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Dominic: How many bits does it take you to communicated the formula you discussed? How many for just the last term of that pattern?

When you wrote “But neither does it seem like the same shade of uncertainty” I suppose you mean that it doesn’t seem that way, to you. Nor does it to me. But before, as a thinking person, I suggest that the difference is meaningful, I need a context or a reason. You haven’t provided one, and that’s why your argument has the flavor of religion, to my palette.

I’d love to see your answer to the actual skeptical argument, rather than the straw man you offer, here. Here you are doing the equivalent of announcing “I’m thinking of a number!..… 5!...… I’m right again! My quest for order is rewarded!”

If you use mathematics to find order in the messy world, and you succeed, does that amount to a proof that the order you found is the actual order? Kepler would have argued yes! So would have Newton. Both were wrong. We know they were wrong. Wrong but their ideas are enduringly useful, as far as we know… so far… The skeptical position is not one of denying the value of ideas, but rather that of continuing the inquiry.

When my inquiry ceases, my beliefs become hardened premises that define my world and prevents me from benefiting from ideas of people with different premises. That’s fine in a simple world. A gamer’s world. I’ve become convinced that there is no simple world, except in our fantasies. Overcoming bias is about finding our center in a messy world. It’s about overcoming fantasy.

I was a little upset when I saw 6 there instead of 3. And I was even more surprised when I saw 24 at the end of the X^4 sequence. Perhaps the whole point is, as the author of this article says, that the beauty that I am looking for is deeper. Perhaps I need to collect all the last levels of sequences and do the same subtraction operations with them, and then I will find the beauty that I would like to find?

Isn’t the last value in the sequence definitionally zero for the first five terms, reducing the entire first term to zero as well and leaving only the n^2?

Does this mean that if we gave you (1, 4, 9, 16, 25, 36...) you would claim the next value in the sequence was 6! plus 49??

Michael: do you think we should decide that the simplest formula is the best?

But then how do we define simple? What do you mean by ‘communicating’ and ‘bits’? Do we assign arbitrary complexity points to the operators? What would be the relative complexity of a power operation as compared to a multiplication? And what of my pet operator I just invented that lets me replace “(n − 1) (n − 2) (n − 3) (n − 4) (n − 5)” with “5##” or something similarly silly?

Ask yourself, how can we be sure we have the simplest explanation? What is the simplest formula for the sequence {1, 2, …}? Is it the powers of two or the natural numbers? What about the sequence {1, …}? Is it really sensible to ask such questions?

Given the set: {1, 4, 9, 16, 25, …} And asked to identify the next number, the answer is: 156 For the sequence is obviously generated by the following formula: ((n − 1) (n − 2) (n − 3) (n − 4) (n − 5)) + (n ^ 2)

It is left to the reader to manipulate the formula into an unreadable form, so that it’s hard to see how it works. Especially fun is adding an irrational multiplier to the ‘(n − 1) … (n − 5)’ part.

And notice this method works for any sequence given to a finite number of elements, for, indeed, there are an infinite number of fully-specified sequences that fit.

That’s what I call beauty.