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Why are rounded pebbles so common? A quick glance on natural shapes, and their durability.

Stones and rocks at various maturation stages

I'm quite sure you noticed it: on average, rounded pebbles are more common than sharp-edged ones.

OK, you're quite right! My statement is not so universal, and I can tell it in my area (a temperate flatland not very far away from the Alps).

Nonetheless, the vast larger amount of rounded pebbles amazed me since childhood.

The reason of this, and its consequences, sounded me thrilling and inspiring in the same time.

Why, then, so many rounded pebbles?

When rocks disintegrate, under the effect of physical erosion like freezing-thawing, the resulting stones are mostly sharp-edged and very irregular. They may stay there, possibly incorporated in some finer grained sediment, and diagenesis (that is, the process of rock formation) will "freeze" them in place, with minimal change of shape.

Or, what happens frequently, they will be transported away by some river, or marine waves. The finer-grained sediment is then washed out, and individual stones are eroded. This is an interesting step: fluvial transport, or wave rework, are not an indifferent "grinding" crushing large stones to sand particles. Rather, stones interact (more specifically, collide) and in the process all irregularities, more exposed to collisions and vulnerable, will eventually be polished out. Eventually, our sharp-edged stone will reduce to a smaller rounded edged stone, plus some sand particles.

From then on, the rounded pebble will continue to erode mechanically, but will do at a much slower rate, no sharp irregularity offering a preferential damage point.

In other words, it takes quite little to reduce a sharp stone to a rounded one, but a much longer one to make the latter into sand. Longer lived, rounded stones are then more common in sediments.

Geologists say the stone has "matured" into a nice, smooth pebble.

Now, let's take a more general standpoint. We may say that the edgy shape of "immature" stones is less durable than a smooth surface. The edgy shape has less entropy than the smooth!

* * * * * * * * *

If you look around in Nature, you seldom find sharp edges.

But to notice it, you should be "objective". We aren't, as our perceptual system gives a higher weight to living beings (and we alive creatures are among the most edgy-shaped objects on the planet: think the many layers and organs we are build from, and the innumerable cells, all characterized by extreme chemical and geometrical gradients).

So, let's turn to "mineral" objects, and look them impassionately. Are sharp discontinuities so common?

On a first glance, mountain faces seem quite common - but if you take really all into account, you invariably find them surrounded by large pancake-shaped, rounded walls. And we have to admit: sharp edges are uncommon.

In addition, when they exist, then there is some process actively maintaining them visible. Like, for example, an active fault. Or a river cutting a very hard rock.

Stop this process, and give time a chance, and these sharp feature will soon vanish.

Of course, this process can be more evident in some places. My brother lives in the Central Alps, and when I go visiting him I always stare at the high faces covered on time to time of snow, in awe. Reflecting, I have to admit the Alps are a very young range, still evolving and lifting. So, a chance is there for sharp edges.

But move North, in Europe, until the Ercinic massifs of Central and Northern Europe... There, landscape is much different, smoother, and pancake-like. The Ercinic mountain lift has long ended, and now erosion dominates. Smooth edges are decidedly dominating. The same will be in our Alps, on some day.

* * * * * * * * *

And technology?

As two examples, chosen at random, let's imagine the latest kind of super-powerful microprocessor, and the huge Rho-Pero exposition building north of Milan.

These two objects have very different scales, but one important thing in common: extremely sharp edges and strong gradients.

The difference is so striking, that I guess even a Venusian would distinguish artificial from natural forms.

The same could be said of most current technology, from clothes to cars to cultivated fields, to literally anything artificial.

So sharp-edged they are, that our technological products demand a continuous flow of energy to maintain them alive, in form of cleaning and repair. The very existence of shapes so far from the natural smooth surfaces and gentle gradients implies a disequilibrium, which in turn obliges to spend an immense amount of money, time and natural resources to maintain it.

The consequence of sharp edges and extreme gradients in artificial objects is their very small durability. As the sharp-edged stone, they are crushed quickly by the normal weathering processes acting on any rock. And, they fail frequently (the sharper the surfaces, the faster the death).

* * * * * * * * *

If smooth forms are more common in nature, why not adopting, copying them in our technology?

I don't know "why", but guess this might be a significant progress: a more lightweight technology, all functions fixed, would be automatically more reliable, durable and possibly less expensive than a sharpy thing. It might require less maintenance, and so the overall environmental impact could be much lower.

Last, and not least, I guess these objects would be beautiful, in their way.

* * * * * * * * *

Technology "is" shapy and sharpy, however.

Form and function obviously intertwine, in so many cases.

I can't exclude they would be also with different kind of shapes, fabrics and textures. But I feel it could be quite difficult, to the untrained eyes of our minds, to figure them out.

Maybe, the apparent connection of sharp forms and functions stems from the way things are manufactured. To date, even the most sophisticated production processes operate by assembling simpler things, or removing some mass from a larger body, or making a liquid into a solid.

Whatever we do, we don't "grow" objects. And by the way, we limit the range of possible forms to a very tiny subset. An optimal one?

"Growing" things, as we find in the biosphere, have inherently complex three-dimensional shapes. They exhibit large gradients, as I mentioned. But they do in a different way than artificial things.

* * * * * * * * *

A smooth surface desn't cut very effectively.

There are cases, in which a sharp blade is more than a necessity (I'm saying this by direct experience after having tries to skin a mature peach with a poorly sharpened knife: a total liquid disaster (not preventing me from eating the peach, of course).

In other instances, the usefulness of a sharp edge is much less clear. Is a sharpy car frame aerodynamical enough?

If we consider external surfaces only, then sometimes a smooth form emerges from trial-and-error, or computer simulation, especially when some tight interaction with a hard medium is in progress. Like airplanes designed for high speed.

The human body, as many other animals, is basically streamlined too. Not as dolphins', sure, but remarkably. Why?

And why, in any population, some individuals are more streamlined than others?

Is it the consequence of subcutaneous fat distribution, and its normal variability? Or, has it some unknown direct adaptive meanings?

* * * * * * * * *

I'd appreciate a lot a technology more akin to nature, and less heavy to the environment. Meanwhile, I wonder whether big investments would be ever placed into it.

It's hard to, but I have to admit to myself that many products of technology have not been developed out some documented, or potential, necessity.

A specific example, in my opinion, is the Messina Strait Bridge, now under design. The most important motivation I see behind of it is celebrating the prestige of a political class, and maybe a single party. Once made, it will stand, and little doubt it will not pass unobserved.

Many other things have been built outside any perceivable necessity, but providing some tangible sign of the persistence of an ego long after his death.

It is not easy for me to buy into this kind of insecurity. I feel having the opposite problem, of leaving not too much traces after my passage (the ones which will remain will mostly be in the form of environmental impact, and resource deprivation to future people and other beings). But, apparently, this is>/em> a motivation. An illogical one, maybe. And perhaps, more conductive to shapes so that no one in the future will mismatch for a natural accident.

This is, I feel, a big, open question.

* * * * * * * * *

Dear friends, I'd like to hear from you about.

The problem is, despite its appearance, deeply physical and mathematical. So, not outside our reach!

I end here, wishing you all any happiness possible (and doing this from a very shapy computer ;-) ).



jap21's picture

Hi Mauri

As our friend Tina would say: This is food for the thought. I usually don´t think about shapes and their relation to math, as my area is more ... "mundane" hehehe. I usually have to take time off to sit down and marvel in nature. But what it usually is on my mind and my heart is a reverence for life. Things that grow are alive. Nowadays, some scientists are trying to convince us that there can be artificial life and we should admit it.

This brings about the question of spirit. Artificial life will have no spirit, and being so, real life will have to fight its way through. Who will win? Honestly, I think if we don´t realize that we have a place in the universe that is very, very special. If we do not find out what our real job is, it will be hard for us to remain on earth. Nature works night and day to protect life. If we do not want to take active part in the protection of life, we will be working against nature (just as we are doing now) and we are more likely to perish than to bloom.

When I think about the Mayans and how they did not work for life, and how nature turned against them, I see a small example of this in this happening. There is just so much that we can do against life without turning on the power of nature to protect it.

When I think about this, I know I have to finish our book soonest.

Hugs my dear friend.


Jacqueline Patiño FundActiva
Tarija - Bolivia
South America

Mauri's picture

Dear, things intertwine so


things intertwine so much, as I see.

That of nature, to me, is one of the most unsolved "problems" of our civilization. And within of it, of life.

Life is "many" things. It's growth (and death). Transformation. Apparent violation of the second principle of thermodynamics. Warmth. Shape, too: we living beings are a geometric contradiction (a "living" contradiction ;-) ), as layered and structured as we are.

Life is, most than all for me, sitting on the verge of night in my magical wood, and listening to the continuum of sounds, of voices. Feeling the trees there. Perceiving their smell. Touching leaves, and furs, mid thinking and mid "just feeling". Being, in some way, close, understanding, to the fear a little animal has of your unexpected presence there.

If you try distancing from all these things, you also see how little is this celebrated, appreciated.

Do we really have a language which allows us to really "understand" life?

My sense of "understanding" is, of course, a bit restrictive, I'm afraid. When a student I remember well the long hours I spent "learning", the way this is done at school. That is, as I realize now, coldly verifying the logics behind some subject, but without any real participation. Needless to say, this barely allowed me to pass my exams and survive the harsh selection. But in the end, I did understand "nothing". Understanding implies some form of deep participatin, not necessarily at conscious level. Some transformation of yourself. An "Aha!", coming from no-one-knows-really-where, in which some deep truth reveals you suddenly...

Are we, socially, equipped for this?

I've seen many attempts to define life logically, in the literature (less and less frequently, I have to add: today science is running fast, under the pressure of publish-or-perish dogma, and almost no time remains for reflection). None of them looked to me "convincing". None, to be precise, was able to "move" me - and it should, for the "definition" to grasp something really useful.

Changing this state of things will be hard, I guess. We are rooted in a culture which places a sharp distinction between the "inside", the "polis", the place of artificial, the conscious ego on a side. And Nature, the unconscious, in the "outside" of the (now imaginary) woodland.

This dualism, in my feeling, is really unnecessary. It denies our naturality (which is foolish, and also deeply unacceptable to me). In denying our naturality, this hard to die pre-cooked concept tramps any possibility to grow a language within which we may "understand" nature, in a participative, connected way.

I don't like imagining myself a sort of "fallen angel", condemned to stay on this planet. I'm alive. I'm a creature of flesh and blood, neither of which is "evil" ("good"?). If I have a spirit, it emerges from this "natural" state (in ways no one has already explained me).

I'm saying this as a personal experience, but feel many of us would say the same, maybe using different words.

* * * * * * * * *

That of artificial life is a point on which I feel a deep agreement with your concern.

I remember an attempt, now failed since when I left the university and began doing something (I hope) useful. People made a lot of talk about fifth-generation computers and artificial intelligence. At that time, it appeared possible to do something as simple as "mechanizing reasoning". I remember a lot of hope was placed in programming languages like Prolog, which allowed you not to give a list of instruction to the computer, as we typically do, but rather a set of "facts" and "deduction rules" (more or less). So instructed, the computer was able to deduce some consequences. More precisely, to enumerate the all, having time enough (infinite).

A little detail emerged from all these studies: "logical reasoning" is not-so-logical, as it does not allow us to "generate all possible consequences given a set of premises". The mess resulting would be so huge (in fact, potentially infinite) to be perfectly useless, with very few pearls of wiseness buried in a monstruous mass of logical rubbish (that is, facts which are "true" from a logical point of listening, but irrelevant-obvious-tautological-useless-unreadable-...).

Even something simple as "logical reasoning" requires mostly a process of "selection". And this can not be described in logical terms. It mainly entails "feeling", aesthetics, and precisely the things the dominant culture undervalues - to the extent of not knowing them.

I'm not in principle contrary to "artificial life", as a phylosophical possibility. But on our current cultural grounds I bet it's not something our generation and the next will see. We may, that's sure, build systems which mimic some aspects of life (self-reproduction and self-repair, enumeration of possibilities with some limited and blind selection criterium, ...). But the real "kernel" of life is still far away - and we currently have no real way to grasp it, given the restriction of our language, mind, and culture.

It might happen that these products will be useful, in many instances. But this is not necessary. As I've heard, some attempts (the more successful ones) or building objects behaving partially as living beings are finding their way in the military. Thing the "reconnaissance bugs", so small and so able to tweak in the rubble after a bombardment to look for "survivors" (for giving their position and allowing someone to kill or capture them). Or the more and more intelligent drones (a case I know is quite interesting: the municipality of Milan bought two mini-helicopters equipped with cameras, to be used for after-match surveillance close to San Siro; these "helicopters", battery operated, have a form not resembling a helicopter even in the idea, and are small enough - less than 1 meter - that from altitude they are completely invisible).

As all science, these "artificial life" objects will be as useful and kind to human kind than the souls of whom designed / bought / operated them is clean. Chance are big some ill-souled individual will leak in, and I'm very worried of this.

* * * * * * * * *

We are at a starting point, however. A "turning" point?

My guess is, in few years Nature will set (herself?) at the centre of our global attention, to an extent we can't imagine now.

We are helping Her, after all. As we occupy land, cover it with concrete, use resources as if they would be infinite, and in other terms act as we do, we more and more blur the once solid boundary between the polis and the outside. All becomes polis, then the outside leaks in everywhere.

This is general, I see.

The very same is occurring to people, and their mind, in a parallel not so incidental: repress humanity more and more (deny passion, kill love and opening, tame receptivity as weak, ...), and what you will invariably obtain is a set of individuals superficially very "fit and optimized" to some criterium (say "tough", "autonomous", "aggressive"), and meanwhile terrified, docile, frail. Dysfunctional. Acting in large groups, unpredictable and overall mad.

The same with any other aspect of nature: the more it is occupied and "disciplined", the higher the exposition of human kind to natural, uncontrollable risks (famine, geological disasters, ...). And the lower opportunities to control things (for example, by retreating to some "safe place") will remain.

I've read some time ago a book on the Mayas, by a German historian. Then, on a travel to Mexico, I had the opportunities to see the traces of their impressive civilization. As you say, all this power vanished, after agricultural production was not able to sustain the "system" - which happened.

The same occurred to Easter Island.

And the same is occurring to us. In this, I agree with you - with a big regret.

What I'm very afraid of, and convinced we have to do something on, is that none of the civilization failures due to environmental causes has produced an increase in wiseness. It seems that catastrophe strikes, kills, and in the same time cancels memory.

So, we should act "in advance".

I invite all, scientists and not, to join in the reflection, the diffusion, the idea-weaving. We need a new language, new paradigms. And, yes, "prophets". Maybe, of the tender type, not crying alone in the desert but showing warmly what is, and what it would be instead if...

So, thank my dear friend of your comment, and hope to see soon your Book on the shelves.

For us all, my invitation is to let our vision and souls to feed the change.



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