Dear Noson,
Thank you for your excellent and insightful question! The answer is yes. If you translate a solution that has survived Occam's Razor into binary form (that is, into software), then the binary form of that solution will exhibit both the brevity and high information of a (near) Kolmogorov minimum.
One can think of the "side trips" of a non-compact message as the information equivalents of the various components of a Rube Goldberg contraption. Simplifying the message thus becomes the equivalent of redesigning an information-domain Rube Goldberg contraption to get rid of unnecessary steps. The phrase "Occam's Razor" even suggests this kind of redesign, since for both messages and physical Rube Goldberg contraptions the goal is to cut away that which is not really necessary.
One point that I think can be a bit non-intuitive is that solutions near their Kolmogorov minima are information dense -- that is, they look like long strings of completely random information. The intuitive glitch comes in here: If the goal of Occam's Razor is to find the simplest possible solution, how can a Kolmogorov minimum that is packed to the gills with information be called "simple"?
The explanation is that to be effective, messages -- strings of bits that change the state of the recipient -- must be at least as complex as the tasks they perform. That means that even an Occam's Razor solution must still encode non-trivial information, and depending on the situation, that in turn can translate into long messages (or lengthy software, or large apps).
If the desired state change in the recipient is simple in terms of how the recipient has been "pre-programmed" to respond (which is a very interesting issue in its own right), then the Kolmogorov minimum message will also be very short, perhaps as short as just one bit. But even though a single bit "looks" simple, it still qualifies as having maximum information density if the two options (0 or 1) have equal probability.
The other extreme for Occam's Razor extreme occurs when the state of the recipient requires a major restructuring or conversion, one that is completely novel to the recipient. That can be a lot of bits, so in that case Occam's Razor will result in a rather lengthy "simplest possible" solution. Notice however that once this new information has been sent, the message recipient becomes smarter and will in the future no longer need the full message to be sent. A new protocol has been created, and a new Kolmogorov minimum established. It's worth pointing out that downloading a new app for your smart phone is very much an example of this scenario!
We see this effect all the time in our modern web-linked world. As globally linked machines individually become more "aware" of the transformations they are likely to need in the future -- as they receive updates that provide new, more powerful software capabilities -- then the complexity of the messages one needs to send after that first large update also shrinks dramatically.
This idea that Kolmogorov messaging builds on itself in a way that over time increases the "meaning" or semantic content of each bit sent is a fascinating and surprisingly deep concept. It is also deep in a specific physics sense, which is this: The sharing-based emergence of increasingly higher levels of "meaning" in messages began with the emergence of our specific spacetime and particle physics, and then progressed upwards over time across a spectrum of inorganic, living, sentient, and (particularly in the last century) information-machine based message protocols. After all, how could we know some of the elements in a distant quasar if the very electrons of that quasar did not share the design and signatures of the electrons within our detection devices? We assume that to be so, but there is no rule that says it must be so. It is for example certainly conceivable that some distant quasar might be made of a completely different particle set from matter in our part of the universe. But if the universe did not provided these literally universally shared examples of "previously distributed" (by the big bang e.g.) information baselines, then such transfers of information would not even be possible.
So here's an important insight into the future of at least our little part of the universe: Meaning, as measured quantitatively in terms of observable impacts on physical reality per bit of Kolmogorov minimum messages sent, increases over time.
This idea of constantly expanding meaning is, as best I can tell, the core message of this year's deeply fascinating essay (topic 3088) by Nobel Laureate Brian Josephson, of Josephson diode fame. His essay is written in a very different language, one that is neither physics nor computer science, so it is taking me some time to learn and interpret it properly. But reading his essay has already prompted me to reexamine my thoughts a year or so ago (on David Brin's blog I think?) regarding the emergence over the history of the universe of information persistence and combinatorics. Specifically, I think focusing on "meaning," which I would define roughly as impact on the physical world per bit of message sent, may provide a better, cleaner way to interpret such expanding combinatoric impacts. When I reach the point where I think I understand Professor Josephson's novel language adequately, I will post comments on it. (I should already note that I am already deeply troubled by one of his major reference sources, though Professor Josephson does a good job of filtering and interpreting that extremely unusual source.)
Please pardon my overly long answer! You brought up a very interesting topic. I'll download your essay shorty and take a look. Thanks again for your comments and question!
Cheers,
Terry