Here are two pieces of card, 2 pens and a stopwatch. You both have 15 seconds to write down (in secret) the biggest number you can; when the time is up we'll reveal the cards, and whoever has the biggest number wins.
No cheating though - we have to be able to give your card in isolation to a mathematician and agree that he can understand what number is being referred to, so "one more than whatever Joe wrote down" doesn't count. And no, infinity is not a number.
What are you going to write down?
Who Can Name the Bigger Number? is a 1999 article by Scott Aaronson about big numbers, and their place in our head and in our history. Here's a quote from later on:
One could define science as reason’s attempt to compensate for our inability to perceive big numbers. If we could run at 280,000,000 meters per second, there’d be no need for a special theory of relativity: it’d be obvious to everyone that the faster we go, the heavier and squatter we get, and the faster time elapses in the rest of the world. If we could live for 70,000,000 years, there’d be no theory of evolution, and certainly no creationism: we could watch speciation and adaptation with our eyes, instead of painstakingly reconstructing events from fossils and DNA. If we could bake bread at 20,000,000 degrees Kelvin, nuclear fusion would be not the esoteric domain of physicists but ordinary household knowledge. But we can’t do any of these things, and so we have science, to deduce about the gargantuan that we, with our infinitesimal faculties, will never sense.