In this series of blog posts, I will try to summarize what might well have been the world's first googological notation to reach beyond the tetration level (some years before the Steinhaus notation that was so famously expanded by Moser) - what I call the Kharms notation (after its author, Daniil Kharms). But first, a bit of background...

The classic (at least relative to your typical online history) Russian source on very large numbers is the Stas article from 2003. It is in the errata to that article that I first found out about Daniil Kharms' 1931 treatise "Lifting of a Number".

Knowing what I knew about Daniil Kharms (a rather famous absurdist poet), I was not expecting any particularly serious mathematics. What I found, however, was an article that, save for being written in a rather archaised version of Russian, would not have been out of place on Aarex's site... it was better than most amateur googology today - for 1931, it was all but revolutionary.

For comparison: 1931 is just three years after the Ackermann function was defined. It is before the Skewes or Steinhaus numbers were a thing (the former are around the lower tetrational level, the latter are bordering on pentation).

Meanwhile, this treatise introduces a well-defined notation up to the hexational level, and with somewhat less certainty extends it up to the limits of what we would know as up-arrow notation (never mind that Graham, Knuth and Conway haven't even been born yet) - and perhaps further (beyond Graham's number).

Sadly, the original link where I'd read the article isn't working anymore. But as of right now, you can read the full Russian text (and some mathematical comments, in a somewhat more modern version of Russian) at this Livejournal post.

And now, we continue on to the next part (where I actually describe Kharms' first major notation - up to the hexational level).

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