People often bounce the idea of soul mates around: *“I think he or she is THE ONE for you.”* But is there such a thing? Yes, absolutely. We can mathematically prove this with a thought experiment. However, just like any other proof, we need to make an assumption:

A human changes through time and we will assume that we know of all changes a human life undergoes in his/her entire life.

Now, take a woman and randomly pull two men from the entire world. If we know exactly how the woman and the two men will change through time, then one of the men will be a better match than the other. Let’s keep the better match and randomly pull another man from the world. We continually do this comparison until there are no more men left in the world. The last man standing is *“The One.”*

Of course, it isn’t very realistic to know that 1 out of billions of people on the planet is best for you. But if you agree with the proof above, then we can reduce the sample size to something more feasible – which includes everyone you will and have met in your entire lifetime. Running through the same analogy again, we come to the same conclusion: One of them will be **The One** for you.

__A rigorous mathematical explanation for the proof given above__

There are * X* traits/personalities/attitudes that exists in a human being which can be scored using

*. The score for a trait is a function of time, therefore, making it a time-dependent variable denoted by*

**S**

**t****.**An ordered pairwise-set for two individuals A and B is created, meaning that

**S**does not equal

_{Xt}(A,B)**S**In other words, Person A’s preference through time does not equal to Person B’s preference through time.

_{Xt}(B,A).We need to find the maximum for this function:

**max ∑ S _{Xt}(A,B) + S_{Xt}(B,A)**

**for all paired individuals A,B with respect to time t scored on traits X**

The world population is estimated to be 7.4 billion and let’s assume that we meet 100,000 people in our lifetime, which is probably a gross exaggeration. This equates to crossing paths with **0.0000142% **of the world’s population! In contrast, we will never meet **99.9999858% **of the world. Wow!

Since the majority never cross paths, they must be independent sets, which then gives us the ability to quantify a score based on the desired traits an individual prefers through time. Using the ordering principle defined above, we can order the scores obtained for each individual to determine the best match between each couple. We then eliminate each person from our set by pairing the highest scored pair first. And continue eliminating them until there are no more possible pairs left to choose from. Each of these pairs will be correctly paired with The One, even though they will never meet.

For the case where a couple does in fact cross paths, it is certainly more complicated in nature. However, we would know that such a pair must have a higher score than any pair of their respective pairs in the 99.9999858% data set. This is certainly less likely to occur, which is why it is considered a rarity to spend one’s life with “**The One**.”

My proof doesn’t state that a person will actually meet their perfect match; instead, my proof shows that such a person exists.

Very interesting! You’ve essentially created a well-ordering principle for human relationships. One thing I’d like to point out, though: You actually make a second, implicit assumption with your proof: That out of any two individuals, one can be definitively picked as best (or, more specifically, you assume that knowledge of two individual’s development through time is sufficient to generate an orderable “matchability” between said individuals). Given the multidimensionality of human behavior and personality traits, I am hesitant to accept this assumption as true (It’s sort of like trying to create an ordering for complex numbers or octonions), and so I am also hesitant to accept your proof as correct. I would also like to point out that the development of an individual depends quite directly on those whom they spend their life with — and more specifically *when* they spend their life with these individuals. It is theoretically envision-able that two individuals may be either an excellent match, or a horrible match, depending upon at what point they meet in their lives. In other words, an individual’s “True One” has the potential to change with respect to time — an implication which on its own would prove the non-universality of the existence of a True One, due to the chronological plurality of True One’s exhibited, for instance, by the example individual above. We could resolve this by reducing the matchability of an individual between two individuals to the matchability of those two at the exact moment they are fated to meet — but the minute we bring fate into the matter, we have already lost; Our True One becomes the one we ultimately end up spending our lives with, regardless of their matchability.

Dear Georges,

Thank you for your comment and interest in my post!

I agree that my initial proof was loosely defined and I’ve added a rigorous explanation for each of the variables above. I would love to hear your comments regarding the extended version of the proof.

Please remember that I am not stating that one will be paired up correctly with the “The One” but rather that such a person exists.

Thanks,

Nima Farzaneh