Correlation is not the same as Causation

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Green houses allow to control the climate inside in a way that is impossible outside. Outside you're a slave to the wheather and the seasons. Inside you set the seasons. So you can grow crops out of season, and grow crops that can't flurish in the local climate otherwise.

Lots of plants from tropical climates have minimum temperature and humidity requirements. Gardeners and farmers in temperate or even polar climates cannot grow these plants outside at all, but greenhouses let them re-create those conditions indoors while still giving plants access to sunlight. Even plants that can survive outside often grow faster under the controlled conditions in a greenhouse. Pest management is also easier in the controlled environment. Some greenhouses can even have extra CO2 piped in for even faster growth.

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Not all paradoxes can be solved with mathematics.

This sentence is false. That's a paradox as well. It cannot be true nor false. No amount of mathematics can make it true or false, it is a logical impossibility.

We use the word paradox in a couple different ways. One is in logical contradictions, i. e. "This sentence is false." It is impossible to have the statement be either true or false, so it is a paradox. "A married bachelor" is another paradoxical statement, as you are definitionally bound by the word "bachelor" to be unmarried.

Another way we use paradoxes is in seemingly contradictory statement that do actually have an answer. Zeno's paradox falls in this category. Like you say, there is the definite answer that Achilles does catch the tortoise, the seemingly contradictory part is the description that you have to cover an infinite number of ever smaller but never 0 distances to go anywhere, so how can you move?

The answer being that the time it takes to move those smaller increments also decreases to 0 at exactly the same rate.

Why should we assume their speed is different if they are both advancing one point at a time? I feel like I’m missing something.

Imagine that I gave you a task:

"Start counting up in integers (1, 2, 3, etc.). When you finish counting all the integers then you can have a slice of cake."

When are you going to have your slice of cake? You are never going to run out of integers since you can keep counting up for an infinite period of time, so in theory you should never reach the point where you can have the cake, right?

Now imagine that as you are counting the time between 1 and 2 takes a second, but you start speeding up so that the time from 2 to 3 is only a half second, from 3 to 4 a quarter of a second, etc. Conceptually this doesn't matter since we didn't really care about how quickly you were counting in the first example, as the issue of the integers being infinite was the real issue. But in this case somehow you "finish" and eat the cake?

This is the idea behind Zeno's Paradox. In order for the hare to pass the tortoise it must first reach the tortoise, and in order to do that it must reach half the distance between it and the tortoise. If it reaches the halfway point then it must next reach the new halfway point, and when it does that reach the new new halfway point, etc. In concept this cycle can be continued infinitely since distance is infinitely divisible and so there are equally an infinite number of steps to this task as there are integers in the previous examples. Yet in this case we know the hare will be able to pass the tortoise. Somehow an infinite series of tasks was completed in finite time.

The paradox is that you have one line of reasoning that shows that Achilles will never reach the Tortoise, and another line of reasoning that shows that Achilles will eventually reach the Tortoise.

If both lines of reasoning are correct, you get a contradiction. But it's not obvious where the mistake is, hence being called a paradox.

The resolution to this paradox is the realization that an infinite series can have a finite sum. That is, the first line of reasoning shows that it will take an infinite number of steps for Achilles to reach the Tortoise, but since each step gets shorter, it can be done in a finite amount of time.

The reason this is a "paradox" is that the logic seems irrefutable although our common sense tells us otherwise. It isn't a true paradox because it isn't a logical contradiction but rather the reasoning seems to go against common sense.

To actually show why this isn't a true paradox involves understanding infinite series. We can build an infinite series out of the sequence 1, 1/2, 1/4, 1/8... Now every term of the sequence is positive. "Logically" adding all the terms would result in "infinity" as there are an infinite number of positive numbers added together.

It actually isn't obvious to a person not familiar with infinite series, why this "logic" isn't true.

Yeah, that's where I was trying to go with it. Better than just giving "Africa" as a gigantic place aid, especially the various corrupt leaders who'll probably take much of it for them and their friends, help smaller communities get what they need to provide better for themselves. That's my belief anyway. I don't live in Africa but I do support a refugee group there, directly.

Like all paradoxes it is only a problem because when proposed there was a lack of mathematics knowledge. Lets look at the paradox in a different way:

How long does it take Achilles to reach the tortoise?

One way to solve this is to just add up all the time intervals for each step. So it takes Achiiles some time, t^1 to get to point A, t^2 to get to point B and so on. Our total time, T, is then:

T= t^1 + t^2 + t^3 .... for an infinite number of intervals.

So how do we get a finite number from adding an infinite number of positive values together? Without calculus we can't solve this and hence the paradox.

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The basic solution to the paradox is integral calculus. The normal statement of the paradox keeps using smaller and smaller time intervals. Integral calculus lets you take an infinite number of infinitely small areas and have it add up to a finite answer. (Which is scary at first, but you get used to it pretty quick.) Once you have that insight, the paradox goes away and the normal view of velocity versus time gets strengthened.

Quality control. Each component is made to specifications, and if it doesn't meet specification, it gets tossed/recycled.

For example, car needs a 50.00mm +/- 0.01mm rod in length, 10.00 +/- 0.01 mm in diameter. Worker makes 10 rods. Quality control checks them, finds that one rod is 50.05 mm long when max permissible is 50.01. Tosses it.

Yeah, I read the wiki, but I still disagree to it. Looking up pickle on Oxford dictionary, merriam-webster, Cambridge or dictionary.com they all say its a vinegar or brine preservation. None of them mention fermentation. I don't know why Wikipedia has decided to bundle the two things together, there's no source to it.

F.ex. Sauerkraut is a salt fermentation, but not with a brine. Yet, Wikipedia says its still a pickled food in contrary to the dictionaries definitions.

In my culture, we have a clear separation between the two ways of preserving food. So I'm just surprised ppl here bundle them into the same thing.

Why do you think it's difficult to make them all nearly identical?

In an automated production line, it's easier to make 100 pieces that are almost identical than 100 pieces that are all visibly different.

Everything is made by machines.

A machine is doing the same motions and using the same tools each time, so the end result is pretty much the same every time.

Something that I think the other answers miss is that often military exercises aren’t about training, at least not entirely. Often they’re constructed to test out possible, sometimes wacky scenarios and evaluate performance. Such as - China is invading Taiwan and our Pacific fleet just simultaneously sank, what do we do? Can we still win and if so how?

This is why sometimes you get those sensational news articles about how “a fleet of speedboats destroyed a US warship!” and the like, not realizing that it was a fleet of literally dozens of boats against a single ship with no other support that wasn’t allowed to use half its weapons and in unfavorable position to maneuver, and also it was a rookie captain vs a guy who literally specializes in rapid motorboat assaults or whatever. That’s the kind of stuff that gets concocted for exercises.

Only if you want your company to fail horribly.

If the process doesn't work right, you fix the process. Someone figures out what went wrong, and they figure out a better way of doing the task, and then that specific problem doesn't happen any more.

Firing people for making mistakes is an effective way to get people to hide mistakes, push blame on others, and otherwise make problems much worse.

There's a management joke: A worker who just caused a million-dollar failure is called into the manager's office. Worker says, "Well, I guess you're going to fire me." Manager laughs and says, "Fire you? We just spent a million dollars training you!"

Just type in google fast food and mental problems linked

This paper also shows a negative correlation between mental issues and fast food https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7041096/

Forgive me for not looking up the full quote. But I strongly object to your suggestion that Africans live in the deserts. Of course there are human population where drinking water is an issue, you mentioned a few places in the US and there are similar locations for cities in Africa. But the idea that Africans live in deserts comes from images from farmlands during severe drought periods or refugee camps from people who have to flee into the barren deserts to avoid racial, religious or political persecution. Somalia, Ethiopia and Kenya is some of the most fertile lands on the planet and some of the greatest food exporters in the world, not unlike the US Midwest or California. And similar to these areas there are occasional droughts when the food harvests fails which can create terrifying images of people living in what looks like a desert.

I wasn't attempting to correct them, I was just sharing. Rumination would be the entire process ;;;;)

They get fired, face a civil lawsuit at the absolute worst.

Well, they don't. They have tolerances. They can spend more time and use tools that were made more carefully to get tighter tolerances.

Every zero added to your tolerances adds a zero to your price, though. A huge part of the engineering process is to figure out just how sloppy they can get away with being.