Just say you recently came into some inheritance and that you are looking into investment opportunities. Then they will expect you to be out of your element, so you won't need to try to pretend you're someone you're not. If they ask about the inheritance, say your grandfather made a fortune selling lumber or something boring like that.
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).
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.
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.
Language parsing is a routine process that doesn't require AI and it's something we have been doing for decades. That phrase in no way plays into the hype of AI. Also, the weights may be random initially (though not uniformly random), but the way they are connected and relate to each other is not random. And after training, the weights are no longer random at all, so I don't see the point in bringing that up. Finally, machine learning models are not brute-force calculators. If they were, they would take billions of years to respond to even the simplest prompt because they would have to evaluate every possible response (even the nonsensical ones) before returning the best answer. They're better described as a greedy algorithm than a brute force algorithm.
I'm not going to get into an argument about whether these AIs understand anything, largely because I don't have a strong opinion on the matter, but also because that would require a definition of understanding which is an unsolved problem in philosophy. You can wax poetic about how humans are the only ones with true understanding and that LLMs are encoded in binary (which is somehow related to the point you're making in some unspecified way); however, your comment reveals how little you know about LLMs, machine learning, computer science, and the relevant philosophy in general. Your understanding of these AIs is just as shallow as those who claim that LLMs are intelligent agents of free will complete with conscious experience - you just happen to land closer to the mark.
Nobody is arguing that a grocery stocker requires less skill and training than brain surgery. Literally nobody. And yet you people repeat this idea over and over.
We know you aren't arguing that every job requires the exact same degree of skill. All that we want to do is say that there are jobs whose required skills are quick to acquire and are therefore easily replaceable. Meanwhile, there are other jobs whose skills take a long time to acquire and are not easily replaceable. We use the term "unskilled labor" to refer to the former group and "skilled labor" to refer to the latter group as a point of convention. When people claim that unskilled labor doesn't exist, they imply that every single job requires skills that are slow to obtain and therefore every worker is difficult to replace, which is clearly false.
I mean this not as an attack on you but a chance to expand your worldview. Cognitive dissonance hurts, and it’s important to recognize when it’s happening so you can ask further questions.
Where is the cognitive dissonance? Where is the contradiction in distinguishing between jobs that require trained applicants and jobs that don't require trained applicants?
There is no such thing as an “unskilled worker” because all jobs require skill. It’s called human skill, and it’s what enables us to build societies greater than the sum of its citizens.
If you decide to use "skilled worker" to mean a worker who has a skill, then you are correct that "unskilled workers" do not exist. Unfortunately, that's not what the phrase "skilled worker" means. If that's how you use the term, then you're talking about something different to everyone else.
The logical conclusion you are suggesting is that because some humans are less capable, they don’t deserve basic needs such as a home, reliable transportation, internet, food, utilities, etc.
The logical conclusion of "unskilled labor exists" is simply that unskilled labor exists. You cannot jump from the observation that "unskilled labor exists" to the claim that "some people don't deserve their basic needs." It's a non sequitur, and it's not a position anyone in this thread would support.
And if your basic premise starts with the notion that society should not be meeting the basic needs of its people, then there’s only one thing that would convince you anyway.
This is a straw man. No one here has expressed the position that society shouldn't meet the basic needs of its people. The position you are arguing against is the position that some jobs require training before hiring and others don't. Again, that's just what people mean when they refer to skilled labor and unskilled labor.
OCB Virgin Slims are my go-to. They're not quite as thin as Raw Blacks, but they have less of a taste in my experience. They also don't tear as easily and stick more reliably than Raws. They're not nearly as common as Raw Blacks, but they're a far superior product in my opinion. It's sad they aren't more popular.
Vote splitting is not a myth. It's just math. Let me explain with an example:
1000 people at a conference are deciding where to order catering and hold a vote:
The restaurants on the ballot are:
If the people who want Asian recognize the strength of their combined numbers, then they can tip the scales by all voting for the favorite between Vietnamese and Thai. In this situation, we get 490 votes Mexican, 510 votes Vietnamese, and 0 votes Thai. This time Vietnamese wins and the majority of people, the 510 who prefer Asian, are either happy or satisfied with the result while only 490 are disappointed.
If everyone votes for their favorite, then we get 490 votes Mexican, 480 votes Vietnamese, and 30 votes Thai. In this case, Mexican wins and the majority of people, the 510 who prefer Asian, are left disappointed while only 490 people are happy with the result. The vote has been split and the result is that the entire conference is worse off for it.
By the way, the ratio of 480 Vietnamese to 30 Thai is irrelevant as long as neither value is 0. That ratio can be fixed to any positive value and a situation can be described in which vote splitting occurs with that specific ratio of Vietnamese supporters to Thai supporters. That's why vote splitting isn't too uncommon - any number of people voting Thai has the potential to split the vote. The one caveat is if literally every Vietnamese supporter decides to vote Thai as well; in that scenario, no vote splitting can occur. Unfortunately, that doesn't happen in practice because it's easier to convert the Thai supporters who are smaller in number than it is to convert the Vietnamese supporters who have greater numbers.
If you want examples from history, there are plenty. Our electoral college amplifies the effect since it breaks one federal election down into a large number of state elections, any of which can exhibit vote splitting. Other people have linked to them in this discussion and you can find more elsewhere online.
Of course! I'm always excited for an opportunity to discuss these sorts of things, so I should be thanking you instead.
As I already mentioned, I'm not talking about situations where your windshield is suddenly obstructed since that situation is especially rare, so if you can see clearly enough to drive safely in the first place, then you can see clearly enough to evaluate your surroundings.
It seems obvious to me that spraying your windshield with soap obstructs your view for a moment, but I'll admit that the occlusion is likely variable depending on the make and model.
I stand by the claim that it is safer to not use your wiper fluid while moving when possible. If you disagree, that's okay. It's a pretty minor point - there are many other driving habits that are far worse in my opinion.
Something has already happened and they didn't touch my rates. I've been saving hundreds of dollars a year. I've saved well into the thousands of dollars at this point. I'm not saying the insurance companies are my friends and while I am better off using the tracker than not using it, that wasn't even my point. My point was that the trackers all function differently and some are better than others.
It's crazy how most of those programs work. The way my insurance handles it is way better. For example, no matter how bad you are at driving, they never raise the premiums above the normal rate, so it almost always makes sense to get the tracker from a finance perspective. (The only exception is that they will raise your rates if you drive farther in 6 months than you estimated on your initial application. The flip side is that they lower your rates if you don't drive very much. I only drive about 1000 miles every 6 months, so my premium is really low.) They also have a Bluetooth device that stays in your car that your phone must be connected to in order for it to record trip data, and if you happen to be riding as the passenger in the car, the app has an option that allows you to clarify for each trip that you weren't the driver. I was surprised to learn they aren't all like that.
While that guy's response to you was completely unacceptable, you should know that there are several reasons not to use the wiper fluid while moving: it obstructs your view of the road for a period of time, in most cases you can and should use the wiper fluid before you start driving (I realize this is not possible if the windshield gets dirty in transit), and it's inconsiderate to other drivers - you don't have to be tailgating someone to be hit with their dirty soap spray and in general it's best not to piss people off on the road if you can avoid it.
It may be unreasonable to ask someone to pull off a highway to use their wiper fluid every time they hit a bug, but it isn't unreasonable to ask someone to consider waiting until there is some free space behind them and it isn't unreasonable to ask them to wait until they are at a stop sign or stop light (if one is coming up).
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.