I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME

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bullhorn

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I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« on: December 05, 2005, 04:42:13 PM »
YOU WILL ALWAYS GET HALF WAY THERE NEVER THE FULL WAY

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #1 on: December 05, 2005, 10:09:46 PM »
Weird: I manage to get home every day without any trouble. Maybe you're forgetting to keep going when you get half-way there.

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bullhorn

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I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #2 on: December 06, 2005, 10:34:30 AM »
you can never get home you can only go half way. then when you go half way you have to go half way again since you always have to go half way then you can never get home

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #3 on: December 06, 2005, 11:09:06 AM »
All true. So how come I manage to make it home every day, then?

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bullhorn

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I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #4 on: December 06, 2005, 01:17:59 PM »
tell me how it is possible if you can only go half way there is always another half way to go if you want to go an inch then you have to go half an inch to get there if you wana go from that half inch to the other half you have to go half way again.  It is impossible to get anywhere due to the fact taht there is always another half way to go to. So it is IMPOSSIBLE that you have ever gotten anywhere in your life

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #5 on: December 06, 2005, 01:47:40 PM »
Gosh: one wonder where you have learned to respond to a question with another question. This is generally considered most impolite.

The problem you state is known as Zeno's paradox, named after the ancient Greek philosopher. The Greeks generally did not have a very good understanding of infinite processes, so this question stumped them, as it seems to have done here also.

The answer to Zeno's paradox is simple: we presume that we are moving at constant speed, which provides the solution. To demonstrate, and to simplify matters, let's say that it takes me one hour to get home. To get to the first half-way point takes half an hour. To get to the next point takes one-quarter of an hour. To get to the next half-way point takes one-eighth of an hour, and so on, all because I am moving at constant speed (which I probably would be if I'm on my way home). It is clear that these are the lengths of time I need to consider since I cover half of the distance in half of the time, one quarter of the distance in one-quarter of the time, and so on.

While I am taking shorter and shorter steps, I'm completing them in shorter and shorter times, since each half step takes exactly half the time that the previous step took. I can then find the amount of time it will take me to complete my journey by adding:

1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + ...

which comes to exactly 1 hour. Thus in 1 hour I appear to be back home. The last steps were getting shorter and shorter, but then, so was the time I took to do them.

It doesn't appear impossible that I got home (which is exactly where I'm sitting right now, enjoying a nice cup of tea, so it's doubly obvious).

Next!

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #6 on: December 06, 2005, 02:49:51 PM »
Nice answer.  I got completely slaughtered last saturday and still made it home.  I was definetely not walking at a constant speed and even at some decisive points ended up moving backwards :lol:
ts obvious isn't it.  No one can prove a damn thing.  Especially in this of all possible worlds. LOL

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #7 on: December 06, 2005, 03:08:54 PM »
My comments above do assume that one is able to move at a constant speed forward. If one is going backward as well, there is definitely no guarantee that one will make it home . . .  :D

One could, of course, just stay out all night and not bother coming back at all, depending on one's luck and/or circumstances. Then there really would be no possibility of getting back. Perhaps bullhorn is right after all.

Or, actually, not. Never mind!

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #8 on: December 08, 2005, 06:20:19 AM »
Hello . . . anyone out there? . . . it seems to have gone very quiet all of a sudden.

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #9 on: December 08, 2005, 05:10:51 PM »
hi Mundi. I made it home despite all possible barriers thuogh sometimes I dont think my next step was even a 1/4 or an 1/8 of the last.  [proof is im now typin on the old comp :D
ts obvious isn't it.  No one can prove a damn thing.  Especially in this of all possible worlds. LOL

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #10 on: December 08, 2005, 05:16:35 PM »
Yup, I'm at home too. The on-going evidence of being able to make it home every day since this thread was posted (and every day in my life before that as well, for that matter) seems to be destroying any chance of bullhorn's theory being correct.

Where is he, by the way? He hasn't replied in days.

I miss him.  :wink:

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #11 on: December 10, 2005, 12:13:25 PM »
This is a philosphical belief that some of the ancients held, and used as a basis for (obviously faulty) proofs of the non-existance of motion.

This argument can be conclusively disprooved with calculus.

The true point of this post, though, I believe, was to ridicule people who believe that the world is flat.  So, as far as that goes, I applaud.

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #12 on: December 10, 2005, 07:06:29 PM »
To be precise, it is not, strictly speaking, calculus which provides the solution to Zeno's paradox. It is the idea of a limit which was missing from the Greeks' mathematical repertoire, and which provides the solution to the paradox. Limits and limiting processes are a very general idea permeating many areas of mathematics, including geometry and metric spaces, topology, and even set theory.

You are, however, quite correct that infinite sums are taught in the calculus syllabus. But even the concept of an infinite collection of objects, which is a very basic idea from something as "simple" as set theory (which actually is highly non-simple) is something that Greek mathematics, which was based in part on the concept of figure and geometry, could not easily cope with. It's all very well to represent a number as a length, and a square number as the area of a square, but an infinite sum of terms is not something which is very easy to draw well.

Hence the problem with Zeno's paradox. One can certainly draw finitely many segments, each of which is half the length of the last. And one can see that the segments do seem to be tending towards a finite length. But since one cannot draw infinitely many segments, one cannot be sure. We can be sure of this with the correct definitions, however, and it was Cauchy who probably provided the best formulation of the limit of a sequence; certainly the whole idea was misunderstood even by great mathematicians before him (and after as well!).

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #13 on: December 10, 2005, 07:38:14 PM »
Thank you Mundi for filling in the details of what I did not know.  Math has never been my high point.

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #14 on: December 11, 2005, 09:47:15 AM »
You're welcome. I just wish that proof were so easy in other areas of life. Mercifully, mathematical proof is (almost) free from ambiguity: if something is proven in mathematics, it's proven irrefutably, is never incorrect in any circumstances or depending on one's viewpoint, and remains true for all eternity.

Not so with most "proofs" in science, for example, as this website goes to show. This website even challenges what we observe as being transitory (for example, when we are no longer present to observe previously-seen phenomena).

That's why I stuck to math. Far simpler.

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pspunit

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I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #15 on: December 13, 2005, 03:07:13 PM »
Quote from: "Talaananthes"
The true point of this post, though, I believe, was to ridicule people who believe that the world is flat.  So, as far as that goes, I applaud.


I find this unlikely. Bullhorn has consistently argued for the flat earth theory (possibly its biggest supporter here). He is probably just being dumb
Three people of different nationalities walk into the bar. Two of them say something smart, and the third one makes a mockery of his fellow countrymen by acting dumb."

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #16 on: December 13, 2005, 03:19:46 PM »
yes, i have since come to the conclusion that you are probably right.  i didnt know who he was at that point.

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #17 on: December 16, 2005, 02:19:23 PM »
I somehow made it home today, despite the weather. This thread made me so curious that I brought chalk with me and marked '1/2', '1/4', '1/8', and so on.
 believe the Earth is round. That must make me... EVIL!!!

By reading this message, you have given me breif control of your mind.

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #18 on: December 16, 2005, 03:06:44 PM »
Quote from: "Anticonspiratator"
I somehow made it home today, despite the weather. This thread made me so curious that I brought chalk with me and marked '1/2', '1/4', '1/8', and so on.


Of course, if you'd marked all of the fractions, you'd still be there, unless you're able to write them down faster and faster. In particular, at the one hundredth stage, you'd be writing 1/1267650600228229401496703205376, and I imagine this would take you a little longer than, say, 1/16.

I guess you stopped when you realised that you were moving less than an atom's diameter at a time . . .

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #19 on: December 16, 2005, 06:13:42 PM »
Quote from: "Mundi"


Of course, if you'd marked all of the fractions, you'd still be there, unless you're able to write them down faster and faster. In particular, at the one hundredth stage, you'd be writing 1/1267650600228229401496703205376, and I imagine this would take you a little longer than, say, 1/16.

I guess you stopped when you realised that you were moving less than an atom's diameter at a time . . .

 :D
ts obvious isn't it.  No one can prove a damn thing.  Especially in this of all possible worlds. LOL

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #20 on: December 16, 2005, 07:26:57 PM »
Thank you, Mundi, for disproving that idiotic Bullhorn. When i first saw this thread i was worried i'd never get back to the frige. I was getting quite hungry when i saw you disprove it. :)
efore making fun of someone, walk a mile in their shoes. Then your a mile away and you have their shoes.

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #21 on: December 17, 2005, 04:35:55 AM »
Quote from: "Mundi"
Quote from: "Anticonspiratator"
I somehow made it home today, despite the weather. This thread made me so curious that I brought chalk with me and marked '1/2', '1/4', '1/8', and so on.


...

I guess you stopped when you realised that you were moving less than an atom's diameter at a time . . .
LOL!

I just figured out another classic paradox that I don't quite understand. I don't think it really describes what human nature provides in knowledge.

Basically, humans come up with the theory that all crows are black. We've seen millions of them, and they're all black. So the more we see a crow that IS black, the chances improve. And whenever we see something that isn't a crow and ISN'T black, our chances improve because we're more used to crows being black. So if we look at an apple, we observe it's red, not black. We also observe that it isn't a crow. So, by looking at that apple, mentally, our chances of crows being black improve. And that just doesn't work. I can look at this web page and it doesn't make me think emoticons are any more yellow.
 believe the Earth is round. That must make me... EVIL!!!

By reading this message, you have given me breif control of your mind.

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #22 on: January 12, 2006, 06:10:04 PM »
that dosnt make very much sense. and you probably found that on some internet site and just tried to explain but failed.
efore making fun of someone, walk a mile in their shoes. Then your a mile away and you have their shoes.

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #23 on: January 13, 2006, 04:22:43 AM »
I agree: I just didn't respond because I wasn't sure if I didn't understand it because of me, or because of him.

I think I know the answer to that question now.

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #24 on: January 21, 2006, 01:48:56 PM »
Quote from: "Mundi"
All true. So how come I manage to make it home every day, then?


Because the universe doesn't give a damn about paradox and does what it bloody well likes.

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #25 on: January 21, 2006, 03:23:55 PM »
Quote from: "Panda
Because the universe doesn't give a damn about paradox and does what it bloody well likes.

You know, I thought for a while what this might mean, and I've finally decided that it doesn't mean anything at all.

Unless you care to expand your statement, I'm at a loss.

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #26 on: January 21, 2006, 03:40:18 PM »
Quote from: "Mundi"
Quote from: "Panda"
Because the universe doesn't give a damn about paradox and does what it bloody well likes.

You know, I thought for a while what this might mean, and I've finally decided that it doesn't mean anything at all.

Unless you care to expand your statement, I'm at a loss.


The reason that one can go home is because what people think has no direct effect on the universe as a whole. Logic is a human thing, not a science. Logic was originally invented as a means for winning debates.

Zeno's Paradox shows that it is impossible to move anywhere (I've always found a drawback being you couldn't go even a FRACTION of a distance - you'd first have to cover a fraction of that fraction and so on... but I'm deviating), whilst it seems obvious that we can.

So, what does this tell us? That it is, logically, impossible to move. That the very idea is paradoxical.

MY POINT is that logic is all very well, but it has no direct effect on the universe. As so, people can move about and go wherever they want to.
It is my dissaproval of the obsession with logic and order in Western society that makes my nihilistic beliefs more adamant.

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Erasmus

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I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #27 on: January 21, 2006, 04:22:33 PM »
Quote from: "Panda"
Zeno's Paradox shows that it is impossible to move anywhere


I guess you missed this, because it was on the previous page of this thread, but Mundi gave a robust rebuttal of Zeno's Paradox, by which rebuttal he showed Zeno's reasoning to be unsound (valid in this case, but based on false premises).

Really, all Zeno's paradox shows is that ancient Greeks and Panda don't have a proper understanding of limiting processes.

Quote
... what people think has no direct effect on the universe as a whole.


True, but irrelevant.  Logic and mathematics are descriptive systems which do have some causal relationship with how the universe works: the way the universe (or really, any possible universe) works causes logic and mathematics to be a certain way.

Of course, there is an as-yet-untested assumption here, which is, that the universe can be described formally, and what set of axioms we should use to describe it.  It may well be the case that the universe is inconsistent, in which case it will probably also turn out that mathematics is inconsistent.  In the meantime, if a logical argument shows that it's possible to move from point A to point B, it's safe to believe it.  Two such arguments have been posted in this thread: Mundi's, and "So how do you explain how I just went from point A to point B?"

-Erasmus
Why did the chicken cross the Möbius strip?

I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #28 on: January 21, 2006, 04:35:02 PM »
Quote from: "Erasmus"
Quote from: "Panda"

Logic and mathematics are descriptive systems which do have some causal relationship with how the universe works: the way the universe (or really, any possible universe) works causes logic and mathematics to be a certain way.


Logic is not a descriptive system. In its simplest form, logic is the study of truth preserving arguments. The first recorded idea of logic is in Aristotle's organon for convincing arguments. Logic is about finding the truth of a given statement.

Mathematics, though seemingly founded on logic, has never been proven using logic. There is no consitent logical base for number - which many would say are the basis of mathematics.

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Cinlef

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I CAN PROVE THAT YOU WILL NEVER BE ABLE TO GO HOME
« Reply #29 on: January 21, 2006, 08:00:33 PM »
Uh logic appears in Platos Socratic dialogues that pre-date Aristotle
An enraged
Cinlef
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