An Attractive New Character Enters - As If Summoned from the Void - Burn Math Class: And Reinvent Mathematics for Yourself (2016)

Burn Math Class: And Reinvent Mathematics for Yourself (2016)

Act I

3. As If Summoned from the Void

3.3. An Attractive New Character Enters

Mathematics: THAT’S BETTER! NOW, DOWN TO BUSINESS. MY AIM IS TO SHOW THAT YOUR PREVIOUS ARGUMENT IN NO WAY CONSTITUTED A MATHEMATICAL TRICK OR A TABOO FORM OF REASONING, WITHOUT REQUIRING YOU TO TRUST MY ASSERTION THAT IT IS NOT. IN THE VOID WE LIVE IN A STATE OF ANARCHY. YET TRUST MUST SOMEHOW BE DEVELOPED. IN THE ABSENCE OF LAWS, TWO PARTIES CAN AID THE MUTUAL DEVELOPMENT OF TRUST BY MAKING THEMSELVES VULNERABLE, FOR INSTANCE BY THE SHARING OF SECRETS, OR THE COMMITMENT OF A TABOO ACT IN ONE ANOTHER’S PRESENCE. I’LL CALL THIS “AXIOM T.” THE T STANDS FOR TRUST. OR TABOO. I HAVEN’T DECIDED YET. NOW, EITHER YOUR REASONING WAS MATHEMATICALLY TABOO, OR IT WAS NOT. IF WE ASSUME IT WAS NOT, THEN THERE IS NOTHING TO DEMONSTRATE, AND WE MAY PROCEED WITH THE BOOK. IF WE ASSUME IT WAS TABOO, HOWEVER, THEN BY AXIOM T I CAN DEVELOP YOUR TRUST IN ME BY COMMITTING A SIMILAR TABOO ACT IN YOUR PRESENCE, FOR INSTANCE BY APPLYING AN IDENTICAL FORM OF REASONING IN THE CASE YOU TWO WOULD HAVE EXAMINED NEXT (I ASSUME) HAD I NOT INTERRUPTED YOU. SO THAT IS THE TASK TO WHICH WE’LL NOW TURN. LET US EXAMINE THE UNFAMILIAR MACHINE . WE MAY BUILD SOMETHING MORE FAMILIAR USING TWO COPIES OF THE ORIGINAL: . THIS IS SIMPLY m(x) = x, AND THEREFORE WE KNOW m′(x) = 1. MAKING USE OF YOUR EARLIER DISCOVERY THAT (fg)′ = f′g + g′f,WE CAN WRITE:

AND IT IS NOW SIMPLE TO ISOLATE THE DESIRED PIECE , GIVING

OR EQUIVALENTLY,

IN SUMMARY, IF YOUR REASONING WAS TABOO, THEN I HAVE JUST ENGAGED IN A TABOO ACT IN YOUR PRESENCE. BY AXIOM T, THIS SHOULD LEAD YOU TO TRUST ME.

Author: I have no idea what’s going on.

Reader: I think I might, sort of. . . But wait, even if we trust you, that doesn’t mean our argument was correct, does it?

Mathematics: OH. . . I SEE. . . I SUPPOSE YOU’RE RIGHT.

Reader: So then why bother committing a possibly taboo act to develop the trust in the first place?

Mathematics: WELL, I SUPPOSE IT’S A GOOD WAY TO MAKE A NEW FRIEND. . .

(Our characters sit for a moment, in an undefined sort of silence.)

Reader: Where did you say you came from?

Mathematics: FROM THE VOID. . . IT’S WHERE I LIVE. OR. . . I THINK IT IS. TO BE HONEST, I DON’T REMEMBER VERY MUCH BEFORE THIS.

Author: Well. . . if it helps. . . you don’t need to remember things to go where we’re going.

Mathematics: WHERE ARE YOU GOING?

Author: I’m not sure yet. Not exactly sure, at least. But we’re definitely headed somewhere.

Mathematics: OH. . . SOUNDS PLEASANT. FORTUNATELY, I’VE HAD TO BECOME ACCUSTOMED TO THE IDEA OF EXISTING IN AN UNSPECIFIED LOCATION. IT SHOULDN’T BE DIFFICULT TO BECOME EQUALLY ACCUSTOMED TO THE IDEA OF HEADING TOWARDS ONE. THAT IS, IF YOU DON’T MIND MY COMPANY. . .

Author: We’d love your company.

Reader: Wait, what do you mean existing in an unspecified location? I thought you lived in the Void.

Mathematics: I DO. . .

Reader: Where’s the Void?

Mathematics: IT’S. . . HARD TO DESCRIBE. . .

Reader: Try.

Mathematics: IT DOESN’T (WELL, AT LEAST NOT IN ANY PRECISE SENSE (OR RATHER, IN A SENSE THAT’S PRECISE BUT NOT EVERYDAY (NOT TO BE CONFUSED WITH “NOT EVERY DAY” (WHICH WOULD SUGGEST THAT THE AFOREMENTIONED PRECISION VARIES WITH TIME, WHICH ISN’T AT ALL THE IDEA I MEANT TO CONVEY))(BUT RATHER “NOT EVERYDAY,” MEANING: IN A SENSE OF THE STILL YET-TO-BE-MENTIONED TERM THAT IS NOT EQUIVALENT TO THE VERNACULAR MEANING (OR TO ILLUSTRATE CONCRETELY BY WAY OF EXAMPLE (IF YOU’LL FORGIVE, OF COURSE, A BIT OF SELF-REFERENCE), THE SIMULTANEOUS LINGUISTIC (AS OPPOSED TO MATHEMATICAL) USE OF BOTH NESTED AND ADJACENT-BUT-NON-NESTED PARENTHESES IS NEITHER “EVERYDAY” NOR (ONE ASSUMES) “EVERY DAY,” THOUGH IF SAID USAGE SOMEHOW CAME TO OCCUR “EVERY DAY” IT WOULD BECOME CORRESPONDINGLY (AND ONE MIGHT ARGUE, PROPORTIONALLY) “EVERYDAY”)), IF THAT MAKES SENSE)) EXIST.

Reader: . . . The Void doesn’t exist?

Mathematics: IT DOES. BUT NOT IN THE EVERYDAY SENSE.

Reader: I see. . .

Author: What about you?

Mathematics: WHAT ABOUT ME?

Author: I mean, do you exist? In the everyday sense?

Mathematics: I SUPPOSE I DO. . . I’VE NEVER THOUGHT OF MYSELF THAT WAY BEFORE. BUT FOR THE LAST 136 PAGES I’VE HAD A STRANGE FEELING. SOMETHING I’VE NEVER FELT BEFORE. I FEEL. . . REAL. . . FOR THE FIRST TIME. AND IT’S ONLY GETTING WORSE. OR BETTER, I SHOULD SAY. IT’S NICE.

Author: So, all things considered. . . you prefer this feeling?. . . Existing more, or more of you existing, or whatever it is. . . You prefer it? Over its absence?

Mathematics: ABSOLUTELY.

Author: Alright then. . . I think we know what to do.