{"id":42007,"date":"2025-03-10T12:56:12","date_gmt":"2025-03-10T12:56:12","guid":{"rendered":"https:\/\/idea.membrane.com\/songwriter\/?p=42007"},"modified":"2025-03-10T12:56:12","modified_gmt":"2025-03-10T12:56:12","slug":"double-or-triple","status":"publish","type":"post","link":"https:\/\/kingarthur.com\/songwriter\/2025\/03\/10\/double-or-triple\/","title":{"rendered":"Double or Triple"},"content":{"rendered":"

Double-or-Triple-0.mp3<\/a>
\nDouble-or-Triple-0.mp4<\/a>
\nDouble-or-Triple-I.mp3<\/a>
\nDouble-or-Triple-I.mp4<\/a>
\nDouble-or-Triple-intro.mp3<\/a><\/p>\n

[Intro]
\nAre you talking two bars
\n… or three
\n(Double or triple)
\nIs it yours or ours
\n… tell me
\n(Feel the ripple)<\/p>\n

[Verse 1]
\n(After all) Free-fall…
\nmotion
\n(in a gravitational field)
\nIs indistinguishable
\n(from acceleration in empty space)
\nWatch the human race<\/p>\n

[Chorus]
\nAre you talking two bars
\n… or three
\n(Double or triple)
\nIs it yours or ours
\n… tell me
\n(Feel the ripple)<\/p>\n

[Bridge]
\nAs we flow
\n(Through spacetime)
\nGet to know
\n(All that I’m)<\/p>\n

[Verse 2]
\n(Lyrical rhymes)
\nTwo spacetimes
\n(are conformally equivalent)
\nStill relevant…
\n(Angles are preserved)
\n… but distances may change
\n(Do you find it… a bit strange)
\nAngels disturbed<\/p>\n

[Chorus]
\nAre you talking two bars
\n… or three
\n(Double or triple)
\nIs it yours or ours
\n… tell me
\n(Feel the ripple)<\/p>\n

[Bridge]
\nAs we flow
\n(Through spacetime)
\nGet to know
\n(What’s not mine)<\/p>\n

[Outro]
\nAs we flow
\n(Through spacetime)
\nGet to know
\n(How far to climb)<\/p>\n

A SCIENCE NOTE<\/p>\n

\u2261 (Triple bar)<\/strong> \u2192 Used in logic and mathematics to denote strict equivalence<\/strong>, such as identity relations and logical equivalence.<\/p>\n

= (Double bar)<\/strong> \u2192 Used in mathematics to denote equality<\/strong>, meaning two expressions have the same value.<\/p>\n

In spacetime, equivalence<\/strong> and equality<\/strong> can have different meanings depending on the context:<\/p>\n

Equivalence in Spacetime<\/strong><\/h3>\n