that race. This week on America Actually, what does being electable actually mean? Let's dig in .So, in our quest to think about American politics beyond the question of Donald Trump, there's no getting around the
Kamala Harris 2028, yay or yikes? That's this week on America Actually. Let's dig in .Now on this show, we like to think about American politics beyond the question of Donald Trump. And yes, that'll be shaped
health of our democratic system. So, who actually has power in our democracy and who has power in name only? Let's dig in .So, here's one thing I never understood about the 2024 election. Why did Democrats spend so much time saying they
I think there has been a reckoning in Hollywood and in publishing that people do want and are thirsty for authentic stories that they can see themselves in .Yeah. No, that's awesome.
But most physics textbooks are wrong. In the 1950s, two physicists came up with a clever experiment.You could have electrons travel through a region with no electric or magnetic fields whatsoever, and yet by flipping a switch, you could change their behavior.
then the solution is easy to find. In fact, the general case was already solved over 300 years ago by Newton himself.- But when Newton added a third body, well, that's when everything fell apart.
- But when Newton added a third body, well, that's when everything fell apart. In the two body case, the forces behaved predictably, always pointing where the system's shared center of mass.But with three bodies, this is no longer the case.
When you try to calculate the forces, they end up being extremely dynamic. In addition to worrying about the magnitude of the forces, you also have to worry about their direction.So you end up with this chaotic mess of vectors.
Well, that's where Joseph-Louis Lagrange comes in . In the 1770s, he was also trying to solve the three-body problem, and he came up with a new approach.It works something like this.
And while they didn't help solve the three-body problem, Lagrange was developing more sophisticated tools. In fact, he developed an entirely new way of doing mechanics.But for that to work, he didn't just need the potential, he needed the potential energy and the kinetic energy too.
So now we have everything we need to try this new method. In fact, we made a whole video on this over a year ago, but for now, all we need to know is thatwe can write down the kinetic minus potential energy to find what's known as the Lagrangian.
- But for all its usefulness, the potential wasn't enough to help Lagrange solve the three-body problem. In 1887, mathematician Heinrich Bruns finally proved that the three-body problem is unsolvable.There are simply too many unknowns and no way to simplify the problem to reduce them.
- If you look at the formula for the electric force, you notice that it's remarkably similar to that for gravity, just with masses and charges swapped. In the 1810s, Simeon Denis Poisson, one of Lagrange's students also noticed the similarity.And he realized that you can define an electric potential phi in a very similar way.
But most physicists might be wrong. - In 1942, 23-year-old David Bohm was hard at work on his thesis in particle physics when one day he received an unexpected visit. - Robert Oppenheimer, who was David Bohm's PhD advisor, wanted to bring him squarely onto the new Manhattan Project efforts.
But fear surrounding his communist sympathies followed him wherever he went. In 1949, he was brought before the House Un-American Activities Committee for questioning.While Bohm was under investigation, Princeton let his professorship lapse.
It's basically just the total energy of the system. In the case where we have both an electric and magnetic potential, the solution to the Schrodinger equation looks something like this.Where this is just a constant.
but there is a potential. In such a setup, if the phase of the particle's wave function started changing slower or faster, that had to be the direct result of the potential itselfbecause there are no fields.
It starts with a beam of electrons, which is split into two. In the middle of these two beams is a tightly coiled wire known as a solenoid.Now, solenoids have an interesting property.
Now take a closer look at the vector potential. In the space the upper beam passes through, the potential points in the opposite direction as the beam.So here the phase changes faster.
- Even Niels Bohr, one of the founding fathers of quantum mechanics, found it impossible to accept that a particle could be influenced by a potential in the absence of any force.But some physicists supported Aharonov and Bohm.
- And that's showing, throwing no shade on their colleague who did these cool experiments. In their case, the magnet is always on, but because of its unique shape, the potential outside the torus is different from the one in the center.
- And that's showing, throwing no shade on their colleague who did these cool experiments. In 2022, researchers at Stanford tested this.
rise of the Normans from Viking raiders to the rulers of kingdoms stretching from England to Sicily. In this conversation, we focus primarily on the Vikings, the seafaring Norse warriors and explorers who, over aperiod of just 300 years, reshaped the medieval world and the trajectory of Western civilization as we know it.
It lasted less than three centuries. So the start is often dated to June 8th, 793. What happened on June 8th, 793? - In June of 793, a group of Vikings, probably originating from Norway, arrived at the Holy Island of Lindisfarne, which was a monastic community, and they essentially slaughtered everyone, burned a couple of buildings and grabbed everything that had any value and left. And that was the first Viking raid that came in force. And I do
Carolingian Renaissance that had done so much to elevate the early medieval world. In fact, the spaces we have, the punctuation we have, spaces between words are likely a result of Alcuin's work. He was an extremely literate man, and you can hear the terrorcreeping into that. Um, and part of that has to do with monastic communities, the Church and the- what they
Do you ever think about trying to put yourself in the mind of those folks and imagining... In that time, you don't have a full map of the world, right? And the oceans are not mapped, and you havea hazy conception of the world. And so out of the darkness from the ocean where you thought nothing can come, comes this terrifying, this brutal force.
- Yeah. Yeah, that... I could not agree more. There are some problems with, ... in history? - I'm a romantic, so I, when I read history, I usually end up rooting for the losers. Um, I want Harold Godwinson to beat No-
- Yeah. Yeah, that... I could not agree more. There are some problems with, in through the Black Sea.
So, this is what it looks like when you use a signal from space to guide human action in real time to changing events.The eye detects change, and the body moves to prevent harm.
Every night before the show starts, I stand backstage getting ready. In my mind, I think about Matilda's life, her love of books, her hatred of bullies, her courage to find her own wayto fight back. I breathe in , I breathe out, and then I step onto the stage.
is included in democracy, who gets to participate, who counts as the people. In the United States, that process has been long.It has taken generations of struggle, abolition, suffrage, civil rights, to
Cuz there is a but. In the US today, your zip code predicts your life expectancy, your race predicts your wealth, and your parents' incomepredicts your future. That ain't democratic.
But that's not the whole story. In fact, that may not even be the story.What I'm going to talk to you today about is some of our work with ketamine, a really remarkable drug that has rapid antidepressant effects.
So things like Prozac, Zoloft, common antidepressants, have been studied for decades, and we've seen ads on TV, in doctor's offices. People openly talk about the idea we're increasing serotonin, we're correcting our chemical imbalance.But here's the thing.
She was an architect of joy, architect of bringing people and things together. In our glass cabinet at home, she would collect objects of memories she treasuredin our show glass.
In our glass cabinet at home, she would collect objects of memories she treasuredin our show glass.My dad worked in retail.
They would simply sit down, say “calculemus” -- “let us calculate,” and get to the bottom of it. In some sense, it was meant to be a universal calculator for truth.Now, Leibniz was a bit of an optimist.
It turns out that AI is the key to making this whole thing work. In the future, AI is not just going to be writing math papers in English for humans to read.They're going to be writing math proofs in Lean for computers to check.
Because when a math AI spits out a proof in Lean of, let's say, the Riemann hypothesis, we're not going to need humans to go through every single line of the proof in painstaking detail, check every single case, and understand the possibly strange and alien logic of the proof just to see if it's correct.Instead, all we're going to do is we're going to take those files, we're going to give them to a Lean compiler, and if it builds,
It turns out that at this year’s International Math Olympiad, automated systems were able to find solutions to five of the six problems in a way that computers could check and require no human review whatsoever.And that’s enough to get a gold-medal-level performance.
And they're pushing back like in Barcelona, with the graffiti asking tourists to go home. In Barcelona, in Italy, in Portugal,residents are pushing back.
you may be wanting to be a part of restoration of an 800-year-old temple like this. In fact, I will seek such an opportunity and bake it in my itinerary because I will love to be part of something like this.The possibilities are infinite.
It's called As the River Flows and it's in support of migrants and refugees and in defiance of racism.And as a river flows, while you and I
irrigation pumps are using 30% less of the fuel than they were 2 years ago. In large part because they've imported millions of cheap Chinese solar panels and gone on YouTube to figure out how toconnect them up. They often lack the money to build the steel scaffolding we're used to seeing
at solar farms. No matter, they just lay them on the ground and point them at the Sun. In a world where many, many big things have taken a very dark turn this decade,this is the one big thing that is going right. We have quite suddenly the
of us don't recognize how huge this moment is. In part, that's because we've spent decades calling this stuff alternative energy and it's blinded us to the factthat it's now the obvious common sense straightforward way to power the future.
out across our hot and tired Earth in the next few years. In advance of your participation in that fight, let me just say thank you.Woo!
in the way that Michelle would have if she had lived or would have told me to do, if she could,
In fact, malnutrition caused by lack of nutrients has all but disappeared in countries where food fortification
In 2009, I was at an event at the University of Southern California, and Mark Hamill was at the adjacent table.