Extending Wednesdays

Money & Science

Today’s Extending Wednesdays topic comes from the Economics section of Ideas Roadshow’s Extended Essay Guide, and features renowned scientist and author Freeman Dyson, Institute for Advanced Study, reflecting on how underlying economic motivations often drive scientific inquiry. 

The fact that science, like any other human activity, is subjected to large-scale economic influences is hardly surprising when one stops to think about it, but often scientific activity is treated as somehow “beyond” standard economic frameworks with incentive structures considered to be based solely on internal scientific criteria or a more abstract, idealistic evaluation of “research interest”.

But Professor Dyson’s comments shed light on several important factors directly correlated with the economics of scientific research, ranging from a waste of human capital on a large-scale sociological level to an increased sense of personal and professional frustration on a personal one. 

This topic bridges Economics, Social and Cultural Anthropology, Geography and Environmental Systems and Societies.  Possible areas of investigation for an extended essay include analytical studies of the influence of economic factors on specific avenues of scientific research and the associated complexities of objectively quantifying innovation and productivity in the context of scientific research.

Related resources that are part of Ideas Roadshow’s IBDP Portal include the clips Too Much String, and Suddenly Fashionable, as well as the hour-long videos and accompanying enhanced eBooks Pushing The Boundaries and The Problems of Physics which include a wealth of additional research materials.

If your school does not have an institutional subscription to Ideas Roadshow’s IBDP Portal you can now sign up for an individual teacher or student subscription. Annual individual subscriptions cost only $99 and provide unlimited access to all resources that are part Ideas Roadshow’s IBDP Portal.

Connecting Thursdays

Fundamental or Accidental?

To what extent can we determine if what we observe is an inevitable consequence of a fundamental law or simply happenstance?

For those who are scratching their heads trying to imagine how principles of TOK can relate to a subject like physics, it’s hard to think of a more illustrative example than Darwin and the Butterfly featuring astrophysicist Scott Tremaine, Institute for Advanced Study. 

Professor Tremaine confronts us with a problem that arises with remarkable frequency in his discipline: how can we be certain that what we detect in a given system is fundamental or accidental? 

He describes how, in our solar system, all the large planets – Jupiter, Saturn, Uranus and Neptune – are all considerably further away from the sun than the small planets like Earth, prompting the key question, “Is that an accident? Do giant planets somehow have to form at large distances away from their star? Or is it just a peculiar feature of the solar system?”    

For those of you who might be thinking that this is just of “academic interest”, in a related Ideas Roadshow’s IBDP clip – Hunting Exoplanets – Professor Tremaine describes how the current search for exoplanets which is garnering widespread interest among scientists and non-scientists alike could, actually, have been successfully conducted decades earlier, but astronomers simply assumed that all solar systems had to be structured similarly to our own.  And it turns out that they don’t. How’s that for TOK in action?

A sample of related Ideas Roadshow’s IBDP resources to integrate TOK across the DP curriculum:  TOK Connections Guide for Physics, TOK Connections Guide for Biology, TOK Connections Guide for Philosophy, Darwin and the Butterfly (TOK), Hunting Exoplanets (TOK), Sherlock Holmes vs. Stamp Collecting (TOK), Deducing Black Holes (TOK), Natural Sciences TOK Sampler.

Extending Wednesdays

Crystallographic Conundrums

Today’s Extending Wednesdays topic comes from the Chemistry section of Ideas Roadshow’s Extended Essay Guide, where Paul Steinhardt, Professor of Physics at Princeton University, gives a detailed description of how a surprising result of his computer model of amorphous metals made him question the limits of the laws of crystallography for solids. 

Professor Steinhardt’s ruminations on whether or not the rules of cryptography could be extended to his computer simulations launched him on a remarkable voyage into the world of “quasicrystals”, a new state of matter which Dan Schechtman serendipitously simulated in a laboratory, a feat for which he was awarded the 2011 Nobel Prize in Chemistry. z

Paul Steinhardt’s path to quasicrystal discovery, meanwhile, went in a strikingly different direction, from the mathematics of symmetries, to theoretical predictions of a diffraction pattern that was unwittingly produced by Schechtman and his colleagues at almost exactly the same moment, to eventually stumbling upon a quasicrystal from a rock in Siberia that turned out to be, quite literally, out of this world.  

Possible areas of investigation for an extended essay include an analysis of the laws of crystallography for solids and the symmetries of materials, X-ray diffraction patterns and their use in material science, Penrose Tiles and their applications, and a history of quasicrystals.  This topic bridges chemistry, mathematics and physics. 

Related Ideas Roadshow content includes the clips Beyond The Textbooks, Natural Quasicrystals, Quasi-Serendipity, Scientific Stubbornness, Scouring Museums and the two hour-long videos Indiana Steinhardt & The Quest for Quasicrystals, along with the corresponding eBook with the same title. 

Extending Wednesdays

Computational Complexity

Today’s Extending Wednesdays topic comes from the Computer Science section of Ideas Roadshow’s Extended Essay Guide, where pioneering “quantum cryptographer” Artur Ekert, Professor of Quantum Physics at University of Oxford & National University of Singapore, describes the notion of computational complexity, a way of objectively distinguishing between “easy” and “hard” mathematical problems.

Well, you might be forgiven for thinking, that is all very interesting in an abstract sort of way, but does it have any real practical value?  The answer turns out to be a resounding “yes” – indeed, it is, quite frankly, hard to think of something that has greater practical value. The entire notion of complexity classes was originally formulated to solve the “key distribution problem” of cryptography and led directly to the development of security protocols that are used to encrypt every current financial transaction on the internet.  

And, as is usually the case for science, developing the idea of computational complexity also helped lead to a whole host of additional intriguing concepts, from quantum algorithms to the very nature of “information”.  

This topic bridges computer science, mathematics and physics.  Possible areas of investigation for an extended essay include an examination of the history of computational complexity, cryptography’s key distribution problem, current public key cryptographic protocols, classical vs. quantum algorithms and quantum cryptography. 

Related Ideas Roadshow content includes the two hour-long videos Cryptoreality Part I and Cryptoreality Part II, as well as the clips The Physics of Information and Applied Philosophy

TOK Tuesdays

Exploring PT 5 – Everything’s A-OK

This is the fifth of six TOK Tuesdays posts that briefly explore various nuances and concepts associated with each of the May 2020 TOK prescribed titles. In each post I will highlight a few specific themes that students may wish to consider related to each title, themes that are fleshed out in considerable detail, together with specific examples, in the corresponding Titled Assistance video available directly on Ideas Roadshow’s IBDP Portal. Subscribers might wish to regard these posts as high-level summaries of those videos, illuminating large-scale structural motivations that can further assist students both before and after watching the associated Ideas Roadshow Titled Assistance video. 

Today we tackle PT 5 for May 2020.  Once again it’s worth emphasizing that these thoughts, together with those in the related Titled Assistance video, are strictly personal opinions and are designed to highlight key conceptual points associated with each title rather than provide any particular thesis or response to the title in question. 

In the video, as always, I explore many aspects and nuances associated with this title, trying to flesh out the various subtleties related to issues such as, What does it mean for a theory to ‘have its limitations? and, What, precisely, does it mean to ‘understand the worldin this context?  These are, of course, very important features of the title that must coherently be addressed by any student in her essay, as are the provocative words “given” and “every”. But that’s not what I’m going to talk about in this post.  

Instead, I’m going to make a lateral move to another aspect of the title before slipping into a higher-level view of things.   

First, the other aspect.  After the claim in quotations comes the obligatory “to-do” message to the student: Discuss this claim with reference to two areas of knowledge. The student, and teacher, might be forgiven for simply glossing this last sentence over, unthinkingly chalking it up to standard TOK title format. After all, every title asks the student to do something, and while “discuss this claim” is clearly more general than “to what extent do you agree with this claim” or even “explore this distinction”, it seems very much of a piece with the general spirit of things.   

But that’s not the part I want to focus on here. For me, a genuine key to this title is the emphasis on “with reference to two areas of knowledge”. At first glance this, too, seems incredibly benign. After all, half of the titles specifically request the student to discuss matters with respect to two AOKs.  So why, on earth, should this stand out here?

The answer, I think, harkens back to the first TOK Tuesdays blog post I wrote at the beginning of October (Theory of Titles) when I stressed the value of trying to understand why the IBO TOK powers that be came up with these particular titles. What were they thinking? What did they have in mind? Why these titles and not similar options?  

My guess is that the titles that specifically ask students to invoke two areas of knowledge indicate those where, by and large, experts pursuing different AOKs will have strikingly different responses to the title in question.   That’s not to say, of course, that the other three titles don’t also present a divergence of views – of course they do – it’s just that, for the most part, that very divergence won’t be so strongly correlated with AOKs. 

And I would further claim that, of the three titles that specifically mandate comparisons across two AOKs, none reveals this correlation as strongly as PT 5. Which leads directly, I think, to an important “way in” to begin addressing the title.  

In other words, I would urge anyone thinking about PT 5 to step back for a moment before plunging into the details, and ask yourself to compare the reactions a typical physicist or biologist would have to the statement “Given that every theory has its limitations, we need to retain a multiplicity of theories to understand the world” with those of a typical historian or social scientist.   

My sense is that, while exceptions definitely abound, most physicists and biologists would strongly disagree with the statement. Some theories, they would admit, have their limitations, but that is more a statement of our current level of ignorance than anything else, and the hope and expectation is that, over time, those limitations will disappear as we better refine our theoretical framework. It is certainly not the case, they would say, that every theory has its limitations.  Most natural scientists would begrudgingly admit that “a multiplicity of theories” is logically necessary during our current period of uncertainty until we sort things out appropriately, but it is hardly desirable, let alone necessary – simply a consequence of not having everything figured out yet

On the other hand, your average historian would likely strongly concur with the claim that every historical theory has its limitations, recognizing two important points:

  • No matter how carefully we sift through the available evidence, there is still the overwhelming likelihood that we don’t have access to all the information necessary to make the best possible judgement.
  • Even those theories that we do develop based upon our available evidence are naturally subjected to our own biases and assumptions that resonate with our own sociocultural values and that historians of both the past and future will naturally come to strikingly different conclusions based upon different interpretations of the same evidence.   

Meanwhile, social scientists tend to come down on various different sides of this question, depending on a combination of their personal attitudes and what sort of research they conduct.  

One of the advantages of having a database filled with hundreds of specific insights of leading experts across different fields is that it’s pretty easy to move beyond one’s gut feelings and check to see if one’s expectations measure up with reality.  Which is why, in our recently released Titled Assistance – Supporting PT 5 video we chose examples from six different experts across the natural sciences, history and human sciences in a deliberate effort to further explore this AOK-related distinction.

Those unfortunate few who have yet to subscribe to Ideas Roadshow’s IBDP Portal will sadly not have the luxury of such concrete examples from expert researchers to support their arguments, but I would nonetheless urge them to trawl through books and YouTube videos to see if they could verify this AOK-related correlation for themselves.  

Because once you spot the roles that different AOKs play in this title, it’s almost like the essay writes itself. 

The Titled Assistance – Supporting PT 5 video is now available on Ideas Roadshow’s IBDP Portal to all individual subscribers and subscribing schools.  It can be found in the general Theory of Knowledge section (under “TOK Compilations”), Student TOK section and TOK Teachers section.  It provides a detailed discussion of PT 5 with 6 specific examples from Ideas Roadshow’s IBDP video and print resources to highlight the concepts under discussion.  It is roughly 40 minutes long.

For information about an affordable individual teacher or student subscription which provides full access to Ideas Roadshow’s IBDP Portal, including all Titled Assistance videos PT 1-6 please visit our website, for students: here, and for teachers: here.

Extending Wednesdays

The Anthropic Principle

Today’s Extending Wednesdays topic comes from the Physics section of Ideas Roadshow’s Extended Essay Guide, where Nobel Laureate Tony Leggett discusses the so-called Anthropic Principle, an idea that begins with the recognition that our current models of particle physics contain within them a number of “fundamental constants” that have no prior explanation – they simply have to be accepted ahead of time, or, as physicists like to say, “put in by hand”.  

Well, most theories have some sort of axioms involved, so that, in itself, is not so significant.  What makes this case potentially different, however, is that the particular values of these constants seem remarkably special (“fine-tuned”, a physicist would say), with only a very narrow range being suitable for not only human life, but even the existence of stars and galaxies. Why, then, do we happen to have the very values of these constants that we seem to “need”? It is this that “The Anthropic Principle” purports to explain? Check out the video called The Anthropic Principle featuring Prof. Tony Leggett.

The recent history of The Anthropic Principle is an intriguing one all by itself, as scientific opinion has oscillated, often very frequently, from utter disdain at its “inherent unscientificness” to a wholehearted embrace. In the 1980s the celebrated science and mathematics writer Martin Gardner wrote mockingly about the “Completely Ridiculous Anthropic Principle” with its vividly ironic acronym (“CRAP”), while many theoretical physicists unquestionably accept it today.

This topic bridges physics and philosophy.  Possible areas of investigation for an extended essay include an examination of the history of the anthropic principle, current levels of acceptance in the scientific community, an analysis of the different types of anthropic principle (e.g. “weak”, “strong”) and a discussion on its compatibility with the scientific method.

Related Ideas Roadshow IBDP resources include the clip The Anthropic Principle, the compilation video Anthropic Reflections, and the eBooks and hour-long videos The Problems of Physics and Pushing the Barriers.

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

Historical Illumination

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.