March 14 is the closest calendrical approximation of pi and this year it falls on Tuesday of 2023. This so called pi-day is celebrated every year by not only the scientifically minded folks but to the general public around the world where pie eating contest is one of the most popular events in this nation. Pi is the most well known transcendental number which is of great interest to mathematicians for a very long time. Pi is the ratio of the circle’s circumference to its diameter- 3.14 followed by an exorbitant amount of decimal places which everyone is familiar with. However, there are bunch of things you might not know about pi :
1) In the 1995 OJ Simpson trial, one witness credibility was called into doubt when he misstated the value of pi. ( How bad was that?) or was it even important? Now I wonder about people like Donald Trump or Betsy Devos will even be able to state the value of pi up to the first two decimal places. Yes, we had two gigantic idiots in this country and it is a good thing that they no longer hold any positions for now.
2) The year ( 2015) I gave a presentation in the afternoon on March 14 about the nature of pi and I informed the audience why that particular morning was so significant, precisely at 9:26:53:58 ( including 1/100 sec) so it was 3/14/15 9265358, representing the first 12 digits of pi. I also informed the audience that this would not happen again for another 100 years until it is 2115, therefore it was a very special moment. Depending on my schedule, perhaps I can give another presentation when that day comes.
3) Richard Feynman, one of the greatest physicists of the 20th century, wanted to memorize pi up to the 762nd digit for there are six nines in a row starting at that point so called ” Feynman point”. He wanted to recite them and say ” nine, nine, nine, nine, nine, nine ” to suggest in a jokingly manner that pi is a rational number. Any challengers here?
4) The genius of all time, Albert Einstein, was born on pi day ( March 14, 1879).
Is there a connection between Einstein and Pi other than his date of birth?
Einstein is famous for his revolutionary discoveries in physics. In 1905, he resurrected the particle model of light by introducing the photoelectric effect and won the Nobel Prize in 1921. In the same year, he formulated the special theory of relativity unifying space and time ( space-time) along with mass and energy. ( E= mc²). In 1915, he included gravity by formulating the General Theory of Relativity, making use of geometry to describe gravity as space-time curvature. The Einstein’s Field Equation in General Relativity does contain pi:
Rμν – ½ Rgμν = 8πG Tμν
Rμν: curvature Tensor Rgμν: gravitational metric Tensor
Tμν: energy-momentum Tensor
This equation says: the amount of gravity( space-time curvature) is proportional to the amount of energy and momentum in which π is part of the proportionality constant. G is the Universal Gravitational constant. By the way, this equation was written before he inserted the cosmological constant to balance the gravitational pull for a static universe. The equation then became : Rμν -½ gμνR + gμνΛ = [8πG/(c²)²] Tμν where Λ is the cosmological constant, although later he mentioned that was the biggest blunder in his life to add the constant into the equation. So what made Einstein put π into the field equation?
Recall that the Gravitational potential field of a single body of mass M which is given by: Φ= -G(M/r) and any object placed in this field will experience an instantaneous gravitational force. The mass density for multiple bodies of M’s is given by: ∇²Φ = 4πGρ. ∇² is the Laplacian operator, Φ is the field, and ρ is the mass density. π appears in many equations in physics and field theory is the best in describing gravity. General Theory of Relativity is a theory of gravity using space-time curvature to describing it and having π in the equation is a necessary consequence of the field theory( it involves integrating over the surface of a sphere). Area of a sphere is 4πr², and the field that is involved in General Relativity is the metric tensor field which describes the geometry of spacetime. That is the connection of π and Einstein in reference to the field theory of gravity.
There is also a mysterious connection between π and Quantum Mechanics which scientists discovered back in last November. ( refer back to my previous blog on the connection between pi and Quantum Mechanics). So π is no longer just a number in mathematics but in physics as well, particularly in Quantum Mechanics and Relativity. The strange connectivity of Quantum Mechanics and π is indeed shocking and we are trying to seek explanations for it. Our jobs as scientists is to formulate the best possible description of the world as it is, not to force the world to bend to our preconception.
So on pi-day, we should focus more on the nature of pi but I am not really a pi person which means I don’t have a thing for pi; in fact, I don’t have a thing for any of the numbers in mathematics. I crunch numbers very well because of what I do from day to day.( ie. analyzing data.) Pi is far from being one of my favorite numbers and I don’t have any favorite numbers.. A few years ago I gave a presentation to a group of audience and it involved number patterns in mathematics. At the end of the presentation came the Q/A session. One person from the audience asked which number do I prefer to be if given a choice, and my response was none. I explained it very clear to the audience that I do not have a favorite number, but I did tell them that I enjoyed looking at palindrome. They are symmetrical and pleasant looking. I was born on Dec 21, so it is 1221. My parking stall number is 121 and one of my security codes is 575 when entering a lab premise ( no worries, you won’t know where the lab is). I do like palindrome but I don’t have a favorite one either. When the person from the audience insisted that I had to pick a palindrome which I prefer to be so I told him i prefer pi. He was shocked as pi isn’t a palindrome and not my favorite number, so why did I pick it? My answer to him once again was ” i prefer pi”, and if he paid more attention to that answer ” i prefer pi” is itself a palindrome. ” i prefer pi” ⇔” i prefer pi”, read it backward.
Have a nice pi day and enjoy eating lots of pies.