Solving 3n+1 - Collatz conjecture.
If you are reading this I assume you have some experience in solving equations. How about a simple one. 3n+1. and the rules are as follows
Here’s how it works:
Start with any positive integer.
If the number is even, divide it by 2.
If the number is odd, triple it and add 1.
Repeat these steps, creating a sequence of numbers. The conjecture states that no matter which positive integer you start with, this process will eventually reach the number 1.
For example, if we start with 6:
6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1
Looks very simple right? Our mathematical geniuses of the century should be able to solve this right? However, despite its simplicity, proving this conjecture for all positive integers remains an open problem in mathematics. It has been verified for numbers up to 2.95 × 10^20, but a general proof eludes us. And in the mathematical world it considered as insane if someone openly agrees they work on proving the conjecture. And more often years of human life have been spent on the problem. So, why is it so hard to solve something looks so simply. And what does this have to do with philosophy?
Approaches to the problem
Let's look at the approaches to the problem by our mathematicians. One thing is clear. The conjecture is either true or false. And there is no middle ground in mathematical world. (Or is there a one?)
Following are the ways used by mathematicians to approach the problem.
They have input thousands and thousands of numbers, into a computer program, to see whether there is any number which doesn't come back to 1. If there is a single number, the conjecture is false. So far, they have checked massive number of numbers with massive number of digits. And computers are working on this problem day in and out.
Second way is to come up with a proof that the conjecture is true, by using other true mathematical proofs.
So far, both these methods have failed either prove or disprove.
Greatest question to answer in philosophy, and in life
Let's stop our math lesson there and turn back to philosophy of life. In a previous article I have discussed about the greatest question to ask, in life in general. And came up to conclusion, that it is asking who am I? Because that is the root cause for all our problems. Not only in mathematics, even in health, even in finance, even in philosophy. And Mindfulness is the tool of philosophy in solving equations of life, harder than 3n+1. Let's apply our new problem-solving skills in our mindfulness practice.
Philosophy of solving equations of life, 3n+1
If you have practiced mindfulness long enough, Or short enough. You would understand that when we question the reality, we end up not finding anything to point as myself within the consciousness. This is what described in the blind persons world. However, this is only one approach to the problem. When we are looking at ourselves, what we are trying to do is either prove the theory of 'me' or disprove it. Just like the way a mathematician does it. However, doing both of these will create a 'me' first. But what if there is a third answer? Although the mathematicians do not have the freedom to go beyond true and false, we as everyday philosophers, of our own minds, can. What if there is just a scarecrow? And we cannot see beyond whatever the 'mind' chooses for us to, see?
Is there a middle ground?
Like one of my dearest friends once told me, it's an automatic living. Like a flag in the wind. A path to relative nothingness of everything.
Let's be mindful today.
Conclusion.
Mathematics, search true or false, as answers. And ignoring the possibility of both be true at the same time, relatively, like in quantum physics.
On the other hand, philosophers are liberal, instead of true or false as an absolute, we have the freedom of looking at life as a relative truth.
And this is true even about a cancer.
Comments