Ah. That makes sense. Thanks for the explanation!

Yeah, I'm gonna need more than your incredulity to convince me. Like, fun that you think it is inconceivable, but your inability to imagine has no bearing on reality. Especially when there is plenty of evidence to suggest they actually filmed and broadcasted it live. For example, the fact that a live television broadcast was a primary goal of the mission, or the fact that RCA made custom TV cameras for the Apollo program , or that the broadcast lasted for hours, or any of the analyses out there that shows the video is likely real. Also, no one suggested that the Apollo astronauts had a camera crew with them - what a bizarre thing to mention.

Housing is taxed at the value of the property, not the difference between the value of the property and the purchase price.

Imaginary numbers are no more imaginary than real numbers. The name trips a lot of people up. If you want to call imaginary numbers "dark unicorns" then you really should say the same thing of the numbers 1, 2, and all other numbers as well.

You're thinking of topological closure. We're talking about algebraic closure; however, complex numbers are often described as the algebraic closure of the reals, not the irrationals. Also, the imaginary numbers (complex numbers with a real part of zero) are in no meaningful way isomorphic to the real numbers. Perhaps you could say their addition groups are isomorphic or that they are isomorphic as topological spaces, but that's about it. There isn't an isomorphism that preserves the whole structure of the reals - the imaginary numbers aren't even closed under multiplication, for example.

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:

• 490 people want Mexican and do not want Asian
• 510 people want Asian:
  • 480 people want Vietnamese, would be satisfied with Thai, and do not want Mexican
  • 30 people want Thai, would be satisfied with Vietnamese, and do not want Mexican

The restaurants on the ballot are:

1. A Mexican restaurant,
2. A Vietnamese restaurant, and
3. A Thai restaurant.

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.

You're mistaken unfortunately. The books don't start that way. They start by describing Arthur Dent's house.

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.

Yeah, you're close. You seem to be suggesting that any measurement causes the interference pattern to disappear implying that we can't actually observe the interference pattern. I'm not sure if that's what you truly meant, but that isn't the case. Disclaimer: I'm not an expert - I could be mistaken.

The particle is actually being measured in both experiments, but it's measured twice in the second experiment. That's because both experiments measure the particle's position at the screen while the second one also measures if the particle passes through one of the slits. It's the measurement at the slit that disrupts the interference pattern; however, both patterns are physically observable. Placing a detector at the slit destroys the interference pattern, and removing the detector from the slit reintroduces the interference pattern.

You have the spirit of things right, but the details are far more interesting than you might expect.

For example, there are numbers past infinity. The best way (imo) to interpret the symbol ∞ is as the gap in the surreal numbers that separates all infinite surreal numbers from all finite surreal numbers. If we use this definition of ∞, then there are numbers greater than ∞. For example, every infinite surreal number is greater than ∞ by the definition of ∞. Furthermore, ω > ∞, where ω is the first infinite ordinal number. This ordering is derived from the embedding of the ordinal numbers within the surreal numbers.

Additionally, as a classical ordinal number, ω doesn't behave the way you'd expect it to. For example, we have that 1+ω=ω, but ω+1>ω. This of course implies that 1+ω≠ω+1, which isn't how finite numbers behave, but it isn't a contradiction - it's an observation that addition of classical ordinals isn't always commutative. It can be made commutative by redefining the sum of two ordinals, a and b, to be the max of a+b and b+a. This definition is required to produce the embedding of the ordinals in the surreal numbers mentioned above (there is a similar adjustment to the definition of ordinal multiplication that is also required).

Note that infinite cardinal numbers do behave the way you expect. The smallest infinite cardinal number, ℵ₀, has the property that ℵ₀+1=ℵ₀=1+ℵ₀. For completeness sake, returning to the realm of surreal numbers, addition behaves differently than both the cardinal numbers and the ordinal numbers. As a surreal number, we have ω+1=1+ω>ω, which is the familiar way that finite numbers behave.

What's interesting about the convention of using ∞ to represent the gap between finite and infinite surreal numbers is that it renders expressions like ∞+1, 2∞, and ∞² completely meaningless as ∞ isn't itself a surreal number - it's a gap. I think this is a good convention since we have seen that the meaning of an addition involving infinite numbers depends on what type of infinity is under consideration. It also lends truth to the statement, "∞ is not a number - it is a concept," while simultaneously allowing us to make true expressions involving ∞ such as ω>∞. Lastly, it also meshes well with the standard notation of taking limits at infinity.

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.

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.