Okay, TIRED poly math geeks gone wild

So, in this entry about finding the formula to determine the total number of possible relationship configurations for any group of n people, blaisepascal observed that the sum we came up with did not consider the case where everyone is involved with everyone else, which is something we had intended to include. The previous equation, therefore, has an off-by-one error. The correct form is:

This is, as many people have observed, essentially the standard “pick r of n permutations” equation, which (had we been thinking along those lines) we likely should’ve recognized from the start. And, to be fair, one of the more math-geeky among us said something like that early on, but it took much scribbling on many sheets of paper to prove it.

28 thoughts on “Okay, TIRED poly math geeks gone wild

  1. Since 0! == 1, you can simply change the upper limit of the sum to be ‘n’ and not need the additional +1 (ie nCn = 1).

    If you consider the case of masturbation then the lower limit could be 1.

    You don’t need the restriction k>=2 since you define n>=2 and k ranges from 2 to n (with my modification) it’s automatically restricted. Without my change you have the potential for k ranging from 2 to 1 (if n==2) which doesn’t make sense.

  2. Since 0! == 1, you can simply change the upper limit of the sum to be ‘n’ and not need the additional +1 (ie nCn = 1).

    If you consider the case of masturbation then the lower limit could be 1.

    You don’t need the restriction k>=2 since you define n>=2 and k ranges from 2 to n (with my modification) it’s automatically restricted. Without my change you have the potential for k ranging from 2 to 1 (if n==2) which doesn’t make sense.

  3. It could be just me, and it’s been awhile, but I think your k parameter is set wrong. Otherwise, you have the summation going from K=2 to 1. And that’s …well unusual.

    Cute shirt idea!! I’m waiting for the tinkertoy shirt to come out personally. I’m a classics kind of person.

    • speaking of tinkertoys, I went out and purchased a set of tinkertoys to build a 3D model of The Squiggle. I have to return it and get a bigger set! But it looks cool so far!

  4. It could be just me, and it’s been awhile, but I think your k parameter is set wrong. Otherwise, you have the summation going from K=2 to 1. And that’s …well unusual.

    Cute shirt idea!! I’m waiting for the tinkertoy shirt to come out personally. I’m a classics kind of person.

  5. speaking of tinkertoys, I went out and purchased a set of tinkertoys to build a 3D model of The Squiggle. I have to return it and get a bigger set! But it looks cool so far!

  6. Hello! I was pointed to this entry by my partner, and it caught my attention. I have some good news and some bad news (and some sad, geeky news).

    The bad news (because I’m a bad-news-first-type-person) is that it seems what you have there is wrong (but feel free to correct me, because I’m really curious about your version of the formula and how it came about).

    The good news is that what looks like a better choice for the enumeration formula is even scarier, and probably more t-shirt-worthy, if we can get it to fit.

    The sad, geeky news is that when I realised the formula didn’t enumerate properly, I sat down with my own wad of paper, went through about 30 sides in the space of two weeks (hey, my Copious Free Time is pretty limited), researched things a bit, and, er, wrote it all up. Yes, I’m sad. You can get the write-up here.

  7. Hello! I was pointed to this entry by my partner, and it caught my attention. I have some good news and some bad news (and some sad, geeky news).

    The bad news (because I’m a bad-news-first-type-person) is that it seems what you have there is wrong (but feel free to correct me, because I’m really curious about your version of the formula and how it came about).

    The good news is that what looks like a better choice for the enumeration formula is even scarier, and probably more t-shirt-worthy, if we can get it to fit.

    The sad, geeky news is that when I realised the formula didn’t enumerate properly, I sat down with my own wad of paper, went through about 30 sides in the space of two weeks (hey, my Copious Free Time is pretty limited), researched things a bit, and, er, wrote it all up. Yes, I’m sad. You can get the write-up here.

  8. Serendipity

    …bizarre. Around the same time that you did this, I also did this with one of my sweeties. Because we were very focused at the time on a person’s relationship with themselves and getting adequate alone-time in the complexifyin’ relationship set, we included each person alone in the equation. When all was said and done, our sum simplified (yay Maple) to 2^n-1.

    • Re: Serendipity

      Yep, the “closed form” Riemann sum simplifies to 2^n-n-1 (if you don’t count singletons) or 2^n-1 (if you count singletons but don’t count the null case). I personally like the summation form better, but the simplified form is a lot…well, simpler. ๐Ÿ™‚

  9. Serendipity

    …bizarre. Around the same time that you did this, I also did this with one of my sweeties. Because we were very focused at the time on a person’s relationship with themselves and getting adequate alone-time in the complexifyin’ relationship set, we included each person alone in the equation. When all was said and done, our sum simplified (yay Maple) to 2^n-1.

  10. Re: Serendipity

    Yep, the “closed form” Riemann sum simplifies to 2^n-n-1 (if you don’t count singletons) or 2^n-1 (if you count singletons but don’t count the null case). I personally like the summation form better, but the simplified form is a lot…well, simpler. ๐Ÿ™‚

  11. Love this post. I am reminded of a Feynman story. He was talking to an artist about her painting of a flower. He started explaining what all the bits are for and she stopped him, telling him he was unable to see the beauty. His thought (and mine) was that knowing what something really *is* is a big part of the beauty.

    For me as a biologist, the magic is in the places where science can currently only say “and then something happens.” That is what fuels the wonder and the desire to know more. Every professional science researcher I have known has had that childlike wonder about their field. They seek out what we do know and are so amazed by what we do not know, that their thirst for knowledge becomes a life-long, passionate pursuit of the information to fill in those gaps.

  12. Love this post. I am reminded of a Feynman story. He was talking to an artist about her painting of a flower. He started explaining what all the bits are for and she stopped him, telling him he was unable to see the beauty. His thought (and mine) was that knowing what something really *is* is a big part of the beauty.

    For me as a biologist, the magic is in the places where science can currently only say “and then something happens.” That is what fuels the wonder and the desire to know more. Every professional science researcher I have known has had that childlike wonder about their field. They seek out what we do know and are so amazed by what we do not know, that their thirst for knowledge becomes a life-long, passionate pursuit of the information to fill in those gaps.

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