CollaboMath Challenge 07: String Theory


Hi everybody! It’s Jason again, from
Collaborative Mathematics. This is Challenge 07. It’s a probability
experiment that I first heard about from a
gentleman named Phil Yasskin. So, thanks for Phil
for the tip! Like I said, this is a
probability experiment so I hope you will try
it out for yourself at home, or at school or wherever
you are right now. I don’t know where you are… But that you’ll try it,
in any case. What you’ll need is
six pieces of string. So here I have six pieces
of yarn that are all about the same length. You’ll need your six pieces
of string, and a partner. And… Here’s my special effects on
Collaborative Mathematics this time. So you have your six pieces of string
and your partner, and the idea is that your partner will hold
the pieces of string in their fist, like this,
in such a way that you can’t tell which strings from the top
connect to which strings from the bottom. So, you might want your partner to
do a little probability shuffle, mix ‘em up a little bit,
before they hold them in their fist like that. You are going to start tying
some knots. Take two strings that are coming out
of the top of your partner’s hand. Pick to strings at random
and tie them together. I’m going to take these two here
and tie them together. Can you see what I’m doing? Here we go, tying them into
a knot like… so. So you take two strings and tie them in
a knot, and then do it again. Pick two more strings from the top,
tie those in a knot. Take the last two strings,
and tie those in a knot. Tie them together, right? So, I’m going to do that.
Please hold. OK. There you go.
That’s the first part. You take these strings that were
coming out of the top of your partner’s hand, in pairs, and you tie
them together. And then…
Do you want to guess what happens next?
You’re going to do it down below. Pick two ends at random,
tie them together, pick two more,
tie them together, and then take the last two
and tie those together. Please hold now while I do that. OK. There you go.
That’s the experiment. The probability question is:
If we do this experiment in this way, what is the probability that
I’ve taken those six pieces of string that we started with and
created one continuous loop of string, like this? That’s the question! Now there’s a couple of ways
we might go about approaching this. We might think about it theoretically,
and if there is anybody that has thoughts about
theoretical probability, I’d love to see some response
videos that discuss that. I’m just as curious to hear about
experimental or empirical results. So if you try this experiment,
then send me your data. Tell me how many times you tried it
and what the outcomes were each time, and I will start to
create some kind of a data table or a spreadsheet on the website
so that we can all look at each others’ empirical data, in addition to maybe
thinking about this theoretically. So you can find me through
Facebook or Twitter, or send me an email. The links are on the website,
somewhere, I don’t know where I’m pointing to,
but they’re on the website. You can find it. I hope people will try this
experiment and share their data. And I look forward to seeing
what happens next. Have fun!

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