Until I took a second year abstract algebra course at university, I would have said 1+1=2 is in the discussion of intuitively obvious. I would have been enormously wrong. The professor, in his cynical way, decided that we should understand math in a more abstract way. He assigned the task of proving 1+1=2 using basic principles.
Three of the people in that class knew of hard to solve math problems only by hearsay. They had never seen one. They did not get this one though.
It is amazingly difficult to prove. Whitehead and Russell in their work Principles of Mathematics provided a proof. This is the last of 362 pages proving the point.
362 pages of fairly dense reasoning. Small wonder we failed.
The point to take from this is there is a great deal that we claim to know for certain that is not exactly certain. I am willing to accept 1+1=2 because a) I have no intention of reading Principles of Mathematics and 2) it serves my day to day purposes fairly well. It is not always right. One drop of water plus one drop of water is still one drop albeit somewhat larger.
Other things we believe fit the same pattern. They are right enough most of the time. Approximations of reality. Approximations are not deterministic, so you cannot rely on them to be always true.
As you will recall from an earlier article on chaos theory and its effects,
Chaos: When the present determines the future, but the approximate present does not approximately determine the future.
In all but the most simple systems, chaos is the real system.
Be a little humble. You cannot know enough to predict the future with certainty. Neither can any of your advisors. The process to success involves iteration. The gradual homing in on the answer you need.
Estimate your reality. Plan. Assign tools and tasks. Record results. Review your reality, your methods and your plan. Revise as necessary. The 3 R’s of planning keep you on track
Douglas Adams seems to get this.
“I may not have gone where I intended to go, but I think I have ended up where I needed to be.”
We know that even simple obvious answers are not necessarily true and we can estimate that complex answers are even less likely to be so. It would behoove us to find a process that causes us to function within reality rather than within our cherished beliefs.
Don Shaughnessy is a retired partner in an international public accounting firm and is now with The Protectors Group, a large personal insurance, employee benefits and investment agency in Peterborough Ontario.
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