Correlation is not causation

[Larry T.]

[Rene]

On 25 Oct 2025, at 02:44, Larry T. <ora...@gmail.com> wrote:

<image of a cat on a damaged roof along with caption, "Correlation is not causation">

The context for Larry's post was Tomchak & Morse's (T&M) article re "some new evidence in favour of group 3 as Sc Y Lu Lr". I now suggest that it's interesting to consider how correlation and causation apply to the periodic table.

Hi Larry

You’re right: correlation isn't causation.

However, I’m not claiming causation—rather I’m using correlation (smoothness) as a diagnostic proxy for periodicity, a long-standing and legitimate practice in periodic-law analysis.

In this instance, there is a causal relationship between Z and the properties of the elements. Each increase in Z introduces an additional proton and electron, altering the electrostatic potential and the way electrons occupy available energy levels. These changes in electronic configuration are associated with the periodic variation in chemical and physical properties that we observe. The correlations we measure—whether in bond energy, ionisation potential, or electronegativity—therefore (as I understand it) trace back to this underlying quantum structure. In the periodic law, correlation isn't a substitute for causation but is its direct empirical expression.

What’s interesting is that when the T&M dataset is expanded to include the additional, relevant carbides, the (much) smoother trendline appears with La, not Lu. This doesn’t undermine their work—they were on the mark in seeking to gauge which of La or Lu appeared to sit better in group 3; rather, it suggests that extending the dataset broadens the perspective and strengthens the analysis.

It reminds me that, as with studies of periodicity generally, our understanding deepens when the evidence is viewed as part of a wider context.

I’m also reminded that Mendeleev discovered the periodic law by noticing correlations long before their theoretical basis was better understood—and that spirit of open-ended discovery still serves us well today.

Thanks for expanding the scope of the discussion.

I look forward to your further thoughts in this matter.

René

[ERIC SCERRI]

Rene

Have you corresponded with the authors of the study?

Eric

On Oct 26, 2025, at 3:23 AM, 'Rene' via Periodic table mailing list <PT...@googlegroups.com> wrote:



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[Rene]

On 27 Oct 2025, at 05:07, ERIC SCERRI <sce...@g.ucla.edu> wrote:

Rene

Have you corresponded with the authors of the study?

Eric

Not yet Eric, but I may do so—thank you. My intent in posting to this thread, in response to Larry’s "cat on a tin roof" 🐈‍⬛ contribution, was to test my reasoning with him and with list members.

There are some further nuances to consider, including your position from 2020 (mentioned below).

Background and earlier work

My suggestion to extend the dataset of Tomchak & Morse in order to broaden the perspective and strengthen the analysis is based on something I’ve learnt to do since my article on the Group 3 question appeared in Foundations of Chemistry in 2020:

https://link.springer.com/article/10.1007/s10698-020-09384-2 (open access)

I said then that:

“The question of the composition of Group 3 has been debated from time to time on the basis of physical (including spectroscopic), chemical, and electronic properties and trends, without resolution.

Scerri (2020, p. 381) observed—and I agree—that the matter cannot be resolved using this rubric, since the two options are effectively indistinguishable."

Scerri E 2020, The Periodic Table: Its Story and Significance (2nd ed.), Oxford University Press, New York

Expanding the 2020 dataset

In that article I examined the trend smoothness of six properties v Z and confined my dataset to Sc-Y-La-Ac or Lu-Lr.

By trend smoothness I mean the degree to which a property varies regularly with Z, quantified by the coefficient of determination (R^2) for a second order polynomial fit. A higher R^2 indicates a more continuous and predictable variation in the property—one of the simplest empirical signatures of periodic regularity.

Since then, I’ve expanded the dataset to 40 properties—22 chemical and 18 physical—going down B-Al-Sc-Y-La or Lu (and sometimes Ac and Lr). I aimed for roughly a 50:50 balance between physical and chemical properties but eventually ran out of physical ones to include.

As I noted, the average smoothness margin is about 6% in favour of La in Group 3.

That may not seem large, but 30 of the trendlines favour La, nine are too close to call, and one favours Lu (first ionisation energy). Excluding ties, the likelihood of 30 of 31 trendlines being in La’s favour on the basis of random variation has a probability of roughly 1 in 67 million.

Caveats on trendline smoothness

I nevertheless do not claim that this is necessarily a categorical argument, given the placement of H over Li and B-Al over Ga.

Thus, while H fits much better over F than Li on the basis of trendline smoothness (John, to note please), the chemical community nevertheless regards H’s proclivity to initially lose its single electron—in the manner of an alkali metal—as being more important; hence H is routinely placed over Li.

Similarly, while the p elements B-Al fit better in terms of trendline smoothness over the d element Sc than the p element Ga, the chemistry community regards block consistency (in this case) as more important so B-Al are positioned above Ga.

Revisiting the Group 3 issue

All that said, I find it hard to conceive of an overriding argument for placing Lu in Group 3. Yes, placing La in Group 3 yields a split d-block in the 32-column periodic table, and this simply reflects the widely noted delayed onset of the first f electron. In contrast, there are no such delayed starts in the other blocks. Philosophically, the combination of (i) the delayed onset of the first f electron and (ii) upholding chemical periodicity are regarded as being more important than diagrammatic tidiness.

Lu can, of course, be placed in Group 3; however, this introduces several irregularities elsewhere including four at the start or end of blocks i.e. having the f-block begin with three d elements (La-Ac, Th) and the 6d row beginning with a p element (Lr).

In contrast, with La in Group 3, such start or end irregularities are limited to three cases within the f-block itself: Th and Lu-Lr.

René