All the Universe on a stick

[wrayal]

There are many simple quines (just about anyting in html as long as you don't use tags ;) For a long list look at http://www.mines.edu/students/b/bolmstea/quines/
But of course, there are many problems inherent in the original question in this topic. Eg Non-discrete data.

[HiddenWarrior]

So far many posts here! I'm glad! You can read about this puzzle in Haruki Murakami book named something like 'Wonderland with no stops and the end of days' (maybe 'Wonderland with no stops and the appocalipsis')

P.S.: And what about word 'yxine'?

[Fusion_power]

I have to disagree with the concept of the universe being represented as "1".

Its like file compression on a computer. The file is only validly compressed when it can be properly uncompressed to reveal the original data. You can't uncompress "1" to reveal the entire universe in all its complexity.

Fusion

[ColdFury]

No, not using digital storage.

However, there's an infinite amount of storage available with analog. Theoretically you could encode all of the world's knowledge as the angle between two objects.

[FeLiNe]

You keep running into the same quantization problems again and again. You cannot define what the term "angle between tow objects" means better than you can define the location of the objects. And that peters out at the level of quantization of matter. Where is the surface of an object if you are looking with a precision that is millionfold smaller than the diameter of a proton? What does "surface" or "location" even mean in this context?

All these naive constructs (angles as much as lengths) may seem obvious when examined from a macroscopic perspective, but are extremely hard to grapple with when you're trying to be really exact about them -- which you will have to be if you want to encode large amount of information in a quantity.

The universe is quantized. That's what everybody has always found who was willing to perform an observation on the universe. There's a large number of "continuous" or "analog" concepts that help us describe the universe when we deal with large qantities of quanta, but they're only approximations and they all seem to break down when you actually examine them closely.

[HiddenWarrior]

Diapozone [0..1] has unlimited number of 'points' as you now from mathematics. The Universe's info is also unlimited. So it value can be placed somewhere on [0..1].

[FeLiNe]

Originally Posted by HiddenWarrior

Diapozone [0..1] has unlimited number of 'points' as you now from mathematics. The Universe's info is also unlimited. So it value can be placed somewhere on [0..1].

Oy, vey ...

"Diapozone" is not an English word. I guess from context that it means "interval" in some language other than English.

The interval [0..1] is a human invention - it does not exist anywhere outside a human mind and it does not exist as anything other than an abstraction. It is not real. It doesn't matter what you can or cannot do with the interval [0..1] as you could not do it anywhere outside your head - not even theoretically. This is not a limitation of technology, it is a limit that physics itself imposes on you.

The claim that the information content of the universe is unlimited is just that: a claim. If you want to build an argument on it, you'll have to show this claim to be true in some fashion. I'd like to note that nobody has (as of yet) seen (heard, measured, tasted, tested, interacted with, found any kind of evidence for) anything "infinite" outside of what people make up.

If the total information content of the universe were found to be "unlimited" (as you write) it would by no means prove that this could be fit into the interval [0..1]. There are different "sizes" of infinities, and they do not all map to each other. There are infinitely many integers, for example, but you cannot represent all real numbers with integers -- there are more real numbers than integers. The cardinality of the one set is larger than the other, even though the naive term people use for both is "infinite". (look up "cantor diagonal" for this one).

[I have a "shrugging smilie", but can't find a way to include pictures here...]

[cheesehead]

Originally Posted by HiddenWarrior

Diapozone [0..1] has unlimited number of 'points' as you now from mathematics.

Well, the cardinality of the number of points in the continuous real interval [0..1] is one of the infinities, and it is no larger than aleph-one. I don't know if the question of whether it is equal to aleph-one has been answered, but it's definitely less than aleph-two.

The Universe's info is also unlimited.

The cardinality of the number of possible states of the universe is also one of the infinities. I think that for a quantized universe, this cardinality is no greater than the cardinality of the number of points in the continuous real interval [0..1].

But if we consider the universe to be continuous rather than quantized, the cardinality of its number of possible states might be greater than aleph-one. I don't know if it is.

So it value can be placed somewhere on [0..1].

If the universe is quantized and the interval is continuous, then yes, it can. But the continuous real interval [0..1] is not the same as a unit interval of real points in a quantized universe, so I think you run into trouble if you try to make a 1-to-1 mapping from the quantized universe to the quantized interval.

[Maybeso]

The answer is no, it can't be done.

You see, to celibrate the millenium, I tried to write the history of the universe on a stick. It took me two years to record everything up to December 31st, 2000, (I'm a very fast writer, and my research team is the best). When I started on the next year, I had to include my work on the stick, which was recording half the history of the universe - of course the research had been done, but I had to record that too...

I gave up when I realized that if I wrote everything through the end of 2003, my stick would have three* copies of history on it, with three more to go...

And now, if anyone else tried to do it...

*Yes, it's three copies, because of my progress through the end of the year.

[patdumpsite]

Originally Posted by cheesehead

Well, the cardinality of the number of points in the continuous real interval [0..1] is one of the infinities, and it is no larger than aleph-one. I don't know if the question of whether it is equal to aleph-one has been answered, but it's definitely less than aleph-two.

Just to nitpick here: The question you're asking is the Continuum Hypothesis. The continuum (i.e. the real line, which has the same cardinality as the interval [0,1]) is at least aleph-one.

Godel (1935ish) showed that CH is consistent with the other axioms of set theory and Cohen (1965ish) showed that the negation of CH is consistent with the other Axioms of set theory. Thus the question you are asking can not be determined and depends on your model of set theory. There are models where the cardinality of the continuum is not even an Aleph! There are other models where this cardinality is aleph-one or aleph-two.

Most mathematicians simply accept the continuum hypothesis and (rather arbitrarily) give it the value aleph-one. However, most logicians that do work in this area, disagree and feel that the continuum has a much higher cardinality than aleph-one.

In short, there is no right answer as to the cardinality of the continuum based on the axioms set theory and mathematics we have now. This does not mean that some day, someone won't come along and reaxiomatize mathematics and settle the issue, but as it stands, there is no answer.

I stand by my earlier comment that the only way we could compile a list of all knowledge forces our list to be countable, but there exists uncountable information to gather and as such it cannot be listed.

[cheesehead]

Originally Posted by patdumpsite

the same cardinality as the interval [0,1]) is at least aleph-one.

Thanks for the correction. I misremembered (from 1966) the subscripts by 1. I really ought not to comment on infinite cardinalities from memory ... sorry.