Professor Wiggly: ” A famous philosopher named Popper added a third world. In addition to World 1 – seeing is believing, and World 2 – believing is seeing, he added a third world made up of mental inventions or abstractions – like mathematics and fantasy stories – which may have no connection with World 1. Although some aspects of mathematics may link to world 1 – like counting rocks, or coins, or ducks or the number of cancer cures. But aspects of mathematics like the square root of -1 have not connection to world 1. Pure mathematics is an invented game of symbols and rules for combining them. Similarly some aspects of fantasy may have links with World 1 like Alice ‘s wonderland houses and cakes, but not other aspects like magical doors and houses that expand and shrink.”

Jenny: ” S0 how do mathematics and science work together – how do World 1 and World 3 get along?”

Peter: “Yeah, earlier you said that scientists use imaginary mathematical bridges to map the future – how so?”

Professor Wiggly: ” Well, so do you. Let’s say that next weekend (the future) you’re planning to drive from New York city to your home out west, which is 3000 miles away. Your girlfriend asks how long it will take. You estimate that you will travel at 50 miles an hour so you trot out your mathematics and **divide 3000 by 50** and get sixty hours – with no stops. So you have an imaginary mathematical bridge (60 hours long) extending into the future. But of course this bridge needs modification because you will have stops to eat, sleep and get gas, so you have to guesstimate the time they will take and extend your bridge into the future **by adding time estimates** to allow for these stops. So this imaginary mathematical bridge helps you and your girl girlfriend manage your uncertainty about the future trip. But if you stop and think about it many uncertainties about the future trip still remain. For instance there may be a number of surprises, like detours caused by road repair, car trouble, accidents that delay traffic, bad weather, your girl friend sometimes gets car sick, etc. So your mathematical bridge becomes more and more imaginary. But if you try to provide for all the ‘what if’s’ , for all possible things that could go wrong you’ll never get on the road – there are always too many possibilities and unknowns for your bounded rationality to consider. You probably know people who drive others nuts by overplanning, or who give up travelling all together – too many uncertainties, no trusted bridges.”

Jenny:” So that’s what you meant earlier when you told us about Herb Simon proclaiming **no decisions without unproven assumptions **and furthermore that there are always too many possibilities to take into account – if we try to prepare for all possibilities we overload our brains – we overload our **bounded rationality – so **we have to take a lot of things on **faith.”**

Peter: ” So you’re saying that when scientists build mathematical bridges they face the same problem, they have to make a lot of unproven assumptions about the future and at lot of crude guesstimates about what may happen, including things they know nothing about. And they have to keep the number of assumptions down to mind size or they become overwhelmed by the complexity and give up.”

Professor Wiggly: “And remember, unlike the guy taking his girlfriend on a trip into familiar territory, scientists are often travelling into unmapped territory where no one has been – so they have to make many more assumptions of what might be out there, about what might happen. But if they think too much they overload their brains – overwhelm their bounded rationality. That’s why they have to rely on simplifying assumptions – on theories. And since some of their bridge building can cost a lot and take a long time they have to trust their theories since they’re making such large investments… in that sense they travel on faith-based bridges. Scientists like to work in laboratories to keep things simple – to keep World 1 junk from mucking up their trip. It’s like growing flowers in a hot-house where you can control the heat, light, humidity, bugs, and wind. So you may learn how to grow those flowers in a controlled hot-house environment, you have **a hot-house truth**. But you don’t know whether they’ll grow outside, outside in the noisy, dusty, buggy, windy World 1.

“Jenny: ” So mathematical bridges and hot-house experiments helps scientists simplify their maps of the future, but they don’t necessarily tells us how their mathematical and hot-house ‘truths’ will survive out in noisy nasty World 1. That helps explain why so many drugs get recalled – researchers tested them on relatively few people under hot house conditions and when they turned them loose out in World 1 involving hundreds of thousands of different people on different diets, different ages, different health problems, different habits (some forgetting to take their pills, or taking them with other pills as well), etc., etc.,)”

Peter: :”So scientists have the same trouble we do in mapping the future… in mapping the changing future of World 1 – the weather, the oil supplies, the engine of my 95 Buick, my ulcer, etc. Scientists have the same trouble mapping the changing future of **World 2 **– marriages, kids future, health, stocks, politics. But scientists can have an easier time playing in **World 3**, horsing around in mathematical space, where they can make up and manipulate that world. That’s why so much scientific theory is based on math. As long as you stay in the make-believe World 3 you can manage your uncertainties much easier than in the unpredictable World’s 1 and 2. That’s why science is becoming more theoretical, more mathematical. And in doing so it may have fewer and fewer connections with Worlds 1 and 2, the worlds the rest of us live in. So as their problems their working on become more complicated they rely more and more on trusted mathematical bridges. That’s what the bankers did and helped cause recent economic meltdowns – the relied on fancy mathematical models of risk written by experts who knew a lot about mathematics but not so much about human behavior. These experts could navigate a lot better in World 3 than the could in Worlds 1 qne 2. “

*Sciencing*

Posted on February 4, 20110