Forums → The Tavern → Maximum Disorder of Dumbbells on a Rack
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Well that title probably didn't bring to you thoughts of, "Oh boy, this will be fun!" But I'm having trouble with a thought and maybe one of you can help. (I'm posting out of curiosity and for fun. And the post sort of rambles, but here goes.)
Sometimes when I'm at a gym I notice that the dumbbells are out of order. Then, one fine day, I started to wonder, "Is there is a point at which the dumbbells on the rack are at maximum disorder. Now I might be using the wrong terminology and I may not have used the proper setup as well and this is were I need help. Here is the in-depth explanation:
- You have 10 pairs of dumbbells (20 dumbbells total) the lowest weight pair of dumbbells is 5 lb and the highest weight pair of dumbbells is 50 lb.
- The weight increments are 5 lb.
- The dumbbell rack has two levels, a top level and a bottom level.
- The top level holds 5 pairs of dumbbells (10 dumbbells) and the lower level holds 5 pairs of dumbbells (10 dumbbells).
- When you are facing the rack the lightest pair should be on the top left and the heaviest pair on the bottom right. In this state the rack is at 100% order and 0% disorder.
- Here is a representation of the rack at 100% order and 0% disorder.
Top Level : (5,5) (10,10) (15,15) (20,20) (25,25)
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Bottom Level: (30,30) (35,35) (40,40) (45, 45) (50,50)
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- Moving one 10 lb dumbbell to the 15 lb dumbbell spot increases the disorder by an interval of 3. (Shown below) Notice how the 10 lb and 15 lb dumbbell are right next to each other.
Top Level : (5,5) (10,15) (10,15) (20,20) (25,25)
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Bottom Level: (30,30) (35,35) (40,40) (45, 45) (50,50)
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- Moving first 5 lb dumbbell to the 50 lb dumbbell spot increases the disorder by an interval of 48. (Shown below) Notice how the are the maximum distance away.
Top Level : (50,5) (10,10]) (15,15) (20,20) (25,25)
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Bottom Level: (30,30) (35,35) (40,40) (45, 45) (50,5)
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- Moving one 10 lb dumbbell to the 15 lb dumbbell spot in this way, increases the disorder by an interval of 2. (Shown below) Notice how the 15 lb dumbbells are still right next to each other.
Top Level : (5,5) (10,15) (15,10) (20,20) (25,25)
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Bottom Level: (30,30) (35,35) (40,40) (45, 45) (50,50)
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- Moving a pair 10 lb dumbbell to the 15 lb dumbbell spot increases the disorder by an interval by only 1. (Shown below) Notice how the 10 lb and 15 lb dumbbell pairs switch exactly.
Top Level : (5,5) (15, 15) (10,10) (20,20) (25,25)
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Bottom Level: (30,30) (35,35) (40,40) (45, 45) (50,50)
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- At which point will it be in dynamic maximum disorder? In other terms, at what point will the dumbbell rack be so out of order that if you were to pick up one dumbbell (or one dumbbell pair) and then return the dumbbell(s) to any spot (the pair can be returned to a spot where they are not next to each other) the dumbbells order and disorder will remain statistically the same (or only move up in order by the smallest amount possible or down in order by the smallest amount possible)?
- I'm not expecting an answer to the question per se (that would be cool, but maybe difficult), but what I would like to know is do I have the set up right? Have I used the proper terminology? Is this entropy, chaos theory, or something else?
- 18 Replies
Isn't this also under the larger umbrella of statistics? So CS computer science or computational statistics? Perhaps both?
I meant Computer Science, because a lot of it deals with various optimization problems.
I feel a chess algorithm/chess program could be modified to determine what moves (on the dumbbell rack) lead closer to organization or disorganization and how much organization or disorganization is introduced in one dumbbell (or dumbbell pair) move.
You're right, you could model a program similar to a chess bot, in that it could evaluate certain moves and finding an optimal solution accordingly. Of course, you'd need to define not only maximum dumbbell disorder, but also a stopping point, because unlike chess there's no "winning condition" to stop the program.
Although admittedly, that's kinda overkill. There's a few simpler ways one could tackle the problem.
But the real question is, do I continue and try to find an actually answer? Would there be an agreed upon answer (different algorithms arriving at the same configuration for maximum disorganization of the dumbbell rack) or would maximum disorganization always be subjective to how a person defines "maximum disorganization (of the dumbbell rack)?"
It isn't so much an issue of what disorder *is*, but rather how you measure any given configurations degree of disorder. If the evaluation is the same, then different algorithms would lead to similar results, depending on how the algorithms in question work.
Sounds like a strange phrasing for the second law of thermodynamics.
Which includes entropy. Yay!
I found this video, it takes a moment but it eventually talks about entropy, although not very in depth.
The Arrow of Time feat. Sean Carroll
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