Can a banana compute?

My teenage daughter was asking me about the philosophical nature of networking and computing. Here I share my answer to one of her tougher questions.

One of the joys of being a parent is being asked supposedly “naive” questions by one’s offspring. Today’s was a simple one, and it took me a while to figure out a satisfactory answer for it. As a bit of fun for the weekend, here is my response.

To make the question more specific, what she asked me was whether it was possible to make a banana compute, and if not, how is the arrangement of atoms in a banana fundamentally different from that in a laptop.

In order to begin to answer the question, we first need to unpack what it means. The starting place is to define “banana” and “compute”, and then consider how these are related.

A banana is clearly a physical thing, and we are here only referring to it in its original edible form. We aren’t allowed to send our banana into a nuclear reprocessing facility for transformation into another substance, be it another botanical berry or dissimilar slither of silicon.

These essential constraining properties of a banana are “cosmic”, in that they are related to the laws of physics. As such, bananas are for the purposes of this question “conserved”. This is not in the sense that we make banana jam, but rather than we can’t combine two bananas into one, or make bananas magically disappear.

An additional cosmic property that we note is that bananas cannot be unsquished once squished, and thus we require our bananas to be maintained in an orderly and undeconstructed condition.

The idea of “compute” splits into two distinct issues: the abstract concept of “computation” (which is a mathematical one), and the physical action of “computing” (which is embodied in a “computer”).

Computation requires a system of state (i.e. a meaning we overlay onto a symbology encoded in the world somehow), together with a set of rules to change that state. By implication there is an arrow of time in which that state evolves (hence the old saying “time flies like an arrow, fruit flies like a banana”).

This abstract “computation” can be seen as a “game”, like Monopoly or chess. That means computation is a “ludic” system. The symbols it manipulates will have to be encoded or mapped into some representation through the physical bananas involved in the computation.

In both the abstract or concrete cases we might be engaged in the act of general computation (which requires Turing completeness), or something less than that in scope and capability.

So when we ask whether bananas can “compute”, there is a trivial “yes”, in that ten bananas could be said to compute the specific function “f(x) = 10”. What we really care about is general computation, i.e. can bananas support the highest level of ludic complexity for computation.

The very act of posing the question implies some form of conscious observer in the universe of inquiry. This turns out to be relevant, since it is clearly possible for a banana to be part of a general-purpose computer. One merely needs to encode ones and zeros by the orientation of the banana’s curve, and have the observer perform the actual computational act in their heads and use the bananas as a state system.

Thus what we are really asking is whether the bananas themselves can fundamentally act as integral mechanisms of a computing machine that performs the general computational act. Absent the bananas, it would not be possible to compute.

Since bananas are a physical item, we are really asking about the potential limits of a physical computer constructed partly or wholly from bananas. In the former case, we might then allow our universe of discourse to also include other mechanisms, say pulleys, pins, levers and strings, which interact with the bananas. You might see this as a Babbage engine transformed into a Cabbage engine, with a banana isomorphism available as the final step.

Such machines are limited by our imagination and creativity, and thus form an “ecological” constraint on banana-based computation.

We can now reposit the original question in a manner that allows it to be answered to a sufficient level of certainty to satisfy an inquiring young mind: Can bananas meet the ludic requirement of general computation, given their innate cosmic constraints and an unbounded level of ecological development in banana-bit processing technology?

If the entire machine is to be constructed of bananas, my suggestion is that the answer is “no”. That is because general computation involves the transformation of information, which inherently demands that information can be destroyed in that process. No possible level of ecological sophistication can overcome the cosmic limits of bananas: you cannot use bananas in your state system as to do so will inevitably demand infeasible acts of banana-bashing.

The answer when bananas are an element of a system that allows for unbounded levels of technological sophistication in the other components then depends on the constraints you pose.

A banana could certainly carry information in the I/O processes of a silicon chip, for instance, and hence a banana might be said to “compute” in this limited sense. Or, in networking, a packet of bananas is helping to compute the identity function at a distance (depending on the cardinality of the bunch).

One could also conceive of machines that use extremely advanced technologies to allow banana-based components to softly interact without causing irreparable damage to the components. Nonetheless, the energy used to advance this mechanical computation would have to be expended in some manner, such as deformation of the skin.

Thus the fundamental difference between a banana and a modern laptop CPU is that the electrical processes of the CPU allow the transformation of information in a manner that is not constrained by the cosmic limits of inviolable physical objects. These ones and zeros can interact with only a byproduct of heat, and that the system only requires (unbounded) levels of electricity and time to produce a general computational capability.