Can There Be Two Ones?
Meditations on Oneness · Local folio mark 111111
Jules's four test gates
On a 15-position Observatory dial, the multiplier machine sends position to the remainder of after division by 15.
The four labels all satisfy
Two different promises
Self-undoing
Two passes return every input.
Identity
One pass leaves every input unchanged.
Separate the promises
Complete the table here. Use scratch paper as needed.
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Complete the table. Which machine is the identity machine? Prove that your choice works for every , and use the input to rule out the other three.
Identity machine? 1 4 11 14
Jules's return test
Use scratch paper as needed.
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Choose one non-identity machine. Write a two-pass journey in which the first pass changes . Explain why “self-undoing” and “identity” do not mean the same thing.
Vivian's Archive note · Forget the dial
Any operation. Any objects.
Let be any operation that combines two objects in a set. An object is an identity when
“If two labels make the same claim, compare the claim—not the labels.” — Vivian Meridian
The uniqueness proof
Use separate paper for your proof.
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Suppose and both satisfy the identity rule. Prove that using only that rule.
Do not assume that the objects are numbers or that is multiplication.