# The Bones Daley hypothesis ...true or false ? **URL:** \ **Category:** Factual Questions\ **Created:** [February 10, 2013, 7:35pm UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893 "2013-02-10T19:35:13Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Bones\_Daley](https://avatars.discourse-cdn.com/v4/letter/b/bc8723/32.png) [@Bones\_Daley](https://boards.straightdope.com/u/Bones_Daley)\ **Post date:** [February 10, 2013, 7:35pm UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/1 "2013-02-10T19:35:13Z")
I am not for one minute suggesting that my hypothesis is anywhere near as important as the Riemann hypothesis or the Goldbach conjecture …but FWIW, here it is. My conjecture is that if a number of irregularly shaped pieces of material, each with uniform density and hardness (although not necessarily of the _ **same** _ density and hardness for every piece) , are tumbled in a jeweller’s tumbler with a matrix of abrasive, for a long enough period of time, then each of these pieces will eventually become perfect spheres. My gut instinct tells me that this end result is inevitable, but I am not sufficiently skilled in math or physics to say why it should be. NB : I am not restricting my hypothesis to pieces with an original cubic shape , my conjecture is that pieces of _ **any** _ shape will eventually become perfect spheres under these conditions. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [February 10, 2013, 8:40pm UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/2 "2013-02-10T20:40:24Z")
More an engineering question than a pure math question, but my guess would be that it’s false–that once the thing reaches a certain degree of smoothness, the abrasive will affect all parts of the surface at an equal rate and so it will retain its shape while simply getting smaller and smaller. ---
**Author:** ![Xema](https://avatars.discourse-cdn.com/v4/letter/x/9de053/32.png) [@Xema](https://boards.straightdope.com/u/Xema)\ **Post date:** [February 10, 2013, 8:50pm UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/3 "2013-02-10T20:50:34Z")
Sounds implausible. I’ll set aside the obvious objection that in the real world there is no such thing as a perfect sphere, and assume that “perfect sphere” can here be taken to mean a spherical shape that varies from perfection by a very small amount: less than, say, 1 part in several thousand of the diameter. If this were true, it would seem to follow that once the pieces have become perfect spheres, no further abrasion happens. I say this because if a perfect sphere undergoes abrasion, it is no longer a perfect sphere - except in the essentially impossible case that the abrasion always magically peels off a perfectly spherical layer at one instant, leaving a smaller perfect sphere. ---
**Author:** ![Duckster](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/duckster/32/1244_2.png) [@Duckster](https://boards.straightdope.com/u/Duckster)\ **Post date:** [February 10, 2013, 8:52pm UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/4 "2013-02-10T20:52:33Z")
Wasn’t it experiments aboard the Skylab or the ISS that actually created perfect spheres because gravity on Earth prevents that from occurring? Seems to me your hypothesis fails because you will not have perfect spheres because of gravity. ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [February 10, 2013, 8:59pm UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/5 "2013-02-10T20:59:20Z")
Given uniform density and hardness – and taking that to mean not having any strong internal “grain” or crystal structure – I’d certainly _guess_ you’re right. Cobblestones in stream-beds seem to approach sphericity over time. Some real life experience with a rock tumbler points in that direction. Basically, anything that sticks out gets abraded away. How would we prove it, though? I can envision a mathematical model of the process…but it would be devised with the desired conclusion already in mind, and thus would be poor science. ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [February 10, 2013, 9:03pm UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/6 "2013-02-10T21:03:36Z")
If the Bones Daley hypothesis were true, wouldn’t approximately - spherical beach pebbles be common? In fact, they’re really rare. ---
**Author:** ![Bob\_X](https://avatars.discourse-cdn.com/v4/letter/b/4491bb/32.png) [@Bob\_X](https://boards.straightdope.com/u/Bob_X)\ **Post date:** [February 10, 2013, 9:44pm UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/7 "2013-02-10T21:44:10Z")
> [@Mangetout](#): > > If the Bones Daley hypothesis were true, wouldn’t approximately - spherical beach pebbles be common? In fact, they’re really rare. Huh? Pebbles are almost all round. ---
**Author:** ![Xema](https://avatars.discourse-cdn.com/v4/letter/x/9de053/32.png) [@Xema](https://boards.straightdope.com/u/Xema)\ **Post date:** [February 10, 2013, 9:52pm UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/8 "2013-02-10T21:52:35Z")
> [@Bob\_X](#): > > Pebbles are almost all round. Roundish, maybe. ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [February 10, 2013, 9:56pm UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/9 "2013-02-10T21:56:29Z")
> [@Bob\_X](#): > > Huh? Pebbles are almost all round. But very rarely close to spherical, regardless of the material of their composition, they’re usually flattened-round, bean-shaped, ovoid, irregular-rounded, etc. ---
**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:** [February 10, 2013, 10:00pm UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/10 "2013-02-10T22:00:04Z")
Is it possible for a diamond to become a perfect sphere? ---
**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:** [February 10, 2013, 10:21pm UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/11 "2013-02-10T22:21:59Z")
The lack of _perfect_ spheres isn’t a problem: We could just tweak the hypothesis to say that “as tumbling time increases, deviations from sphericity approach zero”. I don’t think it’s quite true, though. Certainly, given a non-spherical object, tumbling is more likely to make it more spherical than it is to make it less spherical, but that doesn’t necessarily mean it’s going to trend towards spherical all the way to the end. Eventually, you’re going to get to some limiting “close enough” case where even though marrings are rare, they’re more significant than the original deviation. Your deviation as a function of time is probably going to look like a decaying exponential, but with constant-magnitude noise added to it. **Czarcasm** , a diamond is not isotropic (like all crystals, it has cleavage planes in it), and so I don’t think it would meet the OP’s standards of “ideal material”. ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [February 10, 2013, 10:31pm UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/12 "2013-02-10T22:31:02Z")
**Xema** ’s observation – once the stone is actually spherical, any further abrasion would be away from sphericity – is a good one. It means that the graph of topographical distance from sphericity against time is going to be jagged. It declines in an asymptotic curve…but then spikes upward again, once more to slope downward toward the asymptote of zero. It never arrives at exactly zero, if for no other reason than the lumpiness of atoms themselves, but, worse, it exhibits semi-regular “catastrophes” away from the asymptotic curve. I think the best you can do is say that in nearly all circumstances, the passage of time brings the object closer to sphericity—on the average. In much the same way, the pile of sand in the lower part of an hourglass will approach the shape of a cone, but will constantly be having little catastrophes (mini landslides) that produce larger spikes of topological distance from a perfect cone. Even so, the overall tendency is toward cone-ness. (Conicity?) ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [February 10, 2013, 10:33pm UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/13 "2013-02-10T22:33:25Z")
> [@Bones\_Daley](#): > > … are tumbled in a jeweller’s tumbler… If you revise that to “are subjected to random agitation”, I think you’d be right. Jeweller’s tumblers aren’t random - there’s often a periodic ‘slosh’ and the rotating wall of the tumbler can tend to preserve or accentuate flatness as pieces flip over, slide for a bit, flip, slide, etc. ---
**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:** [February 10, 2013, 10:37pm UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/14 "2013-02-10T22:37:23Z")
> [@Chronos](#): > > The lack of _perfect_ spheres isn’t a problem: We could just tweak the hypothesis to say that “as tumbling time increases, deviations from sphericity approach zero”. > > I don’t think it’s quite true, though. Certainly, given a non-spherical object, tumbling is more likely to make it more spherical than it is to make it less spherical, but that doesn’t necessarily mean it’s going to trend towards spherical all the way to the end. Eventually, you’re going to get to some limiting “close enough” case where even though marrings are rare, they’re more significant than the original deviation. Your deviation as a function of time is probably going to look like a decaying exponential, but with constant-magnitude noise added to it. > > **Czarcasm** , a diamond is not isotropic (like all crystals, it has cleavage planes in it), and so I don’t think it would meet the OP’s standards of “ideal material”. I don’t think the OP didn’t mention “ideal material”-it was “irregularly shaped pieces of material, each with uniform density and hardness” ---
**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:** [February 10, 2013, 11:09pm UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/15 "2013-02-10T23:09:43Z")
Right, but we’re assuming (or at least, **Trinopus** was assuming, but I think it’s appropriate to follow suit here) that “uniform” here means “homogeneous and isotropic”. ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [February 11, 2013, 2:31am UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/16 "2013-02-11T02:31:14Z")
Of course, we have to make assumptions. Uniform density, for instance, doesn’t automatically guarantee uniform malleability or friability. Maybe the mineral has bands of brittleness. But, c’mon. Are we writing a contract with the devil, or can we take some assumptions as part of the spirit of the thing? ---
**Author:** ![Washoe](https://avatars.discourse-cdn.com/v4/letter/w/ecae2f/32.png) [@Washoe](https://boards.straightdope.com/u/Washoe)\ **Post date:** [February 11, 2013, 3:02am UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/17 "2013-02-11T03:02:06Z")
[Unpredicted variables might skew the results.](http://www.google.com/imgres?imgurl=http://1.bp.blogspot.com/_IBVPgalgRAk/TU3CNzU_05I/AAAAAAAADVY/Z4I1OQAkNWA/s1600/Peanuts%2Bcartoon%2Bcroquet%2Bball.jpg&imgrefurl=http://www.deceptology.com/2011/02/charles-m-schultz-skeptic.html&h=431&w=640&sz=111&tbnid=n770TmLmSMlA3M:&tbnh=81&tbnw=120&zoom=1&usg=__bdj9Eu5UG1rBcmDv1GJEdA1QRfs=&docid=atEi00meV4FXHM&hl=en&sa=X&ei=I14YUbn5NcXRigKSs4AY&ved=0CDUQ9QEwAA&dur=673) ---
**Author:** ![Noel\_Prosequi](https://avatars.discourse-cdn.com/v4/letter/n/b19c9b/32.png) [@Noel\_Prosequi](https://boards.straightdope.com/u/Noel_Prosequi)\ **Post date:** [February 11, 2013, 8:34am UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/18 "2013-02-11T08:34:50Z")
I would think that there might also be strange processes that can reinforce non-spherical shapes that might need to be taken into account as well. Idealising, one might think that the more that wind blows across sand, the smoother the sand should become. Yet it doesn’t - little corrugations are set up that become self reinforcing. In the same way, vehicles driving on loose dirt on country roads don’t make the roads approach smoothness, they set up bone jarring corrugations. This is different from asymptotic approach to smoothness with catastrophic variation on the way- here, smoothness is unexpectedly not the asymptote because irregularity is reinforced. While I don’t know the detail of any cognate process in tumbling stones, I would be hesitant to rule out that there might be. ---
**Author:** ![am77494](https://avatars.discourse-cdn.com/v4/letter/a/d2c977/32.png) [@am77494](https://boards.straightdope.com/u/am77494)\ **Post date:** [February 11, 2013, 2:01pm UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/19 "2013-02-11T14:01:13Z")
Based on my prior experience with grinding, I will say that the limiting case will be the binormal distribution of sizes - because it gives the maximum packing efficiency. Binormal as in - there will be 2 sizes of spheres, one twice in diameter than the other. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [February 11, 2013, 2:26pm UTC](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893/20 "2013-02-11T14:26:01Z")
I think sand makes for poor examples. It’s more likely to be the abrasive than the rounded material. So desert sand is just a pile of abrasive with no softer substance to work on. The hypothesis describes the way ball bearings are made (or were, I’m not sure about modern techniques). They were ground with abrasives in batches that contained different sizes (although not all that different), and later sorted by size. However, part of making the process practical was to start with something as spherical as possible. Perhaps oblong shapes will not become more spherical with more grinding, but merely smaller. I would think experiments of this nature have already been conducted. [Next page](https://boards.straightdope.com/t/the-bones-daley-hypothesis-true-or-false/649893.md?page=2)