One of the most annoying debates going on today in the world of science and philosophy is the alleged dilemma between “reductionism” and “holism”.

This debate usually happens as a monologue: those who denominate themselves “holists” differentiate themselves from the opposing group that they call the “reductionists”, and claim that they are capable of studying phenomena that the supposed advocates of the other group can’t even conceive.

I believe humanity is wasting a valuable time in pretending that this dilemma actually exists. The self-denominated holists should stop being paranoid, and those candidates to the other denomination should try to stop the building of this pointless wall.

This is a series of two articles criticizing the idea of holism. In this first one I advocate that what many people perceive as an insufficiency of current science are actually well-known restrictions imposed by ourselves, completely understandable by the so-called “reductionist” framework.

You can read part two of this article at this address .

The hypothesis I present here is that the idea of holism comes from a frustration with the current difficulty of science in finally understanding very complex phenomena. It was created an idea that the scientific knowledge available today has already been exhaustively explored, that it is in fact not enough to handle complex phenomena, and that to finally reach a satisfactory level of understanding of these phenomena it would be necessary to complement this scientific knowledge. We would have to break hidden paradigms, reveal and question implicit assumptions, and make new significant discoveries. It would be necessary something as big as the invention of calculus, or the discovery of the non-euclidean geometries or the atom.

I believe this is not the correct perception of things, although it’s understandable. What happens is that the restrictions perceived by the holists do exist, but they are actually impositions created by scientists to perform certain kinds of studies, and these restrictions are so common and usually innocuous that we sometimes forget about them. The holistic revolution would be, in my point of view, not the discovery of something new that was lacking, but an attempt to finally remove such restrictions, which have been useful for us in other occasions, and were there all this time just waiting for the moment that we would finally be ready to dismiss them to explore new lands.

Those restrictions are related to each other, and they are: the assumption of statistical independence between causes, and the linear superposition of effects. I believe that a good part of the debates between holism and reductionism happens because systems are modeled based on known fundamental rules of interaction, in the “reductionist” way, but with those restrictions further imposed as to facilitate certain analysis. At the same time that those restrictions simplify the models, they ruin the possibility of deduction and representation of certain system characteristics. But the fault is not in the “bottom-up” approach, or in the focus on the knowledge of basic entities and interaction forces. It’s in the ‘naïveté’ and linearization.

STOP BEING NAÏVE

In a bayesian classifier system it is usual assume that the input variables can be considered independent. This means that the probability of a certain effect in a certain given situation p(A|x,y) is proportional to p(x|A)p(y|A), as opposed to p(x|A,y)p(y|A), for example. A model that has this assumption of strong statistical independence between the variables is said to be ‘naïve’ (a word loaned by English speakers from the French. It’s ‘ingênuo’ in Portuguese). This independence brings a lot of benefits to the usage of the system, specially when it has many variables. But naturally there are cases where strong dependencies exist and cannot be ignored. This is when you pay the price for being too naïve all the time.

Recently at Nature magazine there was an article about Chinese medicine… This article and its editorial used the word “reductionism” to refer to the study of the effects of a single molecule in an organism, or something like that. So, traditional western reactionary science would limit itself to isolate interesting specific molecules (“active principles”) and studying its effects in ideal generalized organisms when inoculated in them individually. To consider the effects of a certain cocktail of medicines would be something counter-reductionist, or anti-rationalist, because rationalism would necessarily assume that the effects of a cocktail would be simply the union, the plain and simple ‘superposition’ or ‘sum’ of the predicted effects of each active principle when acting individually.

This makes no sense. This naïve hypothesis is done in superficial preliminary researches only to make things easy at the start, to have a glimpse of some of the characteristics of the system in study. Any sensible scientist can understand that the simultaneous inoculation of two medicines can have an “unexpected” effect, different from the effects of each of the medicines alone. Any doctor would agree that you can’t tell easily what is the effect when you take two pills with opposed effects, for example. What would have happened if Alice had drank from the bottle and eaten the cake at the same time?

This kind of “unexpected” result can be seen as a consequence of some kind of non-linearity, as we will explain below. The reason why these phenomena are unexpected is that people are too used to reason using linear models; or being less nice: are too lazy to consider non-linear possibilities.

STRAIGHTEN UP AND FLY RIGHT

Another way of being naïve in scientific research, other then assuming that simultaneous causes would always lead to a simple union of effects, is to consider that the system you are studying follows a linear model. Linear systems can even be quite complicated, but they are intrinsically easier to handle mathematically. This comes from the most important, fundamental, intrinsic and unique characteristic of linear systems: the superposition.

Superposition means that a certain (continuous) variable being watched presents in time a curve composed by the sum of curves obtained with the convolution of each input variable of the system by functions called “impulse responses”. Those responses can even be measured in a process with a strong reductionist flavor. This is applying impulses in one input variable at a time while the others are in silence.

This means that in linear systems it’s very easy to isolate effects caused by each different input (the causes). If you know a certain impulse response and the corresponding input, you can subtract the contribution of that single input to the output your are analyzing, and what remains is caused only by the other variables.

Non-linear systems can be approximated by linear models in certain conditions, what is good because linear models are so much more easy to deal with. This is an approximation often seen in scientific research, just as statistical independence (naïveté) that we talked about later. The two have much in common, in my opinion, tough linearity is more related to continuous variables, and naïveté to discrete events.

LET’S WORK TOGETHER

Having recalled those two well-known and important concepts of statistical independence and of a linear model, I present again my theory: People got too much used to suppose that their systems have independence and are linear, and create the illusion that the best models offered by contemporary “reductionist” science must have these restrictions. They believe (uncountiously, perhaps) that the best models that exist are those that in fact are simplified versions of more complete models. By the way, those more complete models are not frequently used exactly because they are so much more difficult to work with.

Now, when working with complex systems it’s very easy to hear that a certain phenomenon is not the “simple sum” of certain elements. It’s easy to hear something like that even in your mundane life, specially when people are talking about someone helping someone else. It’s the old “union makes strength” speech… It’s the effect holists love to call synergy, that is one of those things that reductionists wouldn’t be able to conceive.

I just had the opportunity to hear someone saying that: the new coach of the Brazilian woman’s basketball team was interviewed (Globo News TV, 25/09/2007), and he said that the performance of a couple of players in a game is not the “simple sum” of their individual capacities, that the result can be better; or yet, in a declaration that impressed me for its maturity and the insight offered to me related to our topic: the result can be worse. One player can disturb her teammate.

Holists use this kind of appreciation of the possible benefits of cooperation as a proof of the need to seek a new kind of science, one that defies the barriers of the said “rationalism”, or “reductionism”. They rarely talk about the possibility of a setback due to an unhappy cooperation, as did this coach. I believe this reveals the presence of much rhetoric in their speech, and the need to mellow up these arguments.

Reductionism is criticized because it would be incapable of predicting any kind of synergy. Reductionists would only be able to consider a total performance of a team that would be the sum of the performance of each player considered alone.

I believe this thinking is absurd. A reductionist model for the performance of basketball players in a game doesn’t have to be restricted to linearity. It’s very easy to imagine models that can offer non-linear formulas to an overall performance.

For example, imagine that a player has a performance x, and the other has y. A silly linear model would state that their combined efforts must result in a performance D(x,y) = x + y. For example, if x meant 30 points per hour, and y meant 25, then the two players in a team would score 55 points in an hour. It’s not hard to imagine that this model would never work in real life. The mean of the individual performances would be another linear model.

Now, another possible model would be for example to add to the total performance formula an xy term multiplied by a “synergy constant” S:

D(x,y) = x + y + Sxy.

If the performance of one of the athletes is relatively low, just the other one will matter for the result. I they are equal, with x=y, the total performance would be 2x + Sx^2. The larger S gets in this case, the better the overall performance is compared to the linear prediction, meaning that a synergy is happening. On the other hand, S could also be negative, in which case the athletes would perform better playing without interaction.

There is nothing in the so-called “archaic reductionist tradition” that forbids the obtention of a mathematical model for a system that presents characteristics such as synergy. We only have to keep in mind that effects like this can vanish if we make too many simplifications. The simplest model possible is the linear one, and only then our answers will be all “simple sums” of the variables.