Are there a specific number of reincarnations?

 
Thank you so much one and all for the warm reception at Sunday's talk. Some loose ends:
The Theosophical explanations on reincarnation do give a specific number of reincarnations. Is this 777 related to the symbolism of a well-known mystical and biblical number?They do not specifically make the connection. As far as I know, this explanation remains a distinct theosophical view and as offered is succinct and mathematical, and can thus be considered a comparitively pragmatic and rational explanation as far as mystical questions go. (nb. please make allowance for the outdated colonialist anthropoligcal terminology of the time, merely used out of practical semantic necessity. Blavatsky was openly critical of colonialism. According to
Gauri Viswanathan (The Ordinary Business of Occultism, Critical Inquiry, Vol. 27, No. 1 (Autumn, 2000, p. 19), the Mahatma Letters, "brilliantly combine a critique of both colonialism and secularism by admitting the occult into the making of worldly relations and a more inclusive account of the world than the one allowed by imperial, secular histories".( p. 19)

The Mahatma Letters to A.P.Sinnett, (Letter No. 14):

"(7b) However, to set you right so far I will say — one life in each of the seven root-races (nb.race meaning cultural groups or humanities in today's terms - mc); seven lives in each of the 49 sub-races — or 7 x 7 x 7 = 343 and add 7 more. And then a series of lives in offshoot and branchlet races; making the total incarnations of man in each station or planet 777 (...)Not much to divide over some millions of years that man passes on one planet. Let us take but one million of years — suspected and now accepted by your science — to represent man's entire term upon our earth in this Round; and allowing an average of a century for each life, we find that whereas he has passed in all his lives upon our planet (in this Round) but 77,700 years he has been in the subjective spheres 922,300 years. Not much encouragement for the extreme modern re-incarnationists who remember their several previous existences!

Should you indulge in any calculations do not forget that we have computed above only full average lives of consciousness and responsibility. Nothing has been said as to the failures of Nature in abortions, congenital idiots, death of children in their first septenary cycles, nor of the exceptions of which I cannot speak. No less have you to remember that average human life varies greatly according to the Rounds. Though I am obliged to withhold information about many points yet if you should work out any of the problems by yourself it will be my duty to tell you so. Try to solve the problem of the 777 incarnations."

This questions is further discussed in Sinnett's Esoteric Buddhism, p. 51 (which is derived from Letter 14):
https://books.google.ca/books?id=U1IinqCwn-IC&pg=PA51&vq=800&dq=sinnett&output=html&source=gbs_search_r&cad=1

A little bit more is developed in Blavatsky's Secret Doctrine Vol. I, p. 168:
http://www.theosociety.org/pasadena/sd/sd1-1-08.htm

ps.
A nice article in a contemporary context by Jean-Louis Siemons:
The transpersonal model of death as presented in Madame Blavatsky's Theosophy:

http://www.blavatsky.net/index.php/near-death-experiences/36-topics/reincarnation/near-death-exp/62-what-is-death