Now this is a good read...

If you consider a connection as being something binary (two persons involved) then the network value only grows as n^2, n*(n-1)/2 to be precise, not (n-1)!. This is Metcalfe's law: the value of a network grows quadratically with the number of users of the network. This also explains why there are many^2 presents christmas evening if many guests are attending - the number of presents grows quadratically with the number of people if all guests give all other guests one present each.I used a cocktail party example today, regarding bitcoin's utility and adoption:

When 1 person in the ball of 1000 (0.1%) uses bitcoin, it means zero utility and 1 evangelist vs. 999 crowd. It takes 999 one-on-one conversations to tell everybody about a thing that is completely useless, so it is very slow.

When 2 people in 1000 (0.2%) use bitcoin, it means 1 utility (utility is defined by number of connections between bitcoin users, expressed as a

4 people in 1000 (0.4%) -> 6 utility (4-1)!, 4/996. It takes 249 conversations to tell about a thing that is slowly getting useful, and the group pressure begins to form, as the same conversation may have 2 bitcoin users.

8 people in 1000 (0.8%) -> 5040 utility (8-1)!, 8/992. It takes only 124 conversations (8 times faster spread than when bitcoin had 1 user and no utility, and the utility is growing

16 people in 1000 (1.6%) -> 1.3*10^12 utility (16-1)!, 16/984.

When this is reached, the utility tends to infinity.

Notice that it took exactly as much time to reach 2 from 1 as it takes to reach 7 billion from 2.

In this example, we are now half way between 1 and 2 people, and bitcoin is slowly exhibiting any utility whatsoever. If the utility does not correlate with spread, we will reach $300k anyway, but it will be 3 years from now. If it does correlate, bitcoin adoption can and will happen in 3-6 months.

- The utility will grow factorially (factorial growth >> exponential growth(!))

- The spread rate is inversely correlated with the number of current users

When 1 person in the ball of 1000 (0.1%) uses bitcoin, it means zero utility and 1 evangelist vs. 999 crowd. It takes 999 one-on-one conversations to tell everybody about a thing that is completely useless, so it is very slow.

*This must grow by 100% to reach*

When 2 people in 1000 (0.2%) use bitcoin, it means 1 utility (utility is defined by number of connections between bitcoin users, expressed as a

*factorial*(k-1)!) and 2/998. It takes 499 conversations to tell about a practically useless thing.*This must grow by 100% to reach*

4 people in 1000 (0.4%) -> 6 utility (4-1)!, 4/996. It takes 249 conversations to tell about a thing that is slowly getting useful, and the group pressure begins to form, as the same conversation may have 2 bitcoin users.

*This must grow by 100% to reach*

8 people in 1000 (0.8%) -> 5040 utility (8-1)!, 8/992. It takes only 124 conversations (8 times faster spread than when bitcoin had 1 user and no utility, and the utility is growing

*very fast*)*This must grow by 100% to reach*

16 people in 1000 (1.6%) -> 1.3*10^12 utility (16-1)!, 16/984.

**SINGULARITY**When this is reached, the utility tends to infinity.

Notice that it took exactly as much time to reach 2 from 1 as it takes to reach 7 billion from 2.

In this example, we are now half way between 1 and 2 people, and bitcoin is slowly exhibiting any utility whatsoever. If the utility does not correlate with spread, we will reach $300k anyway, but it will be 3 years from now. If it does correlate, bitcoin adoption can and will happen in 3-6 months.

- The utility will grow factorially (factorial growth >> exponential growth(!))

- The spread rate is inversely correlated with the number of current users

And btw, n*(n-1)/2=sum(x,x=1,x=n-1) (the

**sum**of all natural numbers from 1 to n-1, not the product as (n-1)! indicates)