A PROFESSOR WHOSE STUDENTS CALL HIM THE MOST ENGAGING TEACHER THEY HAVE EVER HAD WALKED INTO A LECTURE HALL AND SHOWED WHY A CALCULATOR CAN DRAW ANY CURVE - BUT CANNOT TELL YOU WHY THE CURVE IS SHAPED THE WAY IT IS
He opens with one claim - a calculator will give you the picture, but it will never give you the understanding. To know why a curve rises here and falls there you need the first derivative test. That is what this lecture is about.
He starts with the setup. The first derivative tells you the slope. Positive slope means the function is increasing. Negative slope means it is decreasing. Zero slope means a horizontal tangent - and that is where something interesting might happen. Those are the only three cases. Everything else follows from them.
Then the first derivative test. Take the derivative. Set it equal to zero and solve for the critical numbers. Draw a number line, mark those critical numbers on it, and pick one test point in each interval between them. Plug each test point into the derivative - not the original function, the derivative. You do not care what number comes out. You only care whether it is positive or negative.
Then what the signs tell you. Positive on the left of a critical number, negative on the right - the function was climbing and then fell. That is a relative maximum. Negative on the left, positive on the right - the function fell and then climbed. That is a relative minimum. If the sign does not change, neither maximum nor minimum exists at that point.
Then the case with a denominator. When the derivative is a fraction, set the numerator equal to zero for critical numbers. But also set the denominator equal to zero - because the function can switch from increasing to decreasing at a point where the slope is undefined, not just where it is zero. Miss those points and the table is wrong.
Watch the moment he plugs test values into a derivative with a cube root in the denominator and shows that even though the slope does not exist at zero, the function still has a relative maximum there. Undefined slope does not mean nothing happens. It means you have to check.
A first year engineering student I know rewatched this lecture before a midterm on curve sketching. Said it was the first time the connection between the derivative sign chart and the actual shape of the graph felt obvious rather than memorized.
Free on YouTube.
bookmark this and watch later - after this lecture every curve you draw will feel like a story the first derivative is already telling you
@ArmstrongEcon Sir, now that the boom is lowered, how long ago did Socrates pick up the move? Did any other reason other than ‘Japan decided to defend the yen’ pop up?
A Fields medalist tried to prove a technique was too good to be true. He failed, and the math he uncovered now runs inside MRI machines.
The medalist is Terence Tao. About twenty years ago, engineers kept stumbling onto the same trick: rebuild a sharp, full image from far less data than should be possible.
It kept turning up by accident. In seismology. In astronomy. It worked beautifully, and no one could say why. So each field kept it as a private trick, and it never spread.
Someone brought it to Tao as a pure math problem about random matrices. His first instinct was that they had made a mistake. You cannot get output that clean from input that thin.
So he set out to prove it was impossible. Instead he found the exact conditions where it works, and those were the conditions they had.
He and two colleagues wrote the proof. The moment it had a guarantee, dozens of fields picked it up. Today it is called compressed sensing.
He tried to prove it wrong. The proof he found instead is now inside your MRI.
back in the 70s, game theory was hyped the exact same way AI is today. every genius was obsessed with one thing: how to win.
then one guy watched his kids play with legos and realized everybody was completely missing the point.
in short: if you're constantly trying to "beat the competition," you're playing the wrong game entirely.
hands down one of the clearest explanations of strategic game theory applied to real life by @simonsinek
I mapped out the key rules and action points below.
In 1977, this man told a room of French physicists that reality had been secretly rewritten,
And that he could remember the version before the edit.
The lecture was called "If You Find This World Bad, You Should See Some of the Others."
The man in question?
Philip K Dick.
He delivered it at the Metz science fiction festival in front of an audience that included physicists, philosophers, and journalists who had come expecting a novelist to talk about craft. Instead, the man who wrote *Blade Runner* stood at the podium and calmly explained that the universe is a computed simulation, that the entity running it occasionally rolls back the timeline to try alternate variables, and that most people never notice because their memories get patched to match the new version. Sometimes the patch fails. When it fails, you are left holding a memory of a world that no longer exists.
Half the room thought he was having a breakdown. A quieter half sat forward.
What he was describing, without the vocabulary we have now, was the Mandela Effect twenty years before anyone had a name for it.
He was describing save states and branching timelines before video games gave us the metaphor. He was describing simulation theory a full quarter century before Nick Bostrom made it academically respectable in 2003, when Bostrom argued that any civilization capable of running ancestor simulations would eventually run so many of them that the odds of *you* being the original biological version approach zero.
Dick claimed he had personally experienced the failed patch.
In February 1974, a pharmacy delivery girl arrived at his California apartment wearing a small golden fish pendant called the ichthys, the symbol early Christians used to identify each other under Roman persecution. Sunlight caught the metal.
Dick said something in his mind cracked open. He described a pink beam of information flooding his consciousness, carrying with it medical diagnoses for his infant son that no doctor had made yet. The hospital confirmed those diagnoses days later. He began speaking fragments of Koine Greek, a language he had never studied. He became convinced he was simultaneously living as a persecuted Christian named Thomas in first-century Rome — the same consciousness threaded through two separate slices of time.
He spent the final eight years of his life writing an 8,000-page private journal called the *Exegesis*, trying to reverse-engineer what had happened to him.
Most of it has never been decoded by anyone but him.
What makes the Metz lecture impossible to write off is what physics did afterward.
Everett’s 1957 many-worlds theory suggested each quantum event branches reality. Wheeler’s “it from bit” argued the universe arises from information. More recently, Melvin Vopson claims information has mass and that the cosmos acts like it’s compressing data to save resources. His “second law of infodynamics” says information entropy in closed systems decreases over time (the opposite of matter) and what you’d expect from a simulation optimizing itself.
Experiments probing the discreteness of spacetime at the Planck scale keep producing results that look less like a smooth continuum and more like pixels.
None of this proves Dick was right.
Insrtead, it proves the frame he was speaking from stopped being fringe.
After the lecture, physicists came up to him not for a book signing, but to share their excitement and ask how a novelist without formal training in quantum theory had arrived at ideas they were still exploring at the edges of their own field. He welcomed the question, even if he couldn’t offer a tidy explanation. He told them he had been shown. He said the insight seemed to arrive from beyond the system, from something he sometimes called VALIS ( a Vast Active Living Intelligence System) and other times simply the programmer.
Dick died in 1982 believing he had glimpsed something the rest of us are structurally prevented from seeing.
He invited no worship and sought no followers. He simply left a record for those who came next, ready to notice the same seams in the fabric of the world.
The uncomfortable question isn't whether he was insane.
It's why so many of the things a "madman" said in 1977 keep quietly showing up in peer-reviewed papers forty years later.
A NASA fellow claims 5 equations explain 99 percent of the physics that actually runs your world. Understand them deeply and you are set for life. His words.
And the way he does it is what makes the video worth it.
He does not teach the five as a list. He tells them as one story, where each equation is born from the one before it. F equals ma leads into gravity. Gravity rhymes with the law of electric charge, the exact same shape. That connects to magnetism. Magnetism folds into the wave. And the wave quietly opens the door to relativity and quantum physics.
By the end, all of physics feels like a single sentence written by one hand, not a pile of formulas you were forced to memorize.
The move that stays with you comes first. He says F equals ma is written the wrong way around, and rewrites it. One tiny flip, and the most famous equation on Earth suddenly means something school never told you.
His point for why this matters now: in the age of AI, the people who understand reality itself stay in demand. Everyone else is just memorizing.
Five equations. One thread. It is in the video.
🔥🚨LATEDT: This man uploaded this video appearing to be stunned and amazed when he met a homeless man at a gas station who claims face morphed into Jesus right in front of him.
This man claims the homeless man randomly said “hey boss 13.50” when he arrived at the gas station which he claims ended up being the exact amount of change he has left.
The man claims he gave the homeless man the change of $13.50 and that’s when he morphed into Jesus and told him things so profound that he couldn’t put in ignorant words.
The NSA kept 1 lecture in a vault for 40 years. In 2024 they released it. It's Grace Hopper explaining the future of computing in 1982.
The channel that posted it: the National Security Agency's own YouTube.
Hopper stands at a podium in Navy uniform, a captain, and talks to a room of NSA staff for 90 minutes across 2 reels.
The title: "Future Possibilities: Data, Hardware, Software, and People."
She compares the computer industry to the early automotive one, all custom parts and no standards, and argues software will become the hard problem, not hardware. She was right by decades.
She invented the first compiler and gave COBOL its shape. She kept a clock that ran backwards on her wall to prove rules can be questioned.
The tapes were too degraded for normal release, so the agency restored them before posting.
40 years in an NSA archive. 90 minutes. Now free.
@SusieM414141@RealLAnative Typically, additives are done at the fuel terminal as they are put in the tanker truck; this ensures consistency and proper mixing. Highly unlikely to be the additive that each brand formulates for their stations.
A woman who spent nine years gluing paper models in a print shop just told a room of physicists their whole field stands on a mistake, one line, no hedging:
"Every theory we have takes space and time for granted, like a bagel that forgot it was once a flat sheet of paper."
That's Bianca Dittrich. She has a free lecture course that asks one question: what is left of geometry once you quantize it? The answer is: far less than you can picture.
Quantum gravity looks like one more field theory. Buried inside is something stranger. Every quantum theory we have puts fields on a fixed stage, flat or curved, and does the physics on top of it. Here the stage itself is the thing being quantized.
Your gut reads an atom of spacetime as a tiny grain sitting somewhere. Wrong. It cannot sit anywhere, because it is the somewhere. The move is invisible to human intuition, which is exactly why the people who get anywhere stop asking where the pieces are and start asking what a measurement even means.
In 3D the whole thing collapses in a way that should scare you. No matter, no cosmological constant, and gravity is locally flat everywhere. Six degrees of freedom per point, all of them eaten by diffeomorphism symmetry. A field theory that ends up with finitely many real degrees of freedom, sometimes zero.
None of it is hidden. Cut a parallelogram out of paper, glue the edges, and you have a torus. Flat everywhere, and yet two numbers survive that no local measurement can see. The lecture is free.
Here is the trap: you feel every equation you can solve, every geometry you can draw, as progress. What you cannot feel is the gap you have to cross. Ten to the forty-one, from the Planck scale back up to the world you live in. And crossing it is the only thing that pays.
Almost every approach still cannot show it recovers ordinary physics at the far end, and almost everyone quits long before then.
The math is free to learn. The nerve to stop trusting your picture of space, that part you still have to bring yourself.
"...a small group of scientists here has been investigating a strange new space-age metal, a nickel titanium alloy called Nitinol..."
"...the Department of Energy invited the people of McDonnell-Douglas to investigate the potential for Nitinol heat engines & Nitinol power plants."
Fascinating stuff.
"...no one knows exactly why this machine is working because no one knows exactly why Nitinol behaves the way it does."
Originally produced & aired by CNN in the 70s.
Posted by Kevin Sanders on yt.
In the state of Wyoming, USA, lies a real hydrological oddity. It's a small stream (creek) that is thought to be one of a just a few examples in the world. It is placed so precariously and perfectly that it's hard to believe it is able to exist.
1/n
Globus - The Soviet Mechanical "Space GPS"
Before digital computers took over, Soviet spacecraft used something extraordinary: a fully mechanical navigation computer called Globus.
Installed in missions like Vostok and Soyuz, this device used a system of gears, cams, and rotating mechanisms to calculate the spacecraft's position in real time. As the capsule orbited Earth, Globus would continuously update-showing where the crew was above the planet.
No screens. No software.
Just pure engineering.
By factoring in orbital motion, Earth's rotation, and time, the system could accurately track ground position and even help determine reentry timing and landing zones.
It was reliable, self-contained, and didn't depend on external signals-making it perfect for the early space age.
A reminder that long before digital navigation... spaceflight was powered by clockwork precision.