i think this is an amazing essay. i have a few relatively unrelated thoughts:
1) i wonder to what extent simpson’s paradox depends on a nonlinearity. nonlinearities can often except surprising effects, for example, as demonstrated by perceptrons: a small change of parameter values flips the output in surprising ways. essentially, in simpson’s paradox, there are 2 variables: geographical position and political disposition. if those two functions changed smoothly, rather than abruptly and discretely, can this paradox occur? i’m not quite sure, although i’m fairly sure it would be relatively easy to figure out even analytically for certain simple smooth functions (eg, linear functions). if indeed a nonlinearity is necessary for this paradox to arise, that seems to me to be a very important conceptual point, that could lead to a useful heuristic for people when trying to decide whether any given result is the kind of result that *could* result in simpson’s paradox. for me, for now, the only intuition i have is: is there a latent variable that may have greater explanatory power than the reported variable? if yes, then we are in danger of following into the class of problems for which paradox may arise. but, if we could improve the ‘bounds’ on understand the extent to which such a paradox might arise, i think we would understand the problem much more deeply, and thereby, possibly be better equipped to explain it. perhaps somebody has already investigated this and published something about it, i’ve not read much on the subject.
2) taking seriously idea of making education using current state of the art design and presentation ideas, consider the following. a popular MOOC might get up to 200,000 students registered. coursera now offers certification, that’s $50 per class. students who go for the certification are *much* more likely to complete the course, perhaps because they’ve now invested in the material. let’s just assume for argument’s sake that 50% of the class get’s certified (i’m sure a huge overestimate), so 100,000 people are certified, and let’s assume that the class runs for 10 years, thus a total of 1M people get certified, and $50M are made.
now, consider the time investment given to generate the class. i’ve had friends teach such classes, they spend a few hours per lecture. let’s assume that the course has a total of 50 lectures, so 100 hours total time creating the class. let’s say a professor charges $1000 / hr, so the course costed about $100,000, returned $50M, that ‘s a ROI of 500×1. contrast this to grand theft auto, which had an ROI of 3×1. the point of this all is simply to say, i love the idea of getting the best in business together to design a class. i also think there is a huge untapped financial market. i imagine lots of people are thinking about this. has anybody actually really invested money in teaching a new class to offer on coursera? enough money to have some graphic design, a musical score, an actor presenting the material, etc. (note: the person who writes the lecture obviously need not be the person who gives the lecture).
if each of the above thoughts is worth 1 cent, then you now have my 2 cents 🙂
On point 1, I don’t think this has anything to do with smoothness versus discreteness or anything like that. On confounding variables and the like, I recommend Judea Pearl’s essay: http://ftp.cs.ucla.edu/pub/stat_ser/r414.pdf
On point 2, yup. Courses like http://www.mcb80x.org/ are starting to go down this route; they’re a lot more elaborate than the basic Coursera courses. It’s easy to imagine that costs will gradually rise, so that typical courses start to have a few million invested in them, much more like a relatively low-budget movie today than a traditional class. Of course, this won’t guarantee quality. But it will create interesting opportunities for new types of quality.
ha 🙂 that does seem like the way pearl would explain it!
i don’t, in general, think that saying the word ‘causality’ adds any explanatory power.
this seems to me to be a question about joint distributions, ie, which joint distributions give rise to this kind of situation? the answer doesn’t involve causality, just probability calculus. if other people find talking about causality helpful, that’s fine with me, i just find that it adds an unnecessary layer of complexity. latent variables are sufficient, whether or not they are causal.
Please let me say that “Reinventing Explanation” is one of the very best STEM-related essays that I have read. Thank you!
Particularly germaine is this concluding passage:
“But what the creators of the movies and games appreciate deeply — and what many intellectuals do not — is that emotional involvement is the foundation for understanding. Even when explaining abstract, intellectual subjects — perhaps, especially when explaining abstract, intellectual subjects — creating strong emotional involvement is crucial. If someone’s desire to understand is strong enough, they can overcome tremendous obstacles. Part of what we can learn from the movie and game makers is how important such desires are, and the art of creating them.”
Material that supports this thesis includes:
• Politics Robert Caro’s The Years of Lyndon Johnson, Volume 4, the Passage of Power (1958-1964); the political narratives that passed the Civil Rights Acts.
• Song and Rhetoric Joan Baez and Bob Dylan singing, and Martin Luther King preaching, at the March on Washington for Jobs and Freedom (1963); the societal narratives that passed the Civil Rights Act).
It’s not so easy to extract just one narrative from this material … which is why it’s neither necessary, nor feasible, nor desirable that everyone think alike in this regard.
The same lessons apply more broadly to the 21st century’s STEM narratives, which draw narrative themes from deep wellsprings that include Phillip Pullman’s Dark Materials trilogy and David Deutsch’s TED Lecture A New Way to Explain Explanation (2009).
The former narrative nominally is for children; the latter nominally is for adults, yet the theme of individual and societal growth is central to both narratives. As Deutsch’s TED lecture puts it:
“The tragedy of protracted stagnation isn’t sufficiently recognized”
This is a principle that Philip Pullman’s characters Lyra Belacqua and Will Parry appreciate … and act upon with the fervor of 1960s civil rights activists.
Today, these same powerful, unifying narrative themes motivate us to accept imponderable risks and embrace new creative enterprises that are acting to dispel the stagnation that is harming so many young STEM researchers.
Specifically in regard to quantum dynamical flows, and the 21st century enterprises that are founded upon these flows, an exercise that generates fresh quantum-dynamical narratives — that point toward serious quantum research/enterprise opportunities — is to map Paul Grahams’s celebrated Y-Combinator essays onto quantum-physics narratives. For example:
Exercise 1 Transpose Paul Graham’s essay Beating the Averages (April 2003) into a quantum essay Hilbert-Style algebraic dynamics is Blub; Grothendieck-style algebraic dynamics is Lisp.
Exercise 3 Transpose Graham’s essay Frighteningly Ambitious Startup Ideas (March 2012) into a quantum essay The Transformed Roadmap of QIST-II.
In regard to fresh 21st century narratives (both quantum and otherwise) Graham provides sensible advice:
You’d expect big startup ideas to be attractive, but actually they tend to repel you. And that has a bunch of consequences. It means these ideas are invisible to most people who try to think of startup ideas, because their subconscious filters them out. Even the most ambitious people are probably best off approaching them obliquely. […]
Empirically, the way to do really big things seems to be to start with deceptively small things. Want to dominate microcomputer software? Start by writing a Basic interpreter for a machine with a few thousand users. Want to make the universal web site? Start by building a site for Harvard undergrads to stalk one another.
Conclusion The 21st century’s new quantum devices and quantum systems engineering philosophies — think D-Wave, for example — plausibly comprise “big things that are starting as deceptively small things” … precisely in the sense of Paul Graham, David Deutsch, and of course, Michael Nielsen too.
Thanks John, both for the kind words, and for the many interesting connections. I’ll look into some of them.
A question for you: do you have any recommendations for good books on systems engineering? Big picture, overview style. There’s a type of book I’m particularly thinking of – something like “The Non-designer’s design book” or “Drawing on the right side of the brain” – a book that is reasonably short and compact and sets out enough core principles to give someone an idea of what a field is about, while not trying to make them an expert.
By the way, if you enjoyed the Johnson bio, then I suspect you’ll enjoy Robert Skidelsky’s one-volume bio of John Maynard Keynes. Keynes and Johnson were, of course, completely different, but the bios are similar in that they both convey with great force what was remarkable about their subject.
(Skidelsky has a three-volume bio of Keynes as well. The one volume is adapted from it. This is a rare instance where I believe the adaptation is better than the original.)
In regard to systems engineering, two canonical references are Booton and Ramo’s article (1984) and Johnson’s book (2002).
Ramo What is systems engineering?
Systems engineering is the design of the whole as distinguished from the design of the parts. […] Two major trends may be expected in system engineering. First, the capabilities of the analytical tools of the system engineer will continue to increase. […] The second major trend is the increase in the complexity of systems being developed.
————-
Johnson “Systems approaches emphasize integrative features and the elements of human cooperation necessary to organize complex activities and technologies. Believing that humans are irrational, I find the creation of huge, orderly, rational technologies almost miraculous. I had never pondered the deeper implications of cooperative efforts amid irrationality and conflict, and this project has enabled me to do so.”
“I sincerely hope that this work helps others recognize the the “systems” in which we all take part are our own creations. They help or hinder us, depending upon our individual and collective goals. Regardless of our feelings about them, they are among the pervasive bonds that hold our society together.”
These quotes pretty accurately sum-up my views on quantum systems engineering, particularly in regard to medical applications of it.
@article{Ramo:84,
Author = {R. Booton and S. Ramo},
Journal = {{IEEE} Transactions on Aerospace and Electronic Systems},
Month = jul, Pages = {306–9},
Title = {The development of systems engineering},
Volume = {{AES}–20}, Year = 1984}
@book{Johnson:2002ph,
Author = {Stephen B. Johnson},
Publisher = {JHU Press},
Title = {The Secret of Apollo:
Systems Management in American
and European Space Programs},
Year = {2002}}
Would be interesting to cross-reference with some know examples of excellent explanations by today’s standards: Feynman series on physics; graphics in many Scientific American articles; Hans Rosling TED videos on global trends.
Maybe pull together a team of highly-rated professors (ratings often available on the web) and Hans Rosling; give them some specific problems to study (that are know to trip up students); then create materials they recommend; then have rated by actual students.
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i think this is an amazing essay. i have a few relatively unrelated thoughts:
1) i wonder to what extent simpson’s paradox depends on a nonlinearity. nonlinearities can often except surprising effects, for example, as demonstrated by perceptrons: a small change of parameter values flips the output in surprising ways. essentially, in simpson’s paradox, there are 2 variables: geographical position and political disposition. if those two functions changed smoothly, rather than abruptly and discretely, can this paradox occur? i’m not quite sure, although i’m fairly sure it would be relatively easy to figure out even analytically for certain simple smooth functions (eg, linear functions). if indeed a nonlinearity is necessary for this paradox to arise, that seems to me to be a very important conceptual point, that could lead to a useful heuristic for people when trying to decide whether any given result is the kind of result that *could* result in simpson’s paradox. for me, for now, the only intuition i have is: is there a latent variable that may have greater explanatory power than the reported variable? if yes, then we are in danger of following into the class of problems for which paradox may arise. but, if we could improve the ‘bounds’ on understand the extent to which such a paradox might arise, i think we would understand the problem much more deeply, and thereby, possibly be better equipped to explain it. perhaps somebody has already investigated this and published something about it, i’ve not read much on the subject.
2) taking seriously idea of making education using current state of the art design and presentation ideas, consider the following. a popular MOOC might get up to 200,000 students registered. coursera now offers certification, that’s $50 per class. students who go for the certification are *much* more likely to complete the course, perhaps because they’ve now invested in the material. let’s just assume for argument’s sake that 50% of the class get’s certified (i’m sure a huge overestimate), so 100,000 people are certified, and let’s assume that the class runs for 10 years, thus a total of 1M people get certified, and $50M are made.
now, consider the time investment given to generate the class. i’ve had friends teach such classes, they spend a few hours per lecture. let’s assume that the course has a total of 50 lectures, so 100 hours total time creating the class. let’s say a professor charges $1000 / hr, so the course costed about $100,000, returned $50M, that ‘s a ROI of 500×1. contrast this to grand theft auto, which had an ROI of 3×1. the point of this all is simply to say, i love the idea of getting the best in business together to design a class. i also think there is a huge untapped financial market. i imagine lots of people are thinking about this. has anybody actually really invested money in teaching a new class to offer on coursera? enough money to have some graphic design, a musical score, an actor presenting the material, etc. (note: the person who writes the lecture obviously need not be the person who gives the lecture).
if each of the above thoughts is worth 1 cent, then you now have my 2 cents 🙂
Thanks, Joshua.
On point 1, I don’t think this has anything to do with smoothness versus discreteness or anything like that. On confounding variables and the like, I recommend Judea Pearl’s essay: http://ftp.cs.ucla.edu/pub/stat_ser/r414.pdf
On point 2, yup. Courses like http://www.mcb80x.org/ are starting to go down this route; they’re a lot more elaborate than the basic Coursera courses. It’s easy to imagine that costs will gradually rise, so that typical courses start to have a few million invested in them, much more like a relatively low-budget movie today than a traditional class. Of course, this won’t guarantee quality. But it will create interesting opportunities for new types of quality.
ha 🙂 that does seem like the way pearl would explain it!
i don’t, in general, think that saying the word ‘causality’ adds any explanatory power.
this seems to me to be a question about joint distributions, ie, which joint distributions give rise to this kind of situation? the answer doesn’t involve causality, just probability calculus. if other people find talking about causality helpful, that’s fine with me, i just find that it adds an unnecessary layer of complexity. latent variables are sufficient, whether or not they are causal.
Please let me say that “Reinventing Explanation” is one of the very best STEM-related essays that I have read. Thank you!
Particularly germaine is this concluding passage:
Material that supports this thesis includes:
• Politics Robert Caro’s The Years of Lyndon Johnson, Volume 4, the Passage of Power (1958-1964); the political narratives that passed the Civil Rights Acts.
• Song and Rhetoric Joan Baez and Bob Dylan singing, and Martin Luther King preaching, at the March on Washington for Jobs and Freedom (1963); the societal narratives that passed the Civil Rights Act).
It’s not so easy to extract just one narrative from this material … which is why it’s neither necessary, nor feasible, nor desirable that everyone think alike in this regard.
The same lessons apply more broadly to the 21st century’s STEM narratives, which draw narrative themes from deep wellsprings that include Phillip Pullman’s Dark Materials trilogy and David Deutsch’s TED Lecture A New Way to Explain Explanation (2009).
The former narrative nominally is for children; the latter nominally is for adults, yet the theme of individual and societal growth is central to both narratives. As Deutsch’s TED lecture puts it:
This is a principle that Philip Pullman’s characters Lyra Belacqua and Will Parry appreciate … and act upon with the fervor of 1960s civil rights activists.
Today, these same powerful, unifying narrative themes motivate us to accept imponderable risks and embrace new creative enterprises that are acting to dispel the stagnation that is harming so many young STEM researchers.
Specifically in regard to quantum dynamical flows, and the 21st century enterprises that are founded upon these flows, an exercise that generates fresh quantum-dynamical narratives — that point toward serious quantum research/enterprise opportunities — is to map Paul Grahams’s celebrated Y-Combinator essays onto quantum-physics narratives. For example:
Exercise 1 Transpose Paul Graham’s essay Beating the Averages (April 2003) into a quantum essay Hilbert-Style algebraic dynamics is Blub; Grothendieck-style algebraic dynamics is Lisp.
Exercise 2 Transpose Paul Graham’s essay Black Swan Farming (September 2012) into a quantum essay The Black Swans of Linus Pauling, John von Neumann, and Richard Feynman.
Exercise 3 Transpose Graham’s essay Frighteningly Ambitious Startup Ideas (March 2012) into a quantum essay The Transformed Roadmap of QIST-II.
In regard to fresh 21st century narratives (both quantum and otherwise) Graham provides sensible advice:
Conclusion The 21st century’s new quantum devices and quantum systems engineering philosophies — think D-Wave, for example — plausibly comprise “big things that are starting as deceptively small things” … precisely in the sense of Paul Graham, David Deutsch, and of course, Michael Nielsen too.
Thank you again, Michael, for this fine essay!
Thanks John, both for the kind words, and for the many interesting connections. I’ll look into some of them.
A question for you: do you have any recommendations for good books on systems engineering? Big picture, overview style. There’s a type of book I’m particularly thinking of – something like “The Non-designer’s design book” or “Drawing on the right side of the brain” – a book that is reasonably short and compact and sets out enough core principles to give someone an idea of what a field is about, while not trying to make them an expert.
By the way, if you enjoyed the Johnson bio, then I suspect you’ll enjoy Robert Skidelsky’s one-volume bio of John Maynard Keynes. Keynes and Johnson were, of course, completely different, but the bios are similar in that they both convey with great force what was remarkable about their subject.
(Skidelsky has a three-volume bio of Keynes as well. The one volume is adapted from it. This is a rare instance where I believe the adaptation is better than the original.)
In regard to systems engineering, two canonical references are Booton and Ramo’s article (1984) and Johnson’s book (2002).
These quotes pretty accurately sum-up my views on quantum systems engineering, particularly in regard to medical applications of it.
@article{Ramo:84,
Author = {R. Booton and S. Ramo},
Journal = {{IEEE} Transactions on Aerospace and Electronic Systems},
Month = jul, Pages = {306–9},
Title = {The development of systems engineering},
Volume = {{AES}–20}, Year = 1984}
@book{Johnson:2002ph,
Author = {Stephen B. Johnson},
Publisher = {JHU Press},
Title = {The Secret of Apollo:
Systems Management in American
and European Space Programs},
Year = {2002}}
Thanks for the recommendations, John.
Excellent blog. Very forward-looking perspective.
Would be interesting to cross-reference with some know examples of excellent explanations by today’s standards: Feynman series on physics; graphics in many Scientific American articles; Hans Rosling TED videos on global trends.
Maybe pull together a team of highly-rated professors (ratings often available on the web) and Hans Rosling; give them some specific problems to study (that are know to trip up students); then create materials they recommend; then have rated by actual students.