Skip to content
Do you have adblock enabled?
 
If you can read this, either the style sheet didn't load or you have an older browser that doesn't support style sheets. Try clearing your browser cache and refreshing the page.

(Big Think)   How a simple game of Plinko perfectly demonstrates the power (and randomness) of chaos theory   (bigthink.com) divider line
    More: Cool, Quantum mechanics, Physics, Determinism, Classical mechanics, Chaos theory, Plinko chips, best efforts, initial pricing game  
•       •       •

726 clicks; posted to STEM » on 17 Aug 2022 at 8:33 AM (6 weeks ago)   |   Favorite    |   share:  Share on Twitter share via Email Share on Facebook



13 Comments     (+0 »)
View Voting Results: Smartest and Funniest
 
2022-08-17 8:06:44 AM  
A chaotic system basically means one in which the uncertainty doubles (or more) after a certain time interval. Meaning that no matter how good your initial parameters, eventually you will have no idea what's going on.

For example, let's say you have a ball bouncing around on a circular pool table of diameter 1 meter, and your initial uncertainty in the position of the ball is one millimeter.

If, in this chaotic system, your uncertainty doubles every minute, then after one minute you know the position within 2 millimeters, then 4, 8, 16, 32... Until after 10 minutes your uncertainty in the position of the ball is plus or minus 1.024 meters, which is larger than your table, so the ball could literally be anywhere.

By knowing the initial conditions more precisely, you can push back the "I have no idea" time, but since infinite precision is impossible, especially with a quantum world, you'll always reach a point where you can't give any info on the condition of they system even if it were completely deterministic.
 
2022-08-17 8:57:47 AM  
that isn't a random system.  given enough attempts you'll end up with a standard bell curve distribution.
 
2022-08-17 9:19:53 AM  
TFA: If you take a particle like an electron, you might think to ask questions like:

Me: Well, how did I get here?

/Same as it ever was
 
2022-08-17 9:32:30 AM  
What does Cliffhangers demonstrate?
 
2022-08-17 9:34:49 AM  

sleze: What does Cliffhangers demonstrate?


The awesomeness and nightmare life of a yodeler
 
2022-08-17 10:11:24 AM  
c.tenor.comView Full Size
 
2022-08-17 11:10:42 AM  
Wait what? Plinko is just pool geometry on a large scale. Puck hits peg at angle x and goes in direction y. Repeat till its over. There is nothing random about that in any way. I honestly dont think any human created object or system is capable of being truely random because we hate the very idea of random
 
2022-08-17 11:22:02 AM  

tom baker's scarf: that isn't a random system.  given enough attempts you'll end up with a standard bell curve distribution.


You know what a bell curve does?  It describes the outcome of multiple events from a random system. Just because you can describe the outcomes of system, that doesn't make it not-random.

I would also add to this that you're not exactly correct.  The bell curve only comes out if you drop from the center point each time.  You have a choice of where to drop the disk from when playing Plinko.  If you drop it from an outer edge, you get a half bell curve.  If you drop it 1/3rd away from an edge, the "tail" of the bell curve that falls outside the play area gets reflected inward, so you get something flatter on the edge of the playfield but only tapers on one side.  Its certainly driven by the same math that creates a bell curve, but technically its not a bell curve.
 
2022-08-17 11:26:34 AM  
Yeah? Well, your mom has fat tails on her Guassian envelope
 
2022-08-17 11:42:28 AM  
Also, i wonder if this is a copyright violation on his site since he did this exact article 2 years ago for forbes
 
2022-08-17 2:10:22 PM  

Concrete Donkey: Wait what? Plinko is just pool geometry on a large scale. Puck hits peg at angle x and goes in direction y. Repeat till its over. There is nothing random about that in any way. I honestly dont think any human created object or system is capable of being truely random because we hate the very idea of random


I think the Pinko puck doesn't bounce (or at least that elasticity is minimized), so the pool analogy doesn't work. What the writer seems to have been trying to point out is that even if the puck lands perfectly dead on with respect to the puck, it will still roll one way or another.
 
2022-08-17 2:39:07 PM  

Concrete Donkey: Wait what? Plinko is just pool geometry on a large scale. Puck hits peg at angle x and goes in direction y. Repeat till its over. There is nothing random about that in any way. I honestly dont think any human created object or system is capable of being truely random because we hate the very idea of random


The point is that the more levels you add the more precision you have to specify x to, until it is literally impossible to include enough precision.  Even then, a random sneeze, a wind gust, or a gravitational wave would fark up your calculations.
 
2022-08-17 3:43:02 PM  

davypi: tom baker's scarf: that isn't a random system.  given enough attempts you'll end up with a standard bell curve distribution.

You know what a bell curve does?  It describes the outcome of multiple events from a random system. Just because you can describe the outcomes of system, that doesn't make it not-random.

I would also add to this that you're not exactly correct.  The bell curve only comes out if you drop from the center point each time.  You have a choice of where to drop the disk from when playing Plinko.  If you drop it from an outer edge, you get a half bell curve.  If you drop it 1/3rd away from an edge, the "tail" of the bell curve that falls outside the play area gets reflected inward, so you get something flatter on the edge of the playfield but only tapers on one side.  Its certainly driven by the same math that creates a bell curve, but technically its not a bell curve.


And the TPIR Plinko board is long enough that, even if you do drop from the center, both tails of the distribution are reflected inward.

In fact, a Plinko board of any fixed width will approach a uniform distribution the longer you make it, no matter where the initial drop comes from.  (At least in the narrower rows.  The wider rows are nearly uniform, except that the two edge columns have half the probability of the others.)
 
Displayed 13 of 13 comments

View Voting Results: Smartest and Funniest

This thread is closed to new comments.

Continue Farking




On Twitter


  1. Links are submitted by members of the Fark community.

  2. When community members submit a link, they also write a custom headline for the story.

  3. Other Farkers comment on the links. This is the number of comments. Click here to read them.

  4. Click here to submit a link.