Responding to scientific uncertainty

Science provides an impressive path to certainty in some areas, particularly in physics. However, as scientists seek to describe increasingly complex entities, moving from chemistry to biology, and then to humans and societies, the level of uncertainty increases.

One observes a wide range of responses to scientific knowledge being uncertain. Here are a few.

Denial. Science is about facts and absolute truth. There really isn’t a problem. We should just trust the scientists.

Minimisation. There is some uncertainty, but it isn’t anything to be concerned about. Some scientists will also minimise any uncertainty about their own research. This may occur because of career ambition. Others will minimise public discussion of uncertainty to try and avoid promoting the science scepticism discussed below.

Optimistic perseverance. The uncertainty is openly acknowledged. Some of the uncertainty does not matter for what we need to know. Other uncertainties can be reduced by further scientific work, such by more precise measurements with new instruments or by developing more sophisticated theories.

Total scepticism. There is a suspicion about the validity of most scientific knowledge, particularly that which is perceived to have philosophical, religious, or political implications.

Suspicion about science

In spite of the success of science at describing the material world and leading to powerful and useful technologies, there is much public suspicion of science. On the one hand, this is understandable given that science has led to technologies with undesirable health, environmental and social consequences. Some scientists, governments and companies have lied about these consequences and hidden them from the public. Human subjects have been abused in medical experiments. Drugs that were claimed to be effective and safe turned out to be ineffective or have undesirable side effects. Science has been used for ideological purposes. Sometimes scientists have faked results to advance their own careers. However, these failures should not undermine our trust in reliable scientific knowledge. Distinctions should be made between the bodies of knowledge, the applications of that knowledge, and the actions of institutions. I now discuss several common claims in public discussion that are used to justify scepticism of scientific knowledge.

Science is always changing. 

One day, scientists tell you that chocolate is good for your health, and the next year they say it is bad for you. And that is just the start. Then there are eggs, wine, running marathons, and cheese. They just can’t make up their mind. So why should we trust them? At one time, they believed in phlogiston and the aether. Now they say they don’t exist. Aristotle was replaced by Newton, who was replaced by Einstein. So why believe in human-induced climate change, biological evolution, vaccines, the Big Bang theory, or Einstein’s theories?

It is true that scientific knowledge does develop and change over time. However, today we have incredibly detailed observations and theories in physics, astronomy, chemistry, biology, and geology. Any future changes will be relatively minor because they will have to be consistent with all the knowledge we have now. Furthermore, when theories change, such as when Einstein superseded Newton, they don’t show that the old theory was completely wrong, but rather that it applied in a limited domain. For example, Newton’s theories of motion and gravity are extremely reliable when it comes to objects that are much larger than atoms, less dense than a black hole, and are moving at speeds less than about 10,000 kilometres per second. This is why engineers spend years learning Newton’s theories, not Einstein’s. If you want to build a good bridge or a rocket, Newton is good enough. He is not wrong.

Update. (Jan. 19). I just discovered that the NY Times had a recent op-ed Science Keeps Changing. So Why Should We Trust It?

“Well, that’s just a theory.” 

In popular debate, such a refrain may be applied to the theory of biological evolution, the Big Bang theory in cosmology, or human-induced climate change. The claimant usually wants to dismiss a particular theory as just idle speculation. Here, the term “theory” is used in the same sense as everyday speculations, such as “I have a theory as to why the president resigned,” or “I have a theory about why my computer is running so slowly.” These are just stories that sound somewhat plausible. In contrast, scientific theories in physics, such as quantum theory and Einstein’s theories of relativity, have precisely defined mathematical formulations that have been checked for logical consistency, made specific predictions, and tested to great precision in experiments. They are not “just theories.” For example, for the Big Bang theory about the beginning of the universe and Darwin’s theory of biological evolution and diversity, there are many independent lines of evidence that are consistent with each theory.  

Scientists cannot be trusted. 

They are not committed to the truth, but rather to their own interests and agendas, related to their careers, politics, and religion. They close ranks and support the status quo of current scientific “dogma”, rather than being open to original thinkers who critique it and propose alternative theories. They don’t want to lose their well-paid jobs and lucrative grants. 

On the one hand, scientists can be conservative and resistant to new ideas. On the other hand, there are significant career incentives to overturn existing knowledge and have your radical new theory accepted. That is how some scientists become famous and win Nobel Prizes. The reasons it does not happen very often are not necessarily for social or ideological reasons. Many of the theories we have today can explain an awful lot. It requires a lot of evidence, carefully acquired and checked, to convince people that those theories need to be modified, let alone abandoned. This may take decades. But it does happen. An example is the Big Bang theory of the universe, whose acceptance was initially resisted because it went against the prevailing view that the universe did not have a beginning. In biology, the discovery in 1970 of the enzyme reverse transcriptase went against a popular version of the “Central dogma” of molecular biology that DNA was always converted to RNA and not the reverse. That discovery led to a Nobel Prize.

I don’t trust scientists. I will do my own research. There is lots of good material from unbiased sources on the internet.

The internet provides a range of information and perspectives on practically any issue imaginable, including science. The material is particularly vast and controversial on biological evolution, the beginning of the universe, fundamental physics, the age of the earth, climate change, and medicine. Since the covid-19 pandemic, scepticism of the effectiveness and safety of vaccines has increased. 

Ivermectin is a drug that was developed as a treatment for parasite worms. Its incredible success was recognised by the award of the 2015 Nobel Prize in Physiology or Medicine to William Campbell and Satoshi Omura, who discovered the drug. During the pandemic, high-profile politicians and social media influencers promoted ivermectin as a treatment for covid-19, even after systematic medical studies showed it was ineffective. Recently, it has gained a reputation as a “miracle” drug that can even cure cancer, but this is being suppressed by the medical establishment. All clinical trials have shown the drug is ineffective for human ailments, beyond deworming. Nevertheless, there are groups on social media with hundreds of thousands of members that discuss the conspiracy, how to get the drug, and the experiences of participants using it to treat a wide range of ailments. Danny Lemoi, a founder of one of the largest groups, died in 2023 after taking massive daily doses of the drug for several years to treat a heart condition. Afterwards, one member of the group wrote “No one can convince me that he died because of ivermectin. He ultimately died because of our failed western medicine which only cares about profits and not the cure.”

Fans of ivermectin claim that they are escaping the biases and vested interests of the medical establishment and Big Pharma as they pursue the truth. However, they are not escaping bias and vested interests. Successful social influencers build their reputations and million-dollar incomes from promoting scepticism. If there is no conspiracy, just scientific uncertainty and occasional incompetence and malpractice, their following collapses. Populist politicians build their careers on criticism of and stoking resentment towards elites, such as the medical establishment. The authority of the medical establishment is replaced with the authority of the popular opinion of a group of people whose views are shaped by social media algorithms, intuition, and anecdotal experience.

My purpose in giving the example of Ivermectin is not to start a detailed critique of science scepticism. Rather, it is to illustrate the role that the interplay of trust, authority, and tradition plays in how we determine what is true and what to act on. There are two competing traditions here: the populism of alternative medicine and the elitism of professional medicine. Each has its own sources of authority. In the end, it boils down to who we trust. We do not have the time, energy, resources or inclination to check the veracity of every single piece of information we have access to. We take shortcuts. This is what tradition does for us, for better and worse. Thus, we cannot escape tradition. We are all swimming in traditions, many of which are in conflict with one another. The question is whether we are aware of it and what we do with that awareness.

What is temperature?

Temperature is NOT the average kinetic energy.

When I taught thermodynamics to second year undergraduates one of the preconceived notions that was hard to dislodge from students was that temperature IS a measure of the average kinetic energy of the atoms or molecules in a system.

First, I will give the merits of this view and then explain why it is problematic.

A profound and important insight from Maxwell's kinetic theory of ideal gases was that the average kinetic energy of the atoms/molecules in the gas is related to the absolute temperature defined by Kelvin. This result was important because it provided a microscopic basis for Joule's discovery of the mechanical equivalence of heat.

The result does not just hold for an ideal gas. Classical statistical mechanics can be used to show that for any system of interacting particles, the average kinetic energy of each particle is 3/2 kT. The proof proceeds in the same manner as the equipartition theorem. In the partition function, the integral over momentum factorises and can be evaluated exactly as it is Gaussian integral.

However, this simple relationship between temperature and kinetic energy does not hold for quantum systems. Consider the case of a harmonic oscillator, with frequency omega. By the virial theorem, the average kinetic energy is equal to the average potential energy. Thus, the average kinetic energy is half of the internal energy U(T), which is a universal function f(T/omega). Thus, if we compare two oscillators with different frequencies, at the same temperature, they will have different kinetic energies.

This problem is not just some quantum exotica that is only relevant at extremely low temperatures. Most solids are "quantum" at room temperature because they have a Debye temperature in the range of 200-1000 K.

Temperature is a macroscopic variable, not a microscopic one. It should be defined in terms of the zeroth law of thermodynamics.

Temperature is a state variable associated with a system in thermal equilibrium. It tells us whether that system will be in thermal equilibrium with another system. Consider two separated systems with temperatures T1 and T2. If they are brought into thermal contact, their states will not change if and only if T1=T2.

A thermometer is a system with a single state variable. The value of that variable is an empirical temperature.

Aside. This view of temperature was used by Planck in his book, Treatise on Thermodynamics, first published in 1905.

I am thankful to my undergraduate mentor, Hans Buchdahl for teaching me that thermodynamics is conceptually coherent and beautiful. 

This discussion illustrates that temperature is an emergent property. It is a property of a macroscopic system that the parts of the system do not have. The temperature is independent of the microscopic composition of the system or its history. This universality is a characteristic of many emergent properties.

In another post, I hope to explain what the absolute temperature, first introduced by Kelvin, is.

Maxwell's demon and the history of the second law of thermodynamics

I recently reread Warmth Disperses and Time Passes: The History of Heat by Hans Christian von Baeyer

As a popular book, it provides a beautiful and enthralling account of the discovery of the first and second laws of thermodynamics. The book is a great companion to teaching and learning thermodynamics and statistical mechanics. The narrative is unified by the puzzle of Maxwell's demon.

Aside: The book was first published in 1998 with the title Maxwell's Demon. My guess is that the publisher changed the title because most people have probably not heard of the demon, unlike Schrodinger's cat.

Baeyer captures both the wonder of the subject and the fascinating story of how the science of thermodynamics developed. He describes quirky personalities and illustrates how science proceeds with a mixture of brilliant insights, clever experiments, false leads, and forgotten discoveries. It is easy and compelling reading.

I appreciated that there is a lack of hype, in contrast to too many popular science books.

The book is enhanced by showing that the story is not over. Many reports of the demise of the demon have been premature. The penultimate chapter discusses Zurek's definition of entropy in terms of algorithmic randomness. The last chapter considers molecular motors, such as kinesin, which can be viewed as ratchets driven by thermal noise.

Physical insights

The first and second laws tell us something about the fundamental nature of the universe. Although they are macroscopic and may have some (debatable) microscopic justification,  they can be viewed as fundamental.

Central to the development of the first law was the notion of the mechanical equivalent of heat.

There are three rather different ways to formulate the second law: a Carnot cycle represents an engine of optimal efficiency, heat never passes from a cold to a hot body, and the arrow of time. It is profound that these formulations are equivalent and not something that was anticipated. We should marvel at this.

Entropy can be viewed as the absence of information. Consequently, the second law can be viewed as statistical.

Things I want to understand

A good book stimulates us to want to engage more with its subject. Some things I want to understand are the entropy of the initial state of the universe, Boltzmann's H theorem, Feynman's ratchet, Shannon's information theory, molecular motors, Zurek's definition of entropy, and Gerald Holton's book, Thematic origins of scientific thought.

A recent tutorial is A Friendly Guide to Exorcising Maxwell’s Demon, by A. de Oliveira Junior, Jonatan Bohr Brask, and Rafael Chaves

Beautiful things missed

As a popular book, I think the length and scope of topics are right. Nevertheless, in a longer book, here are some things I would enjoy reading about: the zeroth and third laws, the contributions of Gibbs, the ergodic hypothesis, Brownian motion and evidence for atoms, the role of thermodynamics (and statistical mechanics) in the development of quantum theory (blackbody radiation, Einstein solid, identical particle statistics, and the Sackur-Tetrode equation) and perhaps phase transitions.

Two quibbles

von Baeyer has a somewhat reductionist perspective that the true nature of thermodynamics was revealed by the microscopic descriptions of Maxwell and Boltzmann.

I will write separate posts on why I am not comfortable with the following two statements.

Temperature IS the average kinetic energy of molecules.

Entropy was mysterious until Boltzmann's definition S=k ln W. 

My best blog posts of 2025?

 Best wishes for the New Year!

Here is a list of the posts that I wrote last year that I hope get the most interest.

My review article on emergence. I wrote posts about emergence in a range of systems: thermodynamics, quantum gravity, economics,... They were drafts of sections for my review article. It may be best to just read the article.

Why is the state of universities such an emotional issue for me?

Undergraduates need to learn about the Ising model

I wrote a series of posts on so-called "spin-crossover" compounds. Here are two: Spin crossover is a misnomer, and Elastic interactions and complex patterns in binary systems

2025 Nobel Prize in Physics: Macroscopic quantum effects

As always, I welcome comments, feedback, and suggestions for new posts.