It is interesting, but I'm not clear on the benefit other than aesthetic appeal. I can't see it replacing the Mendaleev system, but it might be useful as an augmentation. Or do you suspect it should replace the traditional table?
On a tangent, the periodic table is not the only thing that's being rethunk. The biological taxonomic system is also being reviewed - because of problems with classification. That is, some things just don't fit well into the system.
Our Linnaean system was established by, well, Linnaeus. Brilliant though he was, he lived and produced his great work before Darwin developed the theory of evolution. I think I recall he was a special creationist - at that time creation was as good an explanation as any.
We might infer then that he believed species were essentially immutable. This makes for a disconnect between the discrete Linnaean taxonomic system and the continuous nature of species being categorized.
Consider the following:
We start with species 'A' someplace way back in time. Through time, the descendents of this species branch all over the place - into a bush, not a tree. Let's follow one of the myriad paths from this relative 'root' to the currently existing leaf species. Say 'Z' is a modern descendent.
So we have A begat B begat C begat .... Z
Now, if the delta T (the elapsed time) has been a long time (on the order of 100s of thousands or millions of years), then A and Z are probably not the same species - they might not even be the same genus. (Note that A and Z *might* be the same species, because there's nothing I'm aware of in evolutionary theory that says that species have to die out.)
However, in each case, A is the same species as B is the same species as C is the same species as D, and so on. Each successor may or may not be assimilating some slight mutation into the gene pool. Eventually there comes a point where, say, X is no longer of the same species as A, even though A is the same species as W and W is the same species as X.
Let the string '<=>' mean 'is the same species as' and let the string '</=/>' mean 'is not the same species as.'
The upshot of my point is that you can have a case where A <=> B and B <=> C, but A </=/> C. In fact, there must have been many such cases. Mathematically we would say that the relationship 'is the same species as' is not transitive.
(It's important to emphasize that this is a thought experiment. I don't think it's possible to look at a fossil, for example, and say with certainty that it was a direct ancestor species of some existing species. The best we might say is that it appears to be at least a cousin, and 'might' be a direct ancestor. This is part of the reason why terms like "missing link" are nonsensical.)
I'm not sure whether a biologist would buy into any of this, btw. But it seems intuitively obvious.
To summarize:
Cause of Problem:
The objects (species) being categorized constitute a continuum, while the taxonomic system assumes discrete units.
Result:
There will be items among the continuum (species) that are putatively difficult to classify.
I reasoned this must be the case some time ago, but then I recently came across the following link at scientific american that pretty much confirmed what I had already thought:
http://makeashorterlink.com/?F20932DB9 Note: In my notation above, the operator "<=>" means "is the same species as" and not "is the same as." If A and B produce viable offspring, then A and B are the same species.
