Algorithmic Reducibility

…the chameleonic nature of numbers [is] so rich and complex that numerical patterns have the flexibility to mirror any other kind of pattern. (Douglas Hoftsadter in I am a Strange Loop, p. 159)

In my last post, I discussed the point of view known as ‘reductionism’ and the problems with that point of view. In summary, reductionism is the false belief that sciences that work with the smallest units of nature – atoms and below – are somehow more fundamental explanations of reality than emergent ones, such as thought or computation.

A few posts ago, I discussed computability and comprehension. My final conclusion was that while algorithms and explanations aren’t the same thing, you can’t have an explanation without having an algorithm. Continue reading

What is Science: Is Science about Reductionism or Holism?

In my last post I discussed Scientific Realism vs. Positivism. The conclusion I drew was that, while both are useful points of view, Scientific Realism is the one you want if your desire is to comprehend reality. In this post, I’m going to discuss Deutsch’s arguments surrounding Reductionism and Holism, two points of view that Deutsch argues are also a hindrance to Scientific Realism.


Deutsch describes Reductionism as the belief that:

…science allegedly explains things reductively – by analysing them into components. For example, the resistance of a wall to being penetrated or knocked down is explained by regarding the wall as a vast aggregation of interacting molecules. The properties of those molecules are themselves explained in terms of their constituent atoms, and the interactions of these atoms with one another, and so on down to the smallest particles and most basic forces. Reductionists think that all scientific explanations, and perhaps all sufficiently deep explanations of any kind, take this form. (The Fabric of Reality, p. 19)

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Positivism vs. Scientific Realism: An Example

In my last post I started to discuss the differences between Positivism and Scientific Realism. To over simplify it, Positivism cares only about the predictive abilities of science and does not care about whether or not science is getting ever closer to some underlying truth. Scientific Realism takes all scientific theories seriously as approximations of an underlying truth.

Actually, despite what Deutsch says (in my last post), I feel Positivism has value. Though I generally agree with Deutsch, sometimes you just want to predict an outcome and you don’t really care about why it works. In fact, I think most people would be shocked to realize that this is how most science and engineering are done. Scientists rarely become philosophical about what their equations mean for reality.

However, Deutsch is right about one thing. Positivism ultimately fails to grasp the value of believing your explanations. It is only through believing your explanations that you can comprehend them. And only by comprehending them can you refine them into something even more useful. Continue reading

Computability and Comprehension – Is Science About Prediction?

Science is the process of how we use reason to find patterns in reality and then to explain them in finite explanations of reality that allow us to represent reality via processes that are computable.

In my last post, I introduced David Deutsch’s book, The Fabric of Reality. Deutsch’s main interest is in understanding – and by that he means understanding everything. Deutsch believes that understanding something is to have an accurate explanation of it and that this, in turn, serves as a sort of algorithmic compression of all observational data.

Deutsch’s point of view falls under what we might call Scientific Realism. It’s the idea that science is not just about coming up with clever predictions about the world, but rather it’s about discovering reality’s true nature and comprehending it. Continue reading

What Does it Mean to Comprehend Something?

In my last post I considered Physicist John Barrow’s view of what science is:

So we find that Barrow’s view of science is that it is the process of how we use reason to find patterns in reality and then to algorithmically compress them into finite steps and formula that allow us to represent reality via processes that are computable.

I am going to suggest this as our starting theory of reality, but there is much that can be challenged about this view and therefore refined.

But first, I want to consider the idea of comprehending something. What does it mean to “comprehend” something? The problem with a word like this is that it’s a single word that maps to multiple possible meanings. Harkening back to my first post, if I ask you if you comprehend PI, what would that mean? Is it even possible to “comprehend PI” at all? It’s an infinitely large number, after all. It is therefore beyond comprehension isn’t it?

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