r/technicallythetruth • u/Dry_Worth_9165 • Jan 28 '23
1/2, 1/4, 1/8, 1/16, 1/32, ... until the end
/img/qxpwgvy61uea1.jpg[removed] — view removed post
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u/PM_NUDES_4_DEGRADING Jan 28 '23
Should’ve suspected something was up when the place was called Zeno’s…
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u/turtle_eating Jan 28 '23 edited Jan 28 '23
When the guinea pig learnt about the Dichotomy paradox.
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u/yarluk990 [Technically] THE [Real] MAN OF THE [PIPIS] Jan 28 '23
what is it
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u/turtle_eating Jan 28 '23
The thing described in the comic, pretty much.
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u/yarluk990 [Technically] THE [Real] MAN OF THE [PIPIS] Jan 28 '23
do you mean, it's like if you're cutting in half, it will never end?
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u/turtle_eating Jan 28 '23
Yes.
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u/yarluk990 [Technically] THE [Real] MAN OF THE [PIPIS] Jan 28 '23
thank you
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u/Soulerrr Jan 28 '23
No need for thanks, the answer was inside you all along :D
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u/Dr_Weirdo Jan 28 '23
Well, half of it was.
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u/RedditedYoshi Jan 28 '23
Oh man I remember trying to teach fractions to an adult man (an "engineer" no less). The pain. I'm shocked you were able to help an internet stranger so quickly and concisely, and with humility. I am in awe lol.
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u/Soulerrr Jan 28 '23
(I'm not u/turtle_eating btw)
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u/RedditedYoshi Jan 28 '23
Oh whoops. Well I'm sure you've patiently helped someone learn something they should already know at great cost to your sanity, too. :I
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u/glimmering_testicles Jan 28 '23
Did that person not go to school for engineering? I'm in the program for civil now and not understanding fractions seems really really unlikely like really really really unlikely.
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u/RedditedYoshi Jan 28 '23
"Engineer" gets thrown around a lot in different industries nowadays eh. ;)
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u/poppoyt Jan 28 '23
There's no chance he could've graduated without knowing limits...
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u/benisco Jan 28 '23
how is that a paradox?
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u/turtle_eating Jan 28 '23
I guess I'm certain no one can be absolute certain they are certain. That is why "yes" might be a paradox. Though I am certain there is a better term for this.
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u/funnystuff97 Jan 28 '23
An infinite number of mathematicians walk into a bar. The first one orders half a pint. The second one orders a quarter of a pint. The third orders ⅛ of a pint, and so on. The bartender, noticing the pattern, pours out one whole pint of beer, and says to everyone, "come on, y'all need to know your limits."
Multivariable calculus version below
An infinite number of mathematicians walk into a bar. The first one orders half a pint. The second one orders a quarter of a pint. Before anyone else can order, the bartender cuts them all off, saying, "I don't serve fractions of a pint of beer." The first mathematician says, "yes, but being a convergent geometric series, you'll find that after an infinite number of us--" The bartender cuts him off. "I know how limits work, this is 8th grade stuff. I'm not serving an infinite number of you", says the bartender.
The infinite number of mathematicians are enraged. Suddenly, they all let out a shriek, and their bodies all morph into an infinite number of mosquitoes, each of varying colors, and they all swarm the bar. "YOU FOOL", booms the now neatly organized rainbow of colored mosquitoes, "BECAUSE YOU HAVE REFUSED TO PARTICIPATE IN THIS JOKE, NOW I WILL INFECT EVERYONE IN THIS NATION WITH MALARIA." The bartender ponders this for a moment. The bartender calmly replies, "But what about the average taxpayer? Won't such a thing drive up public usage of medicare, and equate to the average citizen having to pay even more in taxes as a result?" The swarm is silent for a moment. "A FAIR POINT. FINE, YOUR NATION HAS BEEN SPARED THIS TIME." The mass of mosquitoes slowly vacates the bar, and the bar is once again quiet.
An astonished physicist, who saw the whole thing go down, goes up to the bartender, and asks, "how did you manage to do that?!" The bartender replies, "Easy. I noticed that the set of vectors formed a gradient, and therefore must be conservative."
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u/Baliverbes Jan 28 '23
What vectors ? Do you mean the velocity vectors from the swarming mosquitoes ?
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u/SaloL Jan 28 '23
In epidemiology, a living thing that transfers disease is called a vector.
Additional fun fact, a non-living item that acts as a source of a disease (eg a contaminated needle) is called a fomite.
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u/Baliverbes Jan 28 '23
Alright ! OH ! conservative in the US political sense ? is that why the bit about taxes ? am I reading too much into it or is this it ?
I don't understand the part about the gradient. I know a gradient is a field that changes value/charge over a given dimension. Does that hold here ? How does it connect with the word conservative ?
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u/funnystuff97 Jan 29 '23
The mosquitoes formed themselves into a neatly arranged rainbow, implying a color gradient, where each color fades into each other. In math, a vector gradient (a vector field typically defined by a set of differential equations) is conservative, meaning that its path integral is independent of the direction you take and dependent only on its starting and ending points. For example, gravitational fields are conservative, meaning no matter how you go up between heights 1 and 2, the amount of energy it takes will always be the same. (A steep slope versus a shallow slope to go up 10 meters will both take, say, 100 Joules of energy to go up.)
In politics, conservative people... don't like spending money on taxes? Admittedly I don't know much about politics, but others can chime in on that. I think a key point on conservatism (conservativism?) is that they don't like spending money on the government, because government bad. Or something.
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u/RaeyinOfFire Jan 29 '23
I don't know whether this holds true internationally. In US politics, conservatives want lower taxes and lower government spending. They tend to favor keeping certain spending, like military, the same or increasing it. If they want more military spending, for example, they would want "budget cuts" on something else. They would avoid increased taxes.
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u/vanilla_wafer14 Jan 29 '23
Yes in the US political sense.
And the mosquitos were multicolored in a gradient, and pass along diseases to humans so are vectors. The bartender saw vectors(disease carrying mosquitoes) in the form of a gradient (colors neatly arranged in order) so they must be conservative (the political and math punchline)
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u/R_V_Z Jan 28 '23
I think it does end, in a nuclear explosion. That's the difference between math and physics.
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u/Johannes_Keppler Jan 28 '23
Well just use only half the energy released. Then use the halve of the remaining energy released.Then use the halve of the remaining energy released.Then use the halve of the remaining energy released.Then use the halve of the remaining energy released. Ad infinitum!
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u/Ake-TL Jan 28 '23
Non fissile material atoms don’t produce significant amount of energy if theoretically disjointed
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u/ares395 Jan 28 '23
Maybe that's a whoosh but generally philosophical conundrums don't hold up in real life. They are thought experiments
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u/adalast Jan 28 '23
The fun thing is that the paradox falls apart in the real world because once you do it 115 times or so you get down to the Planck scale and it becomes a binary operation.
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u/XenophonSoulis Jan 28 '23
To make it a paradox, there is a bit more to it. Imagine a different scenario. A runner is running a 100m race. Before they complete 100m, they have to complete half of it, so 50m. After that point, the runner will have 50m left. But before they can complete that, they have to pass from half of that distance now. Again, they will have half of the previous amount left and they will have to complete it. Again, they will first need to complete half of the new amount. And so on. This is clearly an infinite number of smaller parts.
Zeno (the creator of the paradox) claims that the runner cannot complete an infinite number of stuff in a finite time. But we know that they can. So, where's the mistake?
The mistake is that each part of the progress takes less and less time. For simplicity, we'll imagine that the runner has constant speed and that it takes 10s to complete the 100m. The first part takes 5s. The second part 2.5. The next 1.25. And so on. These numbers, while infinite, do have a finite sum and it is 10. So, the runner will complete the course in 10s, as we expected.
This is quite fundamental in modern mathematics, but when Zeno made the paradox 25 centuries ago it was completely incomprehensible to the people. In a way, Zeno was showing everyone the complexity of infinity before it was cool. The result is that everyone was afraid of infinity for many centuries and that his paradoxes took 15-20 centuries to explain fully.
I apologize for rugged explanation. It is quite late where I am. I hope it's somewhat understandable.
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u/trey3rd Jan 28 '23
In the given example you would eventually get down to just one hair to cut, so you would be able to finish cutting so the hair.
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u/EliNNM Jan 28 '23
Yeah it’s basically what it means
Like how multiplying anything by a %, it’ll never reach 100%
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u/ydoiwantreddit Jan 29 '23
It will if you multiply by its reciprocal. E.g. 50% of 200% is 100%
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u/EliNNM Jan 29 '23
Well yes of course that would work
But what would 200% of a hamster look like-
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u/conway92 Jan 28 '23
It turns out people used to never actually get anywhere until Leibniz and Newton invented integration. They just got stuck between infinitely smaller subdivisions of any given distance, having infinite increasingly small segments to traverse, and naturally were unable to accomplish an infinite number of tasks.
It's one of Zeno's paradoxes, probably the most famous one.
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u/grebolexa Jan 28 '23
That’s where the idea of atoms came from. If I cut an apple into half and that half into half again and again then it’ll eventually be so small that I can’t cut it anymore which means that there’s something there yet unseen being the building blocks of the universe
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u/ToebeansInc Jan 28 '23
Yes, and if you add all the fractions up( despite there being infinite number of them) it will equal 1
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u/ydoiwantreddit Jan 29 '23
So, a mathematician, a physicist, and an engineer find themselves standing in a room opposite three drop dead gorgeous 10/10 girls. They are each told that they can, at each step, halve the distance between themselves and the girls, but they can never touch. The mathematician and physicist storm out of the room in a huff; meanwhile, the engineer: "sixteen feet ... eight feet ... four feet ... two feet ... one foot ... six inches ... three inches. Close enough for practical purposes!"
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u/MarcoYTVA Jan 28 '23
If you want to go from here to there, you first need to walk half the distance, then half the remaining distance, then half of that, then half of that at infinitum. How do you get there?
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u/Bob_Chiquita Jan 28 '23
At infinite time, the limit approaches "there," so mathematically you ARE there. In the same way that 0.999... repeating is actually equal to 1.
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u/chez_les_alpagas Jan 28 '23
It's not infinite time because going half the distance takes half the time. It's just arbitrarily dividing the trip up into an infinite number of parts. In the limit, parts are infinitesimally small and take an infinitesimally small amount of time.
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Jan 28 '23 edited Jan 28 '23
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u/TotallyBoat Jan 28 '23
The solution to this specific summation is 1 though lmfao. You are correct in that not all infinite summations equal a finite number but this one in particular does. This can be intuitively imagined by drawing a line dividing a square’s area by half. Then repeat this with that half and so on. Notice how the summation of these halves are the same in a series, 1/2 + 1/4+…1/2n but the total area is still 1 (assuming square side length of 1)
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u/texasrigger Jan 28 '23
1/3 = .333...
.333.... x 3 = .999...
.999... = 1
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u/btveron Jan 28 '23 edited Jan 28 '23
This is just an artifact of using base 10. In base 12, for example, 1/3 = .4 and .4 x 3 = 1
Edit: why the downvotes? .999.... = 1 is not an example of a limit approaching an answer. It's an example of the quirks of decimal representations of fractions in different bases.
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u/Devildawq1 Jan 28 '23
No one is ever going to be on board with 1/3 = .4
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u/texasrigger Jan 28 '23
I love that the same people that will swear by dozenal (base 12 number system) also defend the base 10 metric system as superior. Give me a base 12 metric system!
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u/HamOnRye__ Jan 28 '23
In like third grade my friend had this book weird and creepy stories. One of them was about a boy walking home from school, trying to reach the stop sign at the other end of the street. He was thinking to himself how he only needs to get halfway there and then halfway from there, so on and so forth. It ended implying that he spent an infinite amount of time walking halfway.
That shit blew my little mind and I remember contemplating it for the next several days.
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u/Roflkopt3r Jan 28 '23
And there are two main answers to that:
In descrete systems, there is a minimum step size that you can no longer subdivide. For example the hamster would be down to a single hair at some point. So assuming the barber uses a regular shaver and cannot subdivide hairs, this would be the final step.
In a continuous system like the position of a walking person, an infinitesimally small step would also only take infinitesimally little time. If you walk at 1 meter per second then you also walk at 0.5 m/0.5 s, 0.25 m/0.25s.... but it's all the same, it's all just 1 m/s. You will continue to move as long as time passes.
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u/Babies_Have_No_Teeth Jan 28 '23
Do do an infinite amount of tasks in a finite amount of time/distance etc. For example eat infinite cookies in a few minutes but wait half the time of the previous to eat the next cookie, like this: eat a cookie wait 2 minutes, eat a cookie wait 1 minute, eat a cookie wait 30 seconds, eat a cookie wait 15 seconds etc. By constantly waiting half the time of the previous you could eat infinite cookies in a finite amount of time, when the time is up, the cookies are up. But since its infinite there always is a next step
Source: Vsauce
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u/cimocw Jan 28 '23
At some point the time required for completing the task will be more than the remaining time, so there's a clear and measurable limit.
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u/VRichardsen Jan 28 '23
Also known as Achilles and the turtle. It is used to express the concept of limit in calculus.
https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Achilles_and_the_tortoise
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u/PriusProblems Jan 28 '23
It's a tailless rodent often kept as a pet, but that's not important right now.
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u/anglostura Jan 28 '23
Aka Zeno's paradox of the arrow
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u/Gs305 Jan 28 '23
If infinity taking forever explains a paradox, is it really a paradox?
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u/Clockwork_Firefly Jan 28 '23
But infinity (as understood in the Zeno paradoxes) doesn’t take forever! That’s what makes them unintuitive
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u/No-Olive-4810 Jan 28 '23
Well, sort of. Zeno was approaching a different question: for any two points in space, must there always be a third point in between? If yes, space is uniformly continuous, if no, space is discrete. His argument was that if space was uniformly continuous, the arrow would never hit the wall — but it does, so space must be discrete.
It’s extremely fascinating as a litmus test for determining the topology of infinities, but it doesn’t actually speak to infinities themselves; mathematically, where the number space is continuous, the arrow doesn’t hit the wall, and there’s nothing particularly strange or counterintuitive about that, since we already knew the topology. Zeno was cognizant of this.
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u/BlackH0l Jan 28 '23
Except this is incorrect, because even if you consider space to be continuous the arrow will mathematically hit the wall. It's because if you consider the arrow's speed to be constant, then it will take half the time for it to travel half the distance, meaning the total time it will take to travel the infinite number of half-step to the wall is the infinite sum of 1/(2n) for n going from 1 to infinity, and that sum is finite and equal to 1
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u/No-Olive-4810 Jan 28 '23
It won’t. The mathematical function you have given has a limit of 0 at upper bounds of n, but never actually reaches 0.
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u/BlackH0l Jan 28 '23
It's not a function, it's a sum and it's equal to 1, no limit involved. If you don't want to take my word for it: https://en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/16_%2B_%E2%8B%AF#
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u/T3h_j0k3r Jan 28 '23
Wouldn't at some point have oly one single hair? Is the barber going to cut that is half?
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u/Rigberto Jan 28 '23
Nah, it just agreed to live out it's life casually as a skinny pig, not worrying about paradoxes. Guinea pigs are careless little shits.
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u/bliply
Jan 28 '23
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We can argue if this is possible to make something infinitely small, but in the end we would just be splitting hairs...
PS: getting a haircut when you only have one atom of hair left.. ...would be the bomb, though.
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u/GetsGold Jan 28 '23
A single atom being split won't be a big deal. You need a bunch of them to start causing problems.
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u/Gnoxkulls Jan 28 '23
Is there such thing as a "hair" atom?
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u/bliply Jan 28 '23
https://en.m.wikipedia.org/wiki/Alpha-keratin Technically it is a molecule but molecules are made out of atoms so if you keep taking them apart you get down to a atom eventually, after that it gets kind of Quarky, you wouldn't even understand the gravity of the situation.
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u/WikiSummarizerBot Jan 28 '23
Alpha-keratin, or α-keratin, is a type of keratin found in mammalian vertebrates. This protein is the primary component in hairs, horns, claws, nails and the epidermis layer of the skin. α-keratin is a fibrous structural protein, meaning it is made up of amino acids that form a repeating secondary structure. The secondary structure of α-keratin is very similar to that of a traditional protein α-helix and forms a coiled coil.
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u/Shameboi9739 Jan 28 '23
Is anybody talking about the weird reflection
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u/MaeronTargaryen Jan 28 '23
Yeah I just thought “that’s not how mirrors (or a window I guess) work”
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u/486921 Jan 28 '23
And people don't have two eyes on the side of their face, but that didn't stop Picasso and Peppa! 👁👁👄
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u/Meekman Jan 28 '23
That's what caused me to reread the comic a couple times to understand it. Those panels messed me up.
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u/10gistic Jan 28 '23
Looks like the artist just copied and pasted the layer and inverted it horizontally rather than completely redrawing from another perspective. Which, tbh, I'd probably do. 80% effective with minimal effort.
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u/metatron207 Jan 28 '23
80% puts you firmly in the uncanny valley. A redraw that wasn't as good may have been less noticeable.
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u/unaotradesechable Jan 28 '23
It's not bad of people notice though. If he's getting engagement solely by people complaining about the mirror, that's a net positive.
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u/TheNitroExpress Jan 28 '23 edited Jan 28 '23
Literally forever, yes!
Edit: I'm an engineer, not a philosopher, supertasks are a hotly debated topic in philosophy, but mathematically, this goes on infinitely.
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u/ButteredBagleBoy Jan 28 '23
If the first one took 1/2 a min and second to 1/4 and third 1/8 and soo on it would total 1 min
Edit: According to Netflix
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u/TheNitroExpress Jan 28 '23
You cannot half something out of existence unless you round. Sure the cuts will take less time, but there will be an infinite amount of them.
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u/O_Martin Jan 28 '23
If each haircut takes a decreasing amount of time as suggested, you would have 2 geometric sequences, with no end but one would sum to 1 haircut and the other would sum to the time taken
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u/No-Height2850 Jan 28 '23
Well the end would be the last hair. After that, even if the math can continue, the hair is gone so you have a 3rd geometric sequence of a finite resource.
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u/throwawaysarebetter Jan 28 '23
Cut half the hair.
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u/Not_Sugden Jan 28 '23
while true, with a haircut at some point it would be impossible to indefinetly half it and thus the cut would be complete at some stage. and it will be realistically complete at an even earlier stage due to the fact you will have so little hair its no longer visible that you have any
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u/TheJWeed Jan 28 '23
It would have to get to the point that you split the last atom on this guys head.
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u/No-Height2850 Jan 28 '23
A barber would need to buy an atom splitter, or as a barber, round up on cutting the last hair.
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u/Treacherous_Peach Jan 28 '23
This is called a super task and it can in fact be completed in finite time. Google super tasks to learn more.
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u/ATXBeermaker Jan 28 '23
If the haircut took an amount of time proportional to the amount of hair cut then the infinite sum would only take the time of a single haircut. Once you start taking practical things like wait time, etc into account, you would also need to account for the tolerance in accuracy you would need to call the complete haircut done.
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u/Willis_is_This Jan 28 '23
Eventually you’ll be down to one hair, wouldn’t you? What happens then, if he asks you to cut half? You cut the hair halfway? That’s still a haircut. This wouldn’t go on forever, just a long time, because there’s a finite number of times you can divide the available resources
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u/Ten-2-Ten Jan 28 '23
No it wouldn’t. It would go on forever because they’re only taking 50% off the last amount and will never take off 100%
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u/KrokmaniakPL Jan 28 '23
Technically there is a base case for this recursive situation. It's 1 hair atom left. Unless you want to go all the way to theoretical strings, but still there is an end.
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u/Johannes_Keppler Jan 28 '23
There is no such thing as one 'hair' atom though. Possibly a keratin molecule, but those make up 'only' 95% of hair.
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u/AnUglyDumpling Jan 28 '23
Yes it would. This is the classic Achilles and the tortoise paradox. Even though it'll technically never get to 100%, the time taken is also halving. After 1 minute, all the hair WILL be shaved off.
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u/Ten-2-Ten Jan 28 '23
This is a Zeno Paradox but not the one you’re referring to. This would be under the Dichotomy Paradox example because it is splitting the difference each time they leave the barber.
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u/AnUglyDumpling Jan 28 '23
Correct, but u/ButterflyBagleBoy was talking about if each haircut took half the amount of time as the previous haircut. In THAT case, all the hair WILL be shaved by a minute.
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u/Striking_Plant_76 Jan 28 '23
But they will never reach the minute. Unless all the hair is shaved… which would only be after one minute… but for that all the hair would need to be shaved. It’s a paradox, since both statements depend on the other to be true, but can’t be true without the other being true. Thus, in a real life example all the hair would be cut after one minute simply because it’s almost impossible to shave 1/1024 of a hair, nor to take 1/1024 of a second to do so. However in theory the paradox will only get close to a minute, but will never hit it (same with the hair: it will get close to shaved, but will never hit it). The mathematical way to describe this would be 1 devided by X (basically, it’s an asymptote).
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u/Treacherous_Peach Jan 28 '23 edited Jan 28 '23
You're messing this all up unfortunately. The paradox is that in order to finish a race you must go halfway first. And to finish the second half you must go halfway again. But that suggests you can't finish a race because there's an infinite number of halfways you have to go. But obviously you can finish the race. Thus the paradox.
Anyway it's not really a paradox. Everyone in this thread seems to have half understandings of this all.
What the person earlier in the comment chain described is a super task. Half the hair is being cut but each cut is taking half as much time. You can take a limit of the hair cuts to see it is approach 0 hair, so all the hair will be gone at the end of the supertask. In addition, since each step takes half as long, it will complete in finite time.
The race of Achilles is the common example of the paradox and the supertask that answers it. If Achilles is moving at a constant 10m/s and needs to run 10 meters then he will get halfway there in 0.5s. He will get the next halfway point in 0.25s. Then the next in 0.125s.. etc. As we can see it's the same scenario the limit of the distance as it approaches infinity is 10m. The limit of the time it takes approaches 1s. Which is how long the super task does ultimately task to complete.
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u/Striking_Plant_76 Jan 28 '23
As you have said: in the real world this paradox does not work, since it would be finite (either time, length or amount of hairs just can not get smaller). However, mathematically the paradox does work. If you would put 1 divided by X in a calculator and graph it, it would show you that it never reaches zero. That’s why there are two sides debating here: some people are realists (would this work irl) and some are theorists (would this work if I calculate it). Both sides are right!
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u/bobguy117 Jan 28 '23
The maximum total amount of time would be 1 minute but 1 minute would never be reached
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u/Kilomyles Jan 28 '23
Nah, finite amount of hairs, and the comic established cutting is a clean shave, so no fractional hairs. This seems infinite, but it’ll terminate eventually.
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u/MilkAzedo Jan 28 '23
it's a clean shave because there's more than 1 hair
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u/JavaOrlando Jan 28 '23
But what do you do when there is only 1 stand left? Cut it in half? Then in half again? When that strand is 1/128th of its original length, isn't that basically a clean shave anyway? And if you do keep going (if we pretend it's possible to keep cutting the strand in half) what do you do when you're down to one molecule? Start splitting atoms?
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u/MilkAzedo Jan 28 '23
all the other hairs were cut to the max possible. The remaining one will be cut but will never reach the max. By the time they measure the hair to check if it's right the rest of the hairs will grow again, taking more time to measure and more time to grow
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u/JavaOrlando Jan 28 '23
Sure, but long before then, it would appear to be a complete haircut to the naked eye. But we're both being overly pedantic and ruining the joke.
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u/SkinnyObelix Jan 28 '23
So explain to me when someone throws a ball at my face, I can forever half the distance between the ball and my face, yet I end up with a black eye...
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u/ctharmander Jan 28 '23
Just end with the landing strip. Keeps it sanitary and you can wear the banana hammock to the beach
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u/CaffeinatedGuy Jan 28 '23
It's functionally finite due to the finite number of hairs, but mathematically infinite.
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u/cozy_lolo Jan 28 '23
Incorrect, in my opinion. We’re not cutting the hairs solely as whole strands, but maintaining the concept of reducing the available hair by half, which only initially entails removing whole strands. Whenever there is, say, one strand left, then we begin cutting that strand in half, and if we had the technology, we thus begin cutting the strand into infinitesimally small pieces. I guess the terminus would be eventually arriving at the most fundamental physical particle that cannot be further divided. Only then is the haircut complete!!
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Jan 28 '23
My dad used to say it in golf about putting- you can be short forever, so putt through the hole.
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u/Starik655321 Jan 28 '23
It will eventually reach an equilibrium where hair growth between haircuts equals hair removed per haircut. At this point, the hair would be doubling in length between each cut, only for half of it to be removed each time.
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u/hop_mantis Jan 28 '23
An infinite number of mathematicians walk into a bar. The first one orders a beer, the second one orders a half a beer, the third orders a quarter of a beer, and this trend continues on for some time.
After a while, the bartender gets fed up and hands them 2 beers, shakes his head and says, “You mathematicians just don’t know your limits.”
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u/hackingdreams Jan 28 '23
Zeno's paradox doesn't work on real life objects with physical dimensions. Once you're splitting atoms you're really not talking about hair anymore. It works with distances because they're abstract - you can keep dividing them all the way down to a Planck length (the shortest meaningful distance in the universe).
Realistically after a few dozen iterations there's nothing left worth talking about anyways. That creature would be smoother than me after a close shave.
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u/Baldazar666 Jan 28 '23
Literally not because at one point you will be left with a single atom of hair left.
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u/shadowraiderr Jan 28 '23
Not true. There is a finite amount of hair and even after that, if you keep cutting the last hair in half over and over, its gonna have 1 planck length, which is the smallest size anything can exist in universe.
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u/InfiniteZr0 Jan 28 '23
I wonder what happens as the rest of the hair grows back.
At what point is the grown back hair is cut in half and what kind of trippy patterns you get when the half cuts get half cut.
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u/Sire_Cage Jan 28 '23
In the "very end" you'd have to cut an atom
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u/Rocket-R Jan 29 '23
Local barber shocks scientists as he cuts an electron in half with his scissors
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u/RealHot_RealSteel Jan 28 '23
An infinite number of mathematicians walk into a bar. The first orders a beer. The second orders half a beer. The third orders a quarter, the fourth an eighth. Before the fifth mathematician can order 1/16th of a beer, the bartender cuts him off, pours two beers, and says "y'all need to know your limits."
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u/Enby_Rin Jan 28 '23
I love this comic, I haven't seen it in years! Thanks for making my day better :)
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u/Alive-arrival-forgot Jan 28 '23
One hair, after 50 tries.
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u/Johannes_Keppler Jan 28 '23
I thought about this practical approach too. Makes you wonder why a guinea pig would go to a hairdresser for a full shave in the first place, it would die from hypothermia the same night.
Anyway, after a few more tries the guinea pig would have no noticeable hair left. But that's clearly not thinking in the spirit of the cartoon.
Also, 50 haircuts for 1/2 price is still about 1000 Euro where I live if we take 40 Euro as the full price.
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u/PixelBits89 Jan 28 '23
I imagine the Guinea Pig is getting a haircut because this is a society where they’re the dominant intelligent life. In the same way it’s weird that humans shave their heads when the hair keeps them warm, the Guinea pigs shave themselves. But just like humans, they likely have stuff like clothes or hats
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u/Victor4VPA Jan 28 '23
Se ele ir mais algumas vezes o pelo vai ficar tão pequeno que nem vai dar pra ver mais
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u/Victor4VPA Jan 28 '23
Ah, I forget this is a sub in english, translating: If he goes a few more times, the fur will be so short that you won't even be able to see it anymore
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u/Kingstad Jan 28 '23
I am so bothered by the reflection not facing the same dang direction as him!!
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u/ILikeGuitarAmps Jan 28 '23
Wait till it gets to 2/4, 4/4, 7/4 and if we are a little frisky 9/8
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u/garlic_lollipop Jan 28 '23
Either there'se another guinea pig messing with him, or the author didn't even bother to look at a miror before drawing this.
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u/HubertFiorentini Jan 28 '23
The inaccurate reflection in this comic irritates me every single time.
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u/Turence Jan 28 '23
You will eventually be brought to 1 hair, where they should begin cutting the single hair in half a few times, which is good enough.
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u/villings Jan 28 '23
Ahh so the little guy is walking back in... I thought that was a reflection
Confusing perspective..
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u/andthebestnameis Jan 28 '23
I'm so dumb, I didn't realize the haircut was changing, so the joke made no sense to me...
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u/Granny4TheWin7 Jan 29 '23
If the guinea pig has 200,000 hairs and it goes to the barber to shave half of its hair, it would be left with 100,000 hairs. The next time it goes, it would be left with 50,000 hairs, then 25,000, 12,500, 6,250, 3,125, 1,563, 781, 390, 195, 97, 48, 24, 12, 6, 3, 1.
So he would be splitting hairs if he went 19 times technically.
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u/Crying_eagle Jan 29 '23
Eventually when there is one hair they will cut that hair in half, and then all of his hair would have been cut off
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u/AvocadoSea242 Jan 29 '23
Not exactly on topic, but someone in a bar once asked me "If you could travel at the speed of light, how long would it take to get to the nearest star?" I said "No time at all." He said "You're an idiot. The number of years it takes is the same as the distance in light years." I said "That's your point of view."
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u/Flrere Jan 28 '23
What happens when they get to the last hair? Let's not split hairs over this now
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u/Square-Parfait-4617 Jan 30 '23
I remember a joke where a bunch of scientists and an engineer had this premise but they would walk half of the distance to a naked lady. The scientists have up because they said it's impossible and the engineer said "I eventually would get close enough for practical purposes"
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u/boi012 Jan 28 '23
It will never end until the split an atom and we don’t know what to do with quarks
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