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> Logic itself is a human construct that comes from observing nature - God's surely didn't hand it over to us. I'm not sure that is true. If we estimate Pi by

by mcherm 5y ago

> Logic itself is a human construct that comes from observing nature - God's surely didn't hand it over to us. I'm not sure that is true. If we estimate Pi by tossing needles onto a grid of lines[1] then we are obtaining the value by observing nature. But, while that's a fun exercise, it isn't how mathematicians actually determine the value of Pi. They use formulas[2] based on elementary numbers, such as this: Pi = Sqrt( 6 * Sum[k=1..infinity](1/k^2) ). Maybe you believe that the numbers 1, 2, 3... are different in different universes. Personally, I can't fathom that. But if you accept that the basic counting numbers are fundamental to logic and reason instead of being derived from nature and somehow varying from one universe to another, then simply square those numbers, take the reciprocals, sum the series, multiply by 6 and take the square root -- that's Pi. There ARE various geometries possible. But those consist of different definitions of what terms like "straight line" mean. The geometries all have the same value for the fundamental circle constant, Pi. Whether we choose to talk about Pi or instead about Tau (where Tau = 2Pi) is a social convention. But what the value is (of both constants) is a fundamental property of mathematical reasoning independent of convention. [1] https://www.sciencefriday.com/articles/estimate-pi-by-dropping-sticks/ https://www.sciencefriday.com/articles/estimate-pi-by-droppi... [2] https://mathworld.wolfram.com/PiFormulas.html https://mathworld.wolfram.com/PiFormulas.html

coldtea 5y ago
>But, while that's a fun exercise, it isn't how mathematicians actually determine the value of Pi. They use formulas[2] based on elementary numbers, such as this: Pi = Sqrt( 6 Sum[k=1..infinity](1/k^2) ).* Yes, but this didn't come from God (or the Platonic realm of Ideas) into mathematicians heads. Humans arrived at that by first observing natural laws / behavior (e.g. 1 apple + 1 apple = 2 apples, or observing that somebody can't be A and not A, and so on) and progressing from those into abstractions. Nature comes first, not abstraction. Nor there is some plane where mathematical abstraction or logic exists outside of the universe. It exists only (a) explicitly on people's heads (which, unaraguably, are part of nature), (b) as implicitly observed on natural behavior by said people. >Maybe you believe that the numbers 1, 2, 3... are different in different universes. Personally, I can't fathom that. No, I believe that numbers don't exist. What would "1" even be, as an entity in our very universe? There is a rock or a planet or a tiger, but not an 1. Countable things do (but not necessarily on another universe, where e.g. there might be just a single entity). Also, we already have boolean algebra in this universe, which has different properties compared to regular algebra. In that sense a logic circuit is already a kind of universe where the algebra that governs it is different. One could well imagine a universe that only observes circuit board like behavior.
- lordnacho 5y ago
  Observing that something is either a or not a is not an observation in the empirical sense. Empirical observations suffer from the problem of induction, but neither of us believes that that statement might be disproven someday, in the way that observing a black swan would disprove the statement that all swans are white. Similarly the conservation law of apples is not derived from nature, but from our definition of what an apple is. If you took a heap of sand and added another you would have one heap of sand.

by mcherm 5y ago

coldtea 5y ago

>But, while that's a fun exercise, it isn't how mathematicians actually determine the value of Pi. They use formulas[2] based on elementary numbers, such as this: Pi = Sqrt( 6 Sum[k=1..infinity](1/k^2) ).* Yes, but this didn't come from God (or the Platonic realm of Ideas) into mathematicians heads. Humans arrived at that by first observing natural laws / behavior (e.g. 1 apple + 1 apple = 2 apples, or observing that somebody can't be A and not A, and so on) and progressing from those into abstractions. Nature comes first, not abstraction. Nor there is some plane where mathematical abstraction or logic exists outside of the universe. It exists only (a) explicitly on people's heads (which, unaraguably, are part of nature), (b) as implicitly observed on natural behavior by said people. >Maybe you believe that the numbers 1, 2, 3... are different in different universes. Personally, I can't fathom that. No, I believe that numbers don't exist. What would "1" even be, as an entity in our very universe? There is a rock or a planet or a tiger, but not an 1. Countable things do (but not necessarily on another universe, where e.g. there might be just a single entity). Also, we already have boolean algebra in this universe, which has different properties compared to regular algebra. In that sense a logic circuit is already a kind of universe where the algebra that governs it is different. One could well imagine a universe that only observes circuit board like behavior.

lordnacho 5y ago
Observing that something is either a or not a is not an observation in the empirical sense. Empirical observations suffer from the problem of induction, but neither of us believes that that statement might be disproven someday, in the way that observing a black swan would disprove the statement that all swans are white. Similarly the conservation law of apples is not derived from nature, but from our definition of what an apple is. If you took a heap of sand and added another you would have one heap of sand.