Achilles and the Tortoise Paradox

Achilles paradox, in logic, an argument attributed to the 5th-century-bce Greek philosopher Zeno, and one of his four paradoxes described by Aristotle in the treatise Physics. The paradox concerns a race between the fleet-footed Achilles and a slow-moving tortoise. The two start moving at the same moment, but if the tortoise is initially given a head start and continues to move ahead, Achilles can run at any speed and will never catch up with it. Zeno’s argument rests on the presumption that Achilles must first reach the point where the tortoise started, by which time the tortoise will have moved ahead, even if but a small distance, to another point; by the time Achilles traverses the distance to this latter point, the tortoise will have moved ahead to another, and so on.

The Achilles paradox cuts to the root of the problem of the continuum. Aristotle’s solution to it involved treating the segments of Achilles’ motion as only potential and not actual, since he never actualizes them by stopping. In an anticipation of modern measure theory, Aristotle argued that an infinity of subdivisions of a distance that is finite does not preclude the possibility of traversing that distance, since the subdivisions do not have actual existence unless something is done to them, in this case stopping at them.

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Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
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`\boxed{123}`	$\boxed{123}$

Comments

So the solution is the infinite sum.

A Former Brilliant Member - 11 months, 3 weeks ago

What are you talking about, @Páll Márton?

Debate continues on the question of whether or not Zeno's paradoxes have been resolved. In The History of Mathematics: An Introduction (2010) Burton writes, "Although Zeno's argument confounded his contemporaries, a satisfactory explanation incorporates a now-familiar idea, the notion of a 'convergent infinite series.'"

@A Former Brilliant Member – Ok.

No @Páll Márton, rather the solution is that Zeno considered Achilles' motion as potential and not actual. The difference is Achilles' doesn't even stop for a millisecond when he reaches a the tortoise's previous point, he is in motion till the end of the race.

Achilles' speed would be at around 30 kmph as he was a hero with the Curse of Achilles'. Desert tortoise average speed = 5 kmph. Let's say the race is for 60 km. and the tortoise has a 30 km headstart.

When achilles reaches the 30km mark in one hour, the tortoise will be at 35 km

Achilles - 0 / 30 / 35 / 36.67 Tortoise - 30 / 35 / 36.67 / 37.1

Going on like this, their distances will be so near that they will actually be at the same position (Go to my feed and click 1 = 0.99, to know why), and then Achilles will cross the tortoise.

This is also one of Zeno's Paradoxes, check it out on wikipedia.

A Former Brilliant Member - 11 months, 4 weeks ago

What is the Clash of $\pi$ ? I saw it in your profile.

It is an online math contest. Go to this link - https://www.picirql.com/ Its an All India Contest. Its fun and teaches you a lot. I'm not sure if its available in the UK but you can check. You would have to create a account for yourself and pay some money. There is also a leader board for top 20 students in your grade.

I can't pay money! But, thanks, I now understood what it is.

@A Former Brilliant Member – Try this then, its free - https://in.bricsmath.com/ Its like the fun puzzles in Brilliant, but as a contest, and you have lots of time to do it.

@A Former Brilliant Member – I don't see the UK flag.

@A Former Brilliant Member – Guess it isn't available in UK then. Sorry, I'm not so well-informed on where these exams are available. But i know an English test that's free, that is if you are interested in English.

@A Former Brilliant Member – Sure.

@A Former Brilliant Member – https://www.cambridgeenglish.org/

You can take free tests which will tell you your level of knowledge in English. The International Cambridge English Chart-thingy also tells you the International Cambridge Rankings and stuff. Once you know your level, you can practice at that level and take the test again to get better.

I have passed the FCE exam in my school so I'm almost at the highest level, just one more exam to pass.

Hope you like it.....

@A Former Brilliant Member – I got $\frac{24}{25}$ !

@A Former Brilliant Member – For General English.

@A Former Brilliant Member – Awesome, you beat my progress that took me one year in 15 minutes. You're at the same level as me now I guess. Nice Job!! Does it say that you are eligible for CAE or CPE?

@A Former Brilliant Member – CPE!

Also, I got $\frac{20}{25}$ in For Schools - eligible for B $1/2$ !

@A Former Brilliant Member – I can see you're in 10th so you should consider the For Schools marks. B1/2 means FCE which is the same as me when i tried the For Schools exam for the first time. I got 21.

@A Former Brilliant Member – $\frac{20}{25}$ for Business English! I could take either B $2$ Business Vantage or C $1$ Business Higher!

@A Former Brilliant Member – Business english is for businessmen not high school teens

@A Former Brilliant Member – I am doing Business for GCSE.

@A Former Brilliant Member – Ok. 20/25 is Awesome!!

@A Former Brilliant Member – $\frac{12}{15}$ for Young Learners! It says I should do A $2$ Flyers!

@A Former Brilliant Member – Young learners is for lower grades

@A Former Brilliant Member – Ok. But I wanted to try all the tests.

@A Former Brilliant Member – Ok. There's nothing wrong in it.

I saw that one of your interests is computer programming. What language do you use? I use JavaScript and I'm learning Python and C#.

I use Python. I am doing Computer Science for GCSE.

@A Former Brilliant Member – OK, Good Luck.

@Yashvardhan Pattanashetti, please, don't get angry. I understand that you're angry, and I know you don't care anymore, but can we talk this out? You typing to me in capital letters makes me feel like I have hurt you as well...

Kind of, so i'm back to normal letters, i downvoted this comment of yours.

Please, can we talk this out? When you and @Páll Márton were talking about it, I was on the verge of crying. I feel like that again.

@A Former Brilliant Member – Pall is kind of my only 'closest to friend' person, and just because i don't want you to cry, i forgive you, but we aren't friends anymore.

@A Former Brilliant Member – Ok. I leave you this:

To lose a friend is the greatest of all losses.

@A Former Brilliant Member – Fine, I completely forgive you. But we were never friends in the first place were we? So you never lost a friend(kind of).

@A Former Brilliant Member – Well, to me, you were a friend. It started in this note and it ends here in this note.

@A Former Brilliant Member – Please stop that! I don't like quarells. It's enough at home.

@A Former Brilliant Member – It's not a quarrel, @Páll Márton - it's a farewell.

@A Former Brilliant Member – Its a joke Pall, Hamza and Yajat are having World War 3, and its up to me The UN to stop them. LOL XD LOL XD

@A Former Brilliant Member – Hahaha! It's sad. never joke with a Hungarian about world wars.

@A Former Brilliant Member – Sorry, Think of it as a cat fight(It is kind of like that as its for the pettiest of reasons). LOL

@A Former Brilliant Member – I have a good idea. Maybe I will start to post a problem series by me.

@A Former Brilliant Member – On what topic??

@A Former Brilliant Member – Logic

@A Former Brilliant Member – About what?

@A Former Brilliant Member – You'll see.

@A Former Brilliant Member – Stop acting like a baby @Yajat Shamji and go to Relationships between splitted - whatever Hamza's note is.

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$