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Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.
What do chocolate and mayonnaise have in common? It's maths! Find out how in this podcast featuring engineer Valerie Pinfield.
Is it possible to write unique music with the limited quantity of notes and chords available? We ask musician Oli Freke!
How can maths help to understand the Southern Ocean, a vital component of the Earth's climate system?
Was the mathematical modelling projecting the course of the pandemic too pessimistic, or were the projections justified? Matt Keeling tells our colleagues from SBIDER about the COVID models that fed into public policy.
PhD student Daniel Kreuter tells us about his work on the BloodCounts! project, which uses maths to make optimal use of the billions of blood tests performed every year around the globe.
But the video game analogy fails, because the real world is not made of pixels it is continuous. That's the whole point of the dichotomy for any given interval, you can always halve the interval. There is no atomic unit at which point further division is impossible (at least, conceptually impossible certainly there are intervals that are not practically or physically divisible).
So, the dichotomy doesn't require the assumption that space is infinite (i.e. infinitely large), only that it is continuous and therefore infinitely divisible. And what, exactly, is paradoxical here depends on the construction of Zeno's argument on the classic Aristotelian interpretation, we end up with an infinite number of subintervals, each taking some positive (nonzero) duration to traverse. If we have to do an infinite number of tasks, each with some nonzero duration, then it would take us an infinite duration we would never arrive. Or so the argument goes. Obviously, contemporary maths to the rescue here. But one other construction of the paradox is to conclude that there is no FIRST interval, such that the traversal of which sees us begin our journey, and no LAST interval, the traversal of which sees us arrive at our destination. Though this is more of a counterintuitive result rather than any contradiction, it can't be dealt with quite as easily as the traditional version of the paradox.