In this second article for holism scrutiny I talk about the idea of a “whole larger then the parts”, a subject that almost drove me mad in a recent past. It was trying to explain my rejection to the idea of a “whole larger then the parts”, presented to me in the context of gestalt, that I ended up developing this larger criticism against the idea of the need for a “holism theory” in general.

You can read the part one of this article at this address .

A famous theory that deals with phenomena that are not “simple sums” of things is gestalt (either the original perceptual theory, or the broader one).

The largest part of everything ever said about gestalt, at least in introductory material presented to lame electrical engineers like me, is directed to the idea that the perception of a complex object is not a consequence of the “simple sum” of the perception of its individual isolated elements. For example, in Wikipedia you can read about the “visual recognition of figures and whole forms instead of just a collection of simple lines and curves”.

The eternal example image where one can appreciate the “gestalt effect”, and the impossibility of explaining perception from the isolated perception of small constitutive parts is a black-and-white picture of a Dalmatian dog on a floor covered by dry leaves. It’s the epitome of the defeat of the “archaic reductionist tradition” in its failed attempt to unveil the secrets of the human cognition.

Gestaltic holists accuse the anonymous reactionary reductionism advocates of trying to explain the perception of a picture like this as based only in a “simple” decomposition of the drawing in deformed stains; and the “simple sum of deformed stains” would then be incapable of enclosing the whole process of perception.

Older pre-holism scientists would have been all unable to approach the problem of the perception of a Dalmatian in a monochromatic garden during autumn because they were all restricted to the “ancient rationalist thought”. Archimedes, Galileo, Leibniz, Gauss, Laplace, Babbage and even perhaps Albert Einstein and Avram Noam Chomsky himself would have been all victims of the “anachronistic cartesian reductionism” inherent to our “shallow reactionary western bourgeois culture”, and that would be the reason they had all failed to explain our strange ability to spot a dog in a spotted garden.

This debate is always presented in an introduction to Gestalttheorie — It even seems sometimes that the concept of a Gestalt cannot be communicated directly: It must emerge from this confrontation of complex interacting antagonistic parts. The debate is always presented in classes, but this is actually a finished dispute. Nevertheless, an innocent part is pointed out as guilty in the end…

No reductionist scientist (if there are other kinds) ever defended the idea that perception should happen as a “simple sum” of causes that could be regarded separately. There is no reason to believe that human perception should happen by a linear process. There never was. What could have happened is the wishful thinking that it were linear, because things would be simpler then. But it’s easy to see that this is not the case.

What “reductionism” does is to bring the focus, before anything else, to the most fundamental characteristics of phenomena, and to all possibilities offered by the entities being analyzed. To the eyes of a reductionist a large and complex system has a large number of complex elements, capable of innumerable possibilities, interacting with all of its closer and farther neighbors in complex ways. A model like this can be something very big and intricate, that can easily beat the cognitive power of any mind or machine that try to enclose all its most subtle details.

So the most complete system model a reductionist can offer to the study of any phenomenon is something way beyond a “simple sum” of anything. Gestalt doesn’t require then the abandon of the old way to practice science, but just the use of more advanced models. They may be less familiar models, difficult to use, cryptic, but they are still rationalist, assembled from reductionist atoms.

Now consider the success of neuronal networks to solve problems such as the recognition of letters in images. They are structures that rely not only on the sum of causes, but also on a bunch of sigmoidal functions, such as the hyperbolic tangent.

The question is: gestaltists are against the idea that perception can happen through the “simple sum” of the perception of individual elements. Would they also be against the “sum of the hyperbolic tangents of simple sums” of those same elements? Could the inclusion of this simple non-linearity in a system make the difference between holism and what they call reductionism?

Other then abhor the “simple sums”, holists like to quote the aphorism that “the whole can be larger then the parts”. That is the reason Aristotle in not mentioned in that list of notorious scientific personalities I made previously: he mentions this concept in his Metaphysics, and this is considered as the oldest reference to the idea of holism. I could not determine the oldest reference to the idea of a “whole smaller then the parts”, tough, or even of a “whole of the same size then the parts, but related to them with operations other then ‘simple sums’”.

Before telling you my humble crackpot opinion about this, let me quote Galileo’s advice that sometimes even some great important figures as Aristotle can be proven wrong!… And also let’s not forget Royal Society’s lemma: Nullius in verba. Now, my personal view is that I simply cannot conceive a “whole” that is not composed by its parts, all of them, and nothing more. What lurks behind the enigmatic concept of the cornucopious holistic synthesis would be again the idea of a “simple sum”.

In this holistic myth exists a hidden assumption that the reductionist “whole” is composed through a restrict set of operations. In the holistic “whole”, the interactions between the parts cause emergent miracles, epifaneous epiphenomena and other wondrous wonders. In the rationalist “whole” the parts are inert chunks of matter scattered aimlessly inside a linen bag, without care about their actual states relative to each other.

In heated debates holists give the impression that traditional science can only deal either with the interaction between two single bodies, or make stochastic approximations of the limit behavior of large boiling groups of particles.

This may be perhaps a subconscious denial due to the frustration, after all the expectation since the mechanicism of Laplace, caused by the difficulty met in the study of large systems, as in the 3-body problem famously studied by Poincaré. This “neo-anti-mechanicist” movement seems to ignore that Laplace’s promise involves knowing “all” characteristics of “all” the components of the universe, or closed system in study.

When holists criticize those accused of committing retrograde rationalism, they say that it is not possible to interpret a B&W picture as a “mere juxtaposition of spots”. The implicit statement in that argument makes no sense: rationalism would throw away all the minutia and details of those spots. That is absurd because in principle, the more reductionist you get, the more you should care about the exact state of the components and sub-components of your system, without performing any form of simplifications.

The holist accusation would be equivalent to claiming that reductionist chemists do not care about the structure of their chemical compounds. A traditional chemist would not see any difference between isomers. Chirality would be unconceivable. Molecules would be just “mere agglomerations of atoms”.

It’s undeniable that the detailed study of the structure of molecules and crystals is exactly one of the largest factors in the development of chemistry in its history. And science never ceased to be “reductionist” because of this. It was not necessary to embrace holism to perform that impressive estimate of the shape of the DNA molecule. What was needed was a detailed study of the different possibilities offered by chemical bounds, and the phenomena related to the interaction between light and matter.

Structure is not something that you deny or forget when studying fundamental interactions and properties. It’s something you try to understand based on those basic principles, and on other more advanced ones related to the general behavior of large complex systems.

DNA molecules are not “mere agglomerations” of genes, bases or atoms. They are specific atoms in specific relative positions, with specific non-linear forces of attraction and repulsion acting between them. There is nothing “simple” in that, as in a “simple sum” of atoms.

In the same way, spots in a photograph have specific shapes and positions. The criticism that rationalism only delivers a “bunch of spots” is due to boredom caused by looking into a detailed description of such a picture. Those descriptions seem not to “tell us” anything. Who sees the “bunch of spots” is the critic who is observing a program without seeing anything interesting. Its him who throw away information and regard those spots as just like any other… But to the program that one is a very specific bunch of spots, as all of them are.

The problem in the operation of an AI program is not lack of information. A system capable of recognizing which spots in a picture compose a dog shape starts with the knowledge of the exact location of each spot in the picture, and must also have some good previous information about which sets of spots are acceptable as “dog” shapes. The information in the picture is gradually thrown out until the only data left is either a single bit telling us about the existence or not of a dog in the picture, or a small data structure describing the approximate location of the dog inside the picture, which spots constitute the “dog” set. It’s a great deal of structured and detailed information that exists, and rigorous operations performed, it’s not just “a bunch of spots” from which the program tries to “make sense”. It’s TOO MUCH sense to start with, the problem is to SIMPLIFY.

The program starts with a detailed description of the pictures, and ends up with a small description of the dog inside it. This initial description of all the spots, given in pixels, for example, tell us the whole picture. It’s the “whole”!… As long as a description of the picture has no loss of information, it is the “whole”. You can’t be “larger” then this!!… The fact that “there is more to the picture then the pixels” doesn’t mean that the pixels are insufficient, or “smaller then the whole”. Those information are supplementary. It’s larger then the whole, and not larger then “the sum of the parts”. It’s additional information, and this additional information comes from, for example, the definition of a function that can spot a dog among the spots.

The problem with science is not seeing a “whole” beyond the behaviors of each part. Science understands very well what happens when a large number of particles interact. In fact, too much well. There is nothing “lacking” to finally attain the holistic “whole”. The reductionist “whole” is all, it’s complete. The difficulty resides in the interpretation operations. The identification of similarities between states, or indirect characteristics of states.

In other words, there is no deficiency in the modelling of large systems, but in the identification of what we can call “higher-order abstract attributes”. And they even have specific rigorous mathematical reductionist deterministic mechanicist definitions.

The holists call it a “whole” the picture in question, plus every little thing that can possible be imagined to be said about the picture. I believe the “whole” should be just a set of informations that can fully describe a picture, so it can be stored or transmitted, for example. Every different codification of a picture, be it in raw format, gray coding, RLE, LZW, all those lossless codifications tell the “whole” about the picture. If someone can see a dog before this codification, then another dog finder will be able to find the dog after the codification too, because “it’s all there”.

A program that finds a dog in an image must learn the proper information to consider, and what it can throw away… It’s similar to other stochastic mmeasurements, like finding out the temperature of a gas in a balloon, but much more complex. Why should the information obtained from every operation that we can possibly apply to such a picture to “understand” it be necessary to finally constitute the “whole” of the picture?

The whole should be even less: should be just the necessary information for all the important operators to work. You can still see the dog in a JPEG image, where the distorted spots are distorted even more.

There is a confusion here related to the representation of something, and meaning… The symbol and the content… But I don’t want to get into this because I have some strange opinions regarding semantics.

The biggest problem in accepting the sufficiency of reductionism is chaos, and the inherent computational complexity of all non-trivial, non-linear systems. The biggest problem is the anthropocentric view that if something is difficult, hard to be “understood” by the human mind, than there is something wrong to it… People care too much about the hedonistic pleasure of capturing a seemingly complex phenomenon with a simple mathematical concept. This is great, but it’s not the only acceptable science. Science can be hard, can be difficult, can be sometimes unattainable even to the most seemingly bright minds, geniuses, algebra heroes and pop-stars, including Aristotle and Einstein.

Poincaré once said that avoid suffering is a negative objective, more easily reached by the annihilation of mankind. It’s in the pursue of truth that we should concentrate our efforts. This should be understood as referring to suffering in general, in all aspects of life, but it includes suffering inside science, inside the pursue of truth itself. Do not pursue truth and avoid suffering at the same time. Do the first without caring, and just be glad when your get lucky to have the second. Some mathematical masochism can help sometimes.