# Welcome from

Beyond Infinity

I assume you have come here from the QR code embedded in the book. Firstly, I want to thank you for even reading it! A novel about mathematics? Seriously? Well, why not? Life's too short not to combine things.

The QR code used to direct to an entire website dedicated to exploring the mathematical fun in the book, but alas, there was not enough interest to maintain a separate website. So, I am afraid you've come here instead. Still, I want to share some of the fun that's been a part of my journey.

## Great Stuff

###### One of my favorite websites to go to when I want to learn crazy-cool ideas in math. I like how they explain things in simple terms, often just on a sheet of brown paper. Great for exploring recreational mathematics.

###### One of my new favorite websites for learning. There are a lot of fantastic tools here and each time I learn about a new tool, I am repeatedly impressed.

###### A great website for K-6 games. I am a big fan of providing students with opportunities to play with numbers! Fun and educational - sign me up!

###### A fantastic book for teachers to better plan lessons around mathematical thinking. This is a game-changer!

###### I loved the concept when I saw the idea as an article several years ago. Helping students extract math concepts out of stories is about the most amazing thing I can think of!

###### I often get asked about how to do Socratic Seminars in math class. This article explains how to do a "gallery walk" version of seminars that can be used with most age groups.

## Discover More!

Mathematics is often about finding patterns. For example, if you look at the squared numbers 1, 4, 9, 16, 25, 36, and 49, you might notice that the differences between two square numbers follow an odd number sequence: 3, 5, 7, 9, 11, 13 and so on.

In *Beyond*
*Infinity*, the narrator, Matt, has a habit of collecting examples of various numbers in order to understand their different “personalities.” Whenever he comes across a number fact, such as “There are 7 vital organs,” he writes it down in a notebook or records it on a mobile device. After collecting dozens of examples (sometimes hundreds), Matt then looks for common threads or themes throughout to get a sense of a number’s special properties or traits, and ultimately, a number’s personality.

Collecting examples of numbers and how they appear in the world really isn’t any different than searching for patterns amongst the squared numbers. When collecting examples, try to find what the number itself might mean. As Matt points out in the book: “People a long time ago realized that three pineapples, three llamas, three hiccups and three Neanderthals have something in common - that is, their three-ness.” But beyond measuring such quantities, what do various numbers actually mean?

Not all examples are created equally, though. The strength or quality of an example depends on what kind it is. Here are some guidelines to get things started.

#### Changing vs. Permanent Examples

Most things in life change around us every day. Count the number of clouds in the sky, the number of coins in your pocket, or the number of cars outside your window, and these numbers change constantly. You might count eight swans on a lake, but tomorrow there might only be two. What would be far more interesting is if there were somehow ** always** eight swans on that lake. How weird would that be? Examples that are easily changeable generally do not help establish what the personality of a number really is.

Permanent examples are those that essentially never change, or those that have VERY few or NO exceptions. For example, there are always 60 seconds in a minute and 60 minutes in an hour. Or with very few exceptions, all humans are born with five fingers on each hand. And that number doesn’t change (except through accidents). We don’t, for example, grow more fingers as we age. So, why five? What is it about five-ness that goes with fingers? Why are they different lengths? And why did the ancient Egyptians sometimes depict people with fingers all the same length? Since permanent examples basically never change, they can give us quality insights into various numbers.

#### Natural vs. Human-made Examples

Nature is fact. Nature is free of personal opinions and extraneous emotions. Nature just is. How things turn up in nature is according to patterns that have emerged after thousands or millions of years. For example, white pine trees have 5 needles in a cluster, whereas red pines have 2. Snowflakes are almost always formed based on the number six. Examples from nature are clear and true.

Human-made things, though, can be based in opinion, ego or invention. Just because an architect designs an eight-sided building does not mean that it truly reflects the personality of the number eight. For example, the design of the building might have been influenced by politics, zoning laws, taxes, and so on, so that the eight sides were merely a convenience, rather than an archetypal or symbolic example of the number eight.

#### Collect Your Own Examples!

Collect your own examples of how numbers appear in the world around you. Simply dedicate a few pages to each number and start your lists! Here are some examples of 12 that didn’t make it into the final draft to get you started:

12 months in a year, 12 signs of the zodiac, 12 Olympian gods in Greek mythology, 12 Tribes of Israel, 12 Apostles of Jesus, 12 Days of Christmas, 12 peers of Charlemagne, 12 knights of the round table, 12 ounces in a troy pound, 12 hours in the AM and 12 hours in the PM.

Play around with numbers as well. Notice, for example, that continuously dividing numbers by 2 will demonstrate three different types of even numbers: 12 ÷ 2 = 6 ÷ 2 = 3 (oddly-even). 14 ÷ 2 = 7 (evenly-odd). And 16 ÷ 2 = 8 ÷ 2 = 4 ÷ 2 = 2 (evenly-even).