Among scientists in the US Geological Survey there are two expressions of note: "WAG," which stands for Wild A$$ Guess, and Guestimate.
These are the low-end members of a legitimate - even critical - aspect of science: estimation. You can't predict the future (at least, managers in the US Geological Survey can't), but you can sketch out some possible scenarios and begin planning for them. These include rough guesses of what the annual funding for the US Geological Survey might be. If it includes reduced funding - and senior managers are strongly encouraged to follow the political news for this reason - then you SURE better not plan on hiring new people. This is a form of political estimation that can save you and other people a lot of grief later on.
Estimation is absolutely critical for both advanced math and for all of applied science. With a geophysical instrument inside Mount St Helens crater - or with the $20 billion Large Hadron Collider at CERN in Switzerland - you can ALWAYS get "results", you can ALWAYS come up with "numbers." The problem is that in complex systems, where there are a lot of things affecting the final results, the numbers can add up to something round and steaming.
The critical point of estimation is to set bounds on a reasonable result - a result that is consistent with the real world values already in hand. Example: the conductivity of water and the conductivity of dry rock are well known. If your geophysical box gives you numbers unlike any of these, if you get numbers outside a realistic range, those numbers may be round and steaming: in other words, crap. You then must go back and check your equipment to see what might be wrong, what you must have overlooked when you set up the experiment. Technical review of any scientific manuscript will home in immediately on anything that is unrealistic, so you can save yourself embarrassment if you estimate ahead of time what may be reasonable to expect. Among other things, the preliminary estimate in science is also critical in designing the experiment in the first place. If you are looking for ants, don't build a science experiment to trap mastodons.
It used to be the case that "close" worked in horseshoes, hand grenades, and nukes. Not anymore. Close is usually better than perfect in the real workday, where your data are routinely fuzzy to begin with.
It also is very much the case that "perfect" is the enemy of "good." Scientists worrying about the third decimal place in accuracy on an important number (such as the Hubble Constant) could hold up publication for years - when the number had such approximations in it in the first place that the third decimal place was totally pointless. In other words, trying to get that third decimal place of accuracy was a waste of time.
Sanjoy Mahajan recently published a book "Numbersight" (Subtitle: "A street-fighting mathematician teaches how to make better decisions"). This book sings the praises of estimation. He also points out that to teach kids to do fast math in their heads, it is critical to first teach them how to estimate, and then teach them how to visualize results. If they had no idea what they could expect (for instance multiplying two three-digit numbers is NOT going to give you a four-digit result), then you couldn't be sure that your short-cut math was working in the first place.
Another aspect of estimation - very useful in teaching kids how to do math - is to visualize the result in terms of something that they can relate to. It therefor helps to visualize a football field as being "60 dads long" instead of 100 yards or 91.4 meters in length. In the 1960's physicists spent a lot of time deciding what kind of metric system to use (they had already concluded that all science must be metric to be universally understood, and only in the United States do children still learn distances in "feet" and weights in "pounds"). The argument went something like this: the SI (standard international) system uses meters and seconds and kilograms. The CGS system uses centimeters and grams and seconds. As an old Manhattan Project nuclear physicist gruffly put it, the SI system was appropriate for humans, and the CGS system was appropriate for grasshoppers.
I totally agree with this statement. Working in the engineering field, I often find that people make decisions based on "gut feelings" rather than sound estimates. For instance, do we design a new widget or buy it? A "back of the envelope" calculation based on the number expected to be sold, the ASP, and the estimated development costs (and then multiply the development costs by 2x) provide invaluable information. Instead of doing this calculation, often I am asked to have a financial analyst look at it -- consuming my time and his on often ill-thought out ideas.ReplyDelete
A few other thoughts. If you ask a different question, expect a different answer. You can't optimize on three different variables -- this is an exercise in performing trade studies.