Computational vs Biological Thinking (Man / Machine XII)

Computational vs Biological Thinking (Man / Machine XII)

Our study of thinking has so far been characterised by a need to formalize thinking. Ever since Boole’s “Laws of Thought” the underlying assumption and metaphor for thinking has been mathematical or physical – even mechanical and always binary. Logic has been elevated to the position of pure thought, and we have even succumbed to thinking that is we deviate from logic or mathematics in our thinking, then that is a sign that our thinking is flawed and biased.

There is great value to this line of study and investigation. It allows us to test our own thinking in a model and evaluate it from the perspective of a formal model for thinking. But there is also a risk associated with this project, a risk that may become more troubling as our surrounding world becomes more complex, and it is this: that we neglect the study of biological thinking.

One way of framing this problem is to say that we have two different models of thinking: computational and biological; the computational is mathematical and follows the rules of logic – and the biological is different, it forces us to ask things about how we think that are assumed in computational thinking.

Let’s take a very simple example – the so-called conjunction fallacy. The simplest rendition of this fallacy is a case often called “Linda the bank teller”.

This is the standard case:

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Which is more probable?

Linda is a bank teller.

Linda is a bank teller and is active in the feminist movement.

https://en.wikipedia.org/wiki/Conjunction_fallacy

What computational thinking tells us is that the first proposition is always more probable than the second. It follows from the fact that the probability p is always bigger than the probability p x q if either probability is less than 1.

Yet, a surprising amount of people seem to think that it is more likely that Linda is a bank teller and active in the feminist movement. Are they wrong? Or are they just thinking in a different mode?

We could argue that they are simply chunking the world differently. The assumption underlying computational thinking is that it is possible to formalize the world into single statement propositions and that these formalizations are obvious. We thus take the second statement to be a compound statement – p AND q – and so we end up saying that it is necessarily less probable than just p. But we could challenge that and simply say that the second proposition is as elementary as the first.

What is at stake here is the idea of atomistic propositions or elementary statements. Underlying the idea of formalized propositions is the idea that there is a hierarchy of statements or propositions starting from “single fact”-propositions like “Linda is a bank teller” and moving on to more complex compound propositions like “Linda is a bank teller AND active in the feminist movement”.

Computational thinking chunks the world this way, but biological thinking does not. One way to think about it is to say that for computational thinking a proposition is a statement about the state of affairs in the world for a single variable, whereas for biological thinking it is a statement about the state of affairs for multiple related variables that are not separable nor possible to chunk into individuals.

What sets up the state space we are asked to predict is the premises, and they define the state space we are asked to predict as one that contains facts about someones activism. The premises determine the chunking of the state space, and the proposition “Linda is a bank teller and active in the feminist movement” is a singular, elementary proposition in the state space set up by the premises — not a compound statement.

What we must challenge here is the idea that chunking state spaces into elementary propositions is the same as chunking them into the smallest possible propositions. For computational thinking this holds true – but not for biological thinking.

The result of this line of arguing is intriguing: it suggests that what is commonly identified as a bias here is in fact just a bias if you assume that computational thinking is the ideal to which we are all to be held — but that in itself is a value proposition. Why is one way of chunking the state space better than another?

Another version of this argument is to say that the premises set up a proposition chunk that contains a statement about activism, so that the suppressed second part of “Linda is a bank teller” is “and NOT active in the feminist movement” and cannot be excluded. That you do not write it out does not mean that the chunk does not automatically contain a statement about that as the second chunk and the premises set that up as the natural chunking of the state space we are asked to predict.

The real failure, then, is to assume that “Linda is a bank teller” is the most probable statement – and that is not a failure of bias as such, but an interesting kind of thinking frame failure; the inability to move away from computational thinking instilled through study and application.

It is well-known that economists become more rational than others, that they are infected with mathematical rationality through study. Maybe there is this larger distortion in psychology where tests are infected with computational thinking? Are there other biases that are just examples of being unable to move from the biological frame of thinking?

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