Random sentences
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Re: Random sentences
why you tend to believe that human brain, developed from the same zygote as your lungs and excretory system works using different mechanics?
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mirror retry neighbour shoelace shoelace
error is hex mountain area#$%ainvalid__
mirror retry neighbour shoelace shoelace
"As you have noticed over the years, we are not angry people." (itebygur)

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 Posts: 1483
 Joined: Sun Jan 18, 2009 15:28
 Location: Denmark
Re: Random sentences
It's just in a time loop with the dump truck.
Re: Random sentences
they're afraid to love me
them people
them people
"As you have noticed over the years, we are not angry people." (itebygur)
Re: Random sentences
I hate people's online profiles, but I love all people.
"As you have noticed over the years, we are not angry people." (itebygur)
Re: Random sentences
Now, try to post something completely different to what you want to post and learn to face the results.
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"As you have noticed over the years, we are not angry people." (itebygur)
Re: Random sentences
TO ENTER THE VOID PLEASE REPAIR THE FLUSH VALVE FLAPPER FIRST.
"As you have noticed over the years, we are not angry people." (itebygur)
Re: Random sentences
nouns are male
verbs are female
being is male
overcoming is female
verbs are female
being is male
overcoming is female
"As you have noticed over the years, we are not angry people." (itebygur)
Re: Random sentences
Rule 17H.
For aesthetic reasons always end the paragraph with embarrassing or cryptic sentence.
For aesthetic reasons always end the paragraph with embarrassing or cryptic sentence.
"As you have noticed over the years, we are not angry people." (itebygur)
Re: Random sentences
If matter is a form of energy.
Then information and knowledge are forms of emotion.
Then information and knowledge are forms of emotion.
"As you have noticed over the years, we are not angry people." (itebygur)
Re: Random sentences
The dream of the distant high voltage towers.
"As you have noticed over the years, we are not angry people." (itebygur)

 [insert custom title here]
 Posts: 1483
 Joined: Sun Jan 18, 2009 15:28
 Location: Denmark
Re: Random sentences
What does it mean if you fart in front of a horse?
Re: Random sentences
To understand what is hell you must first make hell out of the lives of other people.
"As you have noticed over the years, we are not angry people." (itebygur)
Re: Random sentences
"pi is certainly a finite real number. It's between 3 and 4. It's not even a particularly large number.
You are correct that it takes an infinite amount of information to specify it in decimal notation. That is, for every counting number n, there's a particular decimal digit in place n. (To the right of the decimal point. We can ignore the 3 for this.) So in decimal notation it takes infinitely much information to specify pi.
But that's just a limitation of the decimal notation. There are many finite ways to define pi. The Internet is full of them. I'm too new to post links, but if you google "formulas for pi" you will find lots of relatively short (in particular, finite) expressions that completely characterize pi.
My favorite is sum(1/n^2; n = 1, 2, 3, ...) = pi^2/6. That's really a cool fact, don't you think? Euler discovered it in 1735. That number is zeta(2), for fans of Riemann's zeta function.
From zeta(2) = pi^2/6 it follows that
pi = sqrt(6 * zeta(2))
I admit that we are still hiding an infinitary process in this notation. We're summing an infinite series of real numbers. But these days, modern math has figured out how to logically derive the operations on infinite series from first principles, using nothing more than the laws of logic and the axioms of set theory. We now have a comprehensive theory of how to represent infinitary processes using finite strings. Or computer programs if you like. We could easily program any of these formulas in a computer and generate as many digits of pi as we want, given constraints on time and electricity. That's a major human intellectual achievement. Not everyone's completely on board with it yet
We have finitized the infinite. That's the important philosophical point. And it's a relatively recent historical development.
Pi isn't "random." Its decimal digits are the result of a deterministic process. Even if the distribution of the digits turns out to be statistically random; those digits are still generated by a deterministic process. And it doesn't require infinite information to specify ... a short mathematical formula does the job perfectly well.
Generally speaking, it's helpful to put aside our highschool understanding of pi as being defined by a circle.
Rather, pi is a particular real number that arises naturally in the study of many mathematical phenomena. It's half the period of the cosine function, for example. And the cosine is not the highschool cosine that's defined by triangles. It's the modern cosine, defined by an infinite series; expressible in finitely many symbols; and (at least in principle) reducible to logic.
In other words, our modern understanding of pi is that it's an algorithm. It doesn't terminate, but it cranks out as many digits as you want. And algorithms are real and solid and they run the world. In that sense, we've tamed pi.
Hope something in here sheds some light."
You are correct that it takes an infinite amount of information to specify it in decimal notation. That is, for every counting number n, there's a particular decimal digit in place n. (To the right of the decimal point. We can ignore the 3 for this.) So in decimal notation it takes infinitely much information to specify pi.
But that's just a limitation of the decimal notation. There are many finite ways to define pi. The Internet is full of them. I'm too new to post links, but if you google "formulas for pi" you will find lots of relatively short (in particular, finite) expressions that completely characterize pi.
My favorite is sum(1/n^2; n = 1, 2, 3, ...) = pi^2/6. That's really a cool fact, don't you think? Euler discovered it in 1735. That number is zeta(2), for fans of Riemann's zeta function.
From zeta(2) = pi^2/6 it follows that
pi = sqrt(6 * zeta(2))
I admit that we are still hiding an infinitary process in this notation. We're summing an infinite series of real numbers. But these days, modern math has figured out how to logically derive the operations on infinite series from first principles, using nothing more than the laws of logic and the axioms of set theory. We now have a comprehensive theory of how to represent infinitary processes using finite strings. Or computer programs if you like. We could easily program any of these formulas in a computer and generate as many digits of pi as we want, given constraints on time and electricity. That's a major human intellectual achievement. Not everyone's completely on board with it yet
We have finitized the infinite. That's the important philosophical point. And it's a relatively recent historical development.
Pi isn't "random." Its decimal digits are the result of a deterministic process. Even if the distribution of the digits turns out to be statistically random; those digits are still generated by a deterministic process. And it doesn't require infinite information to specify ... a short mathematical formula does the job perfectly well.
Generally speaking, it's helpful to put aside our highschool understanding of pi as being defined by a circle.
Rather, pi is a particular real number that arises naturally in the study of many mathematical phenomena. It's half the period of the cosine function, for example. And the cosine is not the highschool cosine that's defined by triangles. It's the modern cosine, defined by an infinite series; expressible in finitely many symbols; and (at least in principle) reducible to logic.
In other words, our modern understanding of pi is that it's an algorithm. It doesn't terminate, but it cranks out as many digits as you want. And algorithms are real and solid and they run the world. In that sense, we've tamed pi.
Hope something in here sheds some light."
"As you have noticed over the years, we are not angry people." (itebygur)
Re: Random sentences
We have a way to accurately define pi and it is π. That's it, no infinite amount of information needed.
We haven't finitized the infinite, on the contrary, mathematics have found a way to work with infinity to the point that they can handle an infinite number of infinites.
However, this does not mean that pi is finite. Curiously, this doesn't matter. Really, it doesn't. The funniest thing ever is that for any calculation we need pi for, 40 digits is enough. And by enough I don't mean good enough, just literally enough for anything in the universe...
We haven't finitized the infinite, on the contrary, mathematics have found a way to work with infinity to the point that they can handle an infinite number of infinites.
However, this does not mean that pi is finite. Curiously, this doesn't matter. Really, it doesn't. The funniest thing ever is that for any calculation we need pi for, 40 digits is enough. And by enough I don't mean good enough, just literally enough for anything in the universe...
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Re: Random sentences
"By touching the pages of the open book, you feel a momentary connection with true meaning that the author was trying to impart to you as he cast his words down the river of time to finally wash up against the shores of your eyeballs."
"As you have noticed over the years, we are not angry people." (itebygur)
Re: Random sentences
Track 6. "How to disagree completely".
"As you have noticed over the years, we are not angry people." (itebygur)
Re: Random sentences
Whoever is addicted and keeps checking this forum on regular basis is doomed and should prepare for more atrocities to come.
"As you have noticed over the years, we are not angry people." (itebygur)