Episode list

Things can get a bit weird when dealing with infinity even in mathematics. In this case Herny does some simple arithmetic with the infinite sequence of powers of two to demonstrate that they don't add up to infinity but rather; negative one. Of course the astute observer will note that with Henry's method the sequence, or any other infinite sequence, could add up to any number you choose. Henry suggests he'll provide some clarity at a later date.

Henry demonstrates that not all infinities are the same, or rather the same size. In this case he demonstrates that there are more real numbers between zero and one than there are whole numbers. He does this by relating all whole numbers to real numbers. But there are still real numbers left over - lots of them.

It seems no one can resist messing with Einstein. So it's nice to see Hery backing him up. Here Herny looks at Einstein's famous equation; Energy equals mass times the speed of light squared. Or rather he looks at the full equation that includes momentum and shows why light has momentum and you can't travel faster than the speed of light.

Today Henry challenges one of the most cherished traditions in mathematics; PEMDAS. He's disturbed that it still leave a lot of room for ambiguity unless you're obsessive about parentheses. But his concern really seems to stem from his belief that humans are a higher form of life than computers.

Henry proposes a game of probability rather than physics. It seems impossible to win but maybe there is a strategy that will at least boost your odds of winning. And since you and 100 friends only risk a dollar to win one hundred dollars, isn't it worth a little thought.

Henry provides the solution to his 100 boxes challenge. And yes, there is strategy that improves you and your friends odds of winning from the barest smidgen above zero to about 37%. Henry explains if you manage to understand it. Or, just give it a try.

Since light sensors and people see brightness differently (linearly versus logarithmically) software programmers took a short cut when storing color brightness to compensate. The method works pretty well. But it makes the mathematics of blending colors a bit more complicated and most programs just do it the easy way which, as Henry points out, is wrong.

The problem with the piano is it has too many strings. You can perfectly tune a few strings like neighboring strings or strings separated by octaves. But that creates a problem for all the other strings. Henry explains the physics. Yes, its all about physics. The usual work around is to use a technique called equal tempered tuning that leaves all the strings just slightly and equally out of tune with all the others. You'll get used to it.

Big airline jet engines move lots of air but not very fast. That's OK since airliners don't need to go all that fast like a fighter jet. So they save lots of energy by not generating hypersonic exhaust. Energy means fuel. And fuel savings is good for the environment and for the airlines' bottom line.

Time travel always seems to become confusing and loaded with paradoxes. Herny decides to tackle on of them and his solution is a concept called superposition as in Schrodinger" have dead half alive cat. Except now you and your grandfather are half alive and half dead. At least it works on paper. Henry even draws it for you.

Max Tegmark joins Henry who wants too know when AI will become so intelligent that it becomes dangerous. Max suggests the question isn't about malevolence. We just need to ensure that human and AI goals are mutually aligned, But that raises the question; exactly what are humankind's collective goals.

A quick look at how to get along with artificial intelligence.

Got some polarized sun glasses? Let's play with quantum mechanics. Follow Henry's instructions to align the lenses in a Venn diagram. Then rotate one 22.5 degrees and another 45 degrees. Voila, you will a see a result that makes absolutely no sense but that quantum theory say is absolutely correct. Henry recruited Grant Sanderson to explain this one.

Tiem travel is featured in some of the world's most popular movies and video games. Henry tries to make sense of them all by diagramming the time travel sequences. He finds there are a variety of different types of time travel with their own set of rules.

Relativity is about the perception of motion by different observers who are themselves in motion. There are various ways to change the perspective of motion between observers using transformations that let speeds change to maintain consistency. But light is special because it is always observed to travel at the same speed. The Lorentz transformation is a special transformation for special relativity that keeps the speed of light unchanged. Henry introduces his space time globe to visually explain motion at near light speeds.

Europe has many, many cracks on it's icy surface that resemble a dent in a ball or the ring of fire on earth. Geometrically the cracks look like cycloids. But rather than resulting from dents or plate tectonics the arcs seem to be caused by tides due the elliptical orbit of Europa around Jupiter. But not tides like on Earth. Henry Explains.

If you think nuclear fusion only occurs in extreme conditions such as hydrogen bombs or the cores of stars let Henry set you straight. As long ago as 1956 scientists performed nuclear fusion at room temperature using muons to bring atomic nuclei closer together so they fuse naturally. Unfortunatly, with current technology it takes more energy to create a muon than is generated in the fusion processes it catalyzes. So muon nuclear reactors are still a distant dream.

Every day particle detectors at the surface of the Earth detect muons created by cosmic rays hitting Earth's upper atmosphere. But muons have very short life spans and should have decayed before reaching the detectors. They are only detected due to time dilation as described by Einstein's theory of special relativity. Elegantly, the muons themselves experience the other feature of special relativity; length contract. So the muons live longer and travel father because they are going really, really fast.

If the famous double slit experiment left you confused, Henry want to double your confusion with help from a scientist name Lucien Hardy. If you add an extra slit to make it a triple slit experiment but control the particles so they can only go through two of the slits then you have a double double slit experiment. And sometimes particles show up where they aren't supposed to. Except quantum mechanics says that's all as it should be.

If you don't know what muons are and what they're good for you're in luck because Henry will explain. Then you will know what to do with them if you want to follow Henry's instructions to make some. Spoiler: you'll need to build, borrow or steal a particle accelerator because I doubt you can afford to buy one.

Here is an introduction to Zermelo-Fraenkel Set Theory which has nine axioms that provide the foundation for mathematics. As will become apparent, ISP marketers are unfamiliar with this theory and so are inclined to violate the axioms in the interest of profit.

This is one of those cases where a concept may be presented in a minute but can't be understood in a minute. You probably don't have a quantum computer either but that's OK because Henry is going to explain the whole process of factoring a large number with Shor's Algorithm on a white board. Oddly enough, to factor a large number it helps to make a much, much, much larger number first following a few 'simple' rules..

The problem with gravity is it's hard to measure. It works well if you wont to track planets and other astronomical objects until you get close to a black hole and the it doesn't work so well. But for everyday objects and distances, or even worse, inside atoms, it's far two weak to measure. Not that scientists don't keep trying. And so far Newton is still good.

Today Henry turns a video game "Portal" into a lesson on frames of reference. Since there's no right answer you get to choose the one you like. But there's a quiz at the end so you better be sure you understand your choice. It's all about a simple question; when an object enters through one portal what happens to it speed when it exists another portal if that portal is moving.

Eistein's biggest blunder wasn't what he thought it was. Rather what he thought was a blunder was correct and his real mistake was thinking he was wrong in the first place. That means Henry is going to explain the cosmological constant Einstein added to his General Theory of Relativity.

How long is a day? Do you mean a calendar day, stellar day or solar day. What the heck is a calendar day, stellar day or solar day anyway. Aren't they just 24 hours. Alas, axial tilts, elliptical orbits and such kinda mess things up. That's why Henry is here to explain.

In a previous video Henry talked about protecting privacy and considered that a good thing. But survey summaries can inadvertently reveal personal information about a person even if she didn't participate in the survey. Example: Hockey players are more likely to have January birthdays. Henry feels this is OK and see it has a good standard for whether a survey is violating individual privacy.

Photons are indifferent to one another. They don't interact or collide so they can't shadow one another. But Henry's a creative guy who comes up with three ways they might. He particularly likes his third prospect where a an extremely high energy photon spontaneously turns into a particle-antiparticle pair of particles which collide with another photon before annihilating to become a high energy photon again.

Redesigning the periodic table of elements is nothing new. All sorts of people have come up with all sorts of different designs. But Henry couldn't resist sharing his spin. After some cutting and taping he winds up at a design called Mendeleev's Flower which he concedes is a little awkward to carry around or even to see very well.

Apparently it's hard for aliens to tell left from right. So in case an alien wants to visit you watch Henry's video so you can give them proper directions. They alien will need to understand the weak nuclear force because it's the only force that knows the difference between right and left. The aliens will also need access to a particle accelerator to make kaons (in case they're made of antimatter). But since they have a space ship that can cross many light years of space that is probably not a problem.

If you feel like the news media reports of CoVid 19 cases isn't really telling you if things are getting better or worse, you're right. Henry has a better way. He demonstrates it in a simple data plot and tells you how to create your own. Now all you need to do is figure out how to get the right data.

It's not the nerdy looking design of N95 masks that make them so effective. It's the fibers and they aren't even woven that close together. But there are many layers of fibers that are very sticky to small particles. They are even permanently electrically charged to capture the more challenging particles you may encounter.

For those of us that don't understand Einstein's theory of Gerenal Relativity Henry takes a novel approach to explaining it. Although he never gets into the math he explains the theory in more and more technical terms. So you can bail out whenever it gets too deep.

Henry doesn't like ANY of the visual depictions of atoms that have been published so far. So he did his own thing, or rather a Shroedinger, De Broglie, Bohm thing to create beautiful, meaningful computer animated images of atomic orbitals. Then he created simplified versions that you can draw by hand that still convey all the relevant information in case you don't have a computer with fancy 3-D graphics software handy.

Bell's spaceship paradox is a special relativity thought experiment that posits two rockets attached by a string that suddenly accelerate simultaneously at the same rate. The question is will the string break due to the length contraction effect of special relativity?

The phase diagram of water ice(s).