The Conceptual Sphere Phenomenon

Thus far, I found this reading segment of Hofstadter's book the most interesting. This is because Hofstadter spends slightly less than the first half of this section discussing real world examples of his ideas instead of number patterns. Even though it all does relate to these number patterns, it is a nice change in his writing style to keep the number pattern ideas from getting too dry. Similar to the previous readings, this "conceptual sphere" provides great insight into some of the finer subtleties of how the human mind works that typically go without notice.

As Hofstadter ideas imply, this "conceptual sphere" boundaries extend to arguably to infinity. Pretty much any two ideas can be connected in some fashion. Obviously, these connections vary greatly from having an obvious direct connection to a very distant that would take deep thought to find the connection. To use simple examples, an obviously directly connected idea would be a brother and sister in a family while the distantly connected one would be two random individuals in two random different continents or even non-human living beings. The simple fact is that one simple idea can be expanded level by level with broader connections being made at each level to infinity. As this relates to number patterns, you can take any segment of a number pattern and make an infinite amount of variations of that pattern. Hofstadter shows this with the base sequence he suggests on page 78 (1,2,2,3,3,4,4,5,5,6,...) and the variant his student Steve comes up with (1,2,2,3,3,3,4,4,4,4,...). While it may not stay true to the core of the original sequence, there are certainly connections. These are just some examples of how this conceptual sphere extending to infinity is one of the core ways of how the human mind works. We are simply making these connections to anything and everything that goes through our mind, whether we realize it or not.