Figuring This All Out

Do you think that you have ever had an original thought?

Yes, it seems like the probability of all of the random events and circumstances in the world eventually engage every person in a completely original thought. It seems like they must be innumerable.

What does innumerable even mean to you?

I attempt to visualize it, even though that defeats the purpose of the idea of an uncountable amount of numbers. I imagine a number line starting with zero and counting by ones until ten that extends out of my frame of reference. Zooming out, the line itself does not shrink but the intervals between the numbers slide closer together as new intervals of tens and hundreds and millions begin to pop up. The intervals continue to slide together until the number line abruptly stops. What comes after this break? Unable to comprehend any larger such entity than already included in the number line, perhaps it you were to zoom out until the number line were near a dot on the page, it would appear to be just one point of ink on a much larger number line that is also numbered from zero to ten by ones. As you continue to zoom out on this impossibly immense piece of paper going through an impossibly immense printer spitting out an infinitely long and fractal-like number line, perhaps at somepoint you will run out of ink and arrive at some number or entity at the end of the line that can be considered innumerable.

Are innumerable and infinity the same thing?

I would venture to say yes, but as I think more, my above description sounds like an attempt to comprehend infinity, rather than innumerability. Innumerable in a sense seems like a human fault, like an inability to count the entirety of some system while infinity is a natural occurence. If a person were asked to count the number of teaspoons of water in a bathtub full of water, albeit tediously, the task could be accomplished and an approximate answer could be found. However, if a person were asked to count the number of teaspoons of water found in Lake Erie, the chances of such an event occuring and producing a correct answer can be assumed to be zero. The person would rather assume the number of teaspoons present in Lake Erie are innumerable rather than an infinite number of teaspoons.

So, is there a difference between innumerability and impossiblity?

Going back to the issue to approximating Lake Erie's volume of water in teaspoons seems to be an impossibility... I'm going to have to think about this one more.