10 Oct 06
Originally posted by ColettiBrings a whole new meaning to the Dave Matthew's Band song, "The Space Between," doesn't it?
There are indeed.
http://mathworld.wolfram.com/ZenosParadoxes.html
http://en.wikipedia.org/wiki/Zeno's_paradoxes
But I think the phrase "Zeno's Paradox" usually refers to the race between Achilles and the tortoise. Most of them involve the same principle.
[quote] Rather, this much simpler paradox simply states that: "for Achilles to capture the ...[text shortened]... n not logically get to the end of an endless series of points, much less get past them.
10 Oct 06
Originally posted by ColettiATY though has offered a potential solution. These points have zero measure.
There are indeed.
http://mathworld.wolfram.com/ZenosParadoxes.html
http://en.wikipedia.org/wiki/Zeno's_paradoxes
But I think the phrase "Zeno's Paradox" usually refers to the race between Achilles and the tortoise. Most of them involve the same principle.
[quote] Rather, this much simpler paradox simply states that: "for Achilles to capture the ...[text shortened]... n not logically get to the end of an endless series of points, much less get past them.
As for knowledge, what's problematic about the statement "Each and every thing which can be known is known by God"?
10 Oct 06
Originally posted by ColettiRead my post. That is false.
The paradox, how is it possible to get past an infinity series of points if infinity by definition means "endless". One can not logically get to the end of an endless series of points, much less get past them.
If time is continuous, then space and time are infinitely divisible (hence the calculus solution is correct), if time is not continuous then there is no paradox.
10 Oct 06
Originally posted by twhiteheadKnowledge is a tricky topic, but here are my 8 points -
Please eplain which paradox you are talking about.
[b]Or - is infinity real?
No, infinity is not real, it is a concept.(And yes the real numbers are infinitate)
Are the set of natural numbers infinite?
Yes the set of natural numbers is infinite. This follows from the definition of infinity and the definition of natural numbers[/b]
...[text shortened]... ng. Merely knowing every natural number would suffice without having to know every real number.[/b]
1) First of all, we throw around the word knowledge, but what is knowledge? What does it mean to know something? Often it seems, for example, in a game of trivia, the contestant will stereotypically say "Oh! I know this one! Hmmm..." Yet they can't think of it. Even if we know something, can we term it as knowledge if we can't think of it at all times?
2) We need to also distinct between knowledge and instinct. In response to a reflex, one may ask, "How did you know to do that?" In defense, the other may say, "Well, I dunno, I just did it."....Just something to think about. It could also be that people use the word know and/or knowledge incorrectly.
3) In response to the question is knowledge countable, I find some problems with the term posed - countable. First of all, in order to come to a conclusion of whether knowledge is infinite, it needs to be compared to some standard to define it as infinite. I guess what I am trying to bring up, is what is infinite? When does something become infinite? Therefore it really is all in what you compare it too because simply "counting" it but not comparing seems useless.....countable just seems like a vague word. Does 1 fact = 1 point of knowledge? I think its hard to put "knowledge" in a box.
4) To answer my question of what is infinite, if I remember correctly from my AP Calculus class last year in high school, it is definite that there are different infinities. When solving a certain equation, such as the limit of (?), we have the symbol infinity at the start of the problem. Then reducing, simplifying, and converting, we may have a number left over, such as 3 that we just add to the symbol infinity creating a new infinity. The same applies in subtraction, division, and multiplication is I am not mistaken. I didn't do superbly in that class, but if this doesn't make sense I will call up my genuis friend, Jon, a math wizard.
5) So in comparing infinites rather than just counting them (because I feel it is impossible to do so), it seems as if something can be more infinite than something else. Such as in that problem where we start with infinity and end up with infinity plus 3.....just something to think about. It could be that although it appears something to be more infinite it is in fact not.
6) Even in the above examples and points, I find myself still being unsatisfied by those certain explanations. Furthermore, there is something that I think we can't extend to in this realm on infinity. We as humans are finite beings. Therefore it can be postulated that we have finite brains, ere go finite knowlege. The brain is a mystery to say the least. I have heard that scientists have discovered that the average human being uses only about 1% of their mental capability. The flaw with their reasoning, is that in order to know what 1% is, you have to know what 100% is in order to compare and term. So I'm not sure if we'll ever figure it out.
7) I failed to explain what I meant by "we can't extend to in this realm on infinity." With us being finite beings and God being a infinite being (or at least it is believed to be so by Christians) that is a bridge that we can't cross with logic. We can't even truly compare the finite with the infinite, and I find taht comparison is truly the only way to understand things and concepts. Most things are defined by their opposites. For example, we don't fully understand the hero aka his characteristics if there isnt a foil character to distinguish him. He isn't appreciated or understood as much if there isn't something to be compared to. Another example is that there would be no smooth without rough, and so on. Basically, heres my point for number 7, we can't even compare.
8) Perhaps this is the answer from the Christian perspective. As God is infinite, absolute, sovereign, immutable, and unchangable, as He is to be believed (although I have contention with a few of those believed qualities), it could be that whatever knowledge God bears is the standard for the infinite. The same logic is justified when Christians say that whatever God does is morally correct, right, and just because He is the standard of morals.
Anyways, this has been a long post, but I hope this adds to the conversation through my 8 different points on the topic. If any of them have not been clear, I will be happy to reexplain and redefine if necessary. Otherwise, I will leave this to be discussed among my fellow reader.
Thank you for your time in reading my post. God bless.
11 Oct 06
Originally posted by DoctorScribblesChristina logic in itself is binding. if you suddenly state that no religion or sect. but your own is true you have inadvertantley cut off unlimited logic. To denie is to be foolsish. When a man looks at a book and reads but does not understand only the words are imprinted upon his mind ,but not their menaing. Even if said man did come to understand he still cannot apply said logic to something that goes against his beliefs as it would be illogical in his frame of mind.
He will remain within the realm of Christian Logic, which knows no boundaries.
11 Oct 06
Now as to the good mans question, yes knowledge is infinite. Though from diffrent point of views knowledge can be finite. As to god yes his knowledge is finite. Due to the infinite chance equals infinite matter and that all things are made of something god !CANNOT! have infinite knowledge. He himself holds a point of view therefore onl a small amount is alloted to him no matter how much you may think he has. The only viewpoint that could ever have all knowledge is sentient energy as it makes up all things therfore all view points.
11 Oct 06
1 edit
Originally posted by Dracos ChikouYou've illustrated the good doctor's point very well. Thank you.
Christina logic in itself is binding. if you suddenly state that no religion or sect. but your own is true you have inadvertantley cut off unlimited logic. To denie is to be foolsish. When a man looks at a book and reads but does not understand only the words are imprinted upon his mind ,but not their menaing. Even if said man did come to understand he ...[text shortened]... logic to something that goes against his beliefs as it would be illogical in his frame of mind.
11 Oct 06
i would like to say that something like knowledge, cannot be infinite (i believe)
it can be total, complete, or whole. GOd can know everything, but there is not an infinite amount of things for him to know, therefore he does not know an infinite amount of things, he knows everything, but that number has (albeit large) a cap
12 Oct 06
Originally posted by mazziewagDoes God know every digit in the number pi?
i would like to say that something like knowledge, cannot be infinite (i believe)
it can be total, complete, or whole. GOd can know everything, but there is not an infinite amount of things for him to know, therefore he does not know an infinite amount of things, he knows everything, but that number has (albeit large) a cap
12 Oct 06
Originally posted by PalynkaThe rational numbers are independant of both time and space. They are also infinite. So knowledge of all rational numbers implies infinite knowlege.
If time was discrete, would Pi be infinitely long?
Would discretion in time mean that there is a logical limit to the division of space?
Freakys 'he created it therefore he knows' it arguement is however just assumption not logical deduction. First of all, 'creation' in terms of some hypothetical being external to the universe creating the universe has no known parrallel within the universe so unless it is fully explained somewhere (in the Bible?) we really have no way of understanding how it worked. Certainly what we term 'creation' within the universe which is normally just 'rearrangement of atoms' or more often imagining and development of a concept, does not in any way imply full knowlege of the resultant creation.
for example the 'creator' of chess could not possibly know all the possible games.
12 Oct 06
Originally posted by twhiteheadI'm just thinking out loud here, and probably wrong, since I've almost no knowledge of physics and my mathematical knowledge is mostly in the realm of statistics.
The rational numbers are independant of both time and space. They are also infinite. So knowledge of all rational numbers implies infinite knowlege.
Freakys 'he created it therefore he knows' it arguement is however just assumption not logical deduction. First of all, 'creation' in terms of some hypothetical being external to the universe creating the un ...[text shortened]... n.
for example the 'creator' of chess could not possibly know all the possible games.
Anyway.
The constructs of mathematics are obviously independant to applications to the real world but Pi is derived from a geometric result, so it's not a merely abstract construct like the rational numbers.
Time being discrete would imply a real lower bound on movement and therefore distance. Space would not be infinitely divisible, so neither a surface or a distance could be described by an infinitely long number. Pi being irrational means that in every circle, either the surface is an irrational number or its radius is.
If space is not infinitely divisible, then I don't see how it's possible for a surface or a length to be irrational.
12 Oct 06
Originally posted by PalynkaMostly right here. Yes space cannot be infinite but it depends on what you are applying infinite too. If you are applying it to a single universe then yes you are correct, but if its being applyed to all exisitence it is quite a reasonbale and true number.
I'm just thinking out loud here, and probably wrong, since I've almost no knowledge of physics and my mathematical knowledge is mostly in the realm of statistics.
Anyway.
The constructs of mathematics are obviously independant to applications to the real world but Pi is derived from a geometric result, so it's not a merely abstract construct like the r ...[text shortened]... y divisible, then I don't see how it's possible for a surface or a length to be irrational.
19 Oct 06
Originally posted by PalynkaI think there is something in what you say. But we may be begging the question when we say that time and space are continuous. But still, this may be the correct answer. One might even ask, if there is anything that is truly finite. (I'm really pushing my limits here.)
Read my post. That is false.
If time is continuous, then space and time are infinitely divisible (hence the calculus solution is correct), if time is not continuous then there is no paradox.
Question: has anyone proven that the value of Pi is an infinite number? We know that it is the ratio of the circumference to the radius. But is the value of the number both infinite (there is no end to it) and finite (we can take the circumference of a circle with a fixed radius, and make it a unit of measure).
It seems we can know exactly ether the radius or the circumference of a circle, but not both at the same time.