(by Eileen Dombrowski, from OSC TOK blog) Mathematician Alex Bellos was intensely irritated by the question. Was that person in the audience mocking him, or possibly ridiculing what he’d been saying about mathematics, to ask such a bizarre and irrelevant question at the end of his lecture? The audience member had asked him, as others had done before, *“What’s your favourite number?” * In this podcast conversation from *Radiolab*, Bellos describes his abrupt shift of perspective as he realizes that the questioner is asking *in sincerity.* Quickly, he discovers that half the members of his audience have “favourite numbers”. And so begins his own investigation into *emotional* and *imaginative* associations with numbers, and the non-rational characteristics that many people attribute to a numbering system he had previously seen exclusively in terms of *reason. *

The ideas in this podcast are surely familiar to most TOK teachers – the emotional associations we gather with symbols within our symbolic systems of representation (which we consider in *WOK language* as it intersects with *WOK emotion* and *WOK imagination*) and the mystic meanings that have been given to numbers in many cultural contexts (which we consider in *AOK mathematics*). What makes this 20-minute podcast of interest to TOK teachers, other than the entertainment listening to it (I liked it!), is that it sets up a quick and easy activity to warm up a class to talking about the intersection of our ways of knowing – and from there about mathematical ideas.

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**“For the love of numbers”, Radiolab podcast, http://www.radiolab.org/story/love-numbers/**

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**Ideas for using the podcast in class**

Listening to the podcast may give you better ideas, but this is what came to my own mind as a class activity. With a light touch and sustained speed, you could fit it into 45 minutes — though an hour would work better.

**1.** Ask your class if any of them has a favourite number, and if so, what makes that number special. (I find a personal and anecdotal opening to class usually brings a group together and “tunes them in”.)

**2.** After their own responses, play for them the first 3 or so minutes of the Radiolab podcast (after the signature opening) – enough to put their own imaginative and emotional associations with numbers (or the absence of such associations) into a larger context of other people’s reactions.

In minutes 1-4:15 Bellos speaks of his reaction to the question “What’s your favourite number?” We hear the voices of people who left messages about what numbers they like best, and why.

**3.** Introduce the class BRIEFLY to examples of different cultures attributing emotional or even mystic significance to numbers. (Warning: Be careful to be clear on what you are exemplifying: you are picking out cultural meanings to illustrate the widespread human tendency to attribute non-rational meanings to numbers, but *not* suggesting to your students that they should take the knowledge claims of numerology or other superstitions seriously.) Some examples:

**Numerology,**or the attribution of mystic properties to numbers, recurs in many cultures. Wikipedia gives a brief introduction (the opening paragraphs are enough for TOK class) and some write-ups on specific numbers such as 108 . Websites abound – far too many! — that list cultural associations or earnestly promote them. (A useful one is a list for the Meaning of Number 3.)

- A striking example is the
**ancient Greek Pythagoreans**(named after mathematician Pythagorus 6^{th}century BCE) attributed special significance to numbers. For them, the associations were more than simply poetic, as they believed that numerical relationships were the essence of reality (Kline, 76):

“The number *one* they identified with reason, for reason could produce only a consistent whole; *two *was identified with opinion; *four* with justice because it is the first number which is the product of equals (to the Pythagoreans one was not a number in the full sense because unity was opposed to quantity); *five* signified marriage because it was the union of the first odd and first even number; *seven* was identified with health, and *eight* with love and friendship…. all the even numbers were regarded as feminine, the odd numbers as masculine.” Morris Kline, Mathematics in Western Culture, page 77.

**4.** Return to a couple more minutes of the podcast (up to 6:40) for snippets of history on numbers and symbols and (up to 8:12) the voices of people explaining how they *think* and *feel* about the numbers 1 and 2.

** 5**. Broaden out to **knowledge questions** for discussion – or else summarize ideas already raised in discussion by connecting them explicitly with knowledge questions.

- Does the existence of “favourite numbers” and numbers to which non-numerical ideas are attached suggest anything about how we use our TOK
*ways of knowing*? In what ways do*emotion*,*imagination,*and*reason*enter our relationship with numbers – as they do for our other symbols, from words to flags? What other ways of knowing may be involved? - What ideas associated with numbers are essentially
*mathematica*l (e.g. relationships such as sequence, symmetries, and factors) and what ideas are*personal or cultural*(including both the sound and the written version of numbers)? - Write a definition of “number”. What is a “good definition” of the
*mathematical concept*of number, and what is the role of a good definition? If possible, submit your class definitions later to your mathematics teacher to ask for his or her thoughts. (Note that the*knowledge framework*for areas of knowledge has a section entitled “language/concepts”.)

**6. Conclusion.** In a written article, Alex Bellos comments, **“We are sensitive to arithmetical patterns, and respond emotionally to them.”** If you have time in class, it would be worthwhile to end by playing the rest of the podcast. It centres on the number 7, the “world’s favourite number” in the online survey with over 30,000 respondents that Bellos ran. In discussion with Radiolab interviewers, he concludes that 7 is the favourite number not because of cultural influences but because of ** mathematical features inherent to the number.** Our arithmetical sense, he thinks, is what influences culture.

**7. Follow-up writing exercise for the class**

I’d suggest a non-mathematical follow-up for a short, reflective piece of writing (outside of class time) to bring the discussion back into students’ personal spheres (and to squeeze more TOK ideas out of the class activity). Suggested guiding questions:

*In what ways is Alex Bellos’ realization that his audience members are sincere in their question (“What’s your favourite number?”) a good example of a shift of perspective as we talk about it in TOK? (IB TOK Course Companion page 28 ) What assumptions was he making? What values were involved in his judgment? What conclusions had he reached? When he suddenly realizes he could have “jumped to conclusions”, how do his assumptions, values, and conclusions abruptly change? link to personal knowledge: Have you ever experienced such a change of mind, or witnessed someone realizing that they had misinterpreted a situation? What are the advantages of keeping an “open mind” – and why is it often difficult?*

**References**

Morris Kline, online book Mathematics in Western Culture.

“For the love of numbers”, Radiolab podcast, http://www.radiolab.org/story/love-numbers/

Alex Bellos, “’Seven’ triumphs in poll to discover world’s favourite number”, Guardian science blog, April 8, 2014.http://www.theguardian.com/science/alexs-adventures-in-numberland/2014/apr/08/seven-worlds-favourite-number-online-survey

**Further Resources**

Eileen Dombrowski, Lena Rotenberg, Mimi Bick. *Theory of Knowledge Course Companion, 2013 edition. *Oxford University Press, 2013. https://global.oup.com/education/product/9780199129737?region=international

I remember listening to this Radiolab one morning to work thinking it would be perfect for TOK class. This happens very often with Radiolab – I highly recommend the programme for TOK enthusiasts — adult and adolescent!

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