"Lessons of Immortality and Mortality From My Father, Carl Sagan"
I have been playing around with Pantheon which is MIT Media Lab’s ambitious effort to visualize cultural production across history. I had pulled comparisons of the most culturally significant industries in various countries before the Middle Ages and after. On the vertical axis, countries were plotted in descending order of cultural power (fewer countries existed before the year 1500) and on the horizontal, each country’s cultural production with the listed occupations and fields. One of the most obvious patterns is the decline of religion as a domain of cultural power and the rise of the natural and social sciences, as well the emergence of the creative arts, from film and theater to design.
I was reminded of something I had read in Carl Sagan’s last book “The Demon-Haunted World: Science as a Candle in the Dark” which he had written primarily to explain the scientific method to laypeople, and to encourage people to learn critical or skeptical thinking. To distinguish between ideas that are considered valid science, and ideas that can be considered pseudoscience. The quote:
"Science is not only compatible with spirituality; it is a profound source of spirituality. When we recognize our place in an immensity of light‐years and in the passage of ages, when we grasp the intricacy, beauty, and subtlety of life, then that soaring feeling, that sense of elation and humility combined, is surely spiritual. So are our emotions in the presence of great art or music or literature, or acts of exemplary selfless courage such as those of Mohandas Gandhi or Martin Luther King, Jr. The notion that science and spirituality are somehow mutually exclusive does a disservice to both.”
It was brought home to me yesterday when I read Sasha Sagan’s essay “Lessons of Immortality and Mortality From My Father, Carl Sagan”. It’s a beautiful piece and relates the story of the Sphinx Head Tomb, repository of her father’s papers, handwritten notes, photographs, to-do lists, birthday cards, childhood drawings, and report cards. The evidence of a great life lived. To read it click here.
How do mathematicians calculate Pi? Well, with a Mossberg 500 Pump-Action shotgun, you idiot!
The task? Calculate:
The method? a Mossberg 500 Pump-Action shotgun:
Having a subscription to the MIT Technology Review opens you to an incredible source of technology and science news, information and reviews. One element is the “arXiv Papers”, a compendium of new research papers, the subject matters being mostly mathematics and physics. I usually scan it once a month. It can be a treasure trove of “technology-soon-on-the-horizon” that often hits the mainstream press months later. All of it just brilliant stuff.
Lately I have been immersed in math due to my work in the field of artificial intelligence. Lately I have been focused on the application of machine learning techniques within the practice of law, as part of a series of presentations our legal group gives on basic principles underlying machine learning methods, in a manner accessible to non-technical audiences.
I have always loved math, and have been fascinated by Pi, and its calculation. Pi Day is celebrated on March 14th (3/14. get it?) around the world. Pi (Greek letter … Pi) has been calculated to over one trillion digits beyond its decimal point. I remember it was one of the first exercises I ever did in “Introduction to Computing” (waaaaaaaaay back in 1972), using a random number generator to find the value of Pi. I did it in FORTRAN back in those days (with punch cards on an IBM370/155). But I got hooked onto Pi years later during a “math in the Bible” course (yes, these courses do exist) when our professor pointed out this passage:
"And he made a molten sea, ten cubits from the one rim to the other it was round all about, and…a line of thirty cubits did compass it round about….And it was an hand breadth thick…." —- First Kings, chapter 7, verses 23 and 26
Research back in the 1930s discovered that there’s more to that verse than appears. In Hebrew, the letters are also numbers, and the number values of letters and words are often very significant to the reading. There is a ‘jot’ (‘jot’ and ‘tittle’ are like diacritic marks) in the original, which here means, “look deeper”. So with a bit of deeper analysis, one finds that the letters there turn out to make up a fraction. I forget what the fraction is, but it’s something like 31/222 or some such, and with the fraction the value is within 1% or less of pi. There is the usual “this-is-numerology-bullshit” debate but still, fascinating stuff.
And then …. ahem … you have people doing a study who are at least one side short of a geometric cube, if you know what I mean. Here follows … from a reader/commentator in the aforementioned “arXiv Papers”, a novel way to compute Pi, with links to Medium which republished it. Medium is one of the best “longread” websites out there. An enormous list of subject areas. Take a look. You’ll subscribe.
"Imagine the following scenario. The end of civilization has occurred, zombies have taken over the Earth and all access to modern technology has ended. The few survivors suddenly need to know the value of pi and, being a mathematician, they turn to you. What do you do?
According to a couple of Canadian mathematicians, the answer is to repeatedly fire a Mossberg 500 pump action shotgun at a square aluminum target about 20 meters away. Then imagine that the square is inscribed with an arc drawn between opposite corners that maps out a quarter circle. If the sides of the square are equal to 1, then the area of the quarter circle is pi/4. Next, count the number of pellet holes that fall inside the area of the quarter circle as well as the total number of holes. The ratio between these is an estimate of the ratio between the area of the quarter circle and the area of a square, or in other words pi/4. So multiplying this number by 4 will give you an estimate of pi.
The result? According to this method, pi is 3.13, which is just 0.33 per cent off the true value. Handy if you find yourself in a post-apocalyptic world.”
Mathematical proof that the Cosmos could have formed spontaneously … from nothing
Pictured: the Universe start button
One of the great theories of modern cosmology is that the universe began in a Big Bang. It’s backed up by numerous lines of evidence, such as the cosmic microwave background and so on.
But what caused the Big Bang, itself? For many years, cosmologists have fallen back on the idea that the universe formed spontaneously; that the Big Bang was result of quantum fluctuations in which the universe came into existence from nothing.
But is this compatible with what we know about the Big Bang itself and the theories that describe it? Now cosmologists have come up with the first rigorous proof that the Big Bang could indeed have occurred spontaneously and produced the universe we see today.
The proof is developed within a mathematical framework known as the Wheeler-DeWitt equation. Heisenberg’s uncertainty principle allows a small region of empty space to come into existence probabilistically due to quantum fluctuations. Most of the time, such a bubble will collapse and disappear. The question these scientists address is whether a bubble could also expand exponentially to allow a universe to form in an irreversible way.Their proof shows that this is indeed possible. There is an interesting corollary: the role of the cosmological constant is played by a property known as the quantum potential. This is a property introduced in the 20th century by the physicist David Bohm, which has the effect of making quantum mechanics deterministic while reproducing all of its predictions. It’s an idea that has never caught on. Perhaps that will change now.
Today’s Google Doodle recognizes the extraordinary works of researcher & chemist, Percy Julian
If you can access Google.com, here is what you’ll find:
Percy Lavon Julian (April 11, 1899 – April 19, 1975) was a U.S. research chemist and a pioneer in the chemical synthesis of medicinal drugs from plants.
He was the first to synthesize the natural product physostigmine, and a pioneer in the industrial large-scale chemical synthesis of the human hormones progesterone and testosterone from plant sterols such as stigmasterol and sitosterol. His work laid the foundation for the steroid drug industry’s production of cortisone, other corticosteroids, and birth control pills.