Zeno Zeno Zeno Can’t you See?
Slaying Ancient Monsters with String Theory.
There’s a class of problems, attributed to Zeno of Elea, who was an ancient philosophical monster. His paradoxes have harassed all of our biggest brains for the last 2500 years.
In their latest iterations, the worlds brainiacs resorted to many ingenious solutions, from Calculus to the Quantum Theory but to no avail. The monsters persist wreaking havoc. Laying waste to everything.
The Vikid Truth, a hero of the ages, has been called to end Zeno’s reign of terror, once and for all.
All he has is a piece of string…
Let the Adventure Begin
To slay the beast, we start with a brief recantation of the paradox itself. We then proceed to show why it’s invertebrate manure and not the dragon everyone takes it to be. Concluding to parse a solution that doesn’t require advanced mathematics or made up physics.
Turtle Soup.
This superhero needs nourishment and he ain’t in no mood for philosophical cuisine. Take the paradox recipe:
Achilles and the Tortoise Paradox:
Our Hero, the speedy Achilles is unable to catch a slow and lethargic tortoise named Timeus.
Arguments and Conclusion:
A race!
In which Timeus has been given a head start…
During the time it takes Achilles to catch up to a given position of Timeus,
Timeus has moved further forward by some distance.
Achilles can never catch Timeus.
Though logically right, the conclusion is obviously wrong.
Achilles will clearly pass Timeus by practical experience.
Leading to Paradox.
See Wolfram (for the original recipe)
Tautologically true and…
therein lies the solution.
String Theory
Let’s for example consider another experiment. I give you a piece of string, asking you to cut it up. Each time you cut it, you throw away one of the pieces, leaving you with a shorter piece of string. Your task is to keep cutting till you have no string. Then you Stop.
The question is, when will you run out of string?
There are two possible solutions to this.
You never run out of string. You can keep cutting and cutting, to the atomic level and below. But you’re always left with something to cut, thus always have a bit of string. You never stop.
You stop, but still possess a bit of string. The atomic level is considered finite. Once you reach the last atom of the string, there is a problem. The activity of cutting no longer works. But you were asked to cut until you have “no string”. Which is impossible.
Hence, you can never cut until you have no string in either case.
Thus the experiment was designed for you to fail.
This is Zeno’s paradox in a nutshell. Asking you to do the impossible, by design, and then concluding that cutting itself or stopping is impossible.
Pure Turtle Poo. Can you see?
Slaying the Beast
Now. Let’s say we have two pieces of string. The first string represents the distance it takes for Timeus to go in some amount of time, say ten minutes.
The second string represents Achilles. For arguments sake let’s say he is twice as fast. So the string is twice the length.
We give Timeus a 5 minute head start. He’s half way up his string before Achilles even starts.
We do the same cutting procedure. In each time Timeus has moved forward along our string. Achilles has tried to catch up. We cut each of the two strings by the amount each racer has covered respectively and discard the part they travelled over.
We notice something silly. As we approach the 10 minute mark. Timeus’s string is reaching a vanishing point. We are using nano-machinery to cut his ever smaller pieces of string whilst Achilles has a whole half (and a tiny bit more) of his yet to go. Remember, Achilles has only been in the race for 5 mins. He was twiddling his thumbs for the first 5 mins.
And there is lies the rub. As long a you never let poor Timeus exhaust his piece of string, because of the asinine nature of the experiment you set up, with autistic rules that don’t remotely match with reality or anything else, of course Achilles can’t catch up!
You gave Timeus a head start in a race with no end.
Now, if we accept the string can’t be cut up infinitely. Poor Timeus will be left with one atom which he must hold onto for each subsequent operation of the experiment. Achilles can keep cutting more and more string at which time he passes Timeus.
This isn’t a paradox. This is an exercise in cutting a finite length infinitesimally. You can’t mix infinities with finite objects.
You will always end up with nonsense.
If infinities exist. They must be matched with other infinities. Infinite cutting operation should be cancelled by an infinite time and space dimensions. Achilles catches Timeus at the limits of infinity. If not. We stop cutting, accept that Achilles caught up with Timeus and then surpassed him.
It is as if we have joined the two ends of a string into a circular loop. Then ask our brave hero to travel along the loop until he reaches the end of it. When he can’t, as we didn’t define an end, we claim that stopping itself is impossible.
There you have it, as promised, the end to 2500 years of terror. No calculus, no made up physics… just some string.
and that’s,
The Vikid Truth
p.s. very few people read this Substack, approximately 40 each post.
So if you do know a brainiac, I would appreciate you sharing with him / her / it.
And as always, I would be humbled by your subscription.
You never know when this superhero will slay ancient monsters. Come and join me!