Mind Matters Natural and Artificial Intelligence News and Analysis

TagElegant program

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Abstract virtual binary code illustration on blurry modern office building background. Big data and coding concept. Multiexposure

Why the Unknowable Number Exists But Is Uncomputable

Sensing that a computer program is “elegant” requires discernment. Proving mathematically that it is elegant is, Chaitin shows, impossible

In this week’s podcast, “The Chaitin Interview IV: Knowability and Unknowability,” Walter Bradley Center director Robert J. Marks interviewed mathematician Gregory Chaitin on his “unknowable number.” That’s the topic of this series, based on the fourth podcast. Last week, we tried getting to know the unknowable number. Today, let’s look at the question of how we know that the number is unknowable — instead of merely non-computable. Lots of things are non-computable but we do not expect that to be true of numbers. Let’s see what’s happening here, as Chaitin offers a walk through his proof that it really is unknowable: https://episodes.castos.com/mindmatters/Mind-Matters-127-Gregory-Chaitin.mp3 This portion begins at 09:43 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks:…

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matrix made up of math formulas and mathematical equations - illustration rendering

Getting To Know the Unknowable Number (More or Less)

Only an infinite mind could calculate each bit

In this week’s podcast, “The Chaitin Interview IV: Knowability and Unknowability,” Walter Bradley Center director Robert J. Marks interviewed mathematician Gregory Chaitin on his discovery of the “unknowable number.” How can a number that is unknowable exist? Some numbers go on indefinitely (.999999999… ) but we can describe them accurately even if they don’t seem to come to an end anywhere. Some numbers, like pi (π), are irrational — pi goes on and on but its digits form no pattern. However, what does it mean to say that a number exists if it is unknowable? How do we even know it exists? That’s the topic of this series, based on the fourth podcast between Dr. Marks and Gregory Chaitin. Note:…