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Is Math flawed? Are we?


Arcesious

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TLDR, but just wanted to say that math is just a toolsuite we use for working with numbers and that there are places where it can and will break down.

 

Math is the science of numbers and its laws are probably the most important discoveries of mankind. And when there's something that can't be described using math it only means "not yet".

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ah, but that is where you are wrong. i thought about that statement for a while. time. time my friend simply does not end

 

If time ends or not... First rule in Philosophical debate... Check your definitions;

 

1. Having no boundaries or limits.

2. Immeasurably great or large; boundless: infinite patience; a discovery of infinite importance.

3. Mathematics

  • a. Existing beyond or being greater than any arbitrarily large value.
  • b. Unlimited in spatial extent: a line of infinite length.
  • c. Of or relating to a set capable of being put into one-to-one correspondence with a proper subset of itself.

 

So your wrong, further more your point is rendered academic unless you can tell me how you know time doesn't end? Regardless the fact that time has a start disqualifies it as an infinite. Even if time doesn't have an end it doesn't qualify under a definition of infinite; Seeing as having a beginning necessitates a boundary and limit so time, therefore is not an infinite. It is also questionable if it is actually possible to be bigger than a arbitrary figure; so an "infinites" own properties would seem to render it impossible.

 

(i messed up my quote in that last post. could a moderater please delete that?)

 

Fixed

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If time ends or not... First rule in Philosophical debate... Check your definitions;

 

 

 

So your wrong, further more your point is rendered academic unless you can tell me how you know time doesn't end? Regardless the fact that time has a start disqualifies it as an infinite. Even if time doesn't have an end it doesn't qualify under a definition of infinite; Seeing as having a beginning necessitates a boundary and limit so time, therefore is not an infinite. It is also questionable if it is actually possible to be bigger than a arbitrary figure; so an "infinites" own properties would seem to render it impossible.

 

 

 

Fixed

 

thank you!

 

but time will not end. even if the world ends time will still be here even if we are not here to record it. the topic is debatable but it will never be proven. so wether we are wrong or right isn't for us to know. but i believe time will never end

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thank you!

 

but time will not end. even if the world ends time will still be here even if we are not here to record it. the topic is debatable but it will never be proven. so wether we are wrong or right isn't for us to know. but i believe time will never end

 

your point is rendered academic unless you can tell me how you know time doesn't end?

 

When in discussion and debate it is useful for the other person to give reasons why you think what you do. In this instance you haven't given me any reasons to back up what you think. Lets imagine Sherlock Holmes points his finger at Moriatti and says he's the murderer - great, he may well be, but without evidence a) No one will believe Sherlock Holmes assertion and b) That wouldn't either cause anyone to change their mind or get you anywhere in a court of law.

 

Key thing here, you said you believe but what are you reasons - you haven't given me any reason why you believe what you do. Indeed I would say this; There is not enough empirical data at this time to say if time is going to end or not; for all you know the Universe could collapse back in on itself and time comes to an end; on the other hand perhaps it will just keep expanding and expanding, and getting colder and colder...

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Proof:

there is no official proof, but even if EVERYTHING in existance is gone, there is still an empty space. and in this space (i really don't think you can kill emptyness) the clock might still be ticking. so really there is no proof for OR against my theory. so this really ISN'T debatable. only arguable. so if there is no life to count time, that dosn't mean time dosn't exist. this really is a confusing topic. my head hurts now :xp: i say we drop this hole time thing and stay on topic :thmbup1:

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Proof:

there is no official proof, but even if EVERYTHING in existance is gone, there is still an empty space. and in this space (i really don't think you can kill emptyness) the clock might still be ticking. so really there is no proof for OR against my theory. so this really ISN'T debatable. only arguable. so if there is no life to count time, that dosn't mean time dosn't exist. this really is a confusing topic. my head hurts now :xp: i say we drop this hole time thing and stay on topic :thmbup1:

 

This isn't a debate, the fact of the matter here is your still young (and won't have done any Astro-physics or Philosophy yet) - and may well struggle to get your head round this; before the big bang there was nothing, time itself did not exsist prior to the big bang, as such given that "there was a period before time" (that in itself is a miss leading statement, as there was no period before time) - it stands to reason that in the "future" time could cease to exsist (again a misleading statement as without time the future doesn't exsist). All this is unquantifiable, so my position is you can't know if time will end or not, I would suggest that should be your position too. However I leave you to think that over ;)

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i've come across this topic many times... i believe that time did not cease to exist. there were just no records of time. in the big bang theory (wich i personally don't believe) it still took time to happen. time could be considered... nothing... and if nothing existed then then the nothingness of time did as well :xp:

 

Doesn't matter if you believe in the Big Bang or not and I'm pretty sure age 13 you haven't actually revied the evidence; all scientific evidence points to it being true. However, if your going to take a YEC line the Bible still supports the assertion that there was a "period" before time;

 

1:1 In the beginning God created the heavens and the earth.

 

The statement "the beginning" means there was nothing before it except God, if there is anything that is "infinite" it would be God and not time.

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Doesn't matter if you believe in the Big Bang or not and I'm pretty sure age 13 you haven't actually revied the evidence; all scientific evidence points to it being true. However, if your going to take a YEC line the Bible still supports the assertion that there was a "period" before time;

 

 

 

The statement "the beginning" means there was nothing before it except God, if there is anything that is "infinite" it would be God and not time.

 

true... :argh: how could i forget that?!?!

but that refers to a time before OUR world (although there is NO time for god)

i still believe there was time. just not in our non-existant galaxy

(and yes i believe in aliens :xp:)

 

I'm pretty sure age...

my friends know me for getting to interested in these for my age :xp:

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I see we've somehow moved to discussing time. Anyhow, since it all started with a reply to this one (especially the bolded part):

 

Infinity is entirely theoretical, even space is not infinite (at least if you accept the Friedmann Lemaitre Big Bang Model). There are no known infinites in the entire universe, indeed I think it is philosophically proovable that the idea of infinity is de fact absurd.

 

and since this thread was originally about math, I'd just like to jump in with this: Numbers. We can't count them. We have no idea which number is the smallest, which is the largest, or if they even exist. So, according to the definition of infinity you provided, it seems numbers are infinite. Right? :)

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What about Zeno's theory (theorem?)--y'know it is theoretically possible to keep dividing by half and still never quite reach zero. Just a whatsit I thought I'd toss in.

 

 

 

Ehh, in terms of infintiy...We're bordering on dimensionality and planes. I'll just interject (correct me if I'm wrong as my math is a tad rusty) a couple basic concepts.

 

It is possible to have a start that goes in one direction indefinitely. (I joke about it being "half of infinity or some fraction thereof" :xp:) This does start at some definite point. There is/was nothing before it. A start could also be an end for which there is/was nothing after it. Whatever it is (like a number line at the simplest) it does not continue any farther in that direction. In the other direction it may go indefinitely.

 

Where you have infinite extension in both direciton, you have no start but rather an origin. For example a number line which extends in both directions indefinitely that have zero at its center, zero is its origin.

 

So far as time is concerned...we have only so much recorded. We don't really know if or when it began. Or if it will come to an end in its essence of what it is. We may die off and be unable to record it. But none of us know how far back or forth time goes.

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I see we've somehow moved to discussing time. Anyhow, since it all started with a reply to this one (especially the bolded part):

 

and since this thread was originally about math, I'd just like to jump in with this: Numbers. We can't count them. We have no idea which number is the smallest, which is the largest, or if they even exist. So, according to the definition of infinity you provided, it seems numbers are infinite. Right? :)

 

Do numbers actually exsist? They are of course just a counting device, so is there anything that would be an infinite to count. I would argue if you accept the Friedmann Lemaître Big Bang Model then I would argue an actual infinite does not exist, so in relation to numbers they would never be required to count an infinite. I'm unaware how familiar you are with this subject so a wiki will suffice for now; Actual Infinity? Obviously I come from the no infinites crowd ;)

 

Aren't black holes supposedly an example of infinity?

 

How so? They are just lots of dense matter from collapsed stars, though they do cause a few interesting questions, like Hawkings disapearing/reapearing particles...

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Do numbers actually exsist?

We use them, so I'd say they exist.

 

They are of course just a counting device, so is there anything that would be an infinite to count.

I guess I see your point. We don't know, or rather as far as we know there isn't an infinite amount of anything, but there's a possibility that we're wrong.

 

I'm unaware how familiar you are with this subject so a wiki will suffice for now; Actual Infinity? Obviously I come from the no infinites crowd ;)

Admittedly, I'm not that familiar with it. I'll have to do some reading before I delve deeper into this.

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We use them, so I'd say they exist.

 

Well, in a physical sense do numbers exsist? They are creation of the human mind to explain and predict our environment. So do they exsist anywhere but in the human mind? This is an age old philisophical question, that doesn't neccasarily have an answer.

 

I guess I see your point. We don't know, or rather as far as we know there isn't an infinite amount of anything, but there's a possibility that we're wrong.

 

There is a possibility, though I would say it exsists as only a hypothetical concept, and that all the evidence we currently have would have lead to the conclusion that there are no "actual infinites".

 

Admittedly, I'm not that familiar with it. I'll have to do some reading before I delve deeper into this.

 

Do its an interesting area :) Related links to this area; Hilberts Hotel - As recorded in that Wiki, Hilberts Hotel is used as an argument against an actual infinite. (I do also agree with Dr Craig's assessment of it, I have had a few conversations with him on the subject, and am sure he is correct :))

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Do its an interesting area :) Related links to this area; Hilberts Hotel - As recorded in that Wiki, Hilberts Hotel is used as an argument against an actual infinite. (I do also agree with Dr Craig's assessment of it, I have had a few conversations with him on the subject, and am sure he is correct :))

 

That was confusing to read... I still don't seem to understand what the paradox means... I kind of understand, but still don't quite get it completely. Could you explain in layman's terms what the paradox means? Also, could you explain why and how Dr. Craig says and knows that time must have 'started' at some point, and also why 'time' cannot be started by any temporal thing?

 

My comprehension of what is being said at this point in this thread is currently limited, and so I just need a little clarification of the key bits of information so that I can contribute meaningful discussion to the topic.

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That was confusing to read... I still don't seem to understand what the paradox means... I kind of understand, but still don't quite get it completely. Could you explain in layman's terms what the paradox means?

 

The paradox is this; lets say you have a hotel with an infinite number of rooms; and then you have an infinite number of guests. All the rooms are full - but what happens if you get more guests? Lets say an infinite number of more guests arrive; what do you do? Well you could move all the guest sequential upto another room, so guest 1 moves to room 2 (leaving room 1 free, and the guest in room 2 to room 4, leaving all the odd rooms free) - so now the infinite number of new guests can move in. So how many people do you have in the hotel? The number remains the same - you still have the same ammount of guests in the hotel; infinite - so despite adding an infinity of of guests you still have the same number - its nonsenseical. You also have a further issue, lets presume that the infinite number of guests from the second set check out - you still have an infinite number of guests in the hotel, despite having an infinite number of rooms both free and occupied. There is the Paradox...

 

As such infinity is absurd. For the record, both Sam D, and myself, who I would say are the forums resident philosophers agree that an "actual infinite" cannot exsist.

 

Also, could you explain why and how Dr. Craig says and knows that time must have 'started' at some point, and also why 'time' cannot be started by any temporal thing?

 

Because nothing temporal exsists before the big bang (this in itself is an innacurate statement) - you will have to read up on the Big Bang Theory if your going to question this...

 

The Big Bang is pretty much prooven now; which causes you a big problem if your an athiest. Firstly the question is Philosophical rather than Scientific - as it goes "beyond the big bang" - what causes the big bang? Nothing is not a sufficient answer, because nothing doesn't explode. So what caused the Big Bang? It has to be an uncaused cause outside of time...

 

Interestingly the Big Bang breaks several rules of science (including that matter cannot be made or destroyed).

 

Kind of linking infinity in at this point, an Eternal Universe model, asside from going against all the scientific data we have with regards the universe - cannot work because if the universe had exsisted for infinity then everything would now be a black holes...

 

My comprehension of what is being said at this point in this thread is currently limited, and so I just need a little clarification of the key bits of information so that I can contribute meaningful discussion to the topic.

 

I hope the above adequatly explains things.

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As such infinity is absurd. For the record, both Sam D, and myself, who I would say are the forums resident philosophers agree that an "actual infinite" cannot exsist.

 

Because nothing temporal exsists before the big bang (this in itself is an innacurate statement) - you will have to read up on the Big Bang Theory if your going to question this...

 

Thanks, that helps a lot.

 

The Big Bang is pretty much prooven now; which causes you a big problem if your an athiest.

 

I consider deism a reasonable position. The thing is that I don't know whether or not a deity exists. Maybe a deity is the cause of all of the universe, maybe not. I'm completely neutral about whether or not a god or gods exist. Claiming specifics about said deity(s) however is where I'm not neutral.

 

Firstly the question is Philosophical rather than Scientific - as it goes "beyond the big bang" - what causes the big bang? Nothing is not a sufficient answer, because nothing doesn't explode. So what caused the Big Bang? It has to be an uncaused cause outside of time...

 

Well, we don't really 'know' that... Yeah, yeah, its the all too typical answer of 'you can't be 100% sure, therefore bla bla bla'. Current understanding of the universe through what instruments we possess to study it with does not allow us to look 'before' the big bang. I, and no one for that matter, can logically claim (yet) to know for sure any facts about the universe 'outside' of the big bang. Maybe we never will. Beyond the visible universe, the only way to make any claims about it (currently) is to attempt to observe the 'effect' that the unseen portion of the universe has on the visible universe.

For example: http://en.wikipedia.org/wiki/Dark_flow

 

This doesn't change anything about the current discussion, but all I can say is this: A deity is an explanation, not necessarily the explanation.

 

Interestingly the Big Bang breaks several rules of science (including that matter cannot be made or destroyed).

 

Which ones, besides the one mentioned? Maybe I can hypothesize some excuses explanations. :p

 

Kind of linking infinity in at this point, an Eternal Universe model, asside from going against all the scientific data we have with regards the universe - cannot work because if the universe had exsisted for infinity then everything would now be a black holes...

 

I don't know enough about physics to say something to the contrary or in agreement at the moment (so I need to research a bit first), so instead I'll ask this: What do you think about Chaotic Inflation theory?

 

Edit: To my knowledge, the age of the universe is somewhere around 13.5 to 14 billion years. It doesn't seem to me that that is enough time for everything to become black holes. Before the Big Bang, perhaps 'time' in the way we perceive it was very different. Perhaps The universe is a part of a multiverse system. This still raises the questions of how the multiverse would be 'caused'. As simple as it goes, binary thought seems to be the most universal way to perceive things. True and false. Maybe the universe isn't binary/polar in its laws.

 

Maybe we humans can't understand it because it exists in a state other than a binary one? Unfortunately, this process of thought ironically favors both a deity-created universe and a deity-less universe, so it doesn't really help us get anywhere, IMO.

 

So, on a different note, if dark matter/energy were discovered/proven, what do you think it would mean for the theories about the universe?

 

I guess this thread isn't very much about math anymore, but I don't want to get into a debate about deities, if at all possible. This adjunct into talking about the nature of the universe in manners of M-theory, etc, etc, seems very interesting though.

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As such infinity is absurd. For the record, both Sam D, and myself, who I would say are the forums resident philosophers agree that an "actual infinite" cannot exsist.
Actually, I'd say it can, as you have shown in your 'paradox'. From a mathematical point of view the infinite is quite easy: you can eternally add something.

 

 

The Big Bang is pretty much prooven now; which causes you a big problem if your an athiest.
Now that's plain wrong.

 

 

Firstly the question is Philosophical rather than Scientific - as it goes "beyond the big bang" - what causes the big bang?
The answer appears to be quite simple -- Big Bang is *not* the beginning of it all, obviously.

 

 

Nothing is not a sufficient answer, because nothing doesn't explode. So what caused the Big Bang? It has to be an uncaused cause outside of time...
The thing is, 'nothing as a cause' is somewhat different from 'exploding singularities'. Also, causality is something tied to time by definition. An 'uncaused cause outside of time' is both, pleonastic and an oxymoron at once. Philosophical nonsense.

 

 

Interestingly the Big Bang breaks several rules of science (including that matter cannot be made or destroyed).
Uh, Big Bang did not create any matter? The Big Bang Theory is a scientific construct, it can't break 'scientific rules'.
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About the infinity thing, a quote from the book "What is Mathematics?" should help:

 

The sequence of positive integers 1...2...3... is the first and most important example of an infinite set. There is no mystery about the fact that this sequence has no end, no "finis"; for, however large be the integer n, the next integer, n+1, can always be formed. But in the passage from the adjective "infinite" to the noun "infinity", we must not make the assumption that "infinity", usually expressed by the symbol ∞, can be considered as thought it was an ordinary number. We cannot include the symbol ∞ in the real number system and at the same time preserve the fundamentals of arithmetic...
This should help explain why Hilbert's paradox is a paradox. It's using infinity as though it were a number, and it cannot be used in that way.
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