http://thetarpit.org/2014/on-numbers-structure-and-induction "Now I feel like I know less about what that blog is about than I did before." Thu, 16 Apr 2026 03:05:43 +0000 http://thetarpit.org hourly 1 http://thetarpit.org/2014/on-numbers-structure-and-induction#comment-16 The mathematics and philosophy of hyperoperations « The Tar Pit Fri, 11 Oct 2019 09:48:54 +0000 http://wp.thetarpit.org/2014/on-numbers-structure-and-induction#comment-16 [...] "On numbers, structure and induction" I give an account on how the concept of numbers is inextricably tied to mathematics. This might [...] [...] "On numbers, structure and induction" I give an account on how the concept of numbers is inextricably tied to mathematics. This might [...]

]]> http://thetarpit.org/2014/on-numbers-structure-and-induction#comment-9 On the difficulty of discussing musical works « The Tar Pit Fri, 11 Oct 2019 09:09:41 +0000 http://wp.thetarpit.org/2014/on-numbers-structure-and-induction#comment-9 [...] Any person with basic musical training can confirm this: scales, modes and the circle of fifths are all part of a mathematical framework used to make sense of how musical "notes" happen, and all this without even discussing rhythm. Furthermore, musical notation is a purely formal construct, not unlike standard mathematical notation, which leads us to the possibility of describing music as algebra. It is very much a miracle, if you will, and one that matters. [...] [...] Any person with basic musical training can confirm this: scales, modes and the circle of fifths are all part of a mathematical framework used to make sense of how musical "notes" happen, and all this without even discussing rhythm. Furthermore, musical notation is a purely formal construct, not unlike standard mathematical notation, which leads us to the possibility of describing music as algebra. It is very much a miracle, if you will, and one that matters. [...]

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