adeledeweylopez

That's probably because they are 3D printed prototypes. He says in the link that they're working on creating the molds for injection molding.

Sure, but when urgency suddenly became necessary, mRNA technology was pursued quickly, which indicates that we already knew it was promising.

Hitler was not good, much less great, for technology. Germany was the scientific center of the world before the Nazis took power, so their successes are mostly attributable to inertia. The Nazis destroyed this on their own with the 1933 Nuremberg laws.

https://physicstoday.scitation.org/do/10.1063/PT.6.4.2018092...

Everything on that website is good like that, but unfortunately I wish I had more like it to recommend.

Yeah, it is different, but once you know what you're after you can measure. It's a "type error" to ask for the number of bits of entropy in a baseball, but if you ask for the bits of entropy of a baseball given everything you know about the baseball (i.e. mass, composition, temperature), then you can measure it. You could even design a special instrument which makes relevant measurements of observable quantities and then calculates the entropy of a given object from those.

Temperature is actually defined from entropy, it's the change in energy per change in entropy. So it too is inherently subjective. One way to think about this is that to a simulator or god outside of our universe, who can precisely see everything happening in the universe, the temperature and entropy of everything is exactly zero (of course, they would be able to predict what we would measure it as). To them, they would see the level of a thermometer as simply a mechanical consequence of all the particles nudging it to that exact place (like you would if you saw someone pump the mercury up the tube -- you wouldn't conclude it must have gotten much hotter suddenly).

Yeah! You can derive the second law from "conservation of information".

This is a great resource about thermodynamics which goes into some of these ideas: http://www.av8n.com/physics/thermo

Entropy is a measure of the uncertainty that an observer has over the microstates (i.e. the exact state of every atom) given their knowledge of the macrostate (i.e. what they are capable of describing: like "the water is just above freezing"). So it's inherently a subjective concept. The most common unit for entropy is the bit, same unit as information.

Anyway, entropy is measurable just like any other physical quantity. You need to determine what your model of the microstates is (often an "ideal gas", with independent molecular point particles with their own positions and velocities, and all interactions are perfectly elastic collisions), what you currently know (stuff like type of gas, pressure/volume/temperature), and then there is a clear answer to what the entropy is.

The true law underlying the second law of thermodynamics is conservation of information. In (classical) physics, this is typically cast as Liouville's theorem, which shows that the area of the phase space of a system must remain constant. (In quantum, it's only true for unitary transformations, which may or may not be everything depending on your interpretation of QM).

Anyway, if you're curious about learning more, I highly recommend http://www.av8n.com/physics/thermo which is an amazing online (and free) book that clarifies the concepts of thermodynamics brilliantly.

And they're getting bought by Intuit (TurboTax)...

One of the major aims of physics is to try to describe reality with mathematical constructs.

If you start with what can be directly observed or experienced, then that's phenomenology.

Those are both valid and interesting ways of trying to understand reality, and I believe they are ultimately fully compatible with each other. But I think you are trying to hold physics to phenomenology standards in a way that doesn't make sense. No one thinks that Newton's theory of gravity "lost contact with empirical reality" because it doesn't have measurements or people as ontological components.

Anyway, that's all beside the point I was trying to make, which was just that the description of the MWI in the article was plain wrong.

"The Many-Worlds Interpretation has it that each time we make a measurement, reality splits into several alternative versions, identical except for the measurement outcome."

That's not right, the Many-Worlds Interpretation is just that the wavefunction in the Schrödinger equation (or its generalizations) is real, and it rejects that there's a separate process that somehow collapses the wavefunction to the single "branch" we perceive ourselves to be in. At the metaphysical level, there's no splitting involved, and no ontological measurements either (much less a "we" to do the measuring).

Memory engrams are thought to be DNA methylation patterns in a neuron's DNA.

http://learnmem.cshlp.org/content/23/10/587.full

https://www.nature.com/articles/s41467-020-14498-4

Nope, black holes have entropy proportional to the surface area of their event horizon. So the more stuff they engulf, the more their entropy increases, and thus they satisfy the 2nd law of thermodynamics just like everything else.

It's a very interesting and active area of physics actually: https://en.wikipedia.org/wiki/Black_hole_thermodynamics

The Bullet Cluster (https://en.wikipedia.org/wiki/Bullet_Cluster) is a big reason why: it's a collision of two clusters of galaxies. We can see where the gas and stars are, but gravitational lensing indicates the bulk of the mass is elsewhere.

But we know that is very possible to do already, via relativistic effects.

I think it's just because hispanic people are poorer and thus more likely to be essential workers.

Honestly I think that will be harder for this kind of system than writing this sort of code. It takes a certain kind of creativity to think of ways that code could potentially fail, and it also requires fairly deep understanding of the intent behind a feature.

As a teen, I was obsessed with knot theory, and Conway's knot notation always felt like magic to me.

The notation works by counting the number of twists in a segment, and then looking for another twist directly connected to the previous twist, and so on.

This gives you a sequence of integers, one counting the number (and direction) of twists.

If the entire knot is made of twists connected this way, then the continued fraction you get from the sequence of numbers is a knot invariant!

https://www.maths.ed.ac.uk/~v1ranick/papers/conway.pdf

For women considering Modafinil, note that it interferes with hormonal birth control.

Terry Tao has a really great post where he depicts group actions (every Rubik's cube move sequence is a group action) as arrows in a graph, and with this picture, commutators can be seen as arrows that make a relatively small change: https://terrytao.wordpress.com/2012/05/11/cayley-graphs-and-... (see figure 14).

If you want to take the arrows very literally, you can think of the commutator as measuring the amount of curvature in the space the arrows lie in. The less of a difference the commutator makes, the less curved - with a commutator that doesn't do anything meaning the space is flat. Expressed in these terms, the two-part algorithm technique amounts to finding places in Rubik's cube algorithm space that are almost – but not quite – flat.

Keisler has a introductory text book (available free here: https://www.math.wisc.edu/~keisler/calc.html) that uses non-standard analysis, which he claims is easier for beginners to understand than the notorious delta-epsilon proofs.

I can't say how effective it is at that goal, but it is all mathematically legitimate, and has a nice intuitive appeal to it.

It seems like they address this issue as well:

"Another key advantage is that most of the solid blanket materials used to surround the fusion chamber in such reactors are replaced by a liquid material that can easily be circulated and replaced, eliminating the need for costly replacement procedures as the materials degrade over time. "It's an extremely harsh environment for [solid] materials," Whyte says, so replacing those materials with a liquid could be a major advantage."