Scientific guesses

Assumptions

Behind every indirect fact (like a calculation) there are a number of assumptions; some of them of minor import, some of them vital. Most people ignore this aspect so much that they don't even realize the assumptions are there. (To paraphrase Ayn Rand, not only don't they "check their premises", they don't even know what those premises are.)

Here's an example: estimating the speed of a moving car. Let's say the car leaves town A at 3pm and reaches town B at 6pm. We can see on a map that the distance between the two towns is 150 miles, therefore we calculate that the car had an average speed of 50 miles per hour (150 miles divided by 3 hours).

What assumptions have we made, and how do they impact our result? For one thing, it is unlikely that the car has moved at a constant speed. It might have slowed down when passing through populated areas and sped up when in between; it might have even stopped for refueling. The actual speed was almost certainly not 50 miles per hour at least some of the time. In itself, this assumption is not so problematic for our result, since we made sure to prefix it with the word "average", acknowledging the possibility of a varying actual speed.

There is a second, more problematic assumption: that the map distance between the two towns is the same as the actual road distance. (I do not know how often this happens to be the case in the US; I know it's almost never true in Romania, where the roads mostly grew up organically, from local necessities, instead of being planned by someone.) This assumption, if incorrect, has the potential to affect the final result quite significantly. To use a distinction I'm fond of making, we're starting to leave the academic towers of science and getting into the murky waters of engineering.

What about a second method of calculating the speed of a car, one that is at the same time more likely to be accepted on its face and carrying a much more vital assumption? The speedometer of a car tells us what the current speed is. It does that by measuring how many times the tire axle revolves per second and multiplying it by the tire circumference to get the distance traveled in that second; another calculation will yield miles per hour.

There are at least two hidden assumptions here. The minor one is about the tire circumference: if you're using a nonstandard tire, e.g. one with a smaller radius, its circumference will be lower than the "known" value, which will affect the final result. Your actual speed will be lower than what the speedometer is showing.

The second assumption can completely destroy the result, though: it's the link between "tire moving" and "car moving". If your car is stuck on snow, or sand, or on a test bench in some garage, the tire will be moving without affecting the car. The speedometer readout will thus be completely useless: a 50 miles / hour with absolutely no significance in reality.

What was the point of all this? Well, just keep it in mind the next time you're reading about Kuiper belts and Oort clouds and dark matter and ...

Comments

Post a Comment

Popular posts from this blog

Posting dynamic Master / Detail forms with Knockout

Image
I have the following dynamic form in my GitHub Inventory project : I created the form with KnockoutJS , using some ideas from this article . The detail view looks like this: <table id="acquisition_items" class="jtable"> <thead> <tr> <th>Product Name</th> <th>Quantity</th> <th>Price</th> <th>Value</th> <th><button data-bind="click: addItem">[+]</button></th> </tr> </thead> <tbody data-bind="foreach: items"> <tr> <td> <input data-bind="value: ProductName" type="text" value="" /> </td> <td> <input data-bind="value: Quantity" type="text" value="" /> </td> <td> ...
Read more

Comparing Excel files, take two

Image
I already wrote this project once, on GitHub , but I can't say that I like the result. I wrote that code without TDD, mostly to see if I can still work in the "normal" fashion. I can, but I had a bug that took me a while to even discover and then was difficult to write tests for. I also hate the temporal dependency in that design (if you don't call the SortBy method first, the ExcludeRecords method will return incorrect results). Anyway; here's attempt number two, writing that code using TDD. Structure I start by creating my usual structure for projects of this type - a library for the logic, a console application for the main program and a test project for tests. I also use the Enable NuGet Package Restore option (right-click on the solution node) to add the three NuGet files that will allow someone to automatically download all the packages I'm referencing without wasting space in the source code repository. (Right now I've only added the Moq pa...
Read more

EF Code First: seeding with foreign keys

This is just a quick tip, more for future reference for myself than anything else. When using Entity Framework Code First, one of the things you might want to do while developing the application is to seed your database with some test data. This can be something as easy as: protected override void Seed(InventoryDB context) { context.Products.AddOrUpdate( p => p.Name, new Product { Name = "Hammer", SalePrice = 11.99m, }, new Product { Name = "Nail Pack x100", SalePrice = 0.05m, }, new Product { Name = "Saw", SalePrice = 19.99m, }, new Product { Name = "Toolkit", SalePrice = 39.99m, } ); //... } (I am using the AddOrUpdate method so the code detects whether those products already exist and doesn't add them again if they do.) The Product class is quite simple and – most importantly – doesn't depend on any other: public class Product { public int Id { g...
Read more