Category: Science

New discoveries, the scientific method, and all matters relating to the scientific study of the physical world

Combinatorial math and the impossibility of rationality

A perfectly rational entity maximizes the expected satisfaction of its preferences over all possible future lives it could choose to lead. I cannot begin to write down a number that describes the complexity of this decision problem, but I find the following thought experiment helpful. First, note that the number of motor control choices that a human makes in a lifetime is about twenty trillion… Next, let’s see how far brute force will get us with the aid of Seth Lloyd’s ultimate-physics laptop, which is one billion trillion trillion times faster than the world’s fastest computer. We’ll give it the task of enumerating all possible sequences of English words (perhaps as a warmup for Jorge Luis Borges’s Library of Babel), and we’ll let it run for a year. How long are the sequences that it can enumerate in that time? A thousand pages of text? A million pages? No. Eleven words. This tells you something about the difficulty of designing the best possible life of twenty trillion actions. In short, we are much further from being rational than a slug is from overtaking the starship Enterprise traveling at warp nine. We have absolutely no idea what a rationally chosen life would be like.

Russell, Stuart. Human Compatible: Artificial Intelligence and the Problem of Control. 2019. p. 232 (italics in original)

Related: How many unique English tweets are possible? How long would it take for the population of the world to read them all out loud?

Game theory and the limits of reason

I myself suffer from a morbid sense of despair, and even now, decades after I worked with von Neumann, I still find myself questioning our central tenet: Is there really a rational course of action in every situation? Johnny proved it mathematically beyond a doubt, but only for two players with diametrically opposing goals. So there may be a vital flaw in our reasoning that any keen observer will immediately become aware of; namely, that the minimax theorem that underlies our entire framework presupposes perfectly rational and logical agents, agents who are interested only in winning, agents who pose a perfect understanding of the rules and a total recall of all their past moves, agents who also have a flawless awareness of the possible ramifications of their own actions, and of their opponents’ actions, at every single step of the game. The only person I ever met who was exactly like that was Johnny von Neumann. Normal people are not like that at all. Yes, they lie, they cheat, deceive, connive, and conspire, but they also cooperate, they can sacrifice themselves for others, or simply make decisions on a whim. Men and women follow their guts. They heed hunches and make careless mistakes. Life is so much more than a game. Its full wealth and complexity cannot be captured by equations, no matter how beautiful or perfectly balanced. And human beings are not the perfect poker players that we envisioned. They can be highly irrational, driven and swayed by their emotions, subject to all kinds of contradictions. And while this sparks off all the ungovernable chaos that we see all around us, it is also a mercy, a strange angel that protects us from the mad dreams of reason.

Labatut, Benjamin. The MANIAC. Penguin Random House, 2023. p. 144-5. (italics in original)

Reading Kahneman’s Thinking Fast and Slow recently, at several points I was struck by what seemed like the unjustified assumption that people are competent at mental arithmetic. Specifically, that you can give a person a list of probabilities and payouts and then find it legitimately surprising that they can’t or don’t pick the best one. For people constantly immersed in calculation this may be puzzling, but I also have personal experience of highly intelligent and knowledgeable people struggling at (or being unwilling to even try) calculating what a certain percentage of a number is, like for a tip. Studies on the numerical literacy of the general public reveal a worrisome inability to properly gauge millions against billions.

When mathematicians, logicians, and game theorists forget that much of the population cannot or will not calculate, they miss the obvious cause of deviations from their predictions and theories.

Travis Rector on fossil fuel abolition

About 90% of climate change is from the extraction and use of fossil fuels. We need to stop. As Chapters 6 and 7 point out, this won’t be easy—especially when fighting against industries that stand to lose trillions of dollars from the energy transition. But the rapid growth of wind and solar shows us that it’s already happening. Our role is to help it happen even faster.

Rector, Travis A. “Preface.” In: Rector, Travis A. Climate Change for Astronomers: Causes, consequences, and communication. IOP Publishing, 2024. p. xxi

Also:

We are at a crossroads in the history of our 4.5-billion-year-old planet. These days in which we are alive are precious beyond measure, especially from the perspective of Earthlings who come after us. Every day the fossil fuel industry continues to exist makes our planet hotter, taking us more deeply into irreversible catastrophe. The only way out is to end the fossil fuel industry; the faster we do, the more we will save… It is incredibly important to fight the fossil fuel industry, which has captured world leaders and international climate negotiations.

Kalmus, Peter. “Foreward.” In: Ibid p. xxii

Our leaders are killing our kids

Oceans of ink have been spilled arguing that social media and smartphones are the reason young people around the world are not doing well.

While there may well be truth to that, to me the whole discussion seems like an evasion of the real issue: we are living in a world where our leaders are killing our kids, because they are unwilling to act on climate change even though it could bring about the end of our civilization. We live in a world where the people in charge are willing to condemn everyone who follows them to torment and destruction, all because they are unwilling to give up the conveniences of fossil fuels. The ‘leaders’ who are doing this are committing history’s most egregious crime against future generations and the natural world, yet our media and society keep treating them as the best of their kind: deserving of praise, wealth, and fancy state funerals when they reach the end.

The lesson that sends to young people is that the system does not value them in any way, and is happy to sacrifice their most vital interests for the sake of further enriching those who benefit from the fossil fuel status quo – which is not just billionaire fatcats, but billions of consumers in rich societies who take it for granted that big trucks and airplanes are the way to get around and who insist on political leaders who pretend to care about climate change, while being privately committed to keep supporting the fossil fuel industry.

Even the RCMP – an institution that sees itself as an ally (p. 41) of the fossil fuel industry – is warning about how our societal disregard for the interests of the young is fueling instability:

There is a notion of the social contract in which each generation is obligated to consider the interests of those who will come after. This covenant has been totally broken, with the almost inescapable consequence that intergenerational conflict will become more and more severe as the damage we have done to the Earth keeps destroying our ability to provide the well-off with what they feel entitled to.

Related:

Taleb on the domain dependence of knowledge

I used to attend a health club in the middle of the day and chat with an interesting Eastern European fellow with two Ph.D. degrees, one in physics (statistical no less), the other in finance. He worked for a trading house and was obsessed with the anecdotal aspects of the markets. He once asked me doggedly what I thought the stock market would do that day. Clearly I gave him a social answer of the kind “I don’t know, perhaps lower”-quite possibly the opposite answer to what I would have given him had he asked me an hour earlier. The next day he showed great alarm upon seeing me. He went on and on discussing my credibility and wondering how I could be so wrong in my “predictions,” since the market went up subsequently. Now, if I went to the phone and called him and disguised my voice and said, “Hello, this is Doktorr Talebski from the Academy of Lodz and I have an interrresting prrroblem,” then presented the issue as a statistical puzzle, he would laugh at me. “Doktorr Talevski, did you get your degree in a fortune cookie?” Why is it so?

Clearly there are two problems. First, the quant did not use his statistical brain when making the inference, but a different one. Second, he made the mistake of overstating the importance of small samples (in this case just one single observation, the worst possible inferential mistake a person can make). Mathematicians tend to make egregious mathematical mistakes outside of their theoretical habitat. When Tversky and Kahneman sampled mathematical psychologists, some of whom were authors of statistical textbooks, they were puzzled by their errors. “Respondents put too much confidence in the result of small samples and their statistical judgments showed little sensitivity to sample size.” The puzzling aspect is that not only should they have known better, “they did know better.” And yet…

Taleb, Nassim Nicholas. The Black Swan: The Impact of the Highly Improbable. Random House, 2007. p. 194-5 (italics in original)

Sagan on self-skepticism

Perhaps the sharpest distinction between science and pseudoscience is that science has a far keener appreciation of human imperfections and fallibility than does pseudoscience (or “inerrant” revelation). If we resolutely refuse to acknowledge where we are liable to fall into error, then we can confidently expect that error—even serious error, profound mistakes—will be our companion forever. But if we are capable of a little courageous self-assessment, whatever rueful reflections they may engender, our chances improve enormously.

Sagan, Carl. The Demon-Haunted World: Science as a Candle in the Dark. Ballantine Books, 1996. p. 21

Canada’s 2023 fires

Oliver Milman writes in The Guardian:

The impact upon the world’s climate will be even more significant than this. According to data from the European Union’s satellite monitoring service, more than 1.7bn tons of planet-heating gases have been released this year by the enormous fires – about three times the total emissions that Canada, a major fossil fuel-producing nation, itself produces each year.

Such huge emissions, eclipsing in a single year any measure, however ambitious, to cut pollution from cars or factories by a country like Canada, are a major drag upon efforts to stem the climate crisis. The majestic boreal forests, much like the Amazon rainforest that now emits as much carbon as it sucks up and is tipping towards becoming a savannah, suddenly appear to be a danger to the world’s climate rather than a key safeguard.

The world has ignored the imperative to stop worsening climate change through fossil fuel use for at least three decades now. The planet is starting to gravely reflect that mistreatment, and doing so in ways that worsen future disruption.

A broad-ranging talk with James Burke

As part of promoting a new Connections series on Curiosity Stream launching on Nov. 9, I got the chance to interview historian of science and technology, science communicator, and series host James Burke:

The more interview-intensive part begins at 3:10.