If we were to choose a set of inconsistent axioms (i.e. By switching axioms it becomes possible to prove different things. But when you get down to it, there are different possible sets of axioms that you can use to define mathematical concepts. Most people think of math as a single, coherent set of rules. That we change which mathematical axioms we use. But this is an extremely boring way to answer this question, reducing it merely to the redefinition of a symbol.ģ. ![]() Of course, π is just a symbol referencing an idea, so if the underlying idea that it references were to change, that would change the value of the symbol. That we change what we mean when we say π. If our universe is not flat, but a curved surface, that could distort the geometric relationships that we measure on physical objects resembling circles.Ģ. It will, in fact, depend on the size of the orange itself. If we allow distances to be measured only along the orange’s surface (disallowing paths that penetrate the orange or go into the empty space around it), then the ratio of the circle’s circumference to diameter is no longer going to be π. For instance, imagine drawing a circle on the surface of an orange. ![]() If space is not flat, that can change geometric relationships. That circular physical objects, as you make them progressively closer to perfect circles, approach a circumference to diameter ratio of something other than 3.14159… If this were the case, it might indicate something about the geometry of spacetime. Mathematician: The idea of giving π a new value of could be interpreted in a few different ways. π shows up in way too many places to make a meaningful statement about the impact on the universe, one way or another. In a very hand-wavy way, if π were bigger, then the universe would be more certain.Īside from leading almost immediately to a whole mess of mathematical contradictions and paradoxes, if π were different it would change the results of a tremendous number of (one could argue: all) calculations, and the fundamental forces and constants of the universe would increase or decrease by varying amounts. In fact, in that last two, π plays a pivotal role in the derivation of the uncertainty principle. A surprising number of calculations and derivations involve “running in a loop”, so π shows up all the time in electromagnetism, complex numbers, quantum mechanics, Fourier analysis, all over. For example, even though doesn’t, on the surface of it, have anything to do with circles, it’s still equal to π (there’s a loop floating around halfway through the calculation). The definition of π seems pretty innocent (the ratio of the circumference of a circle to its diameter), but it shows up over and over in the middle of calculations from all over the place. ![]() ![]() So this question is doubly profound! Unlike other constants, if π were different, then scientists (mathematicians especially) would continually have the sneaking suspicion that there’s something deeply, deeply wrong with the universe. All of the weird places that π shows up track back to this definition. Π is the distance around any circle, C, divided by the distance across that circle, D.
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