Thursday, March 22, 2012

We're Just Getting Started: A Glimpse at the History of Uncertainty

We've had our cerebral cortex for several tens of thousands of years. We've lived in more or less sedentary settlements and produced excess food for 7 or 8 thousand years. We've written down our thoughts for roughly 5 thousand years. And Science? The ancient Greeks had some, but science and its systematic application are overwhelmingly a European invention of the past 500 years. We can be proud of our accomplishments (quantum theory, polio vaccine, powered machines), and we should worry about our destructive capabilities (atomic, biological and chemical weapons). But it is quite plausible, as Koestler suggests, that we've only just begun to discover our cerebral capabilities. It is more than just plausible that the mysteries of the universe are still largely hidden from us. As evidence, consider the fact that the main theories of physics - general relativity, quantum mechanics, statistical mechanics, thermodynamics - are still not unified. And it goes without say that the consilient unity of science is still far from us.

What holds for science in general, holds also for the study of uncertainty. The ancient Greeks invented the axiomatic method and used it in the study of mathematics. Some medieval thinkers explored the mathematics of uncertainty, but it wasn't until around 1600 that serious thought was directed to the systematic study of uncertainty, and statistics as a separate and mature discipline emerged only in the 19th century. The 20th century saw a florescence of uncertainty models. Lukaczewicz discovered 3-valued logic in 1917, and in 1965 Zadeh introduced his work on fuzzy logic. In between, Wald formulated a modern version of min-max in 1945. A plethora of other theories, including P-boxes, lower previsions, Dempster-Shafer theory, generalized information theory and info-gap theory all suggest that the study of uncertainty will continue to grow and diversify.

In short, we have learned many facts and begun to understand our world and its uncertainties, but the disputes and open questions are still rampant and the yet-unformulated questions are endless. This means that innovations, discoveries, inventions, surprises, errors, and misunderstandings are to be expected in the study or management of uncertainty. We are just getting started. 


  1. Hi Yakov. I think you meant to say that the 20th century saw a flourishing, not floresence (the word probably does not exist, but the similar "fluoresence" means something else)

    It is remarkable that the ancient Greeks did not invent or study probability, even though they must have enjoyed games of chance (even athletic competitions, funereal games, and the Olympics had a ton of uncertainty, and if they had none they would have been boring as hell to watch!)

    Games of chance was what really started modern probability theory with Pascal, Laplace, the Bernoullis and others.

    I read a two-volume set of biographies of mathematicians, ancient and modern, and just remembered a story about Bernoulli, who introduced himself to somebody, saying "Hi, I'm Daniel Bernoulli" or something like that, but the other guy did not believe that he was THE Bernoulli, so he replied sarcastically "Hi. (And) I'm Isaac Newton!"

  2. Yakov, hello,
    Science is indeed new, and the science of uncertainty is very young indeed, and I share your optimism in expecting its growth and development. However, the first statement in this blog, that we have our cerebral cortex for only few tens of thousands of years, left me puzzled. I remembered that I had my own cerebral cortex in place for quite a long time... I mean, I remembered learning that our ancestors had an identical anatomy to ours for two hundreds of thousands of years ago.
    So, I searched the literature on recent human evolution, which I have meant to do long ago anyway. I found that in fact there is a hot debate about this very issue. Estimates for the first time when human anatomical structures largely resembled ours, range from as early as 200K YBP (years before present) to as late as 40K YBP. One particularly good article (in my opinion) is:
    It seems to support the notion that early homo sapiens had an anatomy just like ours some 150K YBP, but he mentiones the rationale for the alternative plausible claim, which maintains that the modern homo sapiens were substantially differnt than their predecessors in their materialistic culture and behaviour, implying that they had different brain structures.
    My personal opinion is that human mental capacity is much older than its resulting products and technologies. There are major differences between the Technologies of the 18 century and the 20 century, but we do not invoke brain evolution as an explanation. Yet, some archaeologists interpret any change in the shape of the flint stones at a site as an indication of brain structural change. I understand the frustration of having to learn about such a complex topic as human brain evolution from piles of flint stones. Yet, I believe that humans had the capacity for 'soft hammer flaking techniques' -- long before they have left flaking remains all over the place. So I would think a useful cerebral cortex is as old as homo sapiens, which is believed to be around a quarter of millions years ago.
    I do not imply that we now realize its potential. On the contrary, having this structure for so long, one wonders how come we can not use it wisely to overcome current dilemmas and conflicts. , such as the tragedy of the commons... Perhaps there is a need for a novel expanded cortex, which will enable humans to solve such inherent conflicts…

  3. This blog really captivates readers to read. It gives a lot of information. Thanks for sharing :) #howtocloseteethgap