Originally posted by: EricMartello
Originally posted by: sao123
It is neither paradoxal nor incorrect. Set theory would indicate that your thinking is incorrect. Research the difference between the "small" infinite set called Aleph 0, and the "large" infinite set Aleph 1.
http://mathworld.wolfram.com/CountablyInfinite.html
Both sets are infinite in size, yet one is clearly larger than the other.
Citing another theory and claiming it invalidates another is pretty much bunk. A theory is essentially a guess, and while one may have a higher probability of being "correct", in this case, it really doesn't sway things one way or another.
Here's what I understand you to be saying:
Between 0 and 1 there is an infinite number of fractional numbers.
Between 0 and infinity are also an infinite number of numbers.
0 to infinity, including fractional numbers between the integers is also infinite.
Once you create a SET, you impose limits. You are grouping all numbers, including decimals, between 0 and 1...0 and 1 are the boundaries there...while the potential values WITHIN the set are infinite, there are clearly defined start and endpoint values, which limit the numerical value of the set to <= 1 and >= 0.
The second two sets imply an infinite ray, with 0 as the starting point...this works fine conceptually, and can be used in certain calculations, but has no basis in this discussion...because the starting point is essentially a limit, and true "infinity" has no starting point. There is a difference between infinite precision, and infinity as a numerical concept...just try calculating anything to infinite precision and you'll see what I mean when I say that math isn't really the answer to "everything".
Did you see the questions I asked in a previous post? Try to answer them. Apply any math or accepted theories you want...or even *gasp* some imagination. I'm really interested to see what other people come up with...so far, only StopSign stepped up to the plate.
I purposefully ignored them because they are nonsencial questions without merit or purpose to the question of infinity.
however...
Your theory is flawed and without meaning...
the measurement of time, space, or any property is incapable of being performed if the measuring entity does not have 2 things... a sensory perception capable of quantifying the item to be measured, and a standard to compare it to.
Your infinite number line concept does not conform to the above statement. Zero has been *arbitrarily chosen* as the standard, it could have been any other value, but whatever that value might have been, once a standard has been set, you can measure the distance from that point. I can give you a finite piece of string and a ruler marked 1, 2, 3, 4, 5 and you can measure the string. The string is 4. 4 what? inches? centimeters? seconds? hogaboos? Removing the *arbitrary standard* of the 0 reference point is what makes the numberline meaningless, not the fact that it is infinitely long.
Your time concept exibits the same behavior, there is a point called the present, by which all things can be arbitrarily measured as being past or future, and a quantified means to describe it with.
Infinite scaling - the universe as we know it and measure it have at its very substance & canvas, basic units which are "discrete units", it is not continuous as you would believe. Eventually you will find the smallest particle, even the smallest unit of space, which there is no emptyness between them. Call them packets, pixels, whatever, the canvas of 3 dimentional existence is in discrete units.
To the point of infinite largness, I will defer that answer to laterness because it will be included with one of my other answers.
the videogame analogy is nonsensical. *as a programmer* a video game is a non concious entity which can do nothing more than its defined propertys allow it to. Time will not pass for a videogame, unless it is given a semiphore equivolent, and a reference point to measure it against. This would be no differenct than asking a 2 dimentional drawing how deep are you? **of course the drawing will look at you nonsensically and say, what the hell is deep?**
ah but to your questions:
- It is probable that our Universe has physical bounds that limit its size. What might be BEYOND those bounds?
As in the above example (of the 2 dimentional drawing), in order to exceed the defined limits of 3 dimentional space, one must define a 4th spacial dimention. No matter what you call it, this is the only way to go outside of the defined 3 dimentional existance.
Assuming it is possible at all, Everything which is exclusively in our universe exists with at least 1 or more of the following:
1)A 4th or higher spacial dimention value of 0.
2)The lack of a perception for quantifying the 4th or higher spacial dimention.
3)The lack of a reference in the 4th or higher spacial dimention.
- Is it possible for there to be absolute nothingness, not even space? What would we call that state?
0 Dimentional non-existance, or
4th or higher spacial dimentional existance with at least 1 of the following:
1)zero values for the LWH spacial dimentions
2)The lack of a perception for quantifying the LWH spacial dimentions.
3)The lack of a reference in the LWH spacial dimentions.
- Doesn't infinite scaling make more sense if you consider our universe a point on an infinite number line, rather than a container for that number line?
The universe is the defined boundaries for the existance of LWH dimentional space. Nothing can exist 3 dimentionally without being inside of the LWH defined universe.
Both views of the universe make sense, but neither applies to infinite scaling.
I return to my roots...
If I have a point, which is defined as a singular discrete unit..
Then compare it to an infinite number line which has infinite points. I can see infinity.
Now compare it to an infinite 2 dimentional plane. I now have infinite number lines of infinite points. This is still clearly more points than the first.
now compare it to an infinite 3 dimentional space. I now have still infinitely more points than I had before.
While infinity is a concept and not a number, it still clearly has both a quantifiable perception, and a reference, therefore it is measureable and comparable. As long as you have those 2 properties, meaning has been established.