When Scientists Reject the Mathematical Foundations of Science

The Final Truth of Molecular Mechanisms

The reasonings about the wonderful and intricate operations of nature are so full of uncertainty, that, as the Wise-man truly observes, hardly do we guess aright at the things that are upon earth, and with labour do we find the things that are before us.

- D’arcy Thompson

In my previous post, I introduced Max Born’s 1954 Nobel speech. In it, he warned against the illusion of final truths and called instead for Lockerung des Denkens — a “loosening of thinking.” This wasn’t a call for relativism. It was a demand for rigor — for submission to something greater than ourselves: the probabilistic laws of nature.

Born believed that the higher laws of uncertainty serve as an antidote to the final truths of authoritarianism. But what happens when scientists reject those very laws?

What happens when science itself becomes authoritarian?

The Micro-Macro duality: A Scientific Truth Rejected

More than 25 years ago, we observed in muscle something extraordinary. Its irreversible macroscopic kinetics and energetics follow Boltzmann’s equation, S(t), and cannot be determined from the reversible microscopic kinetics and energetics of its molecular parts, s(t) (here).

We then proved this micro-macro duality mathematically (here and here).

The macroscopic behaviors of muscle emerge from the behavior of all possible molecular configurations, not from deterministic trajectories of individual molecules (here).

No one has ever refuted this model. Not scientifically. Not mathematically.

And yet, it has been categorically rejected.

Why?

Because it removes causal control from the hands of scientists. It places authority in the ensemble, S(t), not in the individual, s(t). It challenges the illusion that we control molecular mechanisms.

Scientists Reject Math and Science in Defense of Their Causal Authority

In 1999, I submitted our first report of the observed micro-macro duality in muscle to Biophysical Journal (here). The reviewers demanded I remove any mention of S(t). In a personal correspondence more than 25 years ago, the editor explained:

Your equations seem to be completely empirical and… don’t force me to abandon my strongly held microscopic thermodynamic (Hill formalism) overall concept of the mechanism.

This admission was revealing: evidence and mathematics were less important than preserving an existing belief.

That belief — codified in Hill’s formalism — grants its believers causal authority over molecules, s(t). It allows them to mathematically instruct molecules how to move, untethered from physical law, S(t).

This is precisely the approach of geocentrists who once believed they could mathematically instruct celestial bodies how to move, untethered from physical law.

But just as Newton’s laws discredited geocentrism, Carnot’s laws — formalized by Clausius and extended by Boltzmann, S(t) — discredit the Hill formalism.

I have since shown that S(t) accurately accounts for most key aspects of muscle contraction (here and here).

And still, Hill’s framework persists — not because it’s right, but because it satisfies scientists’ desire for control over molecules.

The Molecular Power Stroke Illusion

According to Hill’s formalism, muscles shorten via the shortening strokes of molecular springs, s(t). Over the past 70 years one version of this model has replaced another. No consensus. No convergence. Just an endless carousel of different molecular power stroke mechanisms.

These black box power stroke mechanisms are mathematical contrivances designed to force molecular behaviors to recapitulate muscle power output. They give scientists control over nature.

And here’s where it really gets dishonest.

The actual molecular mechanism of muscle contraction is not a black box of shortening springs; it’s a force-generating switch that stretches a spring (here) — a mechanism opposite that of a molecular power stroke.

Absent any evidence for a molecular power stroke mechanism, scientists preserve their mythology of causal control through sleight of hand. They rebrand the observed switch a “power stroke”.

In one paper after another, they maintain the molecular power stroke illusion:

• by concealing from readers the irreproducible black box power stroke mechanisms that generate power output in their models.

• by deceiving readers into believing that the switch they label “power stroke” is the mechanism of power output in their models.

This misrepresentation of their results is intentional. For decades, I’ve argued against this rhetorical fallacy. And for decades they’ve defended it based on their belief in molecular power strokes — a belief so strong that they abandon reason to manifest a molecular power stroke mechanism that isn’t a power stroke.

They Know. They Just Don’t Like It.

For 25 years I’ve presented the data, developed the science, and shown the math demonstrating that muscle’s power stroke is macroscopic and occurs with the shortening of an ensemble of force generating switches, S(t).

A force-generating switch is the opposite of a molecular power stroke mechanism. Force-generating switches do not CAUSE muscle shortening; they occur as the RESULT of muscle shortening (here).

And we’re not the only ones to have observed this.

The editor who rejected S(t) in 1999 wrote of an experimental result of theirs at the time:

This result… raises a question in my mind whether the tilting CAUSES the sliding or is the RESULT of sliding.

Unfortunately, this result and conclusion were never published.

For 25 years, I’ve argued directly with the very scientists who continue to promote molecular power stroke models. They’ve seen the data. They’ve seen the math. They’ve never refuted it.

They simply don’t like what it implies.

This has never been a rational scientific debate. It’s been a decades-long heavy-handed defense of an ideology. They reject math and science, S(t), in defense of their causal authority over molecules, s(t).

When Science is No Longer a Debate

I recently reiterated these concerns in a letter to the editor in response to yet another molecular power stroke model published (here) in the Biophysical Journal by colleagues Walcott and Debold (the three of us were postdocs in the same lab). They and other cosigners replied with an appeal to consensus: WE believe in molecular power strokes!

Just seven months later, circling the wagons, PNAS published still another molecular power stroke model (here).

The lead authors? Walcott and Debold.

The accepting editor? The editor who rejected S(t) in 1999.

The subject? Phosphate binding in muscle under load — the focus of my 25 year research career.

The number of citations to my substantial body of work on the subject? Zero. Out of 82 references listed.

This wasn’t an oversight. We’ve all worked together. For decades we’ve debated this controversy face-to-face in laboratories, at conferences, in bars, and on slopes and trails. They know exactly what they’re omitting — and why.

Molecular springs in muscle randomly fluctuate. They do not directionally shorten. That function belongs to the system, not its parts.

Muscle power output is caused by an increase in macroscopic entropy described by Boltzmann’s equation, S(t), not by deterministic strokes at the molecular level. I’ve demonstrated this experimentally and proven it mathematically.

Defending the Illusion

As I wind down my research program, I reflect not on failed ideas, but on the ones that never made it past these gatekeepers. They include:

• A thermodynamic derivation of irreversible chemical kinetics (here)

• A statistical proof of the micro-macro duality (here)

• A single statistical solution to Maxwell’s demon, Schrödinger’s cat, Gibbs’ paradox, and Loschmidt’s paradox (here)

Over the past several years, six of these manuscripts were back-to-back triaged by editors at PNAS. Other lower tier journals rejected them for reasons ranging from “it would overturn decades of work” and “it’s wishful thinking” to reasons unexplained. An editorial decision in the journal Entropy flipped from a provisional accept to reject followed by radio silence from the journal.

A Biophysical Journal advisory board rejected some of these manuscripts. In one case, an editor explained that a manuscript was rejected — not because the science was flawed but — because the reviewers they would choose would reject it with near certainty. The editor confessed: “I am totally sincere with my advice to look for another journal – BJ is not the right place for this study.”

They could have put a proper scientific end to this 25 years ago by finding a flaw in Boltzmann’s equation, S(t). They never did. They never could.

Instead, these modern day geocentrists intentionally buried the truth in defense of their imagined causal authority. They knowingly and repeatedly chose rhetorical sleight-of-hand over scientific integrity. They maintained their causal authority not by evidence or reason, but by systematically rejecting both.

When Scientists Abandon the Higher Authority of Science for Their Own Authority

Some of these scientists are now retreating to arguments based on postmodern relativism. “There is no truth,” “All models are wrong.”, “It’s just the way we like to think about it.”

But when we trade in the higher authority of science, S(t), for our preferences, s(t), we dismantle the very foundation of science. We no longer discover — we decide. And we decide based — not on nature’s laws of uncertainty but — on our own causal illusion of how nature works.

This is the final truth that Born warned about. It’s the narrowing of Kauffman’s adjacent possibilities. It’s Hayek’s fatal conceit. It’s the scientific authoritarianism — exposed here at its most basic level — that has eroded public trust in science.

Figure generated by ChatGPT with one attempt using the prompt: “create an image of science and the tyranny of human authority”.