Baby, You Incomplete Me

A mathematical look at logic versus emotion

What can Gödel’s Incompleteness Theorem tell us about relationships? Pardon the stereotype, but men tend to be more logical and women tend to be more experiential. If some minds are completely logical and Gödel’s Incompleteness Theorem holds, then it holds there are things which will be completely incomprehensible to those logical minds. Certain things will be magical, seemingly illogical, and maddening.

Of course, if you’re not familiar with Kurt Gödel’s work, we might need some refreshing. I won’t go into anything nearly as complicated as his math, but let’s go over a system that encompasses the idea. Let’s look at prime numbers, and by analogy say that prime numbers are beliefs about aspects and qualities of the world the basis of how ideas and things are built. So then the numbers, 1, 2, 3, 5, 7, 11, 13, and so on, now describe aspects of our world and our beliefs about it. Let’s limit this to only 1, 2, and 3. What numbers (further beliefs, ideas, and physical constructions) can we make with these by only multiplying those numbers and their products? We can make 1, 2, 3, 4, 6, 8, 9, 12, 16, and so on, or 2ˣ3ʸ to be complete.

What about 5? Well, it’s not in the set produced by 2ˣ3ʸ. So it can’t be factored. What about 10? It’s also not in the set, so it also can’t be factored. In this case we don’t know what 10 is, it’s some weird magic. It’s like someone mumbled some nonsense gibberish into our ears expecting it to change our life. If only we extended our system to include 5 we could know that 10 = 2 × 5. Only by including more bits of knowledge as a given to work with can we understand certain experiences.

On the other hand, let’s say we still only have 1, 2, and 3 to work with. Someone comes along and says, “10.” Now we accept that 10 is a valid thought even though we can’t prove it. Later, in the course of speaking with a completely logical person we mention 10, but they vehemently detest the mention of something so illogical. It becomes impossible for them to continue the conversation because, from their beliefs of 1, 2, and 3, it’s impossible to multiply and get 10.

The same thing can happen if, one day, you experience 14. Now, you know it exists. You saw it, maybe even felt it, but it was and is completely incomprehensible without just accepting it as it is. Sometimes this happens, in reality. For some world views, doing yoga makes no sense. Experiencing it and understanding what it does for oneself in spite of that world view, can lead one to embrace it as part of their belief and maybe someday, one will come across the factors which prove why it helps.

If it isn’t obvious by now how this plays out with sensing or intuitive people paired with thinking or judging people, or emotional versus logical people, let’s look at one more example: Dana must go for a walk and sense what the spirits say about her plans before committing to them. Bill, her partner, puts up with this because everything else about their relationship is perfect. Plus, somehow this practice has helped her figure out what’s best for both of them and has benefited Bill, too. Bill knows this. He still can’t wrap his mind around this because it makes no sense. The spirits are not a part of his vocabulary and he doesn’t believe in them. Initially, he struggled with how illogical all of this was. However, eventually he caught onto the larger system of logic that encompassed the human factors of his partner, Dana. She came up with the most rewarding plans and over time Bill came to accept this.

If women are the more intuitive and perceptive sex, then it must hold that we have the better grasp on what reality is despite not having the most logical grasp on what reality is. In fact, it could be stated that the more rigid and logical one’s views and beliefs are, the less of the world and reality one can believe or explain. Logic is incomplete. Constructing some logical models can help in certain cases, but most of the time it’s limiting and could lead to one believing reality and/or certain people are inherently consternating.

Extra Credit

Of course, one can always devise a system in which one can generate statements which are not provable. Assuming we are still using a system like the one above based on multiplication, let us introduce addition by one as a mechanism for discovery. This lets us generate more numbers than we could with multiplication alone and examine what’s produced.

Going back to the system where we only have {1, 2, 3}, let’s generate a few numbers:

1 + 1 = 2
2 + 1 = 3
3 + 1 = 4
4 + 1 = 5
5 + 1 = 6
6 + 1 = 7
7 + 1 = 8

So we have {2, 3, 4, 6, 8} which are a part of 2ˣ3ʸ. However, we’ve discovered {5, 7} which cannot be factored by any of the elements in 2ˣ3ʸ. These must either be discarded or accepted as basic axioms in the system thus making the base set {1, 2, 3, 5, 7} and the possible constructions 2ʷ3ˣ5ʸ7ᶻ.

Assuming we are using the new set, somehow we experience a 154. We also introduce an operation called division. Using the operation of division as a way of exploring how ideas come apart, we can find that 154 is divisible by {2, 7} which leaves us with something called 11. Since 11 is also prime, we can either toss it out or use it as a given.

Of course, none of this kind of analogous work with thoughts and beliefs matters if one’s mind is closed and only uses one kind of logical system. It will never be open to discovering all the crazy unknowns in this universe.