# How may holes are in this shirt? **URL:** \ **Category:** In My Humble Opinion\ **Created:** [July 29, 2026, 6:46pm UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004 "2026-07-29T18:46:55Z")\ **Posts on this page:** 19\ **Page:** 3
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [July 31, 2026, 11:20pm UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004/41 "2026-07-31T23:20:40Z")
I am not sure, but the three circles I described cannot be moved continuously to one another or shrunk to a point. TBH, it surprised me too. The mathematical subject involved is called homotopy theory and I am not an expert in it. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [July 31, 2026, 11:41pm UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004/42 "2026-07-31T23:41:38Z")
Then again, though, if I start with an ordinary sheet of paper and use a hole-puncher on it four times, then I can draw a whole bunch of independent loops on the paper, far more than 5. At least 16, since I can draw loops that encompass any subset of the punched holes, except it’s even more, since I can wrap those loops around the other punched holes in various ways. ---
**Author:** ![Pleonast](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pleonast/32/1183_2.png) [@Pleonast](https://boards.straightdope.com/u/Pleonast)\ **Post date:** [August 1, 2026, 4:08am UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004/43 "2026-08-01T04:08:40Z")
Sounds like knots. ---
**Author:** ![msmith537](https://avatars.discourse-cdn.com/v4/letter/m/d9b06d/32.png) [@msmith537](https://boards.straightdope.com/u/msmith537)\ **Post date:** [August 2, 2026, 3:31am UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004/44 "2026-08-02T03:31:55Z")
Ok, assuming it’s not an unsolvable trick like “oh there’s a cardboard insert so you can’t see the holes in the back”. Topologically I suppose my question is how many “holes” does a garbage bag have? Because it’s the same topological shape as a T-shirt. Since we used to make garbage bags into summer camp by cutting 3 holes in them, the answer to the question is either 15 or 16 depending on whether the bottom counts. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [August 2, 2026, 5:29am UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004/45 "2026-08-02T05:29:02Z")
> [@Chronos](#): > > Then again, though, if I start with an ordinary sheet of paper and use a hole-puncher on it four times, then I can draw a whole bunch of independent loops on the paper, far more than 5. At least 16, since I can draw loops that encompass any subset of the punched holes, except it’s even more, since I can wrap those loops around the other punched holes in various ways. > [@Pleonast](#): > > Sounds like knots. Sounds like the [fundamental group](https://en.wikipedia.org/wiki/Fundamental_group). Now, in knot theory, the “knot group” is just the fundamental group of what is left after cutting out the knot. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [August 2, 2026, 6:31am UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004/46 "2026-08-02T06:31:01Z")
And now it may be worth mentioning that there is a topological theorem that if X is a space, let us say path-connected, then there is a natural map from the fundamental group of X, modulo its commutator subgroup, to H\_1(X) which is an isomorphism. So you can draw a bunch of independent loops, but a loop like aba^{-1}b^{-1} is homologous to zero. The homology class of a closed chain is just determined by how much it winds around each of the holes. ---
**Author:** ![Peter\_Morris](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/peter_morris/32/359_2.png) [@Peter\_Morris](https://boards.straightdope.com/u/Peter_Morris)\ **Post date:** [August 2, 2026, 7:47am UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004/47 "2026-08-02T07:47:01Z")
The answer is zero. Ceci n’est pas une chemise. ---
**Author:** ![Alessan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/alessan/32/465_2.png) [@Alessan](https://boards.straightdope.com/u/Alessan)\ **Post date:** [August 2, 2026, 2:36pm UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004/48 "2026-08-02T14:36:51Z")
If I dig a hole in the ground, is it a hole? ---
**Author:** ![Crafter\_Man](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crafter_man/32/458_2.png) [@Crafter\_Man](https://boards.straightdope.com/u/Crafter_Man)\ **Post date:** [August 2, 2026, 7:27pm UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004/49 "2026-08-02T19:27:37Z")
I guess it depends on the definition of “hole.” Does a sock have a hole? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [August 2, 2026, 7:56pm UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004/50 "2026-08-02T19:56:03Z")
Just remember, a topologist is a guy who can’t tell his ass from a hole in the ground, but can tell his ass from two holes in the ground. Back to the OP, it seems to me that there are two fundamental issues: 1: What counts as a hole? 2: What’s going on with the back of the shirt that we can’t see? And 1: can be further divided into 1a: How are holes counted mathematically? 1b: Do intentional things count as holes, or only unintentional holes? ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [August 3, 2026, 12:04am UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004/51 "2026-08-03T00:04:22Z")
The topology is clear: no. Whether the problem is strictly about topology or is colloquial arm-waving? Aye, there’s the rub. ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [August 3, 2026, 12:26am UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004/52 "2026-08-03T00:26:16Z")
Only if it goes through to China. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [August 3, 2026, 6:27am UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004/53 "2026-08-03T06:27:13Z")
> [@Chronos](#): > > What’s going on with the back of the shirt that we can’t see? I thought the photo, real or not, depicted what we are supposed to thing it depicts > [@Chronos](#): > > How are holes counted mathematically? We can bring mathematics into it, but a punctured sphere and a flat disc are topologically the same, so there may be a philosophical question. ---
**Author:** ![Alessan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/alessan/32/465_2.png) [@Alessan](https://boards.straightdope.com/u/Alessan)\ **Post date:** [August 3, 2026, 10:18am UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004/54 "2026-08-03T10:18:24Z")
Who made topologists the Kings of Holes, anyway? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [August 3, 2026, 9:03pm UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004/55 "2026-08-03T21:03:58Z")
> [@DPRK](#): > > I thought the photo, real or not, depicted what we are supposed to thing it depicts I think that it’s quite the opposite: We’re supposed to be mistaken about what it depicts. After all, “99% get it wrong”. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [August 3, 2026, 9:36pm UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004/56 "2026-08-03T21:36:19Z")
By the way, when you buy a brand-new T-shirt, it may be fair to say that it has _no_ “holes in it”. ---
**Author:** ![Czarcasm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/czarcasm/32/4050_2.png) [@Czarcasm](https://boards.straightdope.com/u/Czarcasm)\ **Post date:** [August 3, 2026, 9:40pm UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004/57 "2026-08-03T21:40:59Z")
Count the total number of holes that exist, subtract the number of holes that do not include the shirt, and the number left will be the number of holes in the shirt. Easy peasy. ---
**Author:** ![Idle\_Thoughts](https://avatars.discourse-cdn.com/v4/letter/i/838e76/32.png) [@Idle\_Thoughts](https://boards.straightdope.com/u/Idle_Thoughts)\ **Post date:** [August 3, 2026, 9:55pm UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004/58 "2026-08-03T21:55:17Z")
> [@Alessan](#): > > If I dig a hole in the ground, is it a hole? Anyone can dig a hole. If I give you a shovel I want to see you trying to dig half a hole. ---
**Author:** ![Peter\_Morris](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/peter_morris/32/359_2.png) [@Peter\_Morris](https://boards.straightdope.com/u/Peter_Morris)\ **Post date:** [August 3, 2026, 10:11pm UTC](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004/59 "2026-08-03T22:11:37Z")
> [@Crafter\_Man](#): > > I see this at least once a day on FB: What is the answer given by the person who posted it, and what is their justification? [Previous page](https://boards.straightdope.com/t/how-may-holes-are-in-this-shirt/1032004.md?page=2)