The letter by Marc Schindler (Very Big Numbers — Jan. 19) makes a valiant attempt in defining a "moser" — but alas, as stated, it is rather complex to describe and Mr. Schindler's understanding of it is in error.
Polish mathematician Hugo Steinhaus defined a number " 'a' inside a triangle" as " 'a' raised to the 'a'th power." The number " 'b' inside a square" was " 'b' surrounded by 'b' triangles." The number " 'c' inside a pentagon" was " 'c' surrounded by 'c' squares." Steinhaus defined a "mega" as "a 2 inside a pentagon." This works out to be a 256 surrounded by 256 triangles. A step-by-step analysis quickly shows that this number is quite different from Mr. Schindler's "X" — 256 with 256 triangles around it is equal to 256 raised to the 256th power with 255 triangles around it. This in turn becomes (256 raised to the 256th power) raised to the power of (256 raised to the 256th power) all surrounded by 254 triangles. And so on . . .
What Leo Moser did was to continue the pattern with hexagons, heptagons, etc.; defining an "n-gon containing the number 'd' " as "the number 'd' with 'd' (n-1)-gons around it." He then defined the "moser" as "a 2 inside a mega-gon."
I leave it to you to calculate how much bigger this is than Mr. Schindler's "moser," that is, X tetrated to the X, where X equals 256 tetrated to the 256; " 'b' tetrated to the 'a' " is an exponentiated stack of "a" many "b"s. These are worked from the top down, although Mr. Schindler's definition is somewhat ambiguous in that regard.
Mr. Schindler gloats about the fact that Leo Moser was a Canadian. Referring to the "moser" he states that "for sheer immensity you can't beat a Canuck." I certainly don't want to take anything away from the likes of Mr. Moser (whatever their nationality, I sometimes think mathematicians live in a country of their very own), but I must point out that anybody can easily come up with finite numbers that would dwarf even a "moser." To wit, let H-1 be a moser inside a moser-gon; H-2 is H-1 inside an H-1-gon; and, in general, H-n is H-(n-1) inside an H-(n-1)-gon. Now a "hoser" is the number represented by H-moser.
Hans Havermann
Weston, Ont.
The above appeared in The Globe and Mail on Saturday, 26 January 1985, page 7.
Here is an in situ facsimile:
Posted here as a historical aside to Tony Padilla's Mega & Moser Numberphile video.
