Connecting Thursdays

A Worrying Lack of Evidence

How can we be certain that we know the true numbers of people suffering from the coronavirus?

Like many people familiar with TOK, I find myself profoundly bemused when someone starts lamenting how difficult it is to “integrate” theory of knowledge within the DP curriculum.   

In an age of increasing pressure to ensure that students learn the required material for their DP courses, I often hear, ruminating on “how we know what we know” is considered something like an intellectual luxury good  – a good idea to indulge in in theory, but in the real world, who has the time to fit such philosophical speculations into a biology or mathematics course? 

Well, sitting in my quarantined house in France, it’s pretty clear that “the real world” has suddenly caught up with all of us with a thud, and navigating the way forwards is going to be nigh on impossible without a clear understanding of core theory of knowledge principles.   

For a good example of what I’m talking about, check out a particularly thoughtful article by Stanford University epidemiologist John Ioannidis called A fiasco in the making? As the coronavirus pandemic takes hold, we are making decisions without reliable data, where he details how major public policy decisions are currently being made in the absence of any solid evidence, warning us that “the data collected so far on how many people are infected and how the epidemic is evolving are utterly unreliable”.   

This article has provoked considerable debate throughout the global health community, but the key point for us is not to directly address its implications for current government policy, but rather to stress that without a rigorous understanding of the true numbers involved it’s impossible to have any real faith in the models being unhesitatingly bandied about in today’s press – a point to most definitely bear in mind the next time you come across an article with eyebrow-raising specifics like, “UK coronavirus crisis to last until spring 2021 and could see 7.9m hospitalised.”

I have never met Dr Ioannidis, and it could well be that he has never heard of “TOK”, let alone the so-called “challenge” of integrating it in today’s Diploma Programme. But it’s hard to think of a stronger argument for its real-world relevance; and I would strongly urge any TOK, biology, business management, chemistry, geography, global politics, mathematics, philosophy, psychology or social and cultural anthropology teachers out there to use this article as a concrete discussion point in their current online teaching.

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Connecting Thursdays

Pondering Proof

How do we know when we’ve proved something?

For most people, it’s hard to think of something more black and white than mathematics, a domain that, with its celebrated distinction between “right answers” and “wrong answers” is often invoked as nothing less than the acme, in some cases even the very definition itself, of objective tests of knowledge. 

And yet, it is not always quite as simple as that.   

You might be relieved to learn that this piece will not try to convince you that claims such as 2+2=4 are merely experientially-determined subjective opinions, but rather explore something somewhat more nuanced: the very notion of mathematical proof itself.   How do we know, in short, when something has been mathematically proven?

If you talk to a mathematician, more often than not this question won’t seem any more profound than asking her what 2+2 is, as she will unthinkingly rattle off a list of the various long-established techniques for mathematical proof that everyone agrees on: deduction, induction, contradiction, and so forth.  

But what about if I do something different from all of that?  What if, as the philosopher of science James Robert Brown suggests, I rely upon a picture instead as proof of my claim?

Well, it’s one thing to discuss these things in the abstract, but quite another to grapple directly with a concrete example, and the one that Professor Brown highlights in the associated video clip Proof by Picture on Ideas Roadshow’s IBDP Portal will, I’m quite certain, make you agree with him: a careful examination of the diagram he provides will convince you, just as much as any other “established” mathematical technique, that the theorem he states at the outset is successfully proven.   

And suddenly, our answer to the question of “how do we know we’ve proved something?” is much less obvious.   Because now we’re aware – at least sometimes and in some cases – that there might be additional ways, much less easy to objectively quantify and assess, that can somehow provide us with that very same sense of certainty that our established mathematical toolkit of proofs does. And suddenly, instead of being in possession of a clear, objective decision procedure for mathematical certainty, our gut feelings have begun to play a curiously significant role in our convictions of what is true. 

For additional examples of how TOK overlaps with mathematics, see Ideas Roadshow’s TOK Connections Guide for Mathematics which you can find in the Teacher Resources section and the Student TOK section of Ideas Roadshow’s IBDP Portal.

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Connecting Thursdays

Objective Progress

To what extent can subjective biases in the arts be objectively measured?

Most people have accepted that the arts is a domain riddled with weird and wonderful combinations of objective and subjective judgements that we will never be able to fully entangle.  

The subjective part is pretty obvious: anyone who maintains that he’s found a way to unequivocally assess artistic beauty or musical genius or theatrical excellence is immediately, and quite rightly, met with an archly-raised eyebrow.  The notion that such things can be rigorously defined, let alone measured, is wholeheartedly counter to virtually all of our experiences, from the diversity of cultural values to the changing winds of artistic fashion.

And yet, there is Titian, and Beethoven, and Shakespeare, to name but three – artists whose achievements are universally recognized as transcending those who came both before and after them.  Few would venture to adopt the unbridled relativist position that these are just three guys who somehow managed to squeak into the cultural pantheon just because they happened to have been at the right place at the right time.

So most of us, prudently enough, recognize the fundamental intractability of the situation and move on with our own personal solution to the subjective/objective artistic divide. 

But nonetheless, if we force ourselves to think sufficiently critically, there are still real opportunities to make progress here.  Take award-winning violinmaker Joseph Curtin’s quest to disentangle “the secret of Stradivarius”.

It turns out that, as Joseph went on to show in several groundbreaking studies with his colleagues, it’s hard to justifiably claim that the “secret of Stradivarius” exists at all.    

The real secret, in other words, is our willingness to question our biases and assumptions.   Which shouldn’t, of course, be a secret at all. 

For additional examples of how TOK overlaps with music, see Ideas Roadshow’s TOK Connections Guide for Music, directly available in the Teacher Resources and Student TOK section on Ideas Roadshow’s IBDP Portal plus the resources highlighted below. 

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