I think the explanation might be that outside of mathematics, our interest in numbers is biased towards accounting for change in new entities…such as a new stock offering. Thus we focus on the early numbers which biases "random" numbers to start with lower lead digits, at whatever their order of magnitude.

By the time a quantity reaches 8 or 9 times 10Ex, where x is the order of magnitude, we are bored with the event or object to which it is attached.

Here’s an example. In the early days of McDonald’s, its outlets carried a sign saying, not "billions and billions served", but the actual number of servings to date, and us kids would pay attention to the number, for example at one of the first outlets in DesPlaines, featured in many histories of McDonald’s.

By the time the number reached billions and billions, McDonald’s publicists realized that the public would no longer pay attention to numbers such as 6,712,104,490. The numbers might even be a negative for the same reason that numbers showing our folly and wastefulness seem to be when expressed precisely, whether at Corey Haines’ site, which identifies the cost of the wat in Iraq so far.

And suppose they reach 666,666,666. The fundies would have a fit.

When a man makes his first million, or his first billion, everybody loves him. But when he like Gates or John D Rockefeller gets up to forty, he’s old news and maybe got rich by sharp dealings.

Benham’s paradox is closely related to Knuth’s point that we are poor makers uppers of random numbers. If I guess a random number such as

the Kantian fact that an active intelligence (or stupidity) was engaged means that I will be trying to hard, whether to avoid ascending sequences so beloved by weary sysadmins when assigning "random" passwords…or to put them in along with repeated sequences just because I’ve read Knuth.

It’s remotely related to John von Neumann’s thesis re random numbers, to wit, that anybunny who thinks to create "random" numbers on a computer, a deterministic machine, is in a state of sin.

The most popular technique, taking the least significant digiit of the time, is by no means foolproof. For suppose you set up a program, which calls the "random number generator", as a scheduled event!

This is why we get to watch cute girls pick balls out of a box worldwide while hoping to win lotteries, where the colored balls dance around on air. It would be much less Fun to have some techie ask a computer for a "random" number, because the techie would clearly have rigged the game.

In fine, programmers are indeed "incompetent" *sub specie aeternitatis*. We messed up on Y2K and missed out on all the parties saving the world and we can’t even make truly random numbers.

The Swedish mathematician Kronecker said, "God made the natural numbers, all else is the work of man", but it appears that only God can make random numbers even in the interval 0..1; any programmer who truly depends on truly random data needs to avoid library functions.

But if Leibniz or Steve Wolfram (A New Kind of Science) are to be believed, G-d is a determinist (perhaps outside of free will) and even airballs can be predicted…perhaps by taking several videos of the lottery and applying a model, and thereby getting rich, and retiring to Bora Bora.

Wow .. Winzip folks could use that to come up with a better compression algorithm.

Cool indeed!

I think the explanation might be that outside of mathematics, our interest in numbers is biased towards accounting for change in new entities…such as a new stock offering. Thus we focus on the early numbers which biases "random" numbers to start with lower lead digits, at whatever their order of magnitude.

By the time a quantity reaches 8 or 9 times 10Ex, where x is the order of magnitude, we are bored with the event or object to which it is attached.

Here’s an example. In the early days of McDonald’s, its outlets carried a sign saying, not "billions and billions served", but the actual number of servings to date, and us kids would pay attention to the number, for example at one of the first outlets in DesPlaines, featured in many histories of McDonald’s.

By the time the number reached billions and billions, McDonald’s publicists realized that the public would no longer pay attention to numbers such as 6,712,104,490. The numbers might even be a negative for the same reason that numbers showing our folly and wastefulness seem to be when expressed precisely, whether at Corey Haines’ site, which identifies the cost of the wat in Iraq so far.

And suppose they reach 666,666,666. The fundies would have a fit.

When a man makes his first million, or his first billion, everybody loves him. But when he like Gates or John D Rockefeller gets up to forty, he’s old news and maybe got rich by sharp dealings.

Benham’s paradox is closely related to Knuth’s point that we are poor makers uppers of random numbers. If I guess a random number such as

490,566,800,123,666,654,800,900,120,780,320,111,222,333

the Kantian fact that an active intelligence (or stupidity) was engaged means that I will be trying to hard, whether to avoid ascending sequences so beloved by weary sysadmins when assigning "random" passwords…or to put them in along with repeated sequences just because I’ve read Knuth.

It’s remotely related to John von Neumann’s thesis re random numbers, to wit, that anybunny who thinks to create "random" numbers on a computer, a deterministic machine, is in a state of sin.

The most popular technique, taking the least significant digiit of the time, is by no means foolproof. For suppose you set up a program, which calls the "random number generator", as a scheduled event!

This is why we get to watch cute girls pick balls out of a box worldwide while hoping to win lotteries, where the colored balls dance around on air. It would be much less Fun to have some techie ask a computer for a "random" number, because the techie would clearly have rigged the game.

In fine, programmers are indeed "incompetent" *sub specie aeternitatis*. We messed up on Y2K and missed out on all the parties saving the world and we can’t even make truly random numbers.

The Swedish mathematician Kronecker said, "God made the natural numbers, all else is the work of man", but it appears that only God can make random numbers even in the interval 0..1; any programmer who truly depends on truly random data needs to avoid library functions.

But if Leibniz or Steve Wolfram (A New Kind of Science) are to be believed, G-d is a determinist (perhaps outside of free will) and even airballs can be predicted…perhaps by taking several videos of the lottery and applying a model, and thereby getting rich, and retiring to Bora Bora.

Bill – When you call reading about floating point numbers and how they group ‘really cool’ That’s proof that your nerd score is too low! ðŸ˜›

Great read BTW, very interesting stuff.