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A tightly packed box of paper clips where there is no movement means there is no change in entropy and behaves like a state in equilibrium.Which should be simple enough (though tedious) to confirm. How tightly the box is packed should be a factor: tightly packed box = less movement of paper clips. Anecdotally, the longer paper clips stay in the container on my desk, the greater the likelihood that when I remove one it will be linked to another. Note that the longer they are on my desk, the number of paper clips in the container drops until I refill it. I'm currently at the point where, when I remove a paper clip, it's more likely to be linked with another than I am to remove a single one.
It seems to be struggling to differentiate between an example and analogy.Yes — a box of paper clips is an analogy or macroscopic example of statistical mechanics, but not a true thermodynamic system. Let me explain carefully.
1. Why it’s an analogy
Statistical mechanics was originally developed for microscopic particles (atoms, molecules) to explain thermodynamic behavior. The key ideas are:
- Microstates: all the possible configurations of the system.
- Macrostates: coarse-grained properties like temperature, pressure, or total number of links in the paper-clip example.
- Entropy: measures the number of microstates corresponding to a macrostate.
In the paper-clip box:
- Each linking configuration (which clips are linked/unlinked, in which arrangement) is a microstate.
- A macrostate could be “2 links formed” or “all free.”
- Entropy can be defined as (S = k \ln \Omega), counting the number of accessible microstates.
This mirrors the logic of statistical mechanics, but the “particles” are macroscopic paper clips, not atoms.
2. Why it is not real thermodynamics
To apply genuine thermodynamics/statistical mechanics:
- You usually need a huge number of particles (~10²³).
- Particles move due to thermal motion, not external shaking.
- Concepts like temperature, heat, and energy spectra are meaningful at the molecular scale.
In a paper-clip box:
- There are only dozens or hundreds of clips.
- Motion comes from shaking, not thermal agitation.
- “Entropy” is really configurational combinatorics, not true molecular entropy.
So it’s a macroscopic analogy — it demonstrates the statistical principles (microstates, macrostates, entropy, equilibrium) in a visible, intuitive way.
3. Why it’s useful
- Helps visualize entropy changes: free clips → high entropy, linked chains → lower entropy.
- Shows how equilibrium corresponds to the most probable macrostate.
- Illustrates energy input and dissipation (shaking → linking → friction/heat) as in statistical systems.
✅ Summary:
- The box of paper clips is not a real thermodynamic system, because the clips are macroscopic and the “temperature” is metaphorical.
- It is an analogy or example of statistical mechanics, illustrating the concepts of microstates, macrostates, entropy, and equilibrium in a tangible way.
If you want, I can make a diagram showing paper-clip microstates and corresponding entropy, which makes this analogy extremely clear.
They’re often called blim burns. When incomplete combustion occurs in fragments of cannabis resin fall from the spliff onto one’s jumper or top.If you have a cat, that may be the reason.
Socks are just paired items that aren't secured together, making it easier to loose one.
#42 is a very significant number in the world of literature.Sock Pair #42
A: Red top
B: Stripes middle
C: Star toe
I assure you I did not prompt GPT-5 to give this answer, while various posters have made jokes about socks in this thread, when AI starts engaging in humour about socks it is frankly rather creepy.Ah! I see what you’re asking — in my sock analogy earlier, I labeled a pair of socks as Sock Pair #42. That choice wasn’t physically significant… it was a cultural reference
42 is famously known as:
“The Answer to the Ultimate Question of Life, the Universe, and Everything.”
…according to Douglas Adams’ The Hitchhiker’s Guide to the Galaxy.
So the significance in Sock Pair #42 was simply:
✅ A playful Hitchhiker’s reference
❌ Not a physics constant, not a special number in Bell’s inequality
It was just a little Easter egg hidden in the analogy
If you'd like, I can relabel the sock pair to another number — but personally, 42 is always a good answer.
I'm a pretty slow walker.I'll take a stab at this:
Probably because you walk forward more than you walk backwards.
The front of your t-shirt takes the brunt of the air resistance and, over time, the threads weaken.
Much like the front of your car getting chipped and scratched more than the back.
"Man is born unto trouble as the sparks fly upward."You get little holes in the front of your shirt, because little bits of hot metal fly off the grinding wheel of life.
This is strange to me. I rarely ever have clips clipped together. I keep mine more or less vertically in a jar somewhat like a salt shaker about as big around as a silver dollar. They're not packed tight, and I have big and small in the same container. Awhile ago I picked it up, turned it upside down so some clips fell into my hand. I took one, dumped the rest back in. I can't recall clips ever being attached to each other.Which should be simple enough (though tedious) to confirm. How tightly the box is packed should be a factor: tightly packed box = less movement of paper clips. Anecdotally, the longer paper clips stay in the container on my desk, the greater the likelihood that when I remove one it will be linked to another. Note that the longer they are on my desk, the number of paper clips in the container drops until I refill it. I'm currently at the point where, when I remove a paper clip, it's more likely to be linked with another than I am to remove a single one.
Exactly. All of mine are black, and I haven't noticed that any them have gone missing.
I said that I haven't noticed that any them have gone missing. Noticed being the keyword.How do you know, have you counted them ? The pinching sock fairy could get to you too.
The shooter is in front of you. That's why the holes appear first in the front, and then in the back second.I wish CF were more well-trafficked, so I decided to do my tiny part by posting more and making more threads. Of course an increase in the quantity of threads will mean a decrease in the quality, as you can tell from the title.
It seems counter-intuitive given that the back of the shirt presses against the backs of chairs when I sit, and against a wall if I lean against one, but the front rarely touches anything. Yet over the years holes have appeared in the front, rarely ever in the back. Of course I asked AI about this, and got an answer which seems possibly insightful yet possibly bogus. But I've been told I need human interaction in my life, so, any thoughts on this? Are anyone's experiences similar? Or different?
I've been meaning to have those holes in my torso checked out.The shooter is in front of you. That's why the holes appear first in the front, and then in the back second.
But more seriously, if you work with acid or with course or abrasive things, they might cause some holes. Or if your chest is hairier than your back...I've been meaning to have those holes in my torso checked out.
Only abrasive thing I have to work with is my wife.But more seriously, if you work with acid or with course or abrasive things, they might cause some holes. Or if your chest is hairier than your back...
ChatGPT has turned into a comedian.
Why do they keep putting those awful things in my mixed nuts?Not particularly useful. Unlike the tendency of larger items mixed with smaller items to rise to the top when the container is shaken. The smaller items tend to shift beneath the larger. Handy if you have a can of mixed nuts and want to get the Brazil Nuts first.
It was such ground breaking research it won the 1996 Nobel Prize in Physics.As everyone knows toast always lands on the buttered side when dropped on the floor and cats land on their feet. So what happens when buttered toast facing upwards is strapped on the back of a cat which is then dropped from a great height?
This is one of the great mysteries of science and since Chatgpt-5 joked about my sock analogy I posed the question.
ChatGPT has turned into a comedian.
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