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Alternatively, you could also consider using multi-letter infix operators, such as c = a <u> b in your union example. This would have the benefit of being easy to type since it's only ASCII characters, but at the same time easy to pretty-print by just converting all instances of <u> to a unicode U+222A symbol using e.g. a regular expression. While this would make your language more original, it would likely be more user-friendly towards people used to other languages if you stuck to a function-like syntax c=union(a,b) though. This would also eliminate the problem figuring out operator precedence in large expressions.

Regarding the last point, about thinking very differently about imaginary numbers and quaternions, you might find this paper interesting; it is a readable and easily accessible introduction to the topic of geometric algebra, with an emphasis on its pedagogical applications in physics. This mathematical formalism goes back over a century to Grassmann and Clifford, and has been repopularized in physics by Hestenes. I believe some people are also using the formalism for computer graphics. The short version is that you can unify vectors, quaternions, and complex numbers into a single geometric formalism, if you just treat scalars, vectors, planes, and cubes all as first-class objects in a general geometric space, and that this leads to more intuitive geometric interpretations.

I wouldn't exactly call it "paranoia", as it's quite well-founded. My friend and I did a motorbike road trip through Vietnam about a year ago, and we didn't get the point of wearing those masks in public, so we just ignored the fact that all the locals were doing it. After a 2000 km trip over 11 days, I developed a tonsil infection, and my friend got a lung infection, so we both had to take antibiotics for the next two weeks. The doctor said that the reason was probably that we had been inhaling too much traffic dust; the dust creates lots of tiny tears in your throat and lungs, which leaves those parts of your body very vulnerable to infections. After that, I've been using a mask when driving through dry areas, and haven't gotten infected again so far :).

There are mathematically precise ways of defining the difference between planets and dwarf planets. If you check the table of planetary discriminants a little bit down the page, you see that there clearly appears to be two groups of planetoids in the list: those with a planetary discriminant of 10,000-1,000,000 which we call *planets*, and those with a planetary discriminant of 0.01-1.00 which we now call *dwarf planets*. Do you still disagree that these two groups, separated by four orders of magnitude in their planetary discriminants, deserve different names?

Sure, I'll give it a try. If you put two bar magnets next to each other, they tend to flip each other around so that they point in the same direction. Now try to picture an infinitely large universe, which is filled with an infinite number of tiny bar magnets. If all of these magnets pointed in the same direction, there wouldn't be much interesting going on; since all the tiny magnets are already aligned, they won't try to flip each other over, and the universe would be a stable place. (You could still have some fun by flipping a few magnets, and watching the ripples spread as a wave throughout the universe; but that's not what I'm gonna talk about now.)

But let us now consider a different scenario: in one end of the universe, all the magnets are pointing "up", while in the other end of the universe, all the magnets are pointing "down". By themselves, both these regions are stable, since there is nothing inherently "better" about pointing up than pointing down. However, somewhere in between these two far ends of the universe, there has to be a region where the magnets change from pointing up to pointing down; and this is a region of higher energy, since you have all these tiny magnets which are constantly fighting among themselves about which way to point, and constantly trying to flip each other over. This is called a "domain wall" in the case of magnetism, which is an example of a "topological defect". This domain wall can be moved and twisted by flipping a finite number of magnets in the vicinty of the domain wall; but you can't truly get rid of it without flipping an infinite number of magnets throughout the universe, which would end up requiring an infinite amount of energy.

In some quantum field theories, you get analogous situations where a theory has multiple stable "vacuum solutions". If the universe contains fields like that, we would then have two possible scenarios: (i) the entire universe has the same vacuum state (corresponding to all the magnets pointing in the same direction); or (ii) the universe could in principle consist of different stable regions with different vacuum states, with an unstable region called a "topological defect" inbetween, where the different vacua fight for dominance.

In general relativity, gravitation is not modeled as a direct force between massive objects.
Instead, any form of energy density (mass according to E=mc^2, electromagnetic fields, and so on) causes spacetime to curve, and this curvature of spacetime then alters the motion of particles through spacetime. I've always liked the summary "energy tells spacetime how to bend, and spacetime tells matter how to move".

So yes, it is true that electromagnetic fields also act as a source of gravity. However, you'll need some*really* crazy field configurations before that effect starts becoming comparable to the gravitation from stars and planets though. For a very rough estimate of the sizes involved, you can try setting the volumetric energy density of an electric field (vacuum permittivity)*(electric field)^2/2 equal to the mean energy density (earth mass)c^2/(earth volume) of the earth, which leads to the result 10^16 V/m for the electric field. This is roughly 10^10 times the electric breakdown voltage of air at standard temperature and pressure...

So yes, it is true that electromagnetic fields also act as a source of gravity. However, you'll need some

wouldn't that make the concept of time fundamentally flawed?

In *any given reference frame*, time is a well-defined quantity. The fundamentally flawed concept here is the idea of some kind of *universal time* that passes at the same rate everywhere in the universe, because relativity tells us that the observed passage of time is affected by things like velocity, acceleration, and gravitation, and therefore varies between different reference frames -- and we have no objective reason to say that any particular reference frame in the universe is inherently superior.

So while the atomic clock might measure the local passage of time with near perfect accuracy in the reference frame where we place it, the results will just be approximate in any other reference frame.

I can imagine a couple of applications of these transistors though...

Many numerical simulations require repeated random sampling of some process, and then combine the results in the end. If you're averaging *some billion simulations*, the result should be quite robust to fluctuations in the results of each simulation. Thus it might well be worth it to use 10 billion unreliable transistors instead of 1 billion reliable transistors, if they cost the same.

Another application could be to generate random numbers. Let's say that you have a pseudorandom number generator with periodicity N, and your unreliable transistors makes the algorithm do a random jump after an average of N/100 numbers. Wouldn't that be "random enough" for more applications than just the pseudorandom number generator itself?

Its DNA sequence has been withheld, until an antidote has been found. [...] Is this the right move?

We arrive at the same question as with security and open source software: if the DNA sequence is withheld, doesn't that reduce the probability of an antidote being discovered?

France regards Scientology as a cult, not a religion

A second woman claimed she was forced by her Scientologist employer to undergo testing and enroll in courses, also in 1998. When she refused she was fired.

It shouldn't matter whether it's a cult or a religion; if someone got fired for not undergoing religious courses and testing, that should be treated the same way by the law.

DIVIDED BY ZERO. No thank you. I'll stick with good old Newtonian physics until you idiots come up with something that accurately explains the laws of motion AND magnetism.

Sticking to Newtonian mechanics because the math looks prettier doesn't sound very scientific. Isn't the point of science to explain and predict the largest number of phenomena, with the smallest number of independent assertions?

Special relativity predicts and explains many phenomena that Newtonian physics doesn't, and even more so for general relativity. The same goes for quantum mechanics and quantum field theory, which can be used to derive all of chemistry and electromagnetism, and is the only theory so far that can predict what happens in particle accelerators. I'm not saying that any of these theories will never be superseded, but so far they explain a lot more than the theories we had in the 1800s.

Actually, he's right, and the analogy is quite good too. Newtonian physics is "wrong" in the sense that it doesn't hold for very massive, very fast or very small objects. However, for medium-sized objects moving at medium speeds, it holds very well.

Similarly, the second law of thermodynamics, that entropy always increases, can be derived in statistical mechanics by assuming that there are an *infinite* number of particles in your system. Thus, it holds for the entire universe, and it holds extremely well for any macroscopic system that I know of. However, for microscopic systems, it becomes quite probable that entropy decreases in small periods of time (the fluctuation theorem tells you the probability for this to happen.)

If you're interested in how this "makes sense": in statistical mechanics, it is shown that entropy is actually just a measure of microscopic disorder. There usually exists a lot more of possible disorderly states than orderly states for a system, so if no particular microstate is preferred (the probability of entering any microstate is equally probable), it's simply more probable that you will observe a transition from an ordered state to a disordered one, not the other way around. For a small system, the discrepancy is small, so you see transitions in both directions on small enough timescales. But as the number of particles in the system grows, the number of disordered states of the total system will grow far faster than the number of ordered states (the discrepancy is O(n!) for n particles in the system), so transitions from disordered to ordered states become extremely unlikely.

Why is it that every time foreign people do something amazing, someone has to question them about the actions of their governments?

Someone in Isreal did science? But they oppress the Palestinians, so it doesn't matter.

Someone in Saudi Arabia did science? But they oppress their women, so it doesn't matter.

Someone in China did science? But they censor their internet, so it doesn't matter.

Someone in Russia did science? But Putin is a fascist, so it doesn't matter.

Assuming that you're american, how would you react if you published a scientific paper after making a great breakthrough, and people started asking why you killed all those people in Afghanistan and Iraq, and why you tortured them without due process at Guantanamo Bay?

Don't get me wrong, I do support human rights; but you shouldn't blame every single individual for the actions of their government.

Special Relativity makes quite clear that if two particles are spacelike separated when measured, that the concept of "instantaneous" is devoid of meaning.

From TFA:

Eisenberg emphasizes that even though in relativity, time measured differently by observers traveling at different speeds, no observer would ever see the two photons as coexisting.

So the separation was timelike, not spacelike.

Thanks for the link to the SR paper! It was a fascinating read :).

"When it comes to humility, I'm the greatest." -- Bullwinkle Moose