Tag Archives: lambda calculus

Coded Math

Is that you, HAL?

Last time, in Calculated Math, I described how information — data — can have special characteristics that allow it to be interpreted as code, as instructions in some special language known to some “engine” that executes — runs — the code.

In some cases the code language has characteristics that make it Turing Complete (TC). One cornerstone of computer science is the Church-Turing thesis, which says that all TC languages are equivalent. What one can do, so can all the others.

That is where we pick up this time…

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Calculated Math

calculation-0The previous post, Halt! (or not), described the Turing Halting Problem, a fundamental limit on what computers can do, on what can be calculated by a program. Kurt Gödel showed that a very similar limit exists for any (sufficiently powerful) mathematical system.

This raises some obvious questions: What is calculation, exactly? What do we mean when we talk about a program or algorithm? (And how does all of this connect with the world of mathematics?)

Today we’re going to start exploring that.

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