Hacking the Common Sense Race Function
or
Why Mathematicians Make Lousy Racists
A Matt and Martha Mathica Dialog.
Hey brother, good news - the bullies only beat up Abraham half as much as they normally do.
MATTHow come ? Did he have twice as much lunch money on him ?
MARTHANo, no. Somehow it came up in class that he's only half Jewish so the bullies decided to decrease their beatings proportionaly.
MATTWell, good for Abraham, but I don't see how anyone can be half Jewish.
MARTHAWell, his father was Jewish and his mother was half Japanese and half Russian, so Abraham is half Jewish, quarter Japanese, and quarter Russian.
MATTWhat ! Being a quarter Japanese makes even less sense than being half Jewish. Sigh. It seems that you're saying that if the mother is M% some race, and the father is F% that race than their kid is going to be (M+F)/2 percent that race ?
MARTHAOf course. Everyone knows this. For being so smart, sometimes you no common sense !
MATTBear with me Sis. Let's call this formula the "Common Sense Race Function". CSRF for short. Ok ? Am I right in thinking that the everyone also thinks that people can have multiple racial backgrounds and that these percentages need to add up 100% ?
MARTHAYes of course. You couldn't well have people running around that were 95% something. Where would the other 5% go, eh ? That would just be silly.
MATTOK. We'll call this the Conservation of Racial Summation. OK ? Is other 'rules of race' I should know about ?
MARTHANo.... Not that I can think of now.
MATTOK then. With these two axioms, I should be able to prove that a person can be 100% Japanese and 100% Russian at the same time !!! I think that would be sufficently absurd to show this whole race concept is hogwash. Agreed ?
MARTHAWhat nonsense !! Of course no one can be 100% of 2 different races - that follows from the Conservation of Racial Summation - 100% + 100% = 200% which isn't 100% I think you've lost it. Did one of the bullies hit you on the head today harder than usual today ?
MATTNo, no. Just hear me out. Let's go back to the CSFR. Remember for a given race, a kid's race is given by k=(m+f)/2 where m is the racial percentage of the mother, and f is the racial percentage of the father.
MARTHAThat was like 10 seconds ago. Of course I remember.
MATTNow let's assume the mother's racial percentage is 100%, and the kid's somehow turns out to be 0%. What would the father's racial percentage need to be ?
MARTHAThat's basic algebra. Let's see start with k=(m+f)/2 ... substituting values... 0=(100+f)/2 ... multiple both sides by 2.... 0 = 100+f. Subtract 100 from both sides.... -100 = f. The father would have to have a racial percentage of -100%. Wait a second.... Negative race makes no sense !!
MATTWhy not ? It flows pretty obviously from the CSRF. You accept negative numbers everyday, and no one's ever handed you -1 apples. Why shouldn't you accept someone having a racial percentage of -100%. At best it might be a convienent fiction.
MARTHAHmmm. There must be another axiom to this racial calculus that I've missed....
MATTWell if you think of it, let me know. In the meantime, it should now be obvious that there can be a person who is 100% Japanese and 100% Russian as long as they are -100% something else, right ?
MARTHAEh ? I guess so, since 100%+100%-100% = 100%, right ?
MATTExactly !! But it gets even better, let's suppose we create a race with no real people, say the Umpalumpa race.
MARTHAThose little orange factory workers from Willie Wonka and the Chocolate Factory ?
MATTYes, exactly. Now let's say there are a total of R races across the entire world. We could say that our person could have a racial percentage of 100% for every race in the world, as long as his Umpalumpa racial percentage was -(R-1)*100 pecent !! The result of would be R*100+ -(R-1)*100 = 100 %
MARTHAActually, I think you glossed over a few steps oh most wise and wonderful brother. You showed that you could have a racial percentage of -100, but I don't see how you can get to -R*100. That seems like a big jump.
MATTUghh. OK, I'll try and spell it out for you. So I've already shown that someone with a racial percentage of -100 is possibile. Now instead of being the kid as before, let's make her a mother, and let's see what percentage the father needs to be for the kid to have a 100 racial percentage.
MARTHAOK, the father would have to have a racial percentage of 300% in this case. -100+300/2 = 100.
MATTYou must be getting tired, Martha. I'd expect you to be jumping up and down at the prospect of someone having a racial percentage over 100% !
MARTHAWell, when you get like this, I've learned it's just best to play along.
MATTGood, good. So it follows that there must also be someone with a -300 RP, so that a child with a percentage of 0 could be born. And then the -300 and -100 people could mate and have a child with -200. At this point I will wave my hands a lot and claim without further proof that you could eventually derive a racial percentage for any negative or positive value, so -R*100 would be allowable.
MARTHAI guess this could be left as an exercise to the reader.
MATTYes, as could the derivation of irrational racial percentages. Just define a multiplication-like version of the CSRF, introduce the concept of squares, and then square roots, and wala, irrational racial percentages. You don't even need the questionable negative race concept to get into trouble this way.
MARTHANext you'll be saying someone can have a racial percentage of i, and that people could have imaginary race.
MATTActually, I don't think so. If both parents have a race of -1, their kid will also have a race of -1, so you don't run into the same problems with squaring negative numbers as with normal numbers. Nice try though. I do think we could probably derive a racial percentage of pi by introducing infinite series. Transcendental race would be pretty trippy.
MARTHAAnd I guess you'ld also be able to introduce uncomputable racial percentages if you use a diagonalization proof over the irrational racial percentages....
MATTHot toasty dang, Martha !! Spoken like a true Mathica ! Perhaps you really are my sister after all !
MARTHASo you've convinced me. This whole racial percentage concept is absurd. reductio ad absurdum...
MATTI suppose you're right. I was starting to like that "100% of every race" concept. Still, I suppose we should keep quiet about it for Abraham's sake.
MARTHAGood point. I'm sure he wouldn't appreciate his beatings going back up to 100%.
The End