Just take my word for it, will you? Assume I’m a genius. - Larry Niven

Forget the infinities: Concentrate on detail.

“For letting us examine their silly records they want to charge us a flat million marks!”
“Pay it.”
“It’s robbery.”
“A Belter says that? Why don’t you have records on Mars?”
“We were never interested. What for?”
“What about abstract knowledge?”
“Another word for useless.”
“Then what makes you want useless knowledge enough to pay a million marks for it?”
Slowly Nick matched his grin. “It’s still robbery. How in Finagle’s name did Earth know they’d need to know about Mars?”
“That’s the secret of abstract knowledge. You get in the habit of finding out everything you can about everything. Most of it gets used sooner or later.”

We follow the scientists around and look over their shoulders. They're watching their feet: provable mistakes are bad for them. We're looking as far ahead as we can, and we don't get penalized for mistakes.