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1153: "Proof"

Posted: Fri Dec 28, 2012 5:11 am UTC
by rhomboidal
Image

Title Text: The prosecution calls Gottfried Leibniz.

William Tell used Zeno's arrow just to mess with his son's head.

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 5:15 am UTC
by ubikuberalles
To save time the judge should have told the lawyer to go to a point twice the distance as the judge's bench. When the lawyer reaches the halfway point, he's at the judge's bench!

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 5:54 am UTC
by sotanaht
ubikuberalles wrote:To save time the judge should have told the lawyer to go to a point twice the distance as the judge's bench. When the lawyer reaches the halfway point, he's at the judge's bench!

But before he can reach that halfway point he first needs to go a quarter of the way...

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 6:15 am UTC
by devious
sotanaht wrote:
ubikuberalles wrote:To save time the judge should have told the lawyer to go to a point twice the distance as the judge's bench. When the lawyer reaches the halfway point, he's at the judge's bench!

But before he can reach that halfway point he first needs to go a quarter of the way...

Maybe he could just walk forward as fast as possible until he is either stopped or dead.

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 6:23 am UTC
by sardia
sotanaht wrote:
ubikuberalles wrote:To save time the judge should have told the lawyer to go to a point twice the distance as the judge's bench. When the lawyer reaches the halfway point, he's at the judge's bench!

But before he can reach that halfway point he first needs to go a quarter of the way...

I never understood why zeno's paradox ever got any discussion as a real paradox, it has as much merit as the free energy myths, aka, none.

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 6:42 am UTC
by ijuin
I think that the point of Zeno's paradox is that, prior to having an understanding of Calculus, it is difficult to wrap one's mind around how an infinite series can converge to a finite value.

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 7:05 am UTC
by Turing Machine
sardia wrote:
sotanaht wrote:
ubikuberalles wrote:To save time the judge should have told the lawyer to go to a point twice the distance as the judge's bench. When the lawyer reaches the halfway point, he's at the judge's bench!

But before he can reach that halfway point he first needs to go a quarter of the way...

I never understood why zeno's paradox ever got any discussion as a real paradox, it has as much merit as the free energy myths, aka, none.


Because obviously space is infinitely divisible. That was proven by ____________

Zeno is hard for some people. Here is a ball. Perhaps you would care to bounce it.

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 7:49 am UTC
by BlueSoxSWJ
This reminds me of a historical Darwin Award winner:
Clement Vallandigham was a well-known Northern Democrat who campaigned for states' rights during the Civil War. In 1863 Vallandigham was convicted of treason for his speeches attacking the administration of President Lincoln. He was banished to the South, where he continued to voice his political views.

After the war, Vallandingham became a lawyer. In his last appearance in the courtroom, he represented a client on trial for murder. The accused man's defense was that the victim had drawn his own gun in a fashion that caused it to fire, killing himself. To prove the defense argument, Vallandigham demonstrated the victim's method of drawing a gun--using the loaded evidence gun as his prop. The firearm went off, and he lost his life--but proved his case.

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 7:58 am UTC
by TimXCampbell
ijuin wrote:I think that the point of Zeno's paradox is that, prior to having an understanding of Calculus, it is difficult to wrap one's mind around how an infinite series can converge to a finite value.

[Emphasis added]

Indeed. Even in this day and age It took me until I was around 50 years old to finally understand (and accept) that .999… actually does equal 1. If I'd told that to a Pythagorean I probably would have been killed.

Turing Machine wrote:Zeno is hard for some people. Here is a ball. Perhaps you would care to bounce it.

Love your nickname. Are you really human? If so, where does the tape come out?

Anyway, I used to have a cat that I named Zeno. When I tossed him a ball he'd simply look at it, and then look at me. I think he was trying to convey that I was asking for the impossible.

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 7:59 am UTC
by Dr What
Laughing my knees off!
Leibniz : "I used to be a philosopher like you, then I ..."

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 8:04 am UTC
by Brian-M
I'm used to seeing it spelled "Xeno". Seeing it as "Zeno" looks strange to me. But since the ancient Greeks didn't use the Latin alphabet, I suppose either way is equally valid.

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 9:30 am UTC
by Kit.
Brian-M wrote:I'm used to seeing it spelled "Xeno". Seeing it as "Zeno" looks strange to me. But since the ancient Greeks didn't use the Latin alphabet, I suppose either way is equally valid.

"Zeno" is actually Zenon, Ζήνων.
"Xenophon" is "Ξενοφῶν".

Not sure where you were seeing "it" spelled "Xeno".

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 10:56 am UTC
by TimXCampbell
Kit. wrote:"Zeno" is actually Zenon, Ζήνων. "Xenophon" is "Ξενοφῶν". Not sure where you were seeing "it" spelled "Xeno".

Perhaps he or she 's thinking of xenon (the element). I guess that would be spelled Ξήνων, though I doubt the ancient Greeks had much use for it. Come to think of it, I don't have much use for it, either. I can't even spread it on a cracker.

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 10:57 am UTC
by squonk
Brian-M wrote:I'm used to seeing it spelled "Xeno". Seeing it as "Zeno" looks strange to me. But since the ancient Greeks didn't use the Latin alphabet, I suppose either way is equally valid.


I prefer Z-Know.

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 11:51 am UTC
by J L
TimXCampbell wrote:
ijuin wrote:I think that the point of Zeno's paradox is that, prior to having an understanding of Calculus, it is difficult to wrap one's mind around how an infinite series can converge to a finite value.

[Emphasis added]

Indeed. Even in this day and age It took me until I was around 50 years old to finally understand (and accept) that .999… actually does equal 1. If I'd told that to a Pythagorean I probably would have been killed.

Thanks for making me feel less lonely down here between all those fine gentlemen riding their stately steeds.

Also:
explainxkcd wrote:Since mathematics started to be able to handle infinite processes, it has been suggested that the Dichotomy paradox is resolved by showing that the infinite number of terms involved add up to a finite sum. However, Zeno is rather saying "it is impossible to traverse an infinite number of things in a finite time", and is so arguably not concerned with finding a sum, but with finishing a task with an infinite number of steps. It remains a question of debate whether a mathematical approach addresses the central points in Zeno's arguments."

I'm note sure if this makes any difference mathematically, but it's a nice illustration of why the paradox seems to be at odds with everyday experience.

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 12:20 pm UTC
by PolakoVoador
This was a very good comic on itself, but the alt-text was unexpected and made me laugh even more. Well done, Randall, well done.

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 12:35 pm UTC
by orthogon
squonk wrote:
Brian-M wrote:I'm used to seeing it spelled "Xeno". Seeing it as "Zeno" looks strange to me. But since the ancient Greeks didn't use the Latin alphabet, I suppose either way is equally valid.

I prefer Z-Know.

Eh? "Zedno"? Oh, right.

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 12:53 pm UTC
by Wooloomooloo
In such matters, perspective is quite important...

A mathematician and and engineer are taking a walk when they suddenly see a beautiful woman some distance away and a voice booms down from above: "there is the woman of your dreams, but you are cursed to always only be able to halve the remaining distance between you". The engineer dashes off. The mathematician yells at him: "Where to? You know you can never reach her...!" to which he responds "Yeah, but I can get arbitrarily close!"

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 1:30 pm UTC
by Throw19289
The most intuitive way to understand Zeno's paradox, for me, was to view it as the slowing of time. Imagine you're looking at film of an arrow flying, but the playback speed gradually slows. Every second of real time the arrow flies half the remaining distance to the target, but each second a shorter amount of film is played back. You're gradually slowing time to zoom in on a specific instant of the video, where time would be at a standstill, and you play back no more video. It's not so much that motion is impossible, but rather, if you slow time to a halt, then no motion happens either. In the real world, time does not become arbitrarily slow, and so the arrow does reach its target.

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 1:32 pm UTC
by Draco18s
TimXCampbell wrote:
ijuin wrote:I think that the point of Zeno's paradox is that, prior to having an understanding of Calculus, it is difficult to wrap one's mind around how an infinite series can converge to a finite value.

[Emphasis added]

Indeed. Even in this day and age It took me until I was around 50 years old to finally understand (and accept) that .999… actually does equal 1. If I'd told that to a Pythagorean I probably would have been killed.


They'd probably have told you that decimal values aren't true numbers. They were all about ratios of things.

Semi-related:
http://www.youtube.com/watch?v=X1E7I7_r3Cw

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 5:30 pm UTC
by bmonk
Wooloomooloo wrote:In such matters, perspective is quite important...

A mathematician and and engineer are taking a walk when they suddenly see a beautiful woman some distance away and a voice booms down from above: "there is the woman of your dreams, but you are cursed to always only be able to halve the remaining distance between you". The engineer dashes off. The mathematician yells at him: "Where to? You know you can never reach her...!" to which he responds "Yeah, but I can get arbitrarily close!"

Also sometimes called, "close enough for all practical purposes"

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 8:06 pm UTC
by dudiobugtron
To really get an understanding of Zeno, we should all play Ancient Greek Punishments. :)

Click 'Z' for Zeno.

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 8:19 pm UTC
by Reecer6
Zeno should be fine, so long as the judge doesn't try to walk away from him.

The thing about Zeno's paradoxes is that, from the ones I've read about, he's either correct or forgets that both time and space are/aren't evenly divisible. Apparently though, he was right about the arrow one. In this comic, however, he can't prove the arrow didn't have direction.
Zeno is a really bad lawyer.

Re: 1153: "Proof"

Posted: Fri Dec 28, 2012 10:05 pm UTC
by mikrit
Brian-M wrote:I'm used to seeing it spelled "Xeno". Seeing it as "Zeno" looks strange to me. But since the ancient Greeks didn't use the Latin alphabet, I suppose either way is equally valid.
Are you a Diskworld fan? Xeno is the name of a philosopher in Small Gods by Terry Pratchett.
http://wiki.lspace.org/mediawiki/index.php/Xeno

Re: 1153: "Proof"

Posted: Sat Dec 29, 2012 1:40 am UTC
by TimXCampbell
dudiobugtron wrote:To really get an understanding of Zeno, we should all play Ancient Greek Punishments. :)

Click 'Z' for Zeno.

Alas, the game didn't work for me in any mode. I also tried the ethical dilemma game — the one with the trolley — and while it saw me press the spacebar to continue in the tutorial, it didn't recognize that key when it was time to throw the switch.

Too bad these didn't work; some of the games looked thought-provoking!

Umm, why doesn't my browser's spell-checker recognize the word "spacebar"? Is that not a real word these days?

Re: 1153: "Proof"

Posted: Sat Dec 29, 2012 3:29 am UTC
by dudiobugtron
Weird - they work fine for me in chrome. What browser/etc are you using? Have you got the latest flash player?

Re: 1153: "Proof"

Posted: Sat Dec 29, 2012 3:44 am UTC
by Arariel
I prefer Diogenes the Cynic's method of resolving Zeno's Paradox.
He walked across the room, and then pointed out that things do, in fact, move.

Firefox's dictionary does not have 'spacebar' in it.

Re: 1153: "Proof"

Posted: Sat Dec 29, 2012 5:15 am UTC
by da Doctah
BlueSoxSWJ wrote:This reminds me of a historical Darwin Award winner:
Clement Vallandigham was a well-known Northern Democrat who campaigned for states' rights during the Civil War. In 1863 Vallandigham was convicted of treason for his speeches attacking the administration of President Lincoln. He was banished to the South, where he continued to voice his political views.

After the war, Vallandingham became a lawyer. In his last appearance in the courtroom, he represented a client on trial for murder. The accused man's defense was that the victim had drawn his own gun in a fashion that caused it to fire, killing himself. To prove the defense argument, Vallandigham demonstrated the victim's method of drawing a gun--using the loaded evidence gun as his prop. The firearm went off, and he lost his life--but proved his case.


And in the process performed the invaluable service of reducing by one the total number of lawyers.

Re: 1153: "Proof"

Posted: Sat Dec 29, 2012 5:29 am UTC
by TimXCampbell
dudiobugtron wrote:Weird - they work fine for me in chrome. What browser/etc are you using? Have you got the latest flash player?

The latest Chrome and I updated the Flash player last week. Windows XP SP3. I'm in the southwest corner of the room.

No biggy. The games looked fun but I can pretty much figure out what they do without playing them. Neat ideas!

Arariel wrote:Firefox's dictionary does not have 'spacebar' in it.

Same goes for Chrome. That strikes me as strange. Time to add it to the dictionary ... problem fixed!

What a weird word to overlook!

Re: 1153: "Proof"

Posted: Sat Dec 29, 2012 7:51 am UTC
by dudiobugtron
If I was a space bar, I'd want a space in my name. :)

TimXCampbell wrote:I'm in the southwest corner of the room.

Well there's your problem. You'll have to call in a Feng Shui expert.


(In all seriousness though, finding out what they do without actually having to play them is probably the best possible scenario... !)

Re: 1153: "Proof"

Posted: Sat Dec 29, 2012 9:58 am UTC
by Beltayn
dudiobugtron wrote:To really get an understanding of Zeno, we should all play Ancient Greek Punishments. :)

Click 'Z' for Zeno.


I was curious what would happen if you kept going until all the significant digits used by the game were filled up with 9's. Game just transitions to using "Half-way" for the target point, and "Almost Half-way" for the starting point.

Re: 1153: "Proof"

Posted: Sat Dec 29, 2012 4:30 pm UTC
by richP
Arariel wrote:I prefer Diogenes the Cynic's method of resolving Zeno's Paradox.
He walked across the room, and then pointed out that things do, in fact, move.


I always wanted to use a method that BHG would probably employ.

BHG (to Zeno fanboy): "ok, so if I were to try and move an object from me to you, it would never reach you?"
ZFB: "yes, because it would have to get halfway there, which takes some time, then it would..."
BHG: Picks up a fist-sized rock "Here's an object..."

Spoiler:
Learning is fun!
or:
Rock beats philosopher

Re: 1153: "Proof"

Posted: Sat Dec 29, 2012 5:22 pm UTC
by keithl
TimXCampbell wrote:Indeed. Even in this day and age It took me until I was around 50 years old to finally understand (and accept) that .999… actually does equal 1. If I'd told that to a Pythagorean I probably would have been killed.


Turing Machine wrote: Zeno is ...


I am skeptical of "..." . In the first case above, it means "0.001" . In the second case, I use it to quote "Turing Machine" without actually quoting her/him/it. In the case of 3.14159... it means "π-3.14159" . Perhaps "..." means "if you are a similarly trained primate, you can guess what this is supposed to mean". Perhaps some kinds of mathematics (like Zeno's "Paradox") are merely aberrant psychology.

Perhaps the Turing test is really a way to detect a peculiar kind of vague primate thinking that no truly intelligent machine would tolerate.

Re: 1153: "Proof"

Posted: Sat Dec 29, 2012 7:07 pm UTC
by dudiobugtron
keithl wrote:
TimXCampbell wrote:Indeed. Even in this day and age It took me until I was around 50 years old to finally understand (and accept) that .999… actually does equal 1.

I am skeptical of "..." . In the first case above, it means "0.001" . ... In the case of 3.14159... it means "π-3.14159" . Perhaps "..." means "if you are a similarly trained primate, you can guess what this is supposed to mean". Perhaps some kinds of mathematics (like Zeno's "Paradox") are merely aberrant psychology.

It doesn't really 'mean' those things, it's just that the intended meaning is equivalent. In the first case, it really means "keep on putting 9s until you have countably infinite 9s." Even though, as Zeno suggests, it's actually impossible to get to infinite 9s just by putting 9s one at a time.

But I agree with your overall point that words and symbols have no intrinsic meaning, and our subjective understanding of them leads to all sorts of "mis"understandings.

Re: 1153: "Proof"

Posted: Sat Dec 29, 2012 7:32 pm UTC
by shokoshu
And then there was Zena, Warrior Princess. She never could hit anything :mrgreen:

(Oh, and BTW, I don't think that Zeno is "solved" whatsoever. The math version of Zeno is
solved more or less to the agreement of mathematicians. The physics...ehem.)

Re: 1153: "Proof"

Posted: Sat Dec 29, 2012 8:43 pm UTC
by TimXCampbell
shokoshu wrote:The math version of Zeno is solved more or less to the agreement of mathematicians. The physics...[not so much].

My uneducated theory is that movement is quantum, with the minimum distance something can move being one Planck unit.

I have no background in physics, so I shouldn't be expressing opinions on such matters. But this is, after all, the internet, where ignorance is no barrier to typing.

Perhaps somebody can tell me if I'm even remotely close to what science says.

Re: 1153: "Proof"

Posted: Sun Dec 30, 2012 8:28 am UTC
by Dryhad
shokoshu wrote:And then there was Zena, Warrior Princess. She never could hit anything :mrgreen:

(Oh, and BTW, I don't think that Zeno is "solved" whatsoever. The math version of Zeno is
solved more or less to the agreement of mathematicians. The physics...ehem.)

Before you can travel a Planck length, you must first travel... um...

Re: 1153: "Proof"

Posted: Sun Dec 30, 2012 12:58 pm UTC
by Nooska
So you are saying that at finitely small increments movement is indistinguishable from teleportation?

Re: 1153: "Proof"

Posted: Sun Dec 30, 2012 1:20 pm UTC
by sometheoreticalphysicist
Well IMHO the jury is still out on whether spacetime is discrete or not, as we keep waiting for the proffesionals to combine quantum mechanis and general relativity

Re: 1153: "Proof"

Posted: Sun Dec 30, 2012 3:54 pm UTC
by ArDeeJ
I think that the "- but never reach it!" ruins the comic, I'd prefer just a "...". Then again, I lol'd.