You cannot make any sense of the periodic table without whole numbers.
Of course you can—just use the subset of reals that have integral values.
I’d have to dig up an old copy of the Brittanica, but IIRC, it didn’t even have one element per square.
This article has some relevant examples of 1880-1930 period tables that are quite different from what we’re used to. You can sorta see how the older ones might have given rise to the current one, but it takes a lot of squinting. It also readily demonstrates how different insights occurring in different orders might have sent things spiralling off in a very different direction.
Clearly it evolved from something and become more correct over time but the original claim was that the current one in the Encyclopedia Britannica would be unrecognizable to Americans. Did British and American scientists ever use substantially different versions?
You may be under the misconception that the Encyclopaedia Britannica is published in Great Britain. It was published in Scotland during the 18th and 19th centuries, but since about the beginning of the 20th century, it’s been published in Chicago.
Ignorance fought. Thanks.
That makes the claim even odder.
I didn’t say the current one; I said the one that was current circa 1990. Which is still pretty recent (at least, recent enough that the actual knowledge behind the table was substantively the same).
EDIT: I think it might have been something like the “short form”, in the first image in @LSLGuy 's link. Though of course with the elements discovered since 1930 also added.
You definitely did say 1990 in a previous post but I am still skeptical that what I now understand to be an American publication had a different periodic table than the one that was in classrooms that I saw starting in the late 1970s.
I first took chemistry in the 1980s and taught chemistry in the 1990s and early 2000s. The periodic table has not changed significantly over that time period.
Sometimes the lanthanides and actinides are included in the table to show how the f-orbital elements fit into the table instead of putting them below. And they renumbered the columns (chemical groups) a while back. That’s about it.
I’ve never seen a “short-period form” of the periodic table in any textbook over the last 40 years.
Now that’s funny …
Back in the 1980s I bought a reprint of the IIRC 1911 EB; might’ve been as early as 1890-something. Three metro phone book sized volumes. It was remarkable how different everything in it was. The prose, the diagrams, the “pedagogy” if you will. Setting aside of course all the stuff that’s part of a 1980 or 2026 EB that was simply unknown in 1911.
So primed by that experience when I read @Chronos comment about different periodic tables, I assumed he’d meant the EB as of about 1890, but had typoed that key digit, inadvertantly transforming his message from a comment about 140+ yo history into one about 40yo history.
Armed with that mistaken notion I went off on a voyage of discovery for 1880s-era periodic tables. Turns out I was barking up the wrong tree.
Co-incidentally, May 2026:
xkcd: Aperiodic Table
“Scientists occasionally invent alternative periodic table layouts, which is usually a sign that they don’t have enough enrichment in their enclosures.”
Agreed, though I would go further.
I think a lot of maths is built on our intuitions. Let me be clear what I mean by that; I’m not saying that maths is subjective.
I mean that the whole reason that maths is so useful is because it enables us to derive non-obvious facts from obvious facts. So it’s like a formalization and augmentation of our reasoning.
I would expect that another intelligent species, with different instincts and cognitive abilities to ours, might consider some of our maths to be so trivial that they never needed to formalize it. But the inverse could be true too: some of the things the human mind does instinctively and easily might be formal mathematical topics to them.
…at least if we’re talking about species of equivalent technological development to us. If we’re talking advanced ETIs then I would expect basically every topic of human study, maths included, to be a tiny and wholly contained subset of their understanding.
Let us take, for example, the prime number theorem that says that for all sufficiently large n, the probability that n is prime is 1/(ln n). Gauss conjectured this around 1800 and two separate proofs appeared in 1896 within a few months of each other. But it is not obvious why primes and their distribution will be important to an alien civilization.
Another such is that fact that every positive integer is a sum of 4 integer squares, nine integer cubes, nineteen integer fourth powers (you need 19 for 79, although it is conjectured that only finitely many require more than 16) and so on. These theorems are clearly no inevitable.