Kolmogorov complexity is a measure of the algorithmic complexity of a particular piece of information, and it is found by identifying the shortest possible representation of that information. For example, if I have a string of characters AAAAA, I can create a compressed representation 5A. The Kolmogorov complexity of AAAAA then is at most 2 because I can represent that same information with only two characters using the shorter version 5A. We can say that 5A is the Kolmogorov string that shows that the Kolmogorov complexity of AAAAA is 2.
Kolmogorov complexity can also give us a sense of the relative complexity of different pieces of information. AAABB can only be compressed down to 3A2B, for a Kolmogorov complexity of 4, making it twice as complex as AAAAA.
Fractals like the one below look complex, and indeed, storing an image of a fractal can take up a lot of space. However, fractals are constructed by following simple rules, and a computer program to execute those instructions can be many orders of magnitude smaller than storing the image itself. This means that the Kolmogorov complexity of fractals can actually be quite low, despite appearances.
It occurred to me to ask—do I have a Kolmogorov complexity? My body and my mind both contain only a finite amount of information, so both could be described in exhaustive detail with only a finite amount of text. A brute-force description of every fiber of my being does not strike me as especially interesting. If I were able to discover my Kolmogorov string though, that does strike me as having some interesting properties.
Such a string would represent my purest and most distilled essence. It would contain every single detail of my existence—since even a single missing bit would disqualify it from being my Kolmogorov string by definition. It is also completely unique, being the shortest possible string. It is so lean that not a single redundant detail remains—otherwise, it would not be the shortest string.
So here we have a total representation of my entire being from which not a single iota can be added or removed; an utterly perfect representation.
One could examine this string and ask any question about my life and get the correct answer in exact detail. The details contained within it would be so exquisite that, even if I were to be utterly destroyed it would be enough to construct an exact replica of me.
One’s Kolmogorov string is an ethereal thing, likely too slippery and ineffable to be truly captured in reality. But, in principle, it does exist and could be found with enough effort. Everything that I am—my memories, my scars, my skills—could be condensed down into its purest essence of information. Despite capturing everything about me, my Kolmogorov string would be a static, unfeeling thing of pure information. Only when that information is situated within a moving, dynamic body would it feel and think.
What is a soul, if not this?
It strikes me just how similar this is to the traditional conception of a soul. Here we have a theoretical object that can perfectly and uniquely capture one’s identity in an abstract and immaterial way. It totally defines us, and yet can never truly be measured.
It also seems to me to be fairly compatible with just about any philosophical background without too much effort. Certainly, an omniscient being would have no difficulty finding one’s Kolmogorov string. At the same time, no appeal to the supernatural is necessary to point out that such a string must almost certainly exist for every individual.
What else could these strings tell us? How big is my soul—what is left of me after you strip away all the fat? How much has my soul grown over my life? How would it change after a major life event? How does it compare to other souls? Would these souls contain similar structures, or would they all be fairly unique? How close can we really get to approximating one? Would someone really be dead if their Kolmogorov string were known?
Kolmogorov Complexity Lays Bare the Soul
Kolmogorov complexity is a measure of the algorithmic complexity of a particular piece of information, and it is found by identifying the shortest possible representation of that information. For example, if I have a string of characters AAAAA, I can create a compressed representation 5A. The Kolmogorov complexity of AAAAA then is at most 2 because I can represent that same information with only two characters using the shorter version 5A. We can say that 5A is the Kolmogorov string that shows that the Kolmogorov complexity of AAAAA is 2.
Kolmogorov complexity can also give us a sense of the relative complexity of different pieces of information. AAABB can only be compressed down to 3A2B, for a Kolmogorov complexity of 4, making it twice as complex as AAAAA.
Fractals like the one below look complex, and indeed, storing an image of a fractal can take up a lot of space. However, fractals are constructed by following simple rules, and a computer program to execute those instructions can be many orders of magnitude smaller than storing the image itself. This means that the Kolmogorov complexity of fractals can actually be quite low, despite appearances.
It occurred to me to ask—do I have a Kolmogorov complexity? My body and my mind both contain only a finite amount of information, so both could be described in exhaustive detail with only a finite amount of text. A brute-force description of every fiber of my being does not strike me as especially interesting. If I were able to discover my Kolmogorov string though, that does strike me as having some interesting properties.
Such a string would represent my purest and most distilled essence. It would contain every single detail of my existence—since even a single missing bit would disqualify it from being my Kolmogorov string by definition. It is also completely unique, being the shortest possible string. It is so lean that not a single redundant detail remains—otherwise, it would not be the shortest string.
So here we have a total representation of my entire being from which not a single iota can be added or removed; an utterly perfect representation.
One could examine this string and ask any question about my life and get the correct answer in exact detail. The details contained within it would be so exquisite that, even if I were to be utterly destroyed it would be enough to construct an exact replica of me.
One’s Kolmogorov string is an ethereal thing, likely too slippery and ineffable to be truly captured in reality. But, in principle, it does exist and could be found with enough effort. Everything that I am—my memories, my scars, my skills—could be condensed down into its purest essence of information. Despite capturing everything about me, my Kolmogorov string would be a static, unfeeling thing of pure information. Only when that information is situated within a moving, dynamic body would it feel and think.
What is a soul, if not this?
It strikes me just how similar this is to the traditional conception of a soul. Here we have a theoretical object that can perfectly and uniquely capture one’s identity in an abstract and immaterial way. It totally defines us, and yet can never truly be measured.
It also seems to me to be fairly compatible with just about any philosophical background without too much effort. Certainly, an omniscient being would have no difficulty finding one’s Kolmogorov string. At the same time, no appeal to the supernatural is necessary to point out that such a string must almost certainly exist for every individual.
What else could these strings tell us? How big is my soul—what is left of me after you strip away all the fat? How much has my soul grown over my life? How would it change after a major life event? How does it compare to other souls? Would these souls contain similar structures, or would they all be fairly unique? How close can we really get to approximating one? Would someone really be dead if their Kolmogorov string were known?
https://sigil.substack.com/p/kolmogorov-complexity-lays-bare-the