The Sock Toe-Hole Symmetry Breaking Problem

[FlexGunship]

I love my nice argyle socks (which I've collected from Christmases passed). But I've noticed a weird inequality in their aging behavior. Toe holes do not form evenly on both sides of the sock.

My socks are not "footed" or "handed." That is to say, I do not have a left-sock, or a right-sock (although, ladies, I assure you that these are the right socks <debonair wink>). So, by random chance, I should expect to put each sock in a pair on each foot equally often.

My understanding is that the big toe degrades the sock's structural integrity until eventually the sock is compromised thus leaving the toe exposed to the interior of the shoe. I believe that repeated wash cycles probably contributes to the effect, but I would think that it would be an exacerbating factor and not an actual causal factor. That is to say, a wash cycle might make a small hole bigger, but won't (in and of itself) create the original hole.

Now, the behavior I have noticed is that, despite the random nature of my sock wearing endeavors, toe-holes do not form symmetrically on both sides of the sock. When taking any given pair, the toe-holes are either on the "inside" or the "outside" (the "outside" being an isometric equal to the "inside" if the pair were left-right swapped).

Why does this happen?!

 

[brewnog]

Because you only ever use one hand (your right?) to hold the scissors to cut your toenails, therefore the burr formed isn't the same on both nails. On average, each sock will be worn on both feet equally, but because the burr pattern doesn't change over time, the wear effect isn't balanced between the two feet.

Easy.

 

[skeptic2]

(the "outside" being an isometric equal to the "inside" if the pair were left-right swapped).

So how do you determine if the holes are on the inside or the outside?

 

[FlexGunship]

Because you only ever use one hand (your right?) to hold the scissors to cut your toenails, therefore the burr formed isn't the same on both nails. On average, each sock will be worn on both feet equally, but because the burr pattern doesn't change over time, the wear effect isn't balanced between the two feet.

Well, that's what I was saying. Is that the toe-holes don't form on the "left" of the sock. They form on the inside, or the outside.

Using this image as a reference:

The "inside" is defined as the parts of the sock closest to the center of the image. This is where my holes are. However, if you translate the socks left and right to swap them, you would find that the hole should be on the "OUTSIDE."

Therefore, after translating socks randomly, I should see equal toe-hole progress on both the "inside" and "outside" of any given arrangement of sock pairing. BUT I DON'T!

 

[FlexGunship]

So how do you determine if the holes are on the inside or the outside?

It's arbitrary but non-trivial. If you hold two socks in a "ready-to-wear" alignment (i.e. heel down, toes pointed out), the holes will be aligned in an "inside" or an "outside" arrangement. Never a "left" or "right" arrangement.

And since swapping socks can only be translation, you would expect the "inside" and the "outside" to wear evenly over time.

Here, the toe hole it on the "inside":

If you swap both socks, then the toe hole will be on the "outside" of the other foot (since heel-orientation must be preserved in sock-swapping).

So, think of a counter on each side of a sock. Every time you wear a sock with the toe on a specific side, you add "1" to the counter. When the counter reaches "10" then a hole forms. If the socks are randomly worn on either foot then why don't holes form symmetrically?

 

[lisab]

You paint your toe nails, Flex?

 

[FlexGunship]

You paint your toe nails, Flex?

No, I stubbed it into submission. Note to self: you can only lose a fight with an appendage.

 

[Gokul43201]

Now, the behavior I have noticed is that, despite the random nature of my sock wearing endeavors, toe-holes do not form symmetrically on both sides of the sock. When taking any given pair, the toe-holes are either on the "inside" or the "outside" (the "outside" being an isometric equal to the "inside" if the pair were left-right swapped).

Why does this happen?!

My guess: Your sock-to-foot pairing is no longer random once a defect starts to form in a sock and breaks the symmetry in the sock shape. Perhaps there is an unconscious urge to make defects be positioned over big toes.

 

[FlexGunship]

My guess: Your sock-to-foot pairing is no longer random once a defect starts to form in a sock and breaks the symmetry in the sock shape. Perhaps there is an unconscious urge to make defects be positioned over big toes.

OKay, I actually thought of this one, and you could be correct. However, if I notice a structural deficiency in the sock, I tend to favor the alternate arrangement. So, it seems that any conscious bias would actually be in the opposite direction.

Does that necessarily override the unconscious bias? Maybe not.

I was recently toying with this idea:

• Socks are weakened evenly, as per intuitive sock toe-hole symmetry theory
• A single discrete event actually causes the initial hole
• This event (for whatever reason) affects both feet simultaneously
• After the initial release of tension in the thread of the socks, there is a strong bias AGAINST future hole formation

EDIT: Flex's actual socks (smell not included). Yes, I have big feet, shut up. You know what they say about big feet, right? Big feet mean big toe-hole symmetry breaking problems.

 

[Gokul43201]

I was recently toying with this idea:

• Socks are weakened evenly, as per intuitive sock toe-hole symmetry theory
• A single discrete event actually causes the initial hole
• This event (for whatever reason) affects both feet simultaneously
• After the initial release of tension in the thread of the socks, there is a strong bias AGAINST future hole formation

I toyed with that idea as well, but abandoned it because I couldn't find any reasonable way to justify point #3 - simultaneity.

 

[FlexGunship]

I toyed with that idea as well, but abandoned it because I couldn't find any reasonable way to justify point #3 - simultaneity.

 

[Gokul43201]

Nice!

 

[FlexGunship]

Nice!

Yeah, I don't do... that.

But, it's a candidate for solving the simultaneity problem. And if there's one solution, there could be others.

 

[mugaliens]

Why does this happen?!

I'd hazard a guess that the holes are more prevalent on the left side of the sock, no? If so, it's probably because you're right-handed, and your big toe on your right foot is slightly longer, thereby causing more wear and tear on the left sides of your sock.

This is also why I'm a fan of cheap, black cotton tube socks. Left, right, right-side-up, upside-down, doesn't matter, and with long pants they go with anything. The only time I wear white tube socks is on those rare days when it's warm enough for shorts but too cool for extended wear of sandals.

 

[turbo]

Holy Socks, Batman!