epistoschizoid

We ‘know’ a near-infinity of truths that contradict our immediate commonsense experience of the world. And yet we have to live and function in the world. So we abstract, compartmentalize: there’s stuff we know and stuff we ‘know’.

Do we really want to say that ∞ exists only in the way that unicorns do, that it’s all a matter of our manipulating abstractions until the noun ‘infinity’ has no real referent?

In short, can thought be so far removed from reality?

the concatenation

Take some such transcomputational number, imagine it’s a grain of sand, conceive of a whole beach, or desert, or planet, or even galaxy filled with such sand, and not only will the corresponding 10x number be <∞, but its square will be <∞, and 10(x(10x)) will be <∞, and so on; and actually it’s not even right to compare 10x and ∞ arithmetically

which means that a hypothetical supercomputer the size of the earth (= c. 6 × 1027 grams) grinding away for as long as the earth has existed (= about 1010 years, with c. 3.14 × 107 seconds/year) can have processed at most 2.56 × 2092 bits, which number is known as Bremermann’s Limit.

Bremermann’s Limit

stay so busy and bombarded with stimuli all the time. Abstract thinking tends most often to strike during moments of quiet repose.