physics vs mathematics

Polylog explains how algorithms can be turned into circuits and encoded as satisfiability problems, which lets you effectively run them backwards. It uses this to motivate breaking RSA, general reductions to SAT, and what P vs NP is really asking.

An animated 11-minute tour of the whole field of mathematics as a single map, showing how pure and applied math and their sub-fields relate to each other.

A Vsauce video exploring whether chairs exist, through metaphysics, mereology and the philosophy of categorizing objects. It runs about 38 minutes and cites academic work on ontology.

Physics Girl compares hydrogen fuel cell cars and battery electric cars after driving 1800 miles in a Toyota Mirai. The video was part of a series sponsored by Toyota.

A two-minute minutephysics video explaining why turning a bicycle requires first steering briefly the other way. It covers counter-steering and balance with slow-motion footage and 3D animation.

An 11-minute animated introduction to P vs. NP and the wider landscape of complexity classes, inspired by the Complexity Zoo wiki. It assumes no background in computer science.

Veritasium explains how trees lift water from roots to the top of tall trunks, using transpiration pull and the negative pressure that liquid water can sustain. It explains why trees do not need pumps or valves.

PBS Space Time, together with It's Okay to be Smart and PBS Eons, asks how a universe drifting toward disorder produced something as complex as life. It presents the idea that the laws of physics, through thermodynamics, may actually favor the emergence of life.

Ben Felix explains how to decide between renting and buying a home, weighing financial and non-financial factors. He argues that renting is often as good or better than owning, both financially and for well-being.

A minutephysics video explaining why a piano cannot be perfectly tuned, comparing equal temperament with just intonation and the math of harmonics.

Veritasium's explainer on entropy, presented as one of physics' most important and least understood concepts. It uses examples such as heat engines and the sun's energy flowing through the Earth.

Technology Connections explains that the so-called EV charger in an electric car's charging cable or wall unit is really an EVSE, a smart switch that safely delivers AC power. The actual charger is inside the car. The video covers the safety signaling and mechanisms involved.

Destin of Smarter Every Day films a cat falling in high-speed slow motion to show how cats right themselves in midair, and introduces the physics behind it.

Veritasium investigates whether a wind-powered vehicle can travel directly downwind faster than the wind, driving the Blackbird craft himself. The video explains the physics behind a claim some physics professors dispute.

Veritasium recounts a $10,000 bet with a UCLA physics professor over whether a vehicle can travel downwind faster than the wind. He presents the professor's reasoning and demonstrations, including one without aerodynamics.

Two Minute Papers covers a paper on speeding up fluid and smoke simulation with convolutional networks. It contrasts the approach with earlier regression forest methods.

A short minutephysics video explaining why bicycles stay upright. It looks at gyroscopic precession, head angle and centre of mass, and shows that bikes self-steer toward the direction they lean.

Not Just Bikes explains how SUVs and light trucks have grown in size and share of US sales, and why that is dangerous for pedestrians, cyclists and city life. He covers the regulatory loopholes, such as fuel economy rules and the chicken tax, that favored them.

An animated visualization of basic quantum mechanics using a free particle, with simulations based on the actual equations. It covers waves, particles, and how measurement collapses the wavefunction.

Ben Felix explains how to compare renting and buying a home by looking at unrecoverable costs, and distills it into the 5% rule of thumb. It is framed for a Canadian audience but broadly applicable.

Tom Scott makes the difference between a million and a billion dollars tangible by using distance on a road trip instead of volume. The drive makes the scale of a billion intuitively felt.

Destin Sandlin of Smarter Every Day explores molten glass and Prince Rupert's drops with a glass artist, including a process that freezes the moment glass shatters and an artisan who makes the drops.

PBS Space Time explains the Standard Model Lagrangian, the single equation encapsulating the particle physics theory, and visualizes what its terms mean.

Engineering Explained follows up on Tesla's claim that a Cybertruck towing a Porsche 911 could beat the 911 alone over a quarter mile. He walks through the MotorTrend drag race and explains why the claim did not hold up.

Vsauce's roughly 24 minute explainer on the Banach-Tarski paradox, building from infinity and set theory to the decomposition of a sphere into pieces that form two spheres.

Vsauce's Michael Stevens takes viewers past infinity using transfinite numbers, ordinals and cardinals, with input from mathematician Hugh Woodin. It is a fast-paced, mind-bending tour of different sizes of infinity.

Vsauce's explainer on Zipf's law, the pattern in which the frequency of a word is inversely related to its rank. It shows the pattern across many domains and discusses why it remains unexplained.

A minutephysics explainer on why the planets orbit in a flat plane. It shows how conserved angular momentum flattens a collapsing cloud of matter into a disk.

Vsauce asks how many holes a human has and uses topology to show the answer depends on what counts as a hole, with animations and expert input.

A minutephysics explainer on the twins paradox in special relativity. It shows why the traveling twin ends up younger and how acceleration resolves the paradox.

Vsauce explores math through card tricks and big numbers, including an animation of how enormous 52 factorial, the number of deck orderings, really is.

Vsauce explores how human reasoning works, drawing on the social theory of reason and the extended mind thesis, made in partnership with Bill Gates around climate change.

minutephysics, in collaboration with the US Census Bureau, explains differential privacy and why the 2020 census adds noise to protect individuals' data. It walks through how statistics can leak private information.

Minutephysics compares how efficiently different processes convert mass to energy per E=mc^2, from fire and fission to fusion, antimatter and black holes, which can convert a large fraction of mass to energy.

A four-minute minutephysics video arguing that causal models and causal networks let statistics infer causation from correlation. It touches on Reichenbach's principle, common causes, feedback and quantum causal discovery.

A three-minute minutephysics video on the orbital mechanics of why crashing into the Sun takes far more energy than leaving the solar system.

Vsauce asks whether music will ever run out of new melodies. It counts the possible note combinations and discusses how common chord progressions and remixing affect originality.

Vsauce looks at 'juvenoia', the exaggerated fear that new media and youth culture are corrupting the young. It gives historical examples of older generations complaining about the next one.

Vsauce explores whether people in past decades really looked older than people of the same age today, or whether photographic and cultural factors make them seem so. It draws on old photos, yearbooks and perception research.

Bill Hammack of engineerguy explains how medieval engineers designed stone cathedrals using rules of thumb, with no science, mathematics or literacy. He uses it to define the engineering method.