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Arcesious
09-11-2009, 07:13 PM
Over the years I've come up with some questions about math, where I seem to think that there are 'flaws' in it. I hope that my questions aren't due to a lack of knowledge on my part about the processes of math. I haven't touched Calculus yet. I know 2 + 2 always equals 4, but that part of math isn't flawed as far as I can comprehend.

Here's a few:

1/3 = 0.333...
however, 1/3 + 1/3 + 1/3 = 1. Infinity sure is confusing.

0.5 x 0.5 = .25
0.3 x 0.3 = 0.09
How can two numbers multipled by each other logically become a smaller number? The math says the answer becomes smaller, but how is that physically possible?

10--10 = 20
1--11 = 12
This kind of problem just bothers the heck out of me. An even amount of subtraction signs suddenly makes it addition? How? Physically, subtraction problems like this can't even be possible. You can't get 20 apples by subtracting negative 10 apples. Said negative apples don't even exist if they're in negative amount... Is double subtraction even logically possible as far as human comprehension goes?

Shouldn't 1--11 equal -10 instead of 12? Mathematically it equals 12, but it seems to me that no matter how many subtraction signs you have, it still boils down to 1 -11 = -10 and not 1+11. Why is it that 1---11 = -10 but 1----11 = 12?

Are there any other 'problems' like these you know of? Do you have solutions that make sense that disprove these examples as problems? What's your opinion? Are we humans simply too limited in comprehension to fully understand the perfect empiricism of math? Or are these problems here because math was created as a flawed process by humans, due to our limited comprehension?

My opinion is that math isn't flawed, but simply our understanding of its quantifing processes is flawed. I wonder how our understanding of math would change if we could mentally comprehend the fourth or fifth dimension...

So what do you think?

Jeff
09-11-2009, 07:25 PM
Think of the multiplication sign as "of" when you say it in your head. 0.3 of 0.3 is 0.09, that makes sense.

Totenkopf
09-11-2009, 07:35 PM
10--10 = 20
1--11 = 12
This kind of problem just bothers the heck out of me. An even amount of subtraction signs suddenly makes it addition? How? Physically, subtraction problems like this can't even be possible. You can't get 20 apples by subtracting negative 10 apples. Said negative apples don't even exist if they're in negative amount... Is double subtraction even logically possible as far as human comprehension goes?

Shouldn't 1--11 equal -10 instead of 12? Mathematically it equals 12, but it seems to me that no matter how many subtraction signs you have, it still boils down to 1 -11 = -10 and not 1+11. Why is it that 1---11 = -10 but 1----11 = 12?

It's the same as a 2x negative. "I ain't got none" doesn't equal "I have none".

Mono_Giganto
09-11-2009, 08:24 PM
1/3 = 0.333...
however, 1/3 + 1/3 + 1/3 = 1. Infinity sure is confusing.


The whole concept of infinity takes a while to get used to; it's pretty theoretical. Try this one:

Start with 1, and add 1/2, then 1/4, then 1/8, then 1/16, etc. Keep doubling that bottom number and adding it to the total. What's the final answer?

0.5 x 0.5 = .25
0.3 x 0.3 = 0.09
How can two numbers multipled by each other logically become a smaller number? The math says the answer becomes smaller, but how is that physically possible?

Like Jeff said, think about when you take half of something (IE multiplying by one-half) you should end up with a smaller value. So using your apples as an example:

0.5 x Apple = Half of an Apple

Half of an Apple < Apple


10--10 = 20
1--11 = 12
This kind of problem just bothers the heck out of me. An even amount of subtraction signs suddenly makes it addition? How? Physically, subtraction problems like this can't even be possible. You can't get 20 apples by subtracting negative 10 apples.

Actually, these problems are entirely possible in the real world. Maybe not with something so mundane as the number of apples in your basket, but there are many things that are considered to exist in negative quantities, especially any quantity that also has a direction associated with it.

Shouldn't 1--11 equal -10 instead of 12? Mathematically it equals 12, but it seems to me that no matter how many subtraction signs you have, it still boils down to 1 -11 = -10 and not 1+11.

The problem here is that -11 =/= 11. They're two different numbers that represent two different things.

So, let me ask you this question. Let's say I took a 12-inch ruler. Let's say I subtracted 11 from all of the values marked on the ruler. Now, instead of going from 0 to 12, it goes from -11 to 1. How long is the ruler now?

jonathan7
09-11-2009, 08:29 PM
The whole concept of infinity takes a while to get used to; it's pretty theoretical.

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.

Litofsky
09-11-2009, 08:29 PM
I know 2 + 2 always equals 4....

So what do you think?

I think that Mr. Blair disagrees with you.

Darth InSidious
09-11-2009, 08:37 PM
I think that Mr. Blair disagrees with you.

Yes, but only because Cherie's rather shady Australian friend tells her it equals giving him all her money...

igyman
09-11-2009, 08:50 PM
Shouldn't 1--11 equal -10 instead of 12? Mathematically it equals 12, but it seems to me that no matter how many subtraction signs you have, it still boils down to 1 -11 = -10 and not 1+11.

As Giganto said, -11=/=11. Basically, they're something along the lines of polar opposites. Think in terms of protons and electrons if you like chemistry, or perhaps Light Side and Dark Side in Star Wars terms. Point being that when you subtract a negative number from a positive number, you are actually increasing the positive side by removing the negative. Another way to look at it is to observe the opposite situation: -11-1=-12. If that seems logical, there's no reason for 1--11=1-(-11)=12 to seem illogical.

Arcesious
09-11-2009, 09:10 PM
Heh, well that solves that... Does anyone know any (nearly) impossible to solve math conundrums?

ForeverNight
09-11-2009, 09:28 PM
Alright. In middle school were you ever taught that you can't get a negative number using exponents only?

Well, they were wrong.

Rather famous equation:

e^((pi)i)=-1

Interesting, no?

I don't know the why behind it (Get's into calculus and I'm only in pre-calc right now) but I do know this equation, and it's more famous cousin, the Famous Five equation:

e^((pi)i)+1=0

That one has everything that you need in math... two basic 'constants' (i and e), pi, and then two universal numbers 1 and 0. Along with the only three operations that are truly used.

Interesting, no?

Mono_Giganto
09-11-2009, 09:40 PM
I don't know the why behind it

Well it's derived from Euler's formula (http://en.wikipedia.org/wiki/Euler%27s_formula):

e^(i x) = cos x + i sin x

Where x = pi, so:

e^(i pi) = cos pi + i sin pi = (-1) + i (0) = -1

Of course, I suppose this is just explaining it in terms of another equation that now needs explaining.... but personally I don't have the willpower to go into greater detail on this particular equation. :p

I did supply a link to the Wikipedia page about the formula if you're that interested.

Det. Bart Lasiter
09-11-2009, 10:16 PM
Heh, well that solves that... Does anyone know any (nearly) impossible to solve math conundrums?

http://en.wikipedia.org/wiki/Hilbert%27s_problems

ForeverNight
09-11-2009, 11:07 PM
Thanks Mono, when I'm not distracted by school work and an upcoming ACT then I'll give it a good look over!

acdcfanbill
09-12-2009, 12:03 AM
Alright. In middle school were you ever taught that you can't get a negative number using exponents only?

I don't recall ever hearing anything like that from anyone. Every odd exponent with a negative input will result in a negative output. Any even exponential powers of i give negative results except 4, 8, 12....

ForeverNight
09-12-2009, 12:13 AM
Alright, since you have to be so smart about it :xp: lemme rephrase:

without starting with a negative number can you make a negative using an exponenet?

Happy? :xp:

acdcfanbill
09-12-2009, 12:26 AM
Alright, since you have to be so smart about it :xp: lemme rephrase:

without starting with a negative number can you make a negative using an exponenet?

Happy? :xp:

Well, in that case, it's pretty much impossible to get a negative number without using one somewhere. If you don't count i as negative, then using that is about your only option. I would think arguments for it's sign could be made both ways though.

ForeverNight
09-12-2009, 12:34 AM
No. It's an imaginary number. There's many different types of numbers, but the two you have to pay attention to right now are Real and Imaginary.

Real Numbers and the numbers that exist: (sq.rt.)7; 4; -1; 100; 1.39; 1.9999999.....;-24.333333333333; and so on.

Imaginary Numbers are numbers that don't technically exist but are used in order to solve important math equations, i is the most famous one that is there... in fact, it's the only one I can think of right now.....

Since Negative numbers are real numbers, i is not negative since it is imaginary.

Darth Avlectus
09-12-2009, 01:10 AM
@ thread I would say:

Flawed, No--incomplete, Yes. Now if you want to view incomplete as flawed, then that is your prerogative but I think that a sweeping generalization discredits the merit it does in fact have.

It's a frustrating subject for me, but what I could find about it, fascinated me. I only wish there weren't so many societal distractions. :xp:

Optics handbooks, though little help to me in my laser hobby, have an intriguing level of math to them. I can hardly understand it, but the descriptions and explanations of the relationships are really something.

Maybe one day in my life, at my leisurely pursuit, I'll finally learn the math required to understand the book.

Point is, it cannot cover every single subject to come up. Or maybe it isn't supposed to. I'm not sure.

acdcfanbill
09-12-2009, 01:10 AM
I understand the difference between real and imaginary numbers and how negative is a subset of reals. Yet squares of imaginary numbers do give negative real results. And since i is a placeholder for sqrt(-1), it can also be -i, that being the nature of square roots.

Jae Onasi
09-12-2009, 05:09 PM
So what do you think?
I think your understanding of math is incomplete at this point and that's why it's confusing. Jeff has the best explanation for why multiplication of fractions or decimals yield smaller fractions--basically, you're taking a portion of a portion. Example--if you multiply 1/2 by 1/2, you're taking half of that half. Think of a pie. If you take half of that half of pie, you end up with a quarter of that pie, hence 1/2 x 1/2= 1/4. The best way to deal with that is keep doing your math exercises. At some point it'll suddenly click. For instance, when I have to solve for x in an equation, it's sometimes easier to think of x as a box with the answer inside of it, and doing the algebraic formulas are your keys to unlocking that box to discover the answer inside.

For negative numbers, sometimes thinking in terms of direction helps. I work with negative numbers all day long so it's second nature for me, now, but if you think of it on an east/west continuum, e.g. the Greenwich mean time is the 0 point, it can help. Negative numbers move you west, positive numbers move you towards the east a certain number of hours. Now, if you have a negative number, say -7 hours, that moves you 7 hours towards the west. Now, take away (subtract) -3 from that. You're taking away 3 western hours from the original (heading back towards the east, now), so now you end up with only -4 hours as a result. I'm not sure if that helps or not. :)

VarsityPuppet
09-12-2009, 07:41 PM
I like your explanation Jae Onasi. Very user-friendly :D

Here's one that's a little hard to wrap your head around.

Where n=any number,


n/0 = undefined


Hint: You have to change the way you think about division for it to actually make sense..

ForeverNight
09-12-2009, 07:56 PM
Alright... so if we divide by zero, that's the same as multiplying by the inverse: so we have n*(1/0) so we still divide by zero... and since zero goes into one an infinite amount of times and yet not once.....

Basically just go with undefined. :xp:

@acdcfanbill: I don't know why we're arguing about what the hell i is, the only number in there that matters if it's positive or negative is e. And since e is positive (~2.71828183) than my assertion and formula still stand. (And -(i^2) would net 1 as opposed to -1 as an answer)

VarsityPuppet
09-12-2009, 08:31 PM
Alright... so if we divide by zero, that's the same as multiplying by the inverse: so we have n*(1/0) so we still divide by zero... and since zero goes into one an infinite amount of times and yet not once.....

Basically just go with undefined. :xp:


True, but not what I was getting at.

Let's go with the apples again: you have 1 apple to divide amongst 3 people.
aka, you have to divide 1 apple into 3 different parts

that of course would be: 1/3= .33333


But let's say you have 1 apple to divide amongst 0 people.
aka, you now have to divide 1 apple into 0 parts. <<< That, my friends is not possible.


idk, that's the way I like to think of it. But yeah, if you take into consideration that multiplication is just division reversed, you can come to a similar conclusion anyways.

Boba Rhett
09-13-2009, 10:34 PM
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.

Darth Avlectus
09-13-2009, 11:23 PM
^^^This coming from an electronics engineer.

Te Je'karta Mand'alor
09-14-2009, 02:40 PM
There are no known infinites in the entire universe

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

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

Marius Fett
09-14-2009, 03:07 PM
time my friend simply does not end

Prove it. :p

Ray Jones
09-14-2009, 03:10 PM
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".

jonathan7
09-14-2009, 03:32 PM
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

Te Je'karta Mand'alor
09-14-2009, 03:53 PM
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

jonathan7
09-14-2009, 04:01 PM
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...

Te Je'karta Mand'alor
09-14-2009, 04:08 PM
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:

jonathan7
09-14-2009, 04:16 PM
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 ;)

Te Je'karta Mand'alor
09-14-2009, 04:31 PM
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:

jonathan7
09-14-2009, 04:41 PM
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.

Te Je'karta Mand'alor
09-14-2009, 04:48 PM
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:

igyman
09-14-2009, 05:29 PM
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? :)

Darth Avlectus
09-14-2009, 05:51 PM
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.

Arcesious
09-14-2009, 05:57 PM
Aren't black holes supposedly an example of infinity?

I wonder what Einstein would have to say if he was still alive and decided to study up on all of the hypothetical formulas that physicists today have about the universe.

Mono_Giganto
09-14-2009, 05:59 PM
Aren't black holes supposedly an example of infinity?

In what way? I was always under the impression that black holes were just lumps of really dense mass.

jonathan7
09-14-2009, 08:14 PM
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? (http://en.wikipedia.org/wiki/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...

Te Je'karta Mand'alor
09-14-2009, 09:34 PM
Aren't black holes supposedly an example of infinity?


i always thought of them as hyperspace... imagine whats inside them... maybe other space :xp:

Darth Avlectus
09-16-2009, 03:23 PM
Aren't black holes supposedly an example of infinity?

I wonder what Einstein would have to say if he was still alive and decided to study up on all of the hypothetical formulas that physicists today have about the universe.

What about white holes?

igyman
09-16-2009, 06:05 PM
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? (http://en.wikipedia.org/wiki/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.

jonathan7
09-17-2009, 10:43 AM
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 (http://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_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 :))

Arcesious
09-17-2009, 11:32 AM
Do its an interesting area :) Related links to this area; Hilberts Hotel (http://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_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.

jonathan7
09-17-2009, 01:33 PM
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.

Arcesious
09-17-2009, 02:53 PM
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.

Ray Jones
09-17-2009, 05:55 PM
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'.

Samuel Dravis
09-17-2009, 07:03 PM
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.

Arcesious
09-17-2009, 08:59 PM
Considering what current information about the universe suggests, the 'Big Rip' idea counteracts the idea of the universe becoming a bunch of black holes after a long time. The universe appears to be expanding rapidly - too much for its own good. Hypothetically, the universe will become 'dust' in 22 billion years.

http://en.wikipedia.org/wiki/Big_Rip

On another subject, mathematics done about galaxies indicate that they need about 95% more gravity (If I read the wiki articles correctly) to hold together. This is where dark matter and dark energy come into hypothesis. Dark matter, which is undefined specifically, is hypothetically what holds galaxies together.

IMO, if dark matter/energy is proven/discovered and data is collected about it, it could very well turn the world of physics on its head.
(Heck, I bet they wouldn't call it dark matter anymore, since its only called that because it is currently undetectable, and thus 'dark' to us.)

Link about dark matter: http://en.wikipedia.org/wiki/Dark_matter

So for us, its kind of like being in a pitch black cave, where you know the rock formations are there, because you can 'feel them' with you 'hands' (hands metaphorically being our observations of galaxies seeming to behave like they have around 95% more mass than they appear to have), but you can't see them without proper illumination. So the key to figuring out what exactly it is that's missing in the cosmological model is figuring out how to build the proper 'flashlight'.

Hypothetically, dark energy is linked to the 'out of control' expansion of the universe.

Yet another link for further info: http://en.wikipedia.org/wiki/Dark_energy

And an overveiw of various ideas about how the might end is here: http://en.wikipedia.org/wiki/Ultimate_fate_of_the_universe

Samuel Dravis
09-17-2009, 10:08 PM
The creation of the universe and physics is interesting but it doesn't seem very "Math, Problems With", if you get my meaning. In the immortal albeit horribly mangled words of some Star Wars character, "Stay on t[opic], stay on t[opic]!"

Darth Avlectus
09-18-2009, 03:09 AM
About the infinity thing, a quote from the book "What is Mathematics?" should help:

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.

That does make sense.

When it is referred to in problems or answers as "an infinite number of", I often tend to think it (infinity) is merely a convenient way of saying "numerically endless" or "numbers theoretically without end". So I do not believe it is being actually used as such when it is said that "variable" represents "such and such to infinity" amount, etc.

Is the paradox of calling infinity itself a number not an obvious thing? To do so is, well, paradoxical even in its plainest form. A value that is unending couldn't be represented as a number by any one value since it is theoretically any and every number in either direction + or -.

Ray Jones
09-18-2009, 03:23 PM
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.For some odd reason I ignored that and had other things in mind. I stopped seeing infinity as a "number" long ago. Nice to learn about Hilbert's paradox though it's pretty useless, IMO. :)

Nedak
09-18-2009, 05:09 PM
I hope it's flawed.

I can't figure it out for the life of me.