…That subjectivity applied to the modern physics bothers me a lot. It is not because I cannot accept the idea of our mind and consciousness are part of the system. No, not at all. I can feel my consciousness so it is part of the real world for me. At least it is real enough for me to accept that it could interact somehow with the physical world around. What bothers me is that there is no math to work with that. In a sense, the science ended at that very moment when you allow any free will to act.

What would you expect? Objectivity is the basis of science.

Yes, but I have been looking for any case when subjectivity and mathematics intersect. I hoped that if I found such an example then may be we can begin to study that subjectivity in a normal scientific way. And guess what? It looks like I found something of that sort! Yesterday I was helping my daughter to do her math homework and there was some of those ‘continue the sequence’ problems. Some short sequence of numbers is given and you have to find out what the next number should be.

O, I remember, I’ve always hated those. Every time when I gave up and somebody showed me the solution, it looked so obvious that I felt stupid.

Right. But here is what I thought: let’s say we have a sequence 2,4,8. What would be the next number?

Simple, 16, of course.

Can you explain why?

That is obvious. You can see that every number doubles, so the next is double of 8, 16.

But what if I tell you that the next number is actually 32?

32? Let me see… Ah I know. The next number is the last one multiplied by the one before! 8 is 4 by 2. Then the next one would be 8 by 4, 32. Right?

The thing is that there is no right solution for that, because your belief in some rule is part of the solution and you are free to come up with any rule you want.

Tell me, what was the answer in the textbook?

Sixteen, of course, but that was wrong. 16 would be correct if the rule of doubling the last number was given, but it was not.

I see. Interesting, but what could you make of this?

Since the solution to the problem depends on the free will of the person who is solving it, we have a clear case of subjective influence on the mathematical result. Isn’t it amazing?

Then I would not call this problem mathematical at all.

Who knows? After all, it was in a mathematics textbook.