How Numbers Work

Numbers are just squiggly lines until you attach them to something. By themselves 5, 19, and 3,046 are meaningless. 5 children, 19 months until retirement, and $3,046 are meaningful

Learn to attach meaning

The examples above are pretty straightforward, but what about thinking about very large numbers with unclear connections to reality. Assessment of public opinion and most data analysis rely on a concept called The Law of Large Numbers. The value to having many examples of something is that you discern direction and a few refinements.

It works like this

Suppose I want to find the percentage of people who will support some program a business wants to offer. Suppose they need 10% of the public to want it before it is profitable. How would they put their mind at ease?

They would do a survey and use what they find to support or deny their plan.

The law of large numbers tells them as they survey more people, their answer will fall into a narrower range. That assumes the people are properly selected and the questions asked are not leading. If you do enough you will have an answer you can rely on. Confidence level.

A large survey for a study like this might be 5,000 people. It might still be wrong but it should be close almost every time. Drug studies are very much larger than that because the precision matters more.

The law of small numbers is the opposite. Suppose you survey 10 people out of the entire population. If you got 1 to think they would buy the product, would you be done?  NO, of course not. If you did it three more times you might get zero twice and 3 once. The average is 10% but would you risk your future on its validity? I hope not.

The law of small numbers is the mathematical model for conclusion jumping. There would be many skilled entrants if that were an Olympic sport.

The law of middle sized numbers is different again. It will approach the law of large numbers result but with more variability. maybe instead of showing an answer of 12% plus or minus 1%, you get 11% plus or minus 2%, and the confidence level would be lower. It’s advantage is it is cheaper. Properly designed and executed studies are very costly.

All of us apply the survey rules.

Unfortunately most of us have a thing called “Confirmation Bias” we believe things that support what we already think very easily and reject most of the rest. Objectively right is not one of the choices. Would a thousand instances of the evidence you believe make much difference. All swans were white until someone found a black one. If you refused to believe you saw a black one, would that make all swans white again?

I have a book here somewhere¬† “Don’t believe everything you think.” It is a sound way to begin improving your results. Even if you get believe everything you think, you will get better results than if you believe everything you feel.

How critical thinking works.

It relies on the idea that education should teach you how to think rather than what to think. If you have to memorize, you are doing it wrong.

Critical thinking uses evidence to develop inferences about what you are seeing. It can also give you a range of possibilities from near certain to probably to improbable to near impossible. If you fall into the true and false only choices, you are doing it wrong. Certainty is a delusion.

Critical thinking uses reason to attach the evidence to the inference. May people have a problem with that. There are many cognition flaws. A common one is “post hoc ergo propter hoc” If B happens after A, A caused it.

There are others. Things we hear many times we treat as more true. Politicians trick you with that one. The importance devalues as the idea grows older, recent flaw. What about the wet roads cause rain idea? Some logic looks like that when you pay attention.

Edward De Bono has opined that the outcome of thinking depends more on how you think about the data than it does about the data itself.

Probably best if you learn to think usefully..

Thinking is hard.

The payback is very large though.

“I suppose that you seldom think. Few people think more than two or three times a year. I have made an international reputation for myself by thinking once or twice a week.” George Bernard Shaw

Don’t give up early. It will take time to make it natural for you.

Start with demanding evidence. Don’t waste your time thinking about things you cannot verify. Opinions are just that. Not evidence. They might hint at a way to think about the problem though. My rule is simple. I trust God, everybody else has to bring evidence.

Using Karl Popper’s idea, if the opinion presents in such a way that if new information could invalidate it, it could be science. Science is always falsifiable given more information. And it only takes one instance.

The takeaway

We are presently faced with turbulent times. Learning to think better will give you an advantage.

Good thinking leads to simplifying methods. There are many that would prefer you not learn to think. Probably best you mistrust them all as soon as you recognize them.


I help people have more retirement income and larger, more liquid estates.

Call in Canada 705-927-4770, or email don@moneyfyi.com 

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