The #mathgeek experiment

I have to say that a number of people, myself included, have been blithely stating that Twitter could be used in class for data-collection, surveys, etc. without actually having fully thought through some of the non-technological challenges that might be involved.  I thought it would be an interesting idea to test it out with a mini-survey of my own, but to include some ‘pitfalls’ or potential barriers to conducting a valid data-collection.  This was definitely my statistician’s geekiness coming to the fore here, I think!

So, in the best traditions of ‘scientific’ data-collection, I started off with some imposed constraints, which could then be varied at a later date if desired, and some hypotheses based on my predictions about the outcomes.  The main idea behind the experiment was to create a kind of mini-manual about what to expect when conducting this kind of activity in future.

Constraints

1. The experiment would run for 24 hours.
2. I would only use the #mathgeek hashtag and rely on my followers to retweet.
3. The instructional tweet would be 140 characters long, requiring editing for retweets.
4. If anyone asked me questions directly about the task, I would respond according to the initial instructions only.
5. Other questions would be answered without ‘giving too much away.’
6. If needed I will provide up to 2 additional prompts by sending the original message again.

Hypotheses

1. Elementary/primary school followers, and non-maths teachers, will probably tweet integers.
2. Followers who tweet integers will probably tweet 7, especially North Americans.
   [Based on other trials such as “Is ‘17’ the most random number?”]
3. No-one will tweet 1 or 10. [Based on intuition.]
4. Secondary or higher level maths teachers will probably make some reference to ‘jargon’ and/or tweet irrational numbers.
   [Because they are more likely to be ‘geeky’!]
5. Followers who tweet irrational numbers will probably chose φ,π or e, or some kind of surd – probably √2 or √5.  It would be interesting, but probably unlikely, to see: ζ(3) [Apéry’s constant], ρ [plastic number, sometimes called the silver number], δ_S [the silver ratio] , δ and α [the first and second Feigenbaum constants].
6. The instructional tweet will be edited at the end rather than the beginning – i.e. the instructions will be ‘lost’.
7. Not everyone will retweet my original tweet as is (possible with Twitter.com, but not where ‘editable’ tweets are available).
8. Not everyone will retweet my original tweet or an amendment of it.
9. Some people will tweet more than once, since no limit was imposed on how many numbers could be tweeted.
10. There will be some extraneous ‘noise’ generated by those participating in the experiment.
11. An Übergeek will probably say that it is numerals rather than numbers which are being tweeted (but only if they are into Number Theory!).

Set-up and preparations

Firstly, I set up an archive on http://twapperkeeper.com/index.php, and also subscribed to #mathgeek using Google Reader (using the Twitter search http://search.twitter.com/search.atom?q=%23mathgeek as an RSS Feed).  I also considered using What the hashtag ?! as an additional backup, since experience with #mathchat moderation suggested that Twitter is not always 100% reliable at keeping all of the tweets!

Then, I sent a test tweet consisting only of the hashtag #mathgeek, to check that the setup worked, and to provide a point of reference for when the experiment was going to begin.

The 140-character tweet I sent out to kick things off was:

Tweet sent out to start #mathgeek

Analysis of Results

The contents of the TwapperKeeper archive of #mathgeek contain duplicated tweets, for some reason, so it required editing before analysis.  The end date in the search had to be extended beyond the 24-hour period, otherwise some tweets sent during the allotted time were missed.  You can carry out your own analysis of the results if you like, by clicking on the link and downloading!

Some special symbols can get distorted by the archiving process, for example:
Ï€ appears instead of π (1-byte versus 2-byte character representations), so it’s best to check with the original when editing any archives for analysis.  Tweets have a unique ID number, so duplicates can be identified easily.  The edited version of the archive is available as a public Google document. One response was sent to me as a Direct Message and not as a Tweet to #mathgeek, but I decided to be kind and include it!

So, after editing and the inclusion of the DM, which was “2 #mathgeek”:

Total responses: 125

Noise/unrelated: 15

Questions/Answers: 9

Retweets: 32

Accepted responses: 68

Discounted: 1 because: (a) it just said “Avogadro”, and (b) Avogadro’s constant, being 6.02214179(30)×10²³, is outside the limits asked for.

Numbers tweeted (frequency):

Integers

1  (3)

2  (4)

3  (2)

4  (6)

5  (4)

6  (7)

7  (11)

8  (5)

9  (1)

10 (0)

Decimals

3.14157 (1)

3.14159 (1) – could be approximation to π?

3.14159… (1) – suggesting non-recurrence, could be π?

7.705519 (1)

8.3  (1)

9.8  (1)

Irrationals

√g (1)

e (5)

phi = [1; 1 1 1 1 …] = {1+sqrt(5)}/2  = 1.61803399… includes “golden ratio” (4)

pi/π (5)

eπ (1)

³√112 (1)

sqrt{42}  (1)

3/e (1)

Test of hypotheses

I do not feel that any statistical significance can be attached to these findings, but if you want to apply tests, be my guest!

1. Still to be analysed but appears to be the case!
2. True, since 7 was the most frequent response amongst the integers – North American-ness to be determined!
3. False – 3 respondents tweeted 1
4. True, first mention of integers came from a secondary maths teacher @TeaKayB, and first irrational number from someone whose job was to promote mathematics in universities @peterrowlett.  Subsequent tweets with irrational numbers seemed to come from people within Peter’s network on Twitter.
5. True φ,π or e, or some kind of surd were tweeted, with e and π being slightly ahead of φ, and also included a single eπ.
6. False, the “Are you a #mathgeek?” was removed from the original when RTed.
7. True, at least 3 different versions of the instructions were available by the end of the experiment.
8. True, 68 responses versus 32 retweets.  This may be because @peterrowlett removed the request to RT in his adaptation of the instructions.
9. True, but only one person did this.
10. True, 15 responses were not directly related to the experiment itself, although some comments were generated by it, including the first two!
11. Undetermined, since there were no Übergeeks!

Observations

As a data-collection activity, I feel this was reasonably successful.  For future experiments to be successful using Twitter, I think:

• a more specialized hashtag would be better.
• instructions should be in a tweet about 120-characters long to reduce chances of re-editing.
• a longer time period could/should be applied with RTing at timed intervals to allow for global participation.
• anyone who ‘hijacks’ the instructions should be contacted and asked to RT original as far as possible.
• Google Reader did not retrieve all of the Tweets sent during the experiment, so it is best to have two or three archives available for analysis.
• graphs and data charts provided by archive software will also contain extraneous ‘noise’, if people ask questions or discuss the activity using the hashtag.
• any archive will probably need to be edited before analysis.

So, over to you now… let me know if you want me to take part in your data-collection activity!

Torture numbers, and they’ll confess to anything! [Gregg Easterbrook]