The sicence behind 1 to 4 to 9 precision (2001 a Space Odyssey)

[benzman]

2 hours ago, HebaruSan said:

I wonder, would aliens consider 1 to be prime? Is our definition of "prime" universal in that sense?

I am no mathematician, but I did hear once that 1 is not a prime and proving that it is not is quite a neat party trick - but only at certain parties!

 

[HebaruSan]

14 minutes ago, Spaceception said:

So I did misinterpret it a bit. But (I don't think) I didn't misinterpret 100%.

Well, that quote is certainly not saying that a 1x4x9 block is "best", which was the meat of the OP.

As for how close we are to being able to manufacture things to extremely precise tolerances, I think we're doing OK. Wikipedia says the machining industry can handle ±0.0005". I think that's for normal everyday orders, so if we wanted to go to extra effort to leave a calling card on an alien moon, I imagine we could improve upon it. And of course there's all the LIGO stuff where we're measuring things to within less than the width of an atom.

10 minutes ago, razark said:

Of course, with the above post actually quoting it, the argument is pointless.  It does say integers, and not primes.

But that's the narrator giving the characters' impression of what it was supposed to be. It doesn't really tell us whether the next in the series is 16 or 25, since only the alien engineers know whether they consider 1 to be prime.

1 minute ago, benzman said:

I am no mathematician, but I did hear once that 1 is not a prime and proving that it is not is quite a neat party trick - but only at certain parties!

Certainly that's the answer that almost any human mathematician will give you. I'm wondering how arbitrary it is, though; we tend to take our own axioms and definitions for granted.

[Kerbart]

4 minutes ago, Spaceception said:

Quote from page 173 from the paperback, Chapter 31, Survival;

So I did misinterpret it a bit. But (I don't think) I didn't misinterpret 100%.

That's the passage I re-read

I guess the statement that humanity was not able to construct an artifact to such precision is where your enthusiasm kicked in and equaled “perfect construction” (in measurements) with “perfect construction” (in mechanical properties).

To be honest, I do think Clarke went a bit overboard with the whole thing, as if any mathematical correlations between the dimensions of TMA-1 were needed to convince others that this was made by intelligent beings. Look! We know math! Yeah, we kinda expected that... The fact that it was artificial, and there, should be enough. A monolith with dimensions 1-2-3 or 1-2-4 would have been equally convincing.

[razark]

18 minutes ago, Spaceception said:

Hey, you're in the 1000 rep group

I hadn't even noticed.  Only 24 to go to a nice round number!

 

8 minutes ago, HebaruSan said:

But that's the narrator giving the characters' impression of what it was supposed to be.

I'd say it could be argued from the passage as quoted.  But it's been a long time since I read it, and I don't know the exact context of the passage (It could be from a less-than-perfect narrator, or it could be the word of the author, which makes it pure truth).

15 minutes ago, benzman said:

I am no mathematician, but I did hear once that 1 is not a prime and proving that it is not is quite a neat party trick - but only at certain parties!

Well, the Sieve of (Some old Greek guy that I can't remember but it begins with an "E") would show that if 1 is a prime number, it is the only prime number.

[Kerbart]

1 hour ago, benzman said:

I am no mathematician, but I did hear once that 1 is not a prime and proving that it is not is quite a neat party trick - but only at certain parties!

What I got from Wolfram is that it's pretty much open for discussion and that the simplest explanation (for 1 not being a prime) is basically “cuz we say so.” I get the impression that general concensus is that 1 is not defined a prime as it makes a couple of other definitions (that include phrases like "all primes") a lot simpler. 

[LN400]

1 was once concidered a prime and now, well, you can choose, apparently, whether to include 1 or not.

 

[p1t1o]

I have read about an interpretation of the Kubric movie that the 4:9 ratio is supposed to represent a movie screen...that is, if a movie is an audience looking through a "window", then the monolith is how that window appears in the observed universe. Or something. It was all very "arty" and convoluted. But an interesting viewpoint.

Even when they find the lunar monolith, the scene is depicted as a "film set" with bright lights illuminating the scene and many video cameras setup around the object.

Anyhoo, I found the interpretation, it is here:

http://2001.a-false-flag-odyssey.com/

 

Kinda explains the part that goes all trippy when the astronaut looks into the monolith/movie screen - back at us! OMG!

"The stargate journey is not just a mental one. Not only does Dave free himself from the figurative confines of the movie screen; there is a sense in which Dave quite literally flies out of the movie screen into the 3-dimensional space of the movie theater. If one were to imagine leaving a movie screen and flying toward the projector, one would see an intense display of colors emanating from a central source, similar in nature to the actual stargate journey."

Edited March 2, 2016 by p1t1o

[Nibb31]

6 minutes ago, p1t1o said:

I have read about an interpretation of the Kubric movie that the 4:9 ratio is supposed to represent a movie screen...that is, if a movie is an audience looking through a "window", then the monolith is how that window appears in the observed universe. Or something. It was all very "arty" and convoluted. But an interesting viewpoint.

Even when they find the lunar monolith, the scene is depicted as a "film set" with bright lights illuminating the scene and many video cameras setup around the object.

Anyhoo, I found the interpretation, it is here:

http://2001.a-false-flag-odyssey.com/

More like nonsensical ramblings from a conspiracy theorist.

[p1t1o]

Just now, Nibb31 said:

More like nonsensical ramblings from a conspiracy theorist.

Its not a conspiracy. Its an interpretation of the movie which includes a conspiracy within the story. Have you tried to interpret the latter portions of the movie? Its "art" so its arguable that no interpretation can be considered "nonsense".

But I dont want to get in a huge debate about it, not being all that arty myself, I just figured it was an interesting counterpoint to all this talk of prime numbers.

[Nibb31]

Just now, p1t1o said:

Its not a conspiracy. Its an interpretation of the movie which includes a conspiracy within the story. Have you tried to interpret the latter portions of the movie? Its "art" so its arguable that no interpretation can be considered "nonsense".

But I dont want to get in a huge debate about it, not being all that arty myself, I just figured it was an interesting counterpoint to all this talk of prime numbers.

The author clearly has an agenda of demonstrating that Kubrick was hiding messages in 2001 to alert the public about false flag operations run by NASA... In conspiracy circles, it is often claimed that Kubrik was hired by NASA to directed the Moon landing movies as a false flag operation. The explanation is not arty, it's just stupid.

[softweir]

19 hours ago, razark said:

With the sequence 1 4 9, you can't really say it's the squares of primes.  It could simply be the squares of integers.  You'd need to know if the next element of the sequence is 16 or 25.

Thanks for that correction! I've amended my post to say "integers".

[p1t1o]

17 minutes ago, Nibb31 said:

The author clearly has an agenda of demonstrating that Kubrick was hiding messages in 2001 to alert the public about false flag operations run by NASA... In conspiracy circles, it is often claimed that Kubrik was hired by NASA to directed the Moon landing movies as a false flag operation. The explanation is not arty, it's just stupid.

On the contrary for me, it helps explain why the Kubrick/moon hoax connection is popular, but I don't think that that is necessarily what the interpretation itself concludes, esp.given that the film was released over a year before the first landings. Anyhoo, each to their own.

 

[softweir]

20 hours ago, peadar1987 said:

Yep, and you can't count in base pi. It just doesn't work.

1 is pi^0

10 is pi^1

100 is pi^2

What is 3? What is 9? If your base isn't an integer, numbers that aren't 1, 10, 100, 1000 etc don't make any sense. If you divide the interval up into chunks, you're no longer working in base pi, you're just giving another name to an integer base system.

Very true! To go further - in order to use base pi one has to be able to count the number of digits, simply because to know the value of a digit, one has to know its position. The only way round that would be to use entirely separate characters for each different power of pi.

Trying to get this back to the OP: the question was about Arthur C. Clarke's intention in choosing those numbers, and whether there was any deeper meaning to it. There wasn't. He chose a sequence of numbers numbers that would be recognisable to a reasonably well educated but not specialised audience, so irrational numbers were out, and "counting in pi" so far out as to be in an as yet unexplored dimension of literature!

[Bill Phil]

8 hours ago, LN400 said:

1 was once concidered a prime and now, well, you can choose, apparently, whether to include 1 or not.

 

According to the definition it isn't, but only because it states any number but 1.

[andrewas]

1 hour ago, softweir said:

Very true! To go further - in order to use base pi one has to be able to count the number of digits, simply because to know the value of a digit, one has to know its position. The only way round that would be to use entirely separate characters for each different power of pi.

You know where the 1's column is, the value of every other position follows from that, just as it does in base 10 or any other base. The only difference is that you don't have unique representations of numbers. 4 is 10.22... by the most intuitive method  , but you could start it 10.13..  carry it out to enough pinary places and it'll evaluate to 4 near enough.

 

[Bill Phil]

For base pi, 2 could be a certain power of pi..... Might not help at though.

[Kerbart]

20 minutes ago, Bill Phil said:

For base pi, 2 could be a certain power of pi..... Might not help at though.

Aside from the incredible difficulties base-pi would impose on day-to-day arithmetic, as a "universal" base it would fail as pi is not a very universal number. I think that e is a more logical choice in that case, as there's only one e. “But Kerbart,” you protest, “surely there’s only one pi either?”

Well, not exactly. Pi is defined as the ratio between the diameter of a circle and it's circumference. But that in itself is open for discussion? Why not define it as the ration between the radius (which is how mathematically a circle is defined in the first place) and the circumference? Proponents of tau instead of pi (one tau equals two pi) do just that. With e, such a discussion is impossible. But if we ever encounter aliens from outer space (bug-eyes, green, et al) the most likely way to exchange numbers would seem to be binary.

[Bill Phil]

1 hour ago, Kerbart said:

Aside from the incredible difficulties base-pi would impose on day-to-day arithmetic, as a "universal" base it would fail as pi is not a very universal number. I think that e is a more logical choice in that case, as there's only one e. “But Kerbart,” you protest, “surely there’s only one pi either?”

Well, not exactly. Pi is defined as the ratio between the diameter of a circle and it's circumference. But that in itself is open for discussion? Why not define it as the ration between the radius (which is how mathematically a circle is defined in the first place) and the circumference? Proponents of tau instead of pi (one tau equals two pi) do just that. With e, such a discussion is impossible. But if we ever encounter aliens from outer space (bug-eyes, green, et al) the most likely way to exchange numbers would seem to be binary.

There is one pi. If tau is equal to 2pi, then it is not equal to pi.

How it's defined may not be the best, but the saje could be said for almost anything. Main sequence stars are dwarf stars, asteroids aren't star like, white dwarves aren't the same as white main sequence stars, which are defined as dwarves, etc. We're just stuck with it.

[lajoswinkler]

On 3/1/2016 at 2:12 PM, Spaceception said:

Well, it is a book written in the 60s.

No difference. Mechanical and structural engineering hundred years ago and today - same things. Same basic principles.

[Kerbart]

7 minutes ago, Bill Phil said:

There is one pi. If tau is equal to 2pi, then it is not equal to pi.

How it's defined may not be the best, but the saje could be said for almost anything. Main sequence stars are dwarf stars, asteroids aren't star like, white dwarves aren't the same as white main sequence stars, which are defined as dwarves, etc. We're just stuck with it.

But the value that is approximately 3.14 would not be a universally chosen one. Unlike e. 

[Bill Phil]

31 minutes ago, Kerbart said:

But the value that is approximately 3.14 would not be a universally chosen one. Unlike e. 

e is strange. It's like an anomaly, showing up in weird places, like the Golden Ratio. 

And 3.14/pi may not be universal, yes, but neither would tau.

[softweir]

Pi is universal in any time-space which is sufficiently flat enough that circles can exist. Some races may use tau instead of pi, but if they do use pi and calculate it then they will get the same answer we do. And if they use tau and calculate it they will get twice the value we use for pi.

Incidentally, tau is a better value than pi. And as for comparison with e, tau turns up in all sorts of weird places you wouldn't expect it either.

[Bill Phil]

2 hours ago, softweir said:

Pi is universal in any time-space which is sufficiently flat enough that circles can exist. Some races may use tau instead of pi, but if they do use pi and calculate it then they will get the same answer we do. And if they use tau and calculate it they will get twice the value we use for pi.

Incidentally, tau is a better value than pi. And as for comparison with e, tau turns up in all sorts of weird places you wouldn't expect it either.

Tau is the ratio of the Circumference divided by the radius, right? If tau shows up in weird spots, so does pi, since they're inherently multiples of each other.

[Kerbart]

3 minutes ago, Bill Phil said:

Tau is the ratio of the Circumference divided by the radius, right? If tau shows up in weird spots, so does pi, since they're inherently multiples of each other.

Nooo, that's not it. I was under the impression that there was a search for an "universal base". Aside from the insanity of picking a ordinal system based on irrational numbers, pi would not be a good choice because there are multiple choices based on circle geometry; pi and tau; so it wouldn't be immediately evident which one was chosen. 

But e doesn't leave such choices. There's no way you can come up with a similar number that has the same properties (unlike the pi/tau couple).

I didn't like the rest of the book, but the first part of The Cassiopeia Affair was wonderful in how it was shown how an alien civilization would communicate a message in such a way that the receivers would not have a tremendous hard time deciphering it.

[Bill Phil]

28 minutes ago, Kerbart said:

Nooo, that's not it. I was under the impression that there was a search for an "universal base". Aside from the insanity of picking a ordinal system based on irrational numbers, pi would not be a good choice because there are multiple choices based on circle geometry; pi and tau; so it wouldn't be immediately evident which one was chosen. 

But e doesn't leave such choices. There's no way you can come up with a similar number that has the same properties (unlike the pi/tau couple).

I didn't like the rest of the book, but the first part of The Cassiopeia Affair was wonderful in how it was shown how an alien civilization would communicate a message in such a way that the receivers would not have a tremendous hard time deciphering it.

But the problems that occur in base tau and base pi are present in base e, too.