URL Shortener Math
So you might have gotten wind that I started tweeting. I’m trying to think of ways of using it productively or at least I’m trying to justify the amount of time I spend on it to myself.
So far I’ve met some very knowledgeable folks and had some interesting conversations (as much as 140 characters will allow). Meaningful conversations can be hard on Twitter. Maybe one day I’ll learn to be more effective with words and to communicate with more precision while using less words. For now, I am using Twitter more for link discovery than anything else. I’ve retweeted some interesting links and I’ve noticed that just about everyone uses an URL shortener.
I’ve never been particularly fond of an URL shortener. Jeff Atwood at Coding Horror has expressed some of my thoughts better on Url Shorteners: Destroying the Web Since 2002, but that’s a whole other post there.
So far I am aware of about 4 URL shortener services frequently used on Twitter. They are:
Bit.ly is the first one that I used. One nice benefit of the service is that you can see the number of times that people have clicked on your link. You can even see the number of clicks from your shortened link compared the the number of total clicks on other shortened links to that same URL. No other service on my list seems to provide this information. But I digress.
I used the 4 URL shortener services to shorten this post’s URL: http://mrho.net/blog/?p=868. There results are below.
Bit.ly produced http://bit.ly/7hFVX7. Seems like it uses 6 upper case, lower case, and number (alphanumeric character) combination to uniquely identify a link. Whether not they will increase to 7 alphanumeric characters when 6 runs out is unknown. Re-entering the same link into the service produces the same shortened link.
The next service is Ow.ly. One nice “feature” of this service is that it uses one less letter in it name than Bit.ly.
The service produced http://ow.ly/Otn1 for this post’s URL. It seems the service uses only 4 upper case, lower case, and number combination to uniquely identify a link. Re-entering the same link into the services produces a different shortened link in a predictable order. This is an interesting “feature” especially for a math class. Some additional testing and we can see the minimum number of alphanumeric characters it will take is 3.
The next service is Im.ly
The service produced http://im.ly/b1fc5/. It seems to use only 5 lower case, and number combination to uniquely identify a link. Re-entering the same link produces the same shortened URL.
Lastly is Is.gd
The service produced http://is.gd/5wSXx. Relatively speaking, it has the more spartan interface of the services in this list. The service uses 5 upper case, lower case, and number combination to uniquely identify a link. Entering the same link again produces the same shortened URL.
| Summary of URL Shortener Services | ||||
|---|---|---|---|---|
| Service | ID Length | Upper Case | Lower Case | Numbers |
| bit.ly | 6 | Y | Y | Y |
| ow.ly | 4 (so far) | Y | Y | Y |
| im.ly | 5 | N | Y | Y |
| is.gd | 5 | Y | Y | Y |
Questions to students:
- Which is the best service? (how do you define best?)
- Which service would you use and why?
- Which service can hold the most links?
- Can we tell how many links are stored in the service as of now? If so how many? (hint: Ow.ly is the only one)
- How many more links needs to be shortened before Ow.ly needs 5 alphanumeric characters?
- Can any service shorten the links to all the pages in the entire web?
- Can any service shorten all the links in the entire web in 5, 10, 20, 50, 100 years? How can you find out? (assuming same rate of growth)
- Is it OK to recycle links like we do with license plates? What are some potential issues? What happens if a service is gone?
- How many unique links do we need to have to accommodate everyone in the world? What if we recycle the links?
- Are there ways to maximize the number of links?
- Could we use a word shortener to “increase” the information density in a single tweet?
- If the alphanumeric characters represent a positional numeral system, what would be its base? What is one hundred/thousand/million/billion/trillion in this base? How does allowing or disallowing upper case and lower case change these numbers?
What other questions would you ask? How would you support students to answer some of the questions above?
UPDATE: A reader points out a WCYDWT (What Can You Do With This) series by Dan Meyer on license plates.
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