Achilles and the Tortoise - 60-Second Adventures in Thought (1/6)

[Rexorsist]

I really don't understand this. Achilles would outrun a tortoise anyday because he's going at a faster speed than the turtle. If the turtle can cover 100m in 1 minutes. Achilles could cover it within 10 seconds. If Zeno was so smart, why didn't he think of this?

[Xzalander]

@Rexorsist See Top Comment #1. Zeno's Theory was ignoring the factor of time. Hence the video mentions that while the original purpose of it was kind of nonsense (Achilles can never pass the tortoise -until- the moment at which Achilles passes the tortoise.) and merely states something is behind until it overtakes, it did give birth to dividing finites by infinites.

[mtubeme]

it's an absurdity in a sense. yes, in order to move somewhere we have to get halfway there first. he seems to be saying that the conquest is fractional, always. and in some ways i can see the truth in that all around me. the further we look into the quantum field the further the goal line seems to be. maybe he was theoretically ahead of his time. on the other hand races are truly won constantly within a set of parameters: distance and time.

[mtubeme]

the problem with this as stated is that there is no limitation put on achilles. so if he is indeed moving at a consistent speed and that speed is faster than the tortoise's speed then he will overtake the tortoise at some point. yes, there is a race that the tortoise would win, depending on their speeds. the length of that race is the longest race the tortoise can win. in the next moment achilles catches, and then passes, the tortoise.

[witzbold91]

@mtubeme Nice explanation, got it now :-) But why didn't Zeno take this into consideration?

[baeronautics]

lets put it this way.. lets say the race is 100m long. Lets assume that Achillies' speed is 50m/min and tortoise 25m/min but the tortoise has to cover 50 m because he is given half the distance head start. It ends up being a Tie between Achillies and the tortoise , then how how does the video say that Achillies will never be able to catch up? plz explain, am I missing something?

[projectbrumaire]

this is retarded, achillies would over take him in 11 sec. in real life it would not even be like how described

[AngryRantingNerd]

Basically it doesn't factor in acceleration, and assumes that both Achilles and the Tortoise are moving at a constant, uniform motion. In the real world, this would obviously not be the case.

[Moshikashitenai]

Oh yeah, cuz everyone covers distance logarithmically... >.>

[Ovalusc1]

What Achilles just covered the distance that would make him equal to the tortoise instead of the distance that would bring him to where the tortoise was when it began?

[MiguelScarpa]

I've actually studied this in filosophy, and it has been proven wrong because if you add an infinite amount on numbers increasingly smaller you will NOT arrive to infinity, so Xeno (Zenone) was wrong.

[alextroch]

this is like a riddle I've heard " if a frog starts out 2 feet from a wall and hops half the distance of where it was to the wall, how many hops will it take for him to reach the wall"

the answer is clearly that he will never reach the wall and his hops will get infinitely smaller

[diljo13]

@alextroch It's not possible to force a quantum solution onto a geometric problem... this "theory" exploits an easily misunderstood concept.

[SkimmerX]

@diljo13 exactly- breaking down the event into little pieces and measurements is only one view of what is taking place, it isn't the real story.

[1marcelfilms]

VEE Saaouwes

[wstmess]

can anyone explain? i dont get it..

[ArndeF]

@wstmess There is a channel on yt called vsauce. Now go and subscribe to it! It's not getting any better.

[Moshikashitenai]

@wstmess You don't get it cuz it's wrong

[MrJinksyJinksy]

Vsauce army passing through

[346Yoman]

*vsauce

[346Yoman]

Sauce

[tooyoungful]

Well this is one of those paradoxes were it is pointless fact.... We know that it is possible, it's like saying everything has to have a halfway point when moving.....

[temperedskinflint]

Is this David Mitchell narrating?

[iKEWTN]

but what if achillies is faster and passes straight away?

im really slow, so my friend let me have a head start, i kept the same pace but he still passed me.???

[sidnet033]

hey what tool has been used to create this animation?

[canadianbacon007]

For if the firstfruit be holy, the lump is also holy: and if the root be holy, so are the branches.

[entmellon]

Thats how math should be taught.

[manoman0]

reality will catch up with the tortoise. eventually.

[woodyeckerslyke]

Practically isn't this solved by the fact that space is *not* infinitely divisible? AIUI there is such a thing as the smallest (quantum?) distance, and once Achilles has bridged that gap to catch the tortoise then he is free to move on and win the race.

[daviangel]

@woodyeckerslyke Last time I checked no one really knows this because the Planck length is so many orders of magnitudes smaller than any currently possible measurement, there is no hope of directly probing this length scale in the foreseeable future. The precise effects of quantum gravity are unknown; often it is suggested that spacetime might have a discrete or foamy structure at Planck length scale. Maybe if someone ever figures out TOE we'll know?

[woodyeckerslyke]

@daviangel Thanks for this. Didn't realise the Planck length was so short (dk.filmomania.pl/j/Scale_of_U­niverse_In93570.swf).

Thoughts:

1. infinite divisibility of space is a Platonic Ideal

2. it's a useful approximation but doesn't stand up to close scrutiny

3. Does the existence of a Planck length (or some other smallest distance) lead to an alternative set of paradoxes or inconsistencies

4. If not then why aren't we operating on the basis that reality is discrete not continuous

[TipsyTulia]

It is based on the assumption that Achilles runs to get to where the tortoise was when he started running. It does not contemplate that Aquilles does not run to catch up, but to pass the tortoise.

[johnnye87]

The problem is it doesn't take time into account. Yes, the tortoise is moving half as far again each time, but it's taking half the time to do it. The time taken shrinks by half for each "step", never reaching (1+(head start)), so this only proves that Achilles can never pass the tortoise -until- the moment at which Achilles passes the tortoise.

[JackieArgent]

@johnnye87 I don't know if you've heard of it but if you are interested in Zeno's paradoxes of motion I'd recommend Adolf Grünbaum's "Modern Science and Zeno's Paradoxes". A pretty good read.

[untilitpasses]

@johnnye87 Correct in your current understanding of Zeno's works. His approach to space was mathematical (or logical whichever you prefer), and not pragmatical as most people think of it. Take the example of a falling glass of water. The measure between the table (where it was resting) and the floor (where it landed) is, let's say 1meter. Mathematically, a segment is made of infinite points. If infinity is reached it isn't infinity. That's what he meant with "movement is an illusion."

[untilitpasses]

@johnnye87 And time, being the measure of movement, is also an illusion.

[Au5tinz]

@johnnye87 yes, while that may be true, zeno also disproves movement through time in another of his pardox's.

[wolfson109]

The calculation for the time taken for Achilles to catch up to the turtle is an infinite sum. However, since each term in the infinite sum describes the function over an period of time which is decreasing as n/2 (where n is the number of the term) and since we are measuring time with a clock (which must have an associated statistical error), we define the mth term such that the time described by all subsequent terms is less than the error in the clock allowing us to truncate the series.

[danthemango]

thanks for the link in the description!

[Fl4dd3rm0uz]

if both always move at equal speed...?

[charlessmyth]

This paradoxical argument is only valid so long as the point of reference is limited to the relative position of the tortoise.