The mathematician moves ideas from the right brain to the left brain. He starts by creatively thinking about about the big picture, the patterns, the relationships. As he processes that thinking he develops symbols, language, formal logic and conclusions.

However, math education rarely reaches the right brain. Educational standards and traditional methods start with the formal language and methods that have already been developed. Students are asked to memorize these formalities. The students do not get involved in the creative and discovery processes that make up real math and real science. They are tested on the formalities, not the deeper understanding or creative processes. They do not get to actually see what real math is.

Goldbach's Conjecture

We have started to examine Goldbach's Conjecture using pattern recursion. We looked for the arrangement of holes (potential prime pairs.) Perhaps, we should have been looking for the arrangement of zeros (convergence of all critical primes.) For example, we can look at the list of holes for G = 2 and critical primes = 2,3,5,7. Each pair below (except S) adds to G and has the critical primes in their factor list.

This list hints at the equivalents for G simply by adding the absolute values. D1 equivalents for G = 2 are 58, 82, 142, 278, 362, and 418.

Stress Limits Profits

We believe in maximizing profits. Our government issue reports on productivity. We believe that maximum productivity means maximum output and maximum profit. But is this assumption correct?
As we push for higher outputs, we increase the stresses on both our workers and our machines.

Fatigued workers are more accident prone, more mistake prone, and more illness prone. Similarly, machines pushed to their limits break down more frequently. Thus, pushing too hard for output rapidly increases stress related costs.

Conversely, the total output does not continue to rise linearly with pressure for more. Only so much juice may be squeezed out of a lemon. After that a lot of energy gets invested into each drop. A person runs out of hours in a day. A machine must be shut down for maintenance. Diminishing returns is reached.

Unemployment

Estimates of unemployment contain too many factors to reliably provide the information we want to see. That's why this site has tracked employment instead of unemployment. But one can put the employment and unemployment numbers back together to see the problems.

The official counts show a drop in the total workforce in 2001 followed by sluggish growth throughout the decade. We have no reason to believe that the number of people needing jobs actually dropped or that the population quit growing.

We can extrapolate the average workforce growth rate from the proceeding years to estimate the probable real workforce. When we do this we see that real unemployment grew to about 10% and remained high throughout the Bush administration. The real unemployment rate was already near 14% the day Obama took office. You may find similar analysis at Shadow Stats.

Climate Change

NASA keeps monthly data. So how does the data compare to either the claims that earth is warming, or the claims that earth is cooling? Here we graph temperatures averaged across a 7.2 year span. (7.2 years was picked because there appeared to be an oscillation at roughly that frequency.) At this interval we see punctuated warming. Periods ending in 2010 are the warmest for land and the globe overall. For the ocean 2008 and 2010 roughly tie as the warmest. (See more)

Peak Oil : In the first decade of this century the rate of production stalled even while demand rose.
Generalization: The rate of rise stalls even while forcing factors should drive continued rising.

• Food Production: The rate of grain production stalled 30 years ago even while population has continued to rise.
• Seasonal Cycles: At the end of the season the fruit tree slows its production, even while people are still searching for fruit.
• Housing Bubble: Housing sales slowed in 2007 even though people still needed houses.

Peak Oil: Prices rose exponentially between 2000 & 2007 with supply & demand factors
Generalization: Secondary measures start to change rapidly, or slow down per situation

• During the first decade prices of many commodities including food and strategic metals rose rapidly.

Peak Oil: The rate of consumption is persisting at about four times the rate discovery
Generalization: Output measures persist higher than input measures.

• Housing Bubble: From 2000 to 2008 real estate values rose rapidly even while wages and employment stagnated.

Peak Oil: Over the last 60 years the sources of oil have moved further away, become riskier to extract, and become costlier to extract (The EROI has dropped.)
Generalization: Sources become costlier and more difficult to acquire.

• Water Supply: Farms in various areas including the Oglalla aquifer and Southern California had had to dig much deeper wells.
• Fishing Industry: Small fishing vessels no longer leave from coastal cities. Larger vessels travel farther to get fish. Fish formerly caught from our own coasts are now imported from other countries.
  

Peak Oil: Since about 1980 new discoveries of oil have become less frequent and smaller.
Generalization: Sources become smaller and less frequent.

• Fishing Industry: Fish caught along the coast and in rivers are smaller and less common than those caught their 50 years ago.
  

Peak Oil: Oil suppliers have changed their behavior in two noticeable ways (1) they are now expressing excitement of low quality sources that they would have ignored in the past (eg: tar sands) (2) they are changing their economic behavior (eg: prospecting on Wall St. and buying back stock.)
Generalization: Experts and experienced workers (1) express excitement over low quality finds, (2) start looking elsewhere for opportunities.

• Seasons: Farm workers leave specific crop behind and move to other more productive crops.
• Fishing Industry: Fishing vessels are larger and travel farther. Some fishing vessels stopped fishing and switched to whale watching and other tourist ventures.
• Housing Bubble: Banks bundled high risk investments with lower risk investments and sold the bundles to other banks. Some banks (Countrywide) habitually changed numbers on documents. Banks started to ask other banks to insure the risks they took on.
  

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