Relating the Sciences: A Compression Theory of Interscientific Reduction

In our project of understanding the world, we have created physics, biology, psychology, and a number of other disciplines. Now we want to turn our project into a rational one, a science that does not only find good hypotheses about the world, but that does so effectively. This requires that we first understand science itself: How do different sciences relate to each other? Why are there different sciences in the first place? And, within a single science, why does it look like we can distinguish ordinary science from scientific revolutions?
One way to ask how biology, psychology and elementary physics relate is the following: Given enough time and space to write, could we translate each biological statement into a statement in terms of physics that is true if and only if the biological statement is true? Likewise, can we translate psychological statements into statements about the physical states and processes of a system? Can psychological statements be translated into statements about biology?
Here is the gist of my thoughts:
The laws of a correct theory of elementary physics must be able to compress complete descriptions of system without loss. A complete description is a description that, in principle, would allow you to recreate the system exactly. It contains all the information there is in the system.
In contrast, inexact physics and special sciences like biology and psychology are lossy compressors of a system’s complete description. Given a lossy description, you might be able to restore certain features of the system, but never recover it completely (except for some degenerate systems).
To make an analogy:
A .png file compresses an image without loss — given the file, you can recreate the original image on the screen perfectly. The price you pay for this ability is that your file is relatively large.
In contrast, lossy image formats like .gif and .jpg create smaller files and they allow you recreate certain features of the original image, but usually do not recover it completely. For example, .jpg is more faithful to the original colors, .gif preserves edges and structural details better, but neither can restore the initial image completely.
Consequently, taking a .jpg image and saving it to .gif will result in loss both of the information that .jpg does not preserve and of the information that .gif does not preserve.

As may already be clear from the analogy, there are implications of the compression view for the relation between the sciences:
Statements from the special sciences and approximate physics can be translated into (possibly very long, disjunctive) statements about elementary physics without additional loss. However, such a translation will not make the statements more exact — information that is not there in a statement from one of the special sciences won’t be there in its translation, so what you get might be something like “it looks like physical situation A, or like physical situation B, or like physical situation C, or …”.
Statements from the special sciences can be translated into each other, but this will result in additional loss of information. In effect, what we need to do here is to first translate into exact physics (without additional loss) and then recompress into the target special science (with loss). Since different special sciences usually keep different structural details of the state intact, such a translation will usually throw away information. The more different the features that the two special sciences keep, the more loss we suffer.
I say usually since it is conceivable that statements formulated within a certain special science contain strictly more information than the translations within another science, just like statements in a correct elementary physics contain strictly more information than any of the special sciences, and just like a .gif format with 8 bits of color information (256 colors) contains strictly more information than a .gif format with 4 bits of information (16 colors). If you’re a philosopher, you might say that the latter, more coarse theory/format supervenes on the former, and if you’re a daring philosopher of mind, you might hypothesize that the relation between biology and psychology is just like this.
Why are there different special sciences? Why do we need special sciences at all?
The analogous question can be asked about image, audio and movie compression algorithms, and here the answer is clear: We don’t have enough space for lossless compression and in the end all we care about are certain features (and in different situations, we care about different features). In the case of audio compression, we only care about sounds within the range of 20 Hz to 20,000 Hz since everything else isn’t perceivable by the human ear.
Similarly, when we want to describe a phenomenon using scientific theories, we cannot use elementary physics as it takes too much time and space (although that would give us the most accurate predictions) and in the end, we do not care about all aspects of the phenomenon equally anyway. In thinking about how the brain works, neuroscientists do not look at the brain as an arbitrary physical system whose behavior is to be predicted, but instead it is certain aspects of this system that they try to explain. The aspects we care about tell us how to compress our observations into theories, and since we are not always interested in the same aspects, we need different ways of compression: different special sciences.
The compression view also gives us a way to think of the difference between ordinary science that discovers new facts within a framework and scientific revolutions that bring conceptual change:
Ordinary science is the process of finding out how the compressed version of interesting situations look like and how lossy the compression is when we apply existing compression algorithms — theories — to different situations. We smooth out small bugs in the compression algorithm, but fundamentally, we don’t change our framework: we use the existing compression algorithm.
Scientific revolutions change how we compress our observations: Every reasonable revolution either improves how strongly we can compress (e.g. by showing that what we thought of as different phenomena can be explained by the same principle) or makes our compressions less lossy (e.g. by replacing a black box term like elan vital with a structured theory). Since compression and prediction are two sides of the same coin, another interpretation of scientific revolutions is that they change the prediction algorithm whereas ordinary science mainly makes and checks predictions.
Now you be the judge how lossy this view on science really is.

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