Bob Schwartz

Category: Mathematics

November 7, 2014

Notes on Interstellar

Interstellar

1

Christopher Nolan’s movie Interstellar is more interesting than it is imperfect. See it if you like space movies, sci-fi movies, intellectually curious movies, spectacular movies, etc.

It is filled with wonders. It is like the car trunk stuffed with luggage for a vacation, so much colorful and significant luggage creatively crammed in that when you open it on arrival you say: Wow, I wonder how we ever got all that stuff in there?

No spoilers here, but a couple of things.

Look for all the tiny (and not so tiny) echoes of space and sci-fi movies past. Star Wars, Close Encounters, etc., but most of all 2001. Why not? Right now, “they” are probably having a good 5th dimensional laugh watching Stanley Kubrick’s proto-human apes tossing that bone.

Interstellar has the most subtly cool robots ever. TARS doesn’t sing like HAL, but he has moves like Jagger and is great with the snappy patter.

2

The movie is much about cosmology—the origin and nature of existence. Cosmology is the domain of all kinds of people, including religionists and philosophers. But in greater part, we have handed over many of those considerations, as in this movie, to theoretical physicists—Einstein, Hawking, etc. I am a big fan of cosmology.

It is not a spoiler to mention that plenty of people, including some in this movie, believe that the Apollo 11 moon landing was faked. Which raises this way-out-there question: What if the moon landing was real but all the cosmological theoretical physics is faked? Going back before Einstein, theoretical physics spends much of its time (as we understand it) looking for physical proof of those theories. What if all the theory is so utterly astounding and enlightening that when the evidence failed to support it, all the scientists engaged in the study conspired to make it seem as if those theories are supported?

Faking the moon landing mission has never been put entirely to rest because, in fact, only three people experienced it first-hand. Everyone else was second-hand or more distanced from the actuality. But the basic elements of it are well within our understanding: astronauts, rocket, spaceship, lunar lander, moon, television pictures. The cosmological speculation and supporting discoveries are so far beyond anything that most of us can fully—or slightly—grasp that we could easily be fooled into taking it for “reality.”

By the way, for those wondering about the earnestness of all that, be assured that I am just playing. Or am I?

3

We don’t have to be space pilots to experience cosmology, or be theoretical physicists or movie directors to think about it. Cosmology is ordinary. Interstellar and other movies and thousands of works of art and literature point to this. Everybody is a cosmologist, like it or not.

Cosmology is an excellent topic that does not necessarily require specialized knowledge. You may not know a worm hole from a black hole. But you already know a ton about time, space, being, and gravity. You just have to know how to know and that you know.

This is from an essay almost 800 years old. No more or less spectacular than Interstellar, it is no more or less a non-theoretical description:

Do not think that time merely flies away. Do not see flying away as the only function of time. If time merely flies away, you would be separated from time. The reason you do not clearly understand the time being is that you think of time only as passing.

In essence, all things in the entire world are linked with one another as moments. Because all moments are the time being, they are your time being….

You may suppose that time is only passing away, and not understand that time never arrives. Although understanding itself is time, understanding does not depend on its own arrival.

People only see time’s coming and going, and do not thoroughly understand that the time being abides in each moment. Then, when can they penetrate the barrier? Even if people recognized the time being in each moment, who could give expression to this recognition? Even if they could give expression to this recognition for a long time, who could stop looking for the realization of the original face? According to an ordinary person’s view of the time being, even enlightenment and nirvana as the time being would be merely aspects of coming and going….

Mountains are time. Oceans are time. If they were not time, there would be no mountains or oceans. Do not think that mountains and oceans here and now are not time. If time is annihilated, mountains and oceans are annihilated. As time is not annihilated, mountains and oceans are not annihilated.

Dogen
The Time Being (1240)
Treasury of the True Dharma Eye

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September 23, 2014

Islamic State: Using Arithmetic to Solve Complex Equations

Riemann - Zeta Function

We are not playing three-dimensional chess in the Middle East—partly because all of us will go crazy if we hear that clichéd term one more time.

Instead, we are using arithmetic to solve very complex equations.

The Clay Mathematics Institute offers the famous Millennium Prizes, $1,000,000 each for solving their current list of unsolved mathematical problems.

Here is description of the Riemann Hypothesis (a manuscript by Riemann of the Zeta function is pictured above):

Some numbers have the special property that they cannot be expressed as the product of two smaller numbers, e.g., 2, 3, 5, 7, etc. Such numbers are called prime numbers, and they play an important role, both in pure mathematics and its applications.

The distribution of such prime numbers among all natural numbers does not follow any regular pattern. However, the German mathematician G.F.B. Riemann (1826 – 1866) observed that the frequency of prime numbers is very closely related to the behavior of an elaborate function

ζ(s) = 1 + 1/2s + 1/3s + 1/4s + …

called the Riemann Zeta function. The Riemann hypothesis asserts that all interesting solutions of the equation

ζ(s) = 0

lie on a certain vertical straight line.

This has been checked for the first 10,000,000,000 solutions. A proof that it is true for every interesting solution would shed light on many of the mysteries surrounding the distribution of prime numbers.

Right now, in the early days of the campaign against the Islamic State, we are using arithmetic that goes something like this:

1 (U.S.) + x (number of participating nations with wildly different involvement and interests) – IS = conditional victory

The truth is much closer to complex mathematics, as complex as any we may have ever seen on the world stage. There are probably behind-the-scenes discussions that are more subtle, but here in the public we are somehow not supposed to bother our heads about that. The question of why we publicly don’t deal with it this way may be because our leaders can’t handle the truth or because they believe citizen/voters can’t handle the truth or, because of politics and wanting to be seen as doing something, a little of both.

Solving the problem is worth much more than a million dollars. But solving it will take more than simple addition, subtraction, multiplication, and division. There was a time when the world was like that, susceptible to those simple solutions. But those days and that world are gone. Our leaders don’t have to be able to attempt a solution to the Riemann Hypothesis. But they do have to recognize when grade school, old school strategies—when simple arithmetic—will no longer work.

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