sets a dangerous precedent where the government knows better than the markets

Wtf. You could say this about literally any law. Outlawing murder-for-hire sets a dangerous precedent where the government knows better than the markets. Making people pay income tax sets a dangerous precedent where the government knows better than the markets. Speed limits set a dangerous precedent where the government knows better than the markets. What a terrible argument.

You're reducing things to a single issue and have the gall to say my political world is narrow. You're unreal.

It's funny you say the philosophy is simple when strategic voting requires multiple layers of analysis and voting for bubblegum ice cream just amounts to what feels good. You can't bring yourself to accept the reality of the situation, so you pretend like the problem is easy to solve if you just ignore it. That's truly simple minded. Pathetic projection on your part.

Doesn't matter where the track leads if the trolley can't get to it. It could lead to rainbows and sunshine, but that isn't where the trolley is headed because there is no possibility that someone other than Trump or Biden is elected president. A few cry babies voting third party won't get some third person elected. A vote for the third track is a vote for a track that will not be ridden.

It's supposed to be E^2 = (mc^2 )^2 + AI^2 , which implies that AI = pc, because AI is the momentum that will carry us into the future. These rookies clearly just took the square root using freshman's dream.

I'll preface this with the fact that I am also not a physicist. I'm also simplifying a few concepts in modern physics, but the general themes should be mostly accurate.

String theory isn't best described as a genre of physics - it really is a standalone concept. Dark matter and black holes are subjects of cosmology, while string theory is an attempt to unify quantum physics with general relativity. Could string theory be used to study black holes and dark matter? Sure, but it isn't like physicists are studying black holes and dark matter using methods completely independent from one another and lumping both practices under the label string theory as a simple matter of categorization.

You are correct to say that string theory is an attempt at a theory of everything, but what is a theory of everything? It's more than a collection of ideas that explain a large swath of physical phenomena wrapped into a single package tied with a nice bow. Indeed, when people propose a theory of everything, they are constructing a single mathematical model for our physical reality. It can be difficult to understand exactly what that means, so allow me to clarify.

Modern theoretical physics is not described in the same manner as classical Newtonian physics. Back then, physical phenomena were essentially described by a collection of distinct models whose effects would be combined to come to a complete prediction. For example, you'd have an equation for gravity, an equation for air resistance, an equation for electrostatic forces, and so on, each of which makes contributions at each point in time to the motion of an object. This is how it still occurs today in applied physics and engineering, but modern theoretical physics - e.g., quantum mechanics, general relativity, and string theory - is handled differently. These theories tend to have a single single equation that is meant to describe the motion of all things, which often gets labeled the principle of stationary action.

The problem that string theory attempts to solve is that the principle of stationary action that arises in the quantum mechanics and the principle of stationary action that arises in general relativity are incompatible. Both theories are meant to describe the motion of everything, but they contradict each other - quantum mechanics works to describe the motion of subatomic particles under the influence of strong, weak, and electromagnetic forces while general relativity works to describe the motion of celestial objects under the influence of gravity. String theory is a way of modeling physics that attempts to do away with this contradiction - that is, string theory is a proposal for a principle of stationary action (which is a single equation) that is meant to unify quantum mechanics and general relativity thus accurately describing the motion of objects of all sizes under the influence of all known forces. It's in this sense that string theory is a standalone concept.

There is one caveat however. There are actually multiple versions of string theory that rely on different numbers of dimensions and slightly different formulations of the physics. You could say that this implies that string theory is a genre of physics after all, but it's a much more narrow genre than you seemed to be suggesting in your comment. In fact, Edward Witten showed that all of these different string theories are actually separate ways of looking at a single underlying theory known as M-theory. It could possibly be said that M-theory unifies all string theories into one thus restoring my claim that string theory really is a standalone concept.

https://twitter.com/latifnasser/status/1750952860131729544

It depends. If the variable names are arbitrary, then a map is best. If the variable names are just x_1, x_2, x_3, ..., x_n, then a list or dynamic array would be more natural. If n is constant, then a vector or static array is even better.

I don't recall any socialized courier or food delivery services.

The major determining factor in the time it takes you to get through the light is the number of cars ahead of you, not the amount of room you have for a run-up. What you're talking about might save you a quarter second at the end of the day, but it more likely to not save any time at all and it unnecessarily contributes to traffic by reducing the effective carrying capacity of the road. There are also situations where hanging back can block a turn onto a minor road or into a parking lot and moving forward may let a person behind you turn off the road thus alleviating traffic. Ultimately, there is nothing you can do to make the person in front of you go faster, so just pull up as far as you safely can to make room for other people to join the queue or get around you.

This is just a continuous extension of the discrete case, which is usually proven in an advanced calculus course. It says that given any finite sequence of non-negative real numbers x,

lim_n(Sum_i(x_i^n ))^(1/n)=max_i(x_i).

The proof in this case is simple. Indeed, we know that the limit is always greater than or equal to the max since each term in the sequence is greater or equal to the max. Thus, we only need an upper bound for each term in the sequence that converges to the max as well, and the proof will be completed via the squeeze theorem (sandwich theorem).

Set M=max_i(x_i) and k=dim(x). Since we know that each x_i is less than M, we have that the term in the limit is always less than (kM^n )^(1/n). The limit of this upper bound is easy to compute since if it exists (which it does by bounded monotonicity), then the limit must be equal to the limit of k^(1/n)M. This new limit is clearly M, since the limit of k^(1/n) is equal to 1. Since we have found an upper bound that converges to max_i(x_i), we have completed the proof.

Can you extend this proof to the continuous case?

For fun, prove the related theorem:

lim_n(Sum_i(x_i^(-n) ))^(-1/n)=min_i(x_i).

2 may be the only even prime - that is it's the only prime divisible by 2 - but 3 is the only prime divisible by 3 and 5 is the only prime divisible by 5, so I fail to see how this is unique.