Tag: Math

Mensa Math

Apologies for links to political blogs. There’s some math here. The question is, what is the probability that one person could have survived two mass shootings (e.g., Gilroy and Las Vegas) ?

One fellow provides this calculation:

Las Vegas 2017 attendance: 20,000
Gilroy 2019 attendance: 80,000

I don’t know how many attendees were actually physically present at each event at the time of the shootings, but I’ll assume two thirds, so 14,520 and 52,800.

Proportion of US population present at LV shooting: 14,520 / 350,000,000 = .000041 or .0041%

Proportion of the population NOT at LV is the inverse or 99.9959%

Likelihood of one person being at both events is then: 1 – (.999959^52,800). Which is 88.8%. The number of times this apparently happened is 3, so it’s 0.888^3, or 70%.

In other words, through purely random chance it is more likely than not that 3 people who were at the LV 2017 shooting would also be present at the Gilroy shooting.

another fellow, who is a member of Mensa, provides this calculation:

The Gilroy Garlic Festival is a three-day event, so that 80,000 is reduced to 26,667 before being reduced another one-third as per Uncephalized’s assumption to account for the timing of the event. This brings us to an estimated 17,787 people present at the time of the shootings. Note that reducing the estimated 20,000 Las Vegas attendance by the same one-third gives us 13,340, not 14,520.
[…]
Gilroy probability: Dividing 17,787 by 350,000,000 results in a probability of 0.00005082, or one in 19,677.
Las Vegas probability: Dividing 13,340 by 350,000,000 results in a probability of 0.00003811428, or one in 26,237
Gilroy AND Las Vegas probability: Multiplying 0.00005082 by 0.00003811428 results in a probability of 0.0000000019369677096, or one in 516,270,868.

Someone posits in a comment to the second calculation, meekly, that perhaps the problem is analogous to the “birthday problem“. The Mensan responds:

No. That’s not relevant here because there is no equivalent to the finite number of birthdays in a year.

I’m personally not smart enough to be admitted to Mensa. However, it seems to me that the number of people in the United States is a finite number.

The Napkin Project by Evan Chen

This is what makes the Internet great:

I’ll be eating a quick lunch with some friends of mine who are still in high school. They’ll ask me what I’ve been up to the last few weeks, and I’ll tell them that I’ve been learning category theory. They’ll ask me what category theory is about. I tell them it’s about abstracting things by looking at just the structure-preserving morphisms between them, rather than the objects themselves. I’ll try to give them the standard example Gp, but then I’ll realize that they don’t know what a homomorphism is. So then I’ll start trying to explain what a homomorphism is, but then I’ll remember that they haven’t learned what a group is. So then I’ll start trying to explain what a group is, but by the time I finish writing the group axioms on my napkin, they’ve already forgotten why I was talking about groups in the first place. And then it’s 1PM, people need to go places, and I can’t help but think:

Man, if I had forty hours instead of forty minutes, I bet I could actually have explained this all.

This book is my attempt at those forty hours.

This project has evolved to more than just forty hours.

The most current draft is also available as a PDF.

Everyone has her price

As an old (before the Web was born) friend of Aziz’ I’ve watched with amusement as he’s become a bit of an Internet celebrity. Even my father, who follows his posts elsewhere, has commented to me about his impressive online presence. Aziz has tried over the years to involve me in this crazy newfangled “blogging” thing he does (in MY day we had to write letters to newspapers to tell people our opinions!). But today Aziz made me the offer I couldn’t refuse. He offered to let me tell you about my Wolfram Alpha Spikey.

Wolfram Alpha Spikey sitting on Fernando's Shoulder
Spikey at the Dojo

Yes, this is a contest. Yes, I’m asking you to vote for my Spikey picture (preferably with every email address you, your friends, your family and all of your co-workers have, every day until January 3rd).

So how did Wolfram get me to do this? What is my price, and how did they meet it?

If you have not used Wolfram Alpha yet, it’s the best-kept search secret on the Internet…despite Wolfram’s attempts to make it NOT a secret. Want to know the average velocity of an unladen swallow? WA knows that. Want to know if you’re pretty? WA thinks you are. Want to use facts and authoritative resources in a discussion about socialized medicine comparing life-expectancy in various countries?  WA can calculate those differences, serve up the facts, show you the references, and point you at other relevant information.

In short, I was hooked on Wolfram Alpha the minute it was born.  This is one sort of potential that computing has to help us leap forward.  It’s the antithesis of Wikipedia (which has another sort of potential for improving our understanding of the world).  This uses the most rigorous and authoritative sources available, and applies Wolfram’s breathtaking calculating algorithms to let you explore it. Yes, a Google result will get you a quick answer (another brilliant outcome of computing), but a Wolfram Alpha result will be either right, or so open about how it was arrived-at that it can be evaluated by those relying on it.  Wikipedia is the “man on the street”, Google is that friend who knows everything, but Wolfram Alpha is the Britcom-loving red-haired research Librarian. The Librarian won’t evaluate your process, but they’ll get you to the best information and be fun doing it.

So when Wolfram Alpha offered to send me a kit to make Spikey, a beautiful red Rhombic Hexecontrahedron, just for picking a neat fact from an Alpha query…well duh.   I spent a week taking pictures of my Spikey in all sorts of places.  It’s amazing how well Spikey fits into my world.  Then I picked one of Spikey hanging out at the dojo with my dear friend Fernando for the contest.  And now I’m evangelizing Wolfram Alpha to get votes for my Spikey . 

But I don’t mind a bit.  Wolfram has done some revolutionary things for mathematics.  I remember struggling mightily with early versions of Mathematica, but they’ve come a loooong way since then.  Those who made it through “A New Kind of Science” see the world differently and perhaps more beautifully now. Wolfram does an array of cool things. But Wolfram Alpha…oh Wolfram Alpha…marries rigorous information, brilliant computing algorithms to explore that information, and a WHOPPING good geeky sense of humor. As Aziz would say…”Awesome!”

So whether you vote for my Spikey, or just go visit Wolfram Alpha, I hope something good comes out of this (like you winning a T-Shirt by voting, or me winning an iPad or Wolfram Stuff because you voted, or you saving the world by researching environment change or nuclear proliferation in Wolfram Alpha). That’s important, because according to Aziz, I will be posting here more in the future.

Sigh. What a geek will do for swag…