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One of my favorite quotes from The Hitchhiker's Guide to the Galaxy: "Population: None. Although you might see people from time to time, they are most likely p
by kk6mrp 5y ago
One of my favorite quotes from The Hitchhiker's Guide to the Galaxy:
"Population: None. Although you might see people from time to time, they are most likely products of your imagination. Simple mathematics tells us that the population of the Universe must be zero. Why? Well given that the volume of the universe is infinite there must be an infinite number of worlds. But not all of them are populated; therefore only a finite number are. Any finite number divided by infinity is zero, therefore the average population of the Universe is zero, and so the total population must be zero."
- xboxnolifes 5y ago> But not all of them are populated; therefore only a finite number are. Isn't this a leap in logic? Not all subsets of an infinite set are finite.
- AnimalMuppet 5y agoDouglas Adams wasn't writing a treatise on mathematics...
- xboxnolifes 5y agoHe was not, but the usage of the quote in this context implies some relevance to mathematical averaging and it's flaws. If the reasoning is not sound, neither is the usefulness in this context.
- kk6mrp 5y agoHow do you mean that not all subsets of an infinite set are finite, or in what cases would this be so?
- xboxnolifes 5y agoEx: {n ∈ R ∣ n is odd}
- jcranmer 5y agoThe set of prime integers is a strict subset of the set of integers, and yet both are infinite (they have the same cardinality even--that is, they are the same size, in one sense of 'size').
- feoren 5y agoTake all the even numbers. That's a subset of all whole numbers. Is it a finite set? Clearly not. Both are infinite; the population of even numbers is 50%. Sometimes infinity/infinity = 0.5.
- HWR_14 5y agoThe universe isn't infinite either. But neither of those is the major error with his reasoning.