I

INFINITY, JUST TO BEGIN

To infinity, and beyond!

Easy, for imaginative cartoonists, to put this challenging cry in the mouth of an improbable, awkward and foolish toy-astronaut, paranoiacally unconscious of its being a toy, and indeed positively and tragicomically identified in its role of interplanetary envoy in defense of the universe, against the forces of evil...

Yes, easy, because this way, thanks to sympathy and smiling, nobody rejects the shocking force of the extraordinary insight − not at all comic − that underlies this apparently innocent motto. But if one stops the smiling and benign sympathy that this novel don Quixote for children (for children?!?) evokes − yes, because he is so serious and naive, and proud and firm, and plump and nonsensical... − then he realizes that the paradox and the explosive contradiction are not at all unacceptable. It may be different for the most logical part of ourselves, but the most open, receptive, intuitive regions of our spirit are perfectly at ease with the idea that infinity can be inhabited, or even that nothing is more precisely natural to our spirit than trespassing in it, and indeed progressing further, well beyond!

It is true, infinity frightens because we cannot embrace it all (comprehend it). But even more upsetting is that, were we ever able to do it, we should stop on its border and admit the vacuum, the nothing, farther on. It is unacceptable that infinity, wide as you wish, enclosed everything. Even more unacceptable, indeed, is that one could not move beyond.

Then yes: beyond infinity, but not into the vacuum. Rather, towards an even wider infinity, outside which even higher infinities are waiting for us. Honestly, one feels much better if infinity, infinite as it may be, does not claim it can encompass everything, and leaves us some more to explore.

An infinity greater that the physical one...

Mathematicians, who can always find some tricks and algorithms to abstractly reproduce the music of spirit, have long solved the problem, elegantly as they usually do it. You write “∞” to say infinity, square it, and there it is: ∞², and go on with ∞³, ∞¹⁰, ∞ⁿ, ∞^∞, and all higher order infinities. Elegant, and vee..ery mathematical, because you do not understand it, unless you decide a priori that you WANT to understand it. What does it mean? it means that it is not even enough saying that there is always something bigger. It is not a matter of being bigger (be rich as you wish, if I give you a dollar you become richer...): here the question is about being definitely bigger, quite a huge lot bigger, intrinsically, foolishly, infinitely bigger, QUALITATIVELY bigger.

Infinity is something else, with respect to any magnitude. Still, an infinity to the second power is conceivable, and it is definitely something different from any simple infinity...

It seems like spewing hot air. Instead, it is an obvious perception, deep in the soul, even for a child, though he can’t tell it.

Take a line. Take it long, but real, real long. Okay, take it infinitely long: will it ever manage to cover just the surface of a toasted bread slice? Take a surface as big as you wish, extending to infinity this side and the other, will you ever be able to play ball with it, if it does not have at least the thickness of a rag, which is no more a surface, but a tri-dimensional object?

No surprise, we know it well: infinity, large as it may be, cannot do it, is not enough, does not reach there. There is always something farther. Always. Anyway.

And after all the dimensions that multiply infinities?

Maybe god, the spirit of the world, the soul...?

Where does this commotion of endlessness come from, where does the visceral certainty of the “beyond” ?

A long-preferred hypothesis is spirit-god, who imposes to intellect, an calls us. This was in the myth of the cavern − we only perceive a limited “reality” of the conceivable, livable experience, and we feel that a truth and reality exist, of a different and more solid, true nature. And this is in every form of religion and mysticism. It seems that man has always needed this: a reality that is immense, higher, to surrender to, and let the spirit wander, relax, dream.

An interesting, alternative secular hypothesis may be defense: we need it, it helps, perceiving something that is greater and beyond infinity is the easiest and most effective way of negating the infiniteness of infinity, and the commotion-confusion that follows.

As it is always the case, there is a third way (is it always the case? here in Italy many of us were convinced there was a third way! now, I think it has remained few of us...). But the third way is always the most demanding, it is the one that many think does not exist at all, and anyway cannot be found, cannot be followed.

The third hypothesis is that infinity is admissible, and real and conceivable, but is irrelevant, it is just the first step. Because no infinity can exclude the possibility of a further dimension, in which all infinities considered hereto just project as a small dot, while the space of the “real” infinitely expands as each new dimension is added. It is not simply a problem of lines that cannot enclose a surface, of infinite surfaces that can wrap an object but cannot fill and pervade it. The question is that no infinite space can encompass more than an instant, or include movement.

The question is that no physical reality in space or time can embrace an emotion, an idea, interpretation, desire, a passion, a dream.

Warning!

We apologize, but is has been necessary to include these “technical” sections, in order to comply with the regulations of the Ministry of Education, in case this were to become − as it should in our most optimistic expectations − the official textbook of neurophysiology, as soon as this topic breaks in into the study programs of high and elementary schools, and possibly in experimental nursery schools.

INFINITE OR NOT?

“Only two things are infinite, the universe and human stupidity, and I'm not sure about the former." (Albert Einstein)

Indeed, scientists do not love infinity: you don’t know how to place it, how to fix it to the bench to make an experiment on it, how to be sure that it does not escape as you try to harness it into a theory.

Scientists like brain more than they like soul. Sure, “soul” directly evokes infinity, and perhaps “mind” plays a similar trick, while “brain” is less dangerous. A grayish and little poetical jelly, it is much easier to trap it into physical schemes: cause-effect, action-reaction, stimulus-response.

We shall discuss later on what a biological system is and how it is characterized, but we can already anticipate some hints. Briefly, it is a system that presents some structural, ordering and functional features that maintain a certain degree of persistence and stability although they continually change and evolve. This is made possible by a complex system of mechanisms that enact physical and chemical responses to any possible stimulus or influence that the external world exerts on the biological system. This way, the system can maintain a number of its characteristics unaltered, while it partially modifies some others, thereby just changing nothing more than what is necessary to survive.

In complex systems, such as multi-cellular organisms, responses cannot be performed by the same sub-system that records external influences (for example the skin is stimulated by the heat of the iron, but to avoid getting burned the muscles must react, and pull the skin away from the contact). Therefore, there must be mechanisms and systems to grant communication among the parts of the organism. The principal such mechanisms are the hormonal and nervous systems.

Hormones are substances that a group of cells produce and release in response to a stimulus. Through blood circulation, hormones reach all cells in the organism, so that they evoke the appropriate responses by the cells that can enact them.

Conversely, the nervous system is a network of cells − neurons. Each neuron can generate an electrical response, if it is appropriately stimulated; it will then propagate such electrical signal along its membrane to several millimeters or even meters away and transmit it to another neuron, or a muscle or gland cell.

The first role played by neurons is therefore to “transfer” a signal from a point to another in the organism.

In many inferior animals several groups of neurons are organized to generate more or less complex responses to external signals, but there is no single control center that organizes and “interprets” all this activity. Typically, in invertebrates, groups of neurons constitute “ganglions” that are located in the distinct portions of the body and coordinate specific local responses.

In vertebrates most of the neurons and their connections are organized to constitute a central axis (neuraxis) that, in addition to producing local responses, also performs a general coordination of all neural activity. This gives rise to a central nervous system (CNS). As one ascends the zoological scale, the mass and complexity of the coordinating and supervising structures grows, until a brain can definitely be recognized, and its complexity tremendously grows, from the few grams of a frog to more than three pounds in human brain.

Classical science does not depart from this vision.

No infinities there.

The nervous tissue is an evolutional conquest that makes it possible to build multi-cellular organisms capable of complex and coordinated functions and responses. Its meaning, goal and fate are to make it possible to generate the appropriate responses to any external (or internal) stimulus.

Stimulus, response.

In between, the nervous system. We study how it perceives and records phenomena, stimuli and conditions from within and outside the organism (sensory systems) and how it produces the appropriate vegetative (autonomic nervous system) or behavioral responses (motor systems).

Classical science does not depart from this view.

Nice and simple way of looking at things. Then, little surprise if none of us is willing to identify himself, his mind, his experience, his identity and conscience with this purely reactive apparatus, made up of sensory, autonomous and motor systems, where no interpretative or creative systems appear to operate, capable of passion, fantasy, desire, dreams and ideals.

Hundreds of billions of neurons are not enough to suggest infinity, if they are indeed organized into a device that is only built to produce responses.

But really there is nothing more than that in the nervous system?

No infinity at all?