explained.
But it wasn't until 1873 that Charles Hermite proved that e was a transcendental (not an algebraic) number, and in 1882 Ferdinand Lindemann was the first to prove that pi was also transcendental.
Of course, in 1874, Georg Cantor shocked (and in some cases enraged) the mathematicians of the world by showing in the set of real numbers (made up of rational and irrational numbers) that the subset of irrational numbers was infinitely greater than the subset of rational numbers because the irrational numbers included the overwhelmingly abundant set of transcendental numbers.
Pie are round
Cornbread are square
Cornbread are square.
22/7 diverges from pi in the third decimal place. It’s a really lousy approximation, despite what we learned in third grade. Better just to memorize 3.141592653 and have more than enough correct digits for any application outside of astronomy or atomic physics.
And you have a “pi” key on your calculator anyway.
Bfl
I thought that an “irrational” number was the square root of a negative number, and could only be expressed as a polynomial equation.
that's the equation of the Edmonton NHL team ...
Pi in the sky....................
square root of a negative number is “imaginary” ...
SQRT(-1) = i
unless you’re an electrical engineer.
then
SQRT(-1) = j
because “i” is current.
I once read a science-fiction novel in which an alien civilization was so enamored of that equation that it became their name for themselves. It was also the key to them and humans learning to communicate with each other.
The humans referred to that particular set of aliens as “Eulers”.
#79 for you.
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