The first thing that comes to mind is the concept of base numbers in any numerical system. Arabic is simply base10, while binary is base2. 11 means Eleven to us because we use base10, but to an extraterrestrial who thought in binary (base2) would know this number to mean Three. I'm not sure this covers what they're speaking about in the quote, as converting from different bases shouldn't be difficult for these higher-density beings.

Makes me wonder though what the practical benefits of a base 7 numerical system would be, considering TLOO posits this number to be integral to the foundation of our reality. True there are seven colours, seven notes on the heptatonic musical scale, and seven levels of energy density within our table of elements. These are supposedly a part of a wider creation in which their are seven primary energy densities, sometimes referred to as dimensions.

Quote: the difficulty, which approaches impossibility, of dealing with your local geometry, arithmetic and numbering system.

Does this imply that higher densities actually contain additional euclidean dimensions? This would correlate with mystical experiences in which the participant reports "impossible geometry" which they cannot properly recall once they are back to their usual reality. I actually have a good friend who claims to have held a pleasant conversation with a hypercube after ingesting dimethyltryptamine.

Interesting thread. I would love to be able to link some of the concepts in TLOO with existing human knowledge of space and time.

Some more thoughts on base7: The counting would go 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14, 15, 16, 20... etc. in which 10 would be known as seven, and 20 something like twoseven, which would equate to fourteen in base10. Now I think about it, converting from different bases, as well understanding and integrating the language and the symbols of the the different cultures on a cosmic scale would actually be an immense task. What a mess. Base7 would be incredibly impractical for mental arithmetic as seven is a prime number, and as such doesn't divide by anything but itself and one. 10/2 in base7 ( which is 7/2 in base10) = 3.5 in base10, but just fries my brain in base7 (edit: the answer is actually 3.333 recurring, which is obvious in retrospect).

Interesting is to look at the numbers in base7 counting and think about Ra's descriptions of the densities. For the first six densities, we have our numbers 123456, but then at the seventh density, the number becomes 10 in base7, correlating with the transitional nature of the density, then the eighth density begins a new octave, symbolised by 11.

Thus in base7 the the creation we're part of could be abstractly represented by an infinite chains of 1s, the number approximating infinity in the sense that it represents a number comprised of sevens within sevens within sevens. This is true of any base, and Ra says there are creations which are founded upon different base numbers, but apparently base7 gives the best experiences. Perhaps this is due the aforementioned difficulty which seven creates as a base number, leading to possibilities which other base numbers can not give. Base5 and Base3 have potential, because they too are prime numbers, as well as base11. Maybe these suffer from some setback due to their relative sizes.

Also check out this neat pdf which lists our planets historical numerical system. You can see an overwhelming affinity to base10 from all the developed peoples as well as some quirky systems from more primitive times.

http://www.math.chalmers.se/Math/Grundutb/GU/MAN250/S04/Number_Systems.pdf