Mathematical Opera


Overview

This is my attempt to make an opera about the Millennium Prize Problems, if you solve any of these problems you get a prize of one million dollars from the Clay Mathematics Institute!

https://en.wikipedia.org/wiki/Millennium_Prize_Problems

So the opera will have seven acts because there are seven such problems, and in each problem the characters will use a time machine to travel to a different period in history, and they will meet with the smartest mathematical genius of that period, and he will help them to solve one of the problems.

The music of the singing parts will be based on the equations of the title problem of that act. for example in the part about the Riemann hypothesis

https://en.wikipedia.org/wiki/Riemann_hypothesis

the equation will be the Riemann zeta function.

https://en.wikipedia.org/wiki/Riemann_zeta_function

basically i will take the pictures in these Wikipedia pages and try to convey them in various ways through music.

The most obvious way is to treat the rise and fall of a graph

https://en.wikipedia.org/wiki/Riemann_hypothesis#/media/File:RiemannCriticalLine.svg

like the rise and fall of the notes on the staff

https://en.wikipedia.org/wiki/Staff_(music)

But maybe I will think of additional ways.

(As you can see this part is similar to my Sonifiquation project)

Main Plot

Remember how Doctor Who always have a woman sidekick? So I’m kidnapping my mythological ex (i apologize that it’s not educational, anyway it’s totally fictional) and our “Tardis” like time machine basically protects the time line inside it, but all the rest of the universe’s time flows in reverse. So outside everything is like a movie that is played backwards. So people are undone (including her kids and husband) and there are very few “stopping stations” that I was able to program into the machine before the process started. and i chose these as the times of those few mathematical geniuses that we’re going to meet.

So time flows in all the world backwards (but inside the time capsule we are protected and time is normal), except for the seven “stopping stations” when time in all the world behaves normally for 24 hours, and then we need to escape to the time capsule again or else we become undone.

Eventually my mythological ex comes up with a way to stop the time machine and restore the time direction back to normal (forward). By then we have returned to the days of the first homo-sapiens humans, and we both start humanity over as the new Adam and Eve! Oh and each time the time machine is working there’s the music of “Ride On Time” the song by Black Box (like instead of the Doctor Who Theme Tune).

Mathematicians (later i will assign them to the 7 problems)

Greece (geometry)
Pythagoras (circa 570-495BC)
Euclid (circa 365-275 BC)
Archimedes (circa 287–212 BC)

India (algebra)
Brahmagupta (c. 598 – c. 668 CE)
Aryabhata (476–550 CE)

England (calculus)
Newton (1642–1727)
Leibniz (1646-1716)

Russia (analysis)
Euler (1707-1783)

France (more analysis)
Lagrange (1736–1813) calculus of variations
Laplace (1749–1827) mathematical astronomy
Legendre (1752–1833)mathematical physics

thank you to Matthew Rave from Many Worlds Theory:
Lagrange, Laplace, and Legendre: which one is which?
https://manyworldstheory.com/2014/11/24/lagrange-laplace-and-legendre-which-one-is-which/

Lagrange: the beauty of math; reformulated mechanics in the Mécanique analytique

Laplace: math as a tool; Newtonian mechanics reaches its zenith in Mécanique céleste; probability theory

Legendre: the creepy looking elliptic integral guy

Germany I ( abstract algebra )
Gauss (1777-1855) everything
Abel (1802–1829) modern algebra
Jacobi (1804–1851) differential equations
Hamilton (1805–1865) mathematical physics
Galois (1811–1832) group theory
Riemann (1826–1866) differential geometry

Germany II (more abstract algebra)
Cantor (1845-1918) infinite sets
Poincaré (1854–1912) everything
Hilbert (1862 – 1943) modern algebra
Noether (1882–1935) modern algebra
Ramanujan (1887–1920) number theory

thank you to Lê Nguyên Hoang from Lê’s Blog
Rigor and Intuition in Mathematics
https://lenhoang.wordpress.com/2013/08/01/rigor-and-intuition-in-mathematics/

A hundred years, two giants of mathematics debated the role of rigor and intuition in mathematics. While the mighty David Hilbert was praising rigorous foundations for the field, the renowned Henri Poincaré was arguing that mathematics was a matter of intuitions.

Reversing Time

In the extremely interesting video by Varitasium about pilot waves:

Is This What Quantum Mechanics Looks Like?

you can see in the last few seconds of the video (starting in minute 6:48), that TIME CAN BE REVERSED!!!

how can we make the droplet land on the back side of the wave? I think it’s enough if we delay the droplet for the right amount of time in the air, then it will land on the back side of the wave. Why is that? because normally the droplet moves forward, so it lands on the forward side of the wave. So that means the wave is moving independently below the droplet while the droplet is in the air (otherwise the droplet will not land in a wave at all, it would have just created a center of a new wave). So if we stop the forward movement of the droplet for a precise fraction of time, let’s call this momentary pause “Switch Direction” (like that special card in the Israeli card game “Taki” ha ha).

I guess it’s half of the time it takes from one bounce to the next. then the wave will not know about this, so it will move forward, and the droplet will stay back, and the droplet will land on the back side of the wave and from that moment on, time is going backwards!

The “Switch Direction” pause is the same length for all the drops. because the time that the drops remain in the air is the same for all the drops. you can see that all the droplets are synchronized to the same frequency in the beginning of the video, when Derek Muller makes big droplets which move a little up and down, and small droplets which move a lot up and down.

it’s similar to the fact that the length of the string of the pendulum dictates dictates the frequency and not the size of the weight. a big weight will move a little left and right, and a small weight will move a lot left and right, but a each cycle will take the same amount of time.

OK so how do we make the “Switch Direction” pause all over the area where all the droplets are jumping, and how do we make this pause at exactly the same time?

for example in Veritasium’s example he uses Silicone Oil

https://en.wikipedia.org/wiki/Silicone_oil

Which is an electric insulator and non flammable, so we could ionize the air above the droplets which will cause the top of the droplets to become ionized. the big droplets will accumulate big ionization, and the small drops a little ionization. oil droplets can be ionized see also in this famous experiment

Oil drop experiment of Robert A. Millikan

https://en.wikipedia.org/wiki/Oil_drop_experiment

So like in the experiment we put the whole thing between two electrodes and then we switch on the current for the exact duration that the “Switch Direction” pause should be.

Or another method, just like Veritasium uses a speaker to vibrate the liquid from below, with pressurized air (the sound waves that push from below) so we can use for a very short duration (again the “Switch Direction” pause duration) a speaker from below that will suck the air and make de-pressurization that will pull the droplets a little upwards. The little droplets by a lot and the bigger droplets by a little as it should be.

So our “time machine” is something that protects whomever is inside it from this time-flowing-backwards that happens everywhere else (outside the time machine). like in the example of the petri-dish it would be some roof on some droplets. In reality the time machine needs to protect all the particles that are within its walls.