
Everything and More

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’.
David Foster Wallace, Neal Stephenson (Introduction) • Everything and More
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?
David Foster Wallace, Neal Stephenson (Introduction) • Everything and More
In short, can thought be so far removed from reality?
David Foster Wallace, Neal Stephenson (Introduction) • Everything and More
the concatenation
David Foster Wallace, Neal Stephenson (Introduction) • Everything and More
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
... See moreDavid Foster Wallace, Neal Stephenson (Introduction) • Everything and More
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.
David Foster Wallace, Neal Stephenson (Introduction) • Everything and More
Bremermann’s Limit
David Foster Wallace, Neal Stephenson (Introduction) • Everything and More
stay so busy and bombarded with stimuli all the time. Abstract thinking tends most often to strike during moments of quiet repose.