Category: Connecting Thursdays

Connecting Thursdays

Historical Illumination

Howard Burton

Under what circumstances can examining the past help guide future discoveries?

It’s most definitely an open question among historians whether or not a careful study of the past can help us in the future.  Some believe that the past must be appreciated and understood solely in its own terms and context and that any attempt to “derive laws of human nature” from its examination that can then be somehow applied to our current situation is bound to fail. 

Others, on the other hand, are convinced that, while rescuing specific “lessons from the past” that can be somehow harnessed in our present is a challenging and complex task, it is not necessarily impossible – certainly not in all instances. 

This debate, which can be traced right back to Thucydides – if not before – rages on.  But meanwhile, a much less recognized question is whether or not historical understanding can help us in other, rather different, spheres of knowledge, such as the Natural Sciences.  Below is University of Pennsylvania physicist Justin Khoury’s intriguing take on how an appreciation of the history of science can better help us frame the current conundrum of dark matter:

Professor Khoury’s explicit invocation of history to help us better appreciate current issues in theoretical physics turns out to be hardly as rare as you might naively believe.  In the TOK compilation Thinking Like A Physicist, particle physicist Nima Arkani-Hamed describes how a thought experiment into the past can help us better understand how to make progress with contemporary challenges, while in the TOK clip New Laws? Physics Nobel Laureate Tony Leggett adopts a strikingly similar thought experiment of returning to the past to illustrate how our current picture of the laws of nature might be more restricted than we currently think.

Your school has not subscribed yet? Visit our website – HERE – to learn more about Ideas Roadshow’s IBDP Portal which offers an extensive database of authoritative video and print resources explicitly created to meet the needs of both teachers and students throughout the Diploma Programme.

Connecting Thursdays

Pondering Proof

Howard Burton

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.

If your school does not have an institutional subscription to Ideas Roadshow’s IBDP Portal yet you can now sign up for an individual subscription. Annual individual teacher or student subscriptions cost only $75 and provide unlimited access to all resources. School-wide subscriptions are affordably priced based on the number of DP students in your school.

 


Connecting Thursdays

Objective Progress

Howard Burton

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. 

Your school has not subscribed yet? Visit our website – HERE – to learn more about Ideas Roadshow’s IBDP Portal which offers an extensive database of authoritative video and print resources explicitly created to meet the needs of both teachers and students throughout the Diploma Programme.


Connecting Thursdays

Misapplications

Howard Burton

Under what circumstances can we be certain that non-specialists understand a given human sciences theory? 

An essential component of TOK is to consider the real-world application of theories.  Do our models correspond to what we actually find in the real world? What sort of real-world evidence exists that can convince us that our theories are correct, and why?  

Looking to concrete applications of our theoretical frameworks in the real world is an essential way of obtaining evidence for their validity. But what happens if “the real world” actually warps our theoretical frameworks out of recognition. What happens if when we think we’re actually implementing or testing our theories, we’re really doing no such thing?

While any theory can certainly be distorted or misinterpreted by other specialists (sometimes deliberately so), this sort of thing most often happens when non-specialists naively try to implement research knowledge that is directly relevant to them, a state of affairs which more often than not happens in the human sciences. 

Carol Dweck who is a renowned social psychologist from Stanford University, has spent much of her research career demonstrating how students can dramatically increase their learning potential by switching from what she calls a “fixed mindset” to a “growth mindset”.  

One key aspect of her theory is that the type of praise that educators give students has a significant effect on their mindset, with praising the effort that led to success much more likely to lead them towards a growth mindset, while simply praising the success itself, or – worse still – the student’s intelligence, is much more likely to reinforce a fixed mindset.

Professor Dweck has good reason to believe that her psychological theory holds water, given that it has been rigorously tested in a number of extensive experiments by both her and others.  The problem, however, is that the greater the public recognition of her mindset work is, the more often it is likely to be misinterpreted.  

(Check out the clip featuring Carol Dweck in this TOK Sampler)

This brings us to an additional feature of the overlap between TOK and the human sciences that is sometimes overlooked.  Normally, we’re primarily concerned with the question of to what extent we can be certain that our theoretical HS frameworks are valid – perhaps there are different sociocultural factors which render them inappropriate in certain instances, or perhaps the evidence that we rely upon contains some hidden assumptions and biases that render our conclusions suspect, or at least limited. 

But now we have something else to consider:  even when we’re confident that our theoretical models are valid, to what extent can we be certain that non-specialists are applying them correctly in the real world?  After all, for a HS theory to have genuine impact, it’s not enough for it to be “abstractly true”. It has to be applicable, not only in principle, but in practice. Which means, in turn, that we have to turn our attention to the overlap of not just psychology and TOK, but also language, the media, and much else besides.  

For additional examples of how TOK overlaps with psychology, language and the media, see Ideas Roadshow TOK Connections Guide for Psychology and Ideas Roadshow TOK Connections Guide for English A: Language & Literature, directly available in the Teacher Resources section and the Student TOK section on Ideas Roadshow’s IBDP Portal.

If your school does not have an institutional subscription to Ideas Roadshow’s IBDP Portal yet you can now sign up for an individual subscription. Annual individual teacher or student subscriptions cost only $75 and provide unlimited access to all resources. School-wide subscriptions are affordably priced based on the number of DP students in your school.


Connecting Thursdays

Historical Imagination

Howard Burton

Introduction

Welcome to the first of our Connecting Thursdays posts, where each week we’ll feature a specific example from one of our many detailed TOK Connections Guides illuminating how TOK thinking can be quickly and easily integrated into courses across the DP curriculum.

These posts will naturally be of direct relevance to DP coordinators, TOK teachers, the subject teachers corresponding to particular posts and DP librarians. 

Historical Imagination 

Many people simply assume that, since the business of history is to understand the past, the only real stumbling block to doing so is finding the appropriate evidence to tell us what precisely occurred. 

Those with a deeper understanding of TOK will appreciate that it’s not quite that simple, as different interpretations of the same results can lead to strikingly different conclusions.  After all, just because we all agree on what actually happened, they will rightfully tell us, hardly means that we will all agree on why it happened.  

But even that is not the end of the subtle story.  Because there are often times that the skillful historian can use her imagination to extract valuable insights from what everyone agrees didn’t actually happen at all.  In other words, they will directly harness imagination as a way of knowing. 

Sir John Elliott, the eminent Spanish historian at the University of Oxford, gives us a concrete taste of how this is done, directly harnessing Sherlock Holmes’ famous technique of paying attention to “the dog that doesn’t bark in the night” in the video clip called Non-Barking Dogs.

This clip not only gives students a clear and penetrating example of how using our imagination can directly assist the knowledge process (a point which often presents significant confusion in TOK courses), it also sheds valuable light on the important use of the counterfactual to develop historical understanding: contemplating the lessons that might be drawn from why some things that could have happened actually didn’t. 

For many more concrete examples of how TOK overlaps with history, see the Ideas Roadshow TOK Connections Guide for History, directly available in both the Teacher Resources section and the Student Section on Ideas Roadshow’s IBDP Portal .

Relevant Ideas Roadshow’s IBDP video resources and supporting materials include TOK Connections Guide for History, History TOK Sampler, Developing Understanding TOK Sampler, Slavery and Revolution, Divining the Date, Knowledge vs. Understanding, Non-Barking Dogs.