Deciding What Close Means

Last timeWorking Without an Answer Key

Every method here is built on a notion of distance, and choosing it, including the scales of the inputs, decides more of the answer than the choice of method does.

Everything here rests on this

A grouping method puts near things together. A reducing method keeps the

directions along which things are far apart. A flagging method reports the

things that are far from everything else.

All three sentences contain the same undefined word, and nothing in any of

those methods defines it. Distance is supplied by whoever runs them, usually

without being noticed, and it decides more of the answer than the choice of

method does.

The ordinary distance

The default is straight line distance: subtract the two rows column by column,

square the differences, add them up, take the square root.

FIG 1Straight line distance between two rows

: how many columns the table has
: the value of column j in each of the two rows

The sum adds a squared difference in pounds to a squared difference in years to a squared difference in counts of purchases. Written out like that the problem is visible: the expression assumes the columns are in comparable units, and a table anybody collected is never in comparable units.

The scales decide the answer

Take two columns, income in pounds and age in years. Income runs from fifteen

thousand to ninety thousand, age from eighteen to eighty. A difference of ten

thousand in income contributes a hundred million to the sum; a difference of

forty years contributes sixteen hundred.

Income therefore decides every distance, and age contributes nothing

measurable. The grouping will be a grouping by income, whatever anybody

intended, and nobody looking at the output will see that.

The lesson stops here

4 more paragraphs to go

You have read the opening. The rest of the argument, the problems that check whether it landed, and the lines worth keeping at the end all come with a plan.

The first lesson of every course in the library reads the whole way through, free, so you can see exactly what the rest of them are.

See the plan The contents

This is the reading half

Starting the course gives you your own copy of it. Every idea on every page has problems standing under it, marked with a reason rather than a tick, and any sentence you do not believe can be opened and argued with. None of that can happen on a page nobody owns.

The contents