Balls! August 18, 2017

What follows is my first crack at developing a thought experiment (cos that’s so “in” right now) that I’ve been thinking about for a while. Feel free to critique, reject, mock… whatever works for you.

Thought Experiment

Imagine a simple thing, a sphere of some kind. Now imagine lots of them, lying gathered on a flat surface. It could a bubble, or it could be a ball bearing, whatever.


Image from: Mike Davies Bearings

Yes, you can argue that there’s not much that is simple about a sphere, but we’ll get to that later.

When I said “lots of them”, I meant a whole bunch of whatever you’ve conjured up (see image above). And I mean identical, actually identical (unlike that one individual in the image above). This is possible in thought experiments, even if not in real life. Again, we’ll get to that in a bit.

Imagine them gathered together on a flat surface, so, in two dimensions, not three… just for now.

If you imagined something like a bubble, then millions and millions of them pressed up against each other will be distorted in uniform ways, and you end up with a honeycomb-like structure. However, if something were to collide against one side of this mass of bubbles, the nearest ones would deform until they break. Only some of the pressure will be dispersed to neighbouring bubbles.


Image from: UniSci

If you imagined something like a ball bearing, then millions and millions of them pressed up against each other will retain their shape. However, if something were to impact against one side of this mass of ball bearings, the furthest ones would break away from the group as the pressure is translated through the neighbouring ball bearings with little deformation of the spheres themselves.

These differences in the basic characteristics of the spheres are what we might call identity.


A problem that arises from the idea that a whole bunch of spheres are completely identical is that no two things are completely identical. If they are identical, they are the same thing (This is a restatement of Leibniz’s Identity of Indiscernibles[i]). Of course, colloquially, when we say identical, we don’t mean actually identical, we mean sufficiently similar for the differences to be overlooked for the purposes of whatever is being discussed.

We might expect that a bubble might be larger, thereby containing more air. If it is made of a fluid with higher viscosity it will remain intact, if not, it will burst before achieving that capacity. Variations in concentrations of key characteritics of the bubble will change what kind of bubble it is. By contrast, it would only take a few changes to a ball bearing for it to no longer be a ball bearing; more impurities or a different admixture of elements would make it weaker, and no use as a ball bearing.

In both cases a collision will cause a change to the collective. They will translate the impact from the sphere nearest the impact, like ripples in a pond, radiating outwards. In the case of the bubbles, those nearest the collision will absorb as much of the impact as they can – and may burst – depending upon the strength (viscosity) of the enveloping fluid. This will happen in concentric rings radiating out from the point of impact until the energy of the impact dissipates, or the bubble bursts. The ball bearings will translate the force of the impact through the collective, and the bearings on the far edge(s) will spin away from the collective, forming their own smaller collectives.


As I mentioned above, you could argue that spheres are not simple. They rely on interactions between the material(s) they are made from and the environment in which they exist. This is very almost the grand point of this thought experiment… almost, but not quite.

It’s possible to imagine the impossibility of millions of identical spheres because it’s simple. We have already added some complexity, the concept of identity (or difference), but only fairly minor difference. We will be adding more complexity, which will have the impact of making it more realistic, but also harder to accurately manipulate.

If you introduce more aspects of the context to the thought experiment, the greater the chance that differences in identity will be highlighted. Under greater pressure (or more collision) more bubbles will burst, and not necessarily those that are directly impacted. In some cases a more robust bubble will translate more energy through to a less robust bubble. The less robust bubble may burst, despite being only indirectly impacted. Equally, under greater pressure, more ball bearings will fly away from the collective, and some may just disintegrate under the pressure.


As we introduce more of the context, and necessarily uncover more identity (through interaction), our mass of spheres takes on a structure. We might not recognise this as a structure in the architectural or engineering sense, but nevertheless it is. This is a direct consequence of differences in the spheres, as uncovered by the context.

Without the commonalities they would not be instances of the same thing, with broadly similar properties. Without the differences, they would all be identical, and thus couldn’t actually exist separately. These individual differences are at the root of complexification. If you ignore the finer details your collective is more like the ball bearings, if you include the finer detail your collective is more like the bubbles.


Image from: All Mac Wallpaper


So far, none of this has required the interference of an intelligence. We are talking about simple objects interacting in a simple context. The complexity is derived from repeated and changing interaction drawing out, or even creating, finer and finer details. The repeated and changing interaction is a product of the changing identity of the individuals, and the group and, eventually, the increase in the number of groups, which changes the environment.

Schisms and Reformations

As we have seen, in the case of the ball bearings, impacts cause the furthest edge(s) to hurtle away from the group. The bubbles are less likely to have sections come away from the collective, though it is not impossible. Because of this, the mass of ball bearings are more likely to have things in their environment to collide with; namely, former members of the collective.

As it happens, the ball bearings that fly away from the collective do so due to their location in the collective. This might be due to their individual features, but that is unlikely. Ball bearings that are significantly different tend to disintegrate under the constant pressure of their neighbours rather than changing neighbourhoods within the collective. As such, whilst such clusters of former members may be, and probably are, the source of future collisions, it is absolutely possible for such former members to rejoin. This is especially the case if the ball bearings have something like magnetism as one of their features.

Bubbles, conversely, relying upon viscosity to retain their shape, and being more inclined to yield to pressure, are more likely to reform, allowing the former members to rejoin the collective.

The Experiment So Far

  • We have collections of spheres, some like bubbles, some like ball bearings, but identical within their respective groupings… at least at first.
  • We have slowly introduced more context, and this has driven greater differentiation within the groups of heretofore “identical” spheres.
  • This differentiation has given rise to differing behaviours that has, in turn, given rise to other smaller groups of also identical objects.
  • These satellite objects were more likely in the case of the ball bearings, and less likely (but not impossible) in the case of the bubbles.
  • These, in turn, in the case of the ball bearings, give rise to more collisions, some of which may lead to the satellite groups rejoining the collective, and some of which might lead to further satellites coming away from other parts of the collective. In the case of the bubbles, it is much more likely that they will rejoin the collective.

The Questions

I’d be interested to hear what spherical things other people came up with, and the properties they assigned, both simple and complex.

  • What can these simple objects, and the groups that they form, be used to illustrate?
  • Do they allow for the necessary complexity to make the illustrations work?
  • At what point does it break down?



There is an argument that this does not hold at the quantum level:

“It is not just that two or more electrons, say, possess all intrinsic properties in common but that — on the standard understanding — no measurement whatsoever could in principle determine which one is which”

This requires the use of the equivocating phrases “on the standard understanding” and “in principle”. Given the enormous difficulty of studying things at the quantum level, I would suggest that this is an open question.

Additionally, given the intention to keep things fairly simple, I’m not going to digress into a discussion on decoherence and all that other fun stuff.

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