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I am slightly shocked by the correct analysis of the incorrect formulation of the liar's paradox.
This incorrect wording sounds like this. “Epimenides of Crete claimed that all Cretans are liars, being himself from the island of Crete. If it's true, then he's a liar himself, and then it's a lie. If this is a lie, then not all Cretans are liars, and then Epimenides ' statement is true.”
The italicized part is wrong; there is no paradox in Epimenides ' statement. It would have been if Epimenides had been the only Cretan, and this statement was the only statement he made; then it would have been the famous paradoxical statement “This statement is false” – it can be neither true nor false, because in both cases there is a contradiction. If it is true, it is false (because when it is true, it asserts it), and if it is false, it is true (because when it is false, it asserts the opposite).
Analysis of incorrect wording is as follows:
If we call someone who lies from time to time a liar, then Epimenides ' statement may even be true (because then just because Epimenides is a liar doesn't mean that he lied right now). That is, now Epimenides may have lied, and maybe not – there will be no contradiction in any case.
Let's assume that we only call someone who lies every time, all the time, a liar.
Then Epimenides ' statement cannot be true: if it were true, it would be false. A contradiction.
But it can easily be false. If it is false, then not all Cretans are liars, there is at least one Cretan who tells the truth from time to time, and there is no contradiction.
Now let's look at the beginning and the end.
Beginning: Epimenides of Crete claims that all Cretans are liars.
End: We draw the strictly logical conclusion that there is at least one Cretan who speaks the truth from time to time. There must be one, because otherwise there will be a contradiction.
WHERE DID WE GET THIS FROM?
From an aesthetic point of view, I admire Zeno's paradox about Achilles and the Tortoise: Let's say Achilles runs ten times faster than the tortoise, and is behind it at a distance of a thousand paces. In the time it takes Achilles to run this distance, the turtle will crawl a hundred paces in the same direction. When Achilles has run a hundred paces, the turtle will crawl another ten paces, and so on. The process will continue indefinitely, and Achilles will never catch up with the turtle.
The effect of oxygen on the body.
RNA and other elements of cells are destroyed due to the fact that oxygen enters it.But the paradox is that if you don't breathe, your brain cells will die.That is, we are forced to breathe oxygen, which destroys us.�And that's fair enough?
I've been struggling with the Simpson paradox for a month wikipedia.org, and he seemed wildly strange-until he understood the problem (see my edits wikipedia.org from 10.02.17).
https://www.youtube.com/embed/BABu3bNoaBg?wmode=opaque
In a nutshell, the effect (drugs, promotions, etc.) in comparison with the control group in each of the subsegments can have one sign, and the average effect in general is the opposite.
The reason is that the control group was chosen unrepresentatively for sub-segments (the share of controls in one segment differs significantly from the share of controls in another segment). In the video screenshot, 150 out of 200 men (75%) received a placebo, while only 50 out of 200 women (25%) received a placebo. As a result, you can't just average such data.
Equalizing the proportion of controls in sub-segments using weighted averages eliminates the paradox. And it allows you to successfully predict the total effect for the future.
The skewed share of controls is often found in spontaneous samples, when a significant factor affects both the choice of controls and the target indicator. For example, prices and sales of tangerines increase before the New Year (external factor). While price increases reduce sales in each period separately, total sales at high prices will be greater than at low prices. This may lead to the erroneous conclusion that higher prices for tangerines in the future will lead to higher sales.
For this reason, on the one hand, stratification of control observations before the experiment is very important. On the other hand, in this subtle and not very well-known moment, there is a risk of manipulating the results.
A digital photo consists of a sequence of zeros and ones. 2 digital photos differ if they contain at least one digit at the same position. Obviously, for a sequence of length n, 2^n photos can be encoded. The number is large, but finite. Now let's take a camera and start photographing everything we see from different angles, in different parts of the world. The number of points on the globe is infinite (moreover, it is uncountable, that is, it has a continuum cardinality). Obviously, we can photograph every point on the globe, that is, set it to a sequence of zeros and ones. Thus, we can define a one-to-one correspondence of a finite set to an infinite one!
There is an equivalent paradox. Let us take for granted that human thought is infinite and can be expressed on paper. So, on paper, you can express any idea you want. But a sheet of paper can fit a limited number of characters, and the number of possible combinations of characters is also finite. This means that by going through all possible symbols, we can eventually express all possible human thoughts (including all works, both created and not yet created), but at the same time we will still reach the end. (this paradox is sometimes referred to as “monkeys with typewriters”.)