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When I was 18, I "discovered" three-value Boolean logic by thinking about what it would mean to have three signs in arithmetic. I called them positive, negative

When I was 18, I "discovered" three-value Boolean logic by thinking about what it would mean to have three signs in arithmetic. I called them positive, negative and urgative and had a symbol for urgative so I could write expressions. I worked out truth tables and had a lot of fun. Later I brought this up with one of my math professors and he encouraged me to study methods of proof so I could understand my results better. To his credit, he didn't say "this is already already all worked out," he sparked an interest that led to me studying a lot more mathematics (like abstract algebra and non-euclidean geometry) than I had planned when I started college.

oarabbus_ 7y ago
I'm not sure I follow. What is negative 1 plus positive 5 plus urgative 3?
- knodi123 7y ago
  it's boolean logic, not integer math. think "true/false/interesting", instead of using numbers
  - jdblair 7y ago
    I replied to the commenter. I started thinking not about boolean logic, but about a third arithmetic sign. I was thinking, if there are conceptual dimensions we can't perceive, maybe there are directions in those dimensions we also can't perceive.
- jdblair 7y ago
  When I started thinking about it I made a number "line" that had an origin (0) with positive in one direction, negative in another, and urgative in a third. The reasoning is that a different sign takes you towards the origin, then in the direction of the new sign. The answer to your question is: -1 + +5 = +4 +4 + urg3 = +1 to illustrate some other examples: +5 + urg10 = urg5 -5 + urg10 = urg5 urg5 + -10 = -5 urg5 + +10 = +5 I never actually proved that the arithmetic was consistent, or even useful in any way. Multiplication was much easier to reason about because setting the sign was just the result of a truth table. This is when I figured out the true/false truth tables extended the 3 symbols pretty trivially. I worked through boolean logic and then got bored with it and forgot about it until that time talking to my Calc 3 teacher during office hours.

oarabbus_ 7y ago

I'm not sure I follow. What is negative 1 plus positive 5 plus urgative 3?

knodi123 7y ago
it's boolean logic, not integer math. think "true/false/interesting", instead of using numbers
- jdblair 7y ago
  I replied to the commenter. I started thinking not about boolean logic, but about a third arithmetic sign. I was thinking, if there are conceptual dimensions we can't perceive, maybe there are directions in those dimensions we also can't perceive.
jdblair 7y ago
When I started thinking about it I made a number "line" that had an origin (0) with positive in one direction, negative in another, and urgative in a third. The reasoning is that a different sign takes you towards the origin, then in the direction of the new sign. The answer to your question is: -1 + +5 = +4 +4 + urg3 = +1 to illustrate some other examples: +5 + urg10 = urg5 -5 + urg10 = urg5 urg5 + -10 = -5 urg5 + +10 = +5 I never actually proved that the arithmetic was consistent, or even useful in any way. Multiplication was much easier to reason about because setting the sign was just the result of a truth table. This is when I figured out the true/false truth tables extended the 3 symbols pretty trivially. I worked through boolean logic and then got bored with it and forgot about it until that time talking to my Calc 3 teacher during office hours.