Posts Tagged ‘law of error’
Posted on 21 February 2012 by cjf
It may be that the presumed dichotomy between determinism and randomness is superficial and illusory. Determinism is the world view that events result from an unalterable causal chain. It models the world as a clock whose behavior can be inferred by scientific investigation. Stocasticity or randomness is the world view that uncertainty pervades experience. It models the world as a dice game with unpredictable behavior.
Many thinkers including Einstein, Buckminster Fuller, and D’Arcy Wentworth Thompson have argued in support of the traditional deterministic world view. However, Quantum mechanics, machine learning, and behavioral economics are three prominent areas which have helped realign modern thinking to apprehend that randomness and uncertainty may be fundamental and pervasive. Leonard Mlodinow in a 2008 book goes further and argues that randomness rules our lives.
In preparing for and discussing randomness at a recent meetup of the Ben Franklin Thinking Society, I started to gravitate to the hypothesis that uncertainty and determinism may be like inside and outside or concave and convex. They may be both real, both partially right and partially wrong, both revelatory and misleading. It may be that each perspective is a “tuning in” to only part of a reality that is both-neither.
Here are several ways to see the dual and co-occurant qualities of the stochastic and deterministic models or world views.
In a deterministic model of the world, the fixed set of laws that govern everything apply to every quanta of energy or their constituents. So computing the state of the world requires applying these fixed laws to each such quanta from some initial state and iterating through each picosecond of time. Clearly, this is computationally infeasible except for the computer known as Universe itself. So any effective simulation or calculation will entail estimates and approximations, that is, randomness. Unwittingly, randomness imposes itself into the system!
Conversely, in a stochastic model the relationships between data are given by frequencies with respect to their sample space, the set of possible outcomes. What could be more deterministic than the elementary counting of frequencies? Indeed probability is basically a form of advanced counting in ratios. Deterministic indeed!
Now consider measurement. The basis of a scientific model involves measurable parameters. Data are measurements. Science has determined that all measurements involve uncertainty. MIT physicist Walter Lewin puts it emphatically: “any measurement that you make without any knowledge of the uncertainty is meaningless!” Measurement theory is built upon the law of error which is a principle of the science of randomness. Hard data acquires its validity and persuasiveness from the science of chance!
On the other hand, the law of error is a central principle in statistics, the science of inferring probabilities from observed data. Such inference is the gold standard of scientific truth. The techniques of scientific inference are based on the mathematics of randomness. Like all mathematics, the theory is definite, rigorous, and repeatably verified by logic, proof and experiment. The sciences of probability and statistics are rigorous and deterministic like all mathematics!
Even in a fundamentally deterministic world, our understanding, decision-making, strategies, predictions, measurements, and designs are predicated upon uncertainty and randomness. To be effective we must be cognizant of these lingering unavoidable uncertainties.
Conversely, even in a fundamentally uncertain world ruled by randomness, pattern and order emerge and can be identified. To be effective we can and should seek the design and structure permeating through the apparent randomness.
From these considerations, I conclude that randomness and determinism always and only coexist. They are inseparable. Each provides a spectacular, incisive perspective on reality. The careful thinker or practitioner should be facile in using both types of models to get a more wholistic, more complete picture of the world in which we find ourselves. This is evidence that both-neither should be our guiding principle in seeking truth!
Do you find the argument compelling? Is it sound? Can you help me improve it? Do you see other ways in which these two models interpenetrate and interaccommodate? How do you see the interrelationship between determinism and randomness?
To better develop my understanding of a more complete set of models (beyond superficial determinism vs. stochasticity), I am excited about Scott E. Page‘s new and just started on-line video course on Model Thinking. I think we need many diverse models to sharpen our thinking and uncover subtleties in the complex systems and theories upon which our civilization is built. I am looking forward to wrapping my head around the 21 or so models in this course. You can register for the Model Thinking course by filling out the form at http://www.modelthinker-class.org/.
Finally, here are three good audio-visual resources that explore issues of randomness further:
 Click here to read my previous essay on randomness where arguments for determinism are discussed.
Posted on 20 April 2011 by cjf
The view that randomness impacts and shapes our lives in profound ways has been gaining traction since 2002 when Daniel Kahneman won the Nobel prize in Economics for his work with Amos Tversky in characterizing human weaknesses when facing uncertainty. My thinking on the subject was first awakened by reading Nassim Nicholas Taleb’s book Fooled by Randomness which will give anyone who imagines they can think “rationally” a healthy dose of humble pie. A more helpful discussion can be found in Jonah Lehrer’s How We Decide which pays heed to our brain’s strengths while acknowledging our weaknesses. As I relayed in a post on the brain, mind and thinking, Lehrer recommends thinking about your thinking process to strengthen its decision-making function. Recently I finished reading Leonard Mlodinow’s The Drunkard’s Walk: How Randomness Rules our Lives which provides an accessible, historically detailed, and elementary introduction to the sciences of randomness and uncertainty and shows how they rule our lives.
These books have started to change my thinking about the nature of reality itself: I see now that randomness and uncertainty have an essential role to play. Interestingly, I shunned probability and statistics, the sciences of randomness and uncertainty, in college because I was steeped in Euclid, logic, and Buckminster Fuller’s “generalized principles” in Synergetics. I wanted to design destiny with deliberate application of knowledge … to worship at the altar of scientific determinism. Fortunately, Bucky taught me to “dare to be naïve” so I have been open to the new evidence about randomness. Now I suspect that Bucky and I were a little off about this subtle subject. It isn’t surprising, probability and statistics are among the newer branches of mathematics having developed mostly after the calculus was well established. They have not had enough time to pervade our collective consciousness.
Do you think the world is fundamentally deterministic or random? What influences have shaped your thinking and biases about the subjects of randomness, uncertainty, probability, and statistics? Do you think the increasing focus on the role of randomness and uncertainty in our lives is an important trend?
Randomness Rules Our Lives
Is Mlodinow’s thesis that randomness rules our lives really so convincing? Evidently so. Mlodinow finds dramatic evidence of randomness in our economic lives. He retells the poignant story of Sherry Lansing who led Paramount Pictures to huge successes in seven consecutive phenomenal years. Then after three years of bad results, she left the company. Did Paramount let her go too quickly? Evidently so because the pipline she left behind was full of new hits that restored Paramount’s revenue and market share. Shouldn’t seven years of success earn the right to forgive a few bad years? What if another great leader happened to have their three consecutive bad years at the beginning of their tenure? Do we replace them before their ship comes in? Mlodinow cites many other examples including the fact that “And to Think That I Saw It on Mulberry Street” was rejected by publishers some 27 times before Dr. Seuss’ career launched. Mlodinow also shows that student grades are often random and independent of their skill and knowledge.
Should we insist that our students, our schools, and our business leaders perform, perform, and perform with no “bad” years allowed? Do you believe that performance results are somewhat random? We invest a lot in exam and executive performance. Given the evidence, is that wise?
One part of Kahneman’s Nobel-prize winning work addressed the conjunction fallacy. Let A, B, and C be statements represented by a colored circle in the venn diagram to the right. The only case in which they can be simultaneously true is in the small area where all three colors overlap. So it is much less likely (less area) for three statements to be simultaneously true than for any one of them to be true. However, when someone weaves a story filled with a lot of concrete details, it seems more vivid and hence more believable than the statements considered separately: that’s the conjunction fallacy. Evidence of people falling for this fallacy has been documented widely even in medicine and the court room. We humans are easily duped by a good story!
It is surprising that the Nobel prize for the work showing how “blind” humans are to the elementary logic of the conjunction fallacy was only awarded one decade ago! Humanity has only just yesterday identified this basic weakness in our cognitive function! Add to the conjunction fallacy the many other fallacies and biases that Taleb, Lehrer, and Mlodinow show us to be subject to and one can see that Emanuel Lasker who was world chess champion for 27 years got it right: “In life we are all duffers”!
What is the significance of our weakness in understanding uncertainty? Do these weaknesses of the human mind subject us to the ravages of randomness? Are they a consequence of an inherent randomness in reality? Or do they simply lead to the appearance of randomness?
Our weakness extends to our sensory organs and perception as well. Mlodinow notes
Human perception … is not a direct consequence of reality but rather an act of imagination. Perception requires imagination because the data people encounter in their lives are never complete and always equivocal.
Mlodinow illustrates the problem by explaining that the human visual system sends “the brain a shaky, badly pixelated picture with a hole in it” (due to the relative weakness of our vision outside the fovea and the blind spot). In addition to conjunction bias, the sharp shooter effect, the hot-hand fallacy, availability bias, confirmation bias, and more, it becomes evident that “When we look closely, we find that many of the assumptions of modern society are based … on shared illusions.” And his conclusion
It is important in our own lives to take the long view and understand that streaks and other patterns that don’t appear random can indeed happen by pure chance. It is also important, when assessing others, to recognize that among a large group of people it would be very odd if one of them didn’t experience a long streak of successes or failures.
What shared illusions do we hold? How often are our lives subject to pure chance events? How important is serendipity? Do you believe that a long series of failures or successes is just the result of luck? When is it luck and when is it skill? How can we tell the difference?
The problem of randomness is deeper still: even machine-enhanced human sensing and measurement are fundamentally random! In Walter Lewin’s excellent video introducing physics and measurement in MIT OCW’s Physics I course, he says “Any measurement that you make without any knowledge of the uncertainty is meaningless.” Understanding uncertainty is at the heart of scientific measurement. No physics experiment ever found an exact match between theory and the laws of nature: data points always appear at random! Then add in effects like Heisenberg’s uncertainty principle and we see that randomness and uncertainty are vital elements of experience: they are pervasive.
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