The Beatles famously shared songwriting credits for all of their songs; throughout history, it’s been gradually revealed whether or not John Lennon or Paul McCartney wrote each famous Beatles song. However, there’s one song that they were never able to agree on. Hear how mathematicians have determined who actually wrote The Beatles’ hit “In My Life”.
Listen to the song above. Then you should read this NPR article and/or listen to the interview (top left of page).
Write a brief paragraph summary explaining in your own words how mathematicians determined the authorship of “In My Life”. Write a second paragraph hypothesizing: Where else might this statistical method be used? Think not just in music, but in the written word as well. How might historians and archaeologists use this method in other instances?
Finally check out this post, wherein the author used a technique similar to “Bags of Words” to see if a machine could read recipes and create new ones. The results are…interesting.
A mathematician/musician has taken the infinite decimal digits of Pi and composed a song based on them. Take a look and listen to the song here:
(This badge will likely go much smoother for you if you’re musically inclined or have some basic training in reading music.)
Watch the video above.
- First, reflect on what you think of the song. Do you like it? Is it pleasant to listen to? In general, what are your feelings on using mathematics to help create a song? Answer in a few sentences.
- Pause the video at the 9 second mark and look at the scale he used to compose his song (A Harmonic Minor Scale). Hypothesize in a sentence or two why he used this scale to compose his song rather than a “simpler” one (like, for example G Major).
- Pick another irrational number besides Pi (Phi, e, the square root of two, etc.) Using the same scale and time signature (4/4) as the song above*, compose at least 8 bars of a song based on this irrational number. You may print off sheet music here.
- I need to hear this song. You can record it, you can bring in an instrument and play it, or you can bring in the sheet music and I can play it on guitar (just give me a heads up so I can bring in a guitar that day).
- Reflect on your new song in a couple of sentences. Do you like it? Is it better or worse than the Pi song? Has it changed the way you feel about math being used to create music?
* use a different scale and time signature if you really want to, but that seems more complicated and difficult than I am intending this to be. But go for it if you want! Likewise, you don’t have to worry about harmonies like you can hear in the original video, but if you’re capable and interested you are welcome to try!
This badge was suggested by USN Class of 2023 Colette. Thanks, Colette!
Chefs in Great Britain have used “maths” to determine the best way to cook roasted potatoes. See the magic formula here (courtesy of the Sun).
Watch the video and read the accompanying article. Write a paragraph that explains the difference between the “traditional” way of making roasted potatoes and the “new, mathematical” way. What changes were made and what is the advantage? How did chefs determine that the new way was in fact “better”?
In a second paragraph, describe another food that you think might be improved using mathematics to aid in the preparation. Describe a hypothesis you might have about how that food might be improved using mathematics and why you think it would be an improvement. Give a diagram if it helps your explanation.
STOP! If you plan on finishing this badge, right now I want you to take a blank sheet of paper and draw any THREE (3) of the following company logos from memory (including color — not just black and white drawings unless the logo itself is black and white). Don’t look them up, just draw what you can remember of any three of these logos:
Apple, Adidas, Burger King, Domino’s, 7-11, Foot Locker, Starbucks, Walmart, Target, IKEA.
People all over the country were asked to do this activity, and the results are interesting. After you’ve drawn your logos from memory, click HERE to compare your drawings to everyone elses.
Draw the logos before reading the article, then look at the article. You don’t have to read the whole thing — but read the introduction, then skip to the three sections that correspond to the three logos that you drew (You can use the icons near the top of the article to “jump” to that section”)
Answer these questions:
- How did you do? Compare any mistakes you made to the most common mistakes made by other people.
- Write a few sentences comparing common mistakes you noted between the three logos that you read about. Do humans have any common tendencies? Notice any patterns you see in the mistakes that people tended to make. What were the easiest parts of each logo to remember? Why do you think that is?
- Read the Summary at the bottom of the page and “place yourself” on the table/chart that they showed. Do you think you have a better- or worse-than average memory?
- Take the interactive quiz underneath the summary How did you do? Better or worse than you expected?
When you turn in your badge, be sure to include your original drawings-from-memory.
Did you know the color distribution of M and Ms has changed over the years? Quartz has a breakdown, and how you can which factory your candy originates from (including one right here in Tennessee)! (Thanks to Bowman Dickson for sharing this link on Twitter!)
Read the article linked here or above.
Answer the following questions in a couple of sentences each.
- Compare the color distribution for M and M’s in 1997 compared to the color distribution in 2008. What changed? Why do you think it changed (hypothesize)?
- Why does Mars no longer publish the color data for M and Ms? (In other words, what’s true about the two different plants that manufacture M and Ms?)
- Buy a bag of M and Ms and before you eat it, count the colors. Create a data display (bar graph, pie graph, etc) to show the color distribution in your bag (you can use Excel or some other program to help you do this, or you can do it by hand). State whether or not you think you are eating New Jersey or Tennessee M and Ms based on your results, and explain your reasoning.
So there’s this Twitter feed that tweets out the prime numbers…in order…on the hour…every hour. Friend of Pre-Algebra.info David Butler analyzed the data from this Twitter feed to see which prime numbers were the most popular (via Likes and Re-Tweets). See the results in his blog post.
`1. Before you visit the blog post linked above, visit the Twitter feed that lists primes. Out of the most recent 15 primes listed, which one is your “favorite”? (You can decide how to interpret “favorite”. Just decide which of the most recent 15 primes you like the best).
2. Now visit Dr. Butler’s blog post where he analyzes the prime data. Read the blog post and look at the data displays. List at least four characteristics he noticed about the “most liked” primes, and give an example from the data to support each claim.
3. Refer to your prime choice from question #1. Does your choice fit any of the four categories from the second question? Which ones?
4. Hypothesize: Why do you think certain patterns or arrangements of primes are more “likeable” than others? What might this have an impact on subjects like cryptography (internet passwords or even locker combinations)?
5. Here’s a link to ten random ten-digit prime numbers? Using what you’ve learned so far, which one do you think would be the “most liked”? Explain your reasoning.
Via CityLab comes a bunch of infographics that examine how different flags around the world are constructed. Pretty cool stuff!
Pick the United States and one other country (Your choice! Maybe this is a country that you’ve visited, one where you have lived at one time in your life, one where a family member lives, or just one you are interested in for any reason).
Look through the infographics at the link above and answer the following questions about the flags for the USA and the other country that you chose.
- Do your countries’ flags (USA and the other one you chose) have any of the five most typical layouts? If so, which ones?
- Do your countries’ flags have any of the most typical colors included in them? Which ones?
- Research what the colors on your countries’ flags are used to represent. Are they the most typical meaning behind those colors, or a less-used meaning?
- Do your countries’ flags include any of the five most common symbols? Which ones?
- How complex are your countries’ flags? If they are more than just “Child’s Play”, what elements do you think made the flags more complicated?
- Finally, imagine you were going to create a new country and had to design a flag. Given what you learned about flag design from these infographics, how would you design your flag so that it was similar enough to other world flags (doesn’t feel like a huge outlier) but still different enough to be recognizable and unique (doesn’t feel like a copycat) ? Draw/color a sketch of your new flag after you print out your answers to the previous five questions.