Physics and Jazz
Stephon Alexander is an Associate Professor of Physics at Haverford College, focusing on theoretical cosmology, quantum gravity and particle physics. He is also an Assistant Professor (Adjunct) of Physics at Penn State University. Stephon has studied at Brown University and done postodoctoral research at Imperial College, London and at the Stanford Linear Accelerator Laboratory. He is on the Board of Directors for the Network for the Improvement of World Healthare, an action-driven organization that forges global partnerships to address local health challenges. He also plays jazz saxophone and sees improvisation as an extension of his scholarship.
Stephon Alexander: So, it’s interesting that a lot of modern jazz composers; some names that immediately come to mind; people like John Coltrane, Wayne Shorter; there was always directly; Sun Ra; and a deep appreciation, and even a very deep, intuitive understanding, of modern physics into their music.
And one of the things I like to do for fun is actually look for those connections, like literally- I talk to music composers and it’s like this hobby of mine, where I will take a Coltrane song, or the chord changes, and try to relate it to music theory and physics.
One thing I found interesting is the notion that Coltrane came up with, was something called; it was a sort of a musical illusion device in saxophone playing. See, a saxophone can’t play more than one note at a time. It’s a monophonic instrument. But what Coltrane was able to do was to come up with illusory effects on the saxophone--I call it that--and it was called sheets of sound. Or another thing that he did was figure out ways in which you can go to higher notes that a sax was wasn’t built to make.
And this uses ideas in physics, like non-linearity, for example, that there isn’t always a one-to-one correspondence between a wave and a note, and I mean, one wave- if I add two waves together, I get a third wave. There’s not always a one-to-one correspondence; that’s the difference between linear and non-linear.
And since music is a way a culture is able to figure out techniques to do that, ways in which, you know, you can hear more than one note at a time--and how is that related to physics? Well, quantum mechanics is exactly an example of that. A particle really can be; there’s a probability, in a sense, of a particle being here or here, then in a sense, you can think of it as occupying two places at the same time; until you go and measure it.
And the question is, well, that’s not hard to get your mind around, but in a sense that’s what the sheets of sound Coltrane was doing was like; because you are playing many ways, many different notes, on an instrument that can only play one note at a time. But there’s this overall effect in which all those notes are co-existing.
What the sheets of sound is; I’m going to be switching between different individual notes. So, for example, I’m going to play a “D”.
And I’ll play a “G”- I’m sorry, a “G.”
All right, and that’s a “C”- and if I play them very quickly.
But if Coltrane figured out alternative fingerings while playing those notes in a rapid succession that you get an effect that it sounds like this. So that’s an example of sheets of sound. Altissimo was basically that the sax normally can just go up to, say, this high F sharp. That’s a high F sharp for me.
But then you can go further by using a non-linear effect by, you know, using your diaphragm, down here, by forcing the resonance from down here. So I can go up to my high F sharp.
Stephon Alexander: Actually, I’m working on a little album project--it’s almost done, and the title of the album is called-- and a lot of the songs are inspired by my love for great cool ideas in physics and how it’s connected to jazz music, in particular--but actually it has a lot of. It also explores the idea of diversity and creativity, so it uses modern rhythms, like a Brazilian beat versus a Reggaeton beat versus a hip-hop beat. So it uses modern rhythms with jazz improvisations, combining it with themes and impressions--having to do with cosmology and particle physics and string theory. And the title of the album will be called Mathematics!
Because when I grew up in the Bronx in the Eighties, hip-hop music; there was a part of rap music where guys would battle each other on the streets, and sometimes the battling would go into the subject matter would be talking about science, for example, and they even called it droppin’ science, like Eric B and Rakim.
I used to take the bus home from school and these guys would be on the back of the bus around, rappin’ and battling each other- droppin’ science, so to speak, and one day, you know, I heard someone say, “Yeah, man, ‘cause I got enough mathematics.”
So it also captures a big part of my, you know, what inspired me, was that I was already living in sort of a- this rappin’ and improvisational rappin’- and talking about things around you in the universe, and stars exploding. But I’m like the star exploding. Planet Rock Afrika Bambaataa- one of the first rap songs out there.
So, that title of Mathematics sort of brings it all together.
Recorded June 2, 2008.
Alexander shares the music that most reminds him of physics. He even plays a few notes.
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What is human dignity? Here's a primer, told through 200 years of great essays, lectures, and novels.
- Human dignity means that each of our lives have an unimpeachable value simply because we are human, and therefore we are deserving of a baseline level of respect.
- That baseline requires more than the absence of violence, discrimination, and authoritarianism. It means giving individuals the freedom to pursue their own happiness and purpose.
- We look at incredible writings from the last 200 years that illustrate the push for human dignity in regards to slavery, equality, communism, free speech and education.
The inherent worth of all human beings<p>Human dignity is the inherent worth of each individual human being. Recognizing human dignity means respecting human beings' special value—value that sets us apart from other animals; value that is intrinsic and cannot be lost.</p> <p>Liberalism—the broad political philosophy that organizes society around liberty, justice, and equality—is rooted in the idea of human dignity. Liberalism assumes each of our lives, plans, and preferences have some unimpeachable value, not because of any objective evaluation or contribution to a greater good, but simply because they belong to a human being. We are human, and therefore deserving of a baseline level of respect. </p> <p>Because so many of us take human dignity for granted—just a fact of our humanness—it's usually only when someone's dignity is ignored or violated that we feel compelled to talk about it. </p> <p>But human dignity means more than the absence of violence, discrimination, and authoritarianism. It means giving individuals the freedom to pursue their own happiness and purpose—a freedom that can be hampered by restrictive social institutions or the tyranny of the majority. The liberal ideal of the good society is not just peaceful but also pluralistic: It is a society in which we respect others' right to think and live differently than we do.</p>
From the 19th century to today<p>With <a href="https://books.google.com/ngrams/graph?year_start=1800&year_end=2019&content=human+dignity&corpus=26&smoothing=3&direct_url=t1%3B%2Chuman%20dignity%3B%2Cc0" target="_blank" rel="noopener noreferrer">Google Books Ngram Viewer</a>, we can chart mentions of human dignity from 1800-2019.</p><img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDg0ODU0My9vcmlnaW4ucG5nIiwiZXhwaXJlc19hdCI6MTY1MTUwMzE4MX0.bu0D_0uQuyNLyJjfRESNhu7twkJ5nxu8pQtfa1w3hZs/img.png?width=980" id="7ef38" class="rm-shortcode" data-rm-shortcode-id="9974c7bef3812fcb36858f325889e3c6" data-rm-shortcode-name="rebelmouse-image" />
American novelist, writer, playwright, poet, essayist and civil rights activist James Baldwin at his home in Saint-Paul-de-Vence, southern France, on November 6, 1979.
Credit: Ralph Gatti/AFP via Getty Images
The future of dignity<p>Around the world, people are still working toward the full and equal recognition of human dignity. Every year, new speeches and writings help us understand what dignity is—not only what it looks like when dignity is violated but also what it looks like when dignity is honored. In his posthumous essay, Congressman Lewis wrote, "When historians pick up their pens to write the story of the 21st century, let them say that it was your generation who laid down the heavy burdens of hate at last and that peace finally triumphed over violence, aggression and war."</p> <p>The more we talk about human dignity, the better we understand it. And the sooner we can make progress toward a shared vision of peace, freedom, and mutual respect for all. </p>
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With just a few strategical tweaks, the Nazis could have won one of World War II's most decisive battles.
- The Battle of Britain is widely recognized as one of the most significant battles that occurred during World War II. It marked the first major victory of the Allied forces and shifted the tide of the war.
- Historians, however, have long debated the deciding factor in the British victory and German defeat.
- A new mathematical model took into account numerous alternative tactics that the German's could have made and found that just two tweaks stood between them and victory over Britain.
Two strategic blunders<p>Now, historians and mathematicians from York St. John University have collaborated to produce <a href="http://www-users.york.ac.uk/~nm15/bootstrapBoB%20AAMS.docx" target="_blank">a statistical model (docx download)</a> capable of calculating what the likely outcomes of the Battle of Britain would have been had the circumstances been different. </p><p>Would the German war effort have fared better had they not bombed Britain at all? What if Hitler had begun his bombing campaign earlier, even by just a few weeks? What if they had focused their targets on RAF airfields for the entire course of the battle? Using a statistical technique called weighted bootstrapping, the researchers studied these and other alternatives.</p><p>"The weighted bootstrap technique allowed us to model alternative campaigns in which the Luftwaffe prolongs or contracts the different phases of the battle and varies its targets," said co-author Dr. Jaime Wood in a <a href="https://www.york.ac.uk/news-and-events/news/2020/research/mathematicians-battle-britain-what-if-scenarios/" target="_blank">statement</a>. Based on the different strategic decisions that the German forces could have made, the researchers' model enabled them to predict the likelihood that the events of a given day of fighting would or would not occur.</p><p>"The Luftwaffe would only have been able to make the necessary bases in France available to launch an air attack on Britain in June at the earliest, so our alternative campaign brings forward the air campaign by three weeks," continued Wood. "We tested the impact of this and the other counterfactuals by varying the probabilities with which we choose individual days."</p><p>Ultimately, two strategic tweaks shifted the odds significantly towards the Germans' favor. Had the German forces started their campaign earlier in the year and had they consistently targeted RAF airfields, an Allied victory would have been extremely unlikely.</p><p>Say the odds of a British victory in the real-world Battle of Britain stood at 50-50 (there's no real way of knowing what the actual odds are, so we'll just have to select an arbitrary figure). If this were the case, changing the start date of the campaign and focusing only on airfields would have reduced British chances at victory to just 10 percent. Even if a British victory stood at 98 percent, these changes would have cut them down to just 34 percent.</p>
A tool for understanding history<p>This technique, said co-author Niall Mackay, "demonstrates just how finely-balanced the outcomes of some of the biggest moments of history were. Even when we use the actual days' events of the battle, make a small change of timing or emphasis to the arrangement of those days and things might have turned out very differently."</p><p>The researchers also claimed that their technique could be applied to other uncertain historical events. "Weighted bootstrapping can provide a natural and intuitive tool for historians to investigate unrealized possibilities, informing historical controversies and debates," said Mackay.</p><p>Using this technique, researchers can evaluate other what-ifs and gain insight into how differently influential events could have turned out if only the slightest things had changed. For now, at least, we can all be thankful that Hitler underestimated Britain's grit.</p>
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