The first example involves a contractor bidding on a $3 million dollar construction project. He offers to build the building by working for a penny the first day, doubling that each day for a month. After a month he'll work for free until the building is completed. If you work out the day by day pay, it is going to grow slowly for the first 20 days. From that point on, the curve of actual dollars per day grows very sharply upward. The pay for day 10 is $5.12, for day 20 $5,242.88. Day 25 pay is $167,772.16. Day 31 pay is $10,737,418.24 and the total paid is over 20 million dollars.

Another example is the pond lily, which grows so fast during the summer that the leaf surface area doubles every day. The lily is inconspicuous during the first 20 days, but during the last 5 days of growth will cover 1/16, 1/8, 1/4, 1/2 and then the full surface area of the pond. To the casual observer the pond is "suddenly" overgrown during just a few days. In fact it has been growing at the same rate for a long time, but the effects were not easily detectable until the end where the magnitude became large.

Computer processing power (speed) has been doubling every 18 months for many years (Moores's law). Skeptics have pointed out that physical limits prevent this, but each time we appear to be at the limit someone discovers a new method that overcomes the obstacle. We are at approximately the 20th doubling starting from the first PCs in the early 1970's. This means that during the next 10 doublings (15 years) we'll see the explosion similar to the last few days of the pond lily's growth or the construction project's pay. Processor power in 2010 will be approximately 256 times faster than today's 300 MHz speed. This is 76,000 MHz! In the year 2018 the processor speeds will be 8000 times faster than today at 2.5 million MHz.