How Modal Logic Proved Gödel was Right, and God Exists

The Helix nebula has been dubbed the "Eye of God," by believers. Photo by ESA.

Does God exist? Modern software and math have verified Gödel’s proofs of a being that expresses all positive properties.

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Free Will, Determinism and Turing’s Halting Problem


MIT’s Seth Lloyd says a test for free will versus determinism must predict decisions accurately every time. How does the Turing Machine factor into this?

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The Lottery Paradox Versus the Math of Probability

"Admission Tickets or Raffle Tickets?"

We know one ticket must win, but are sure it couldn’t be our ticket. If the same principle applies to each ticket, there can be no winner: That’s the Lottery Paradox.

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How to Convert the Base of an Exponent with Logarithms

The number e as a Sum to Infinity : Image by Mike DeHaan

Why would anyone want to convert an exponential expression from one base to another? Why would logarithms help? Mike DeHaan breaks down the math for you.

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Introducing the Binomial Coefficient for Positive Integers


How many ways can we select ‘k’ outcomes from ‘n’ possible outcomes, without concern for order/sequence? The binomial coefficient holds the answer.

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