Learning this yourself

Most people choose their first book by one test: does it explain what things mean. There is a better test you can use in the shop. Open the book in the middle. Does any page there ask you to work something out, with a table or a sum? If not, you are holding a dictionary of meanings, which is the easiest thing to read and close to the least useful in a first year.

Meanings cannot correct you. A calendar can. So an honest first year runs almost backwards from the usual order.

Begin with the panchang, the Indian almanac, sold cheaply near most temples. Read one day at a time, the day you are actually in. A panchang is a page of statements that can be checked. It says a lunar day ends at 09:48 tomorrow, and either you can work out why or you cannot yet. Three months of that and you have been quietly corrected several dozen times.

Then do one piece of arithmetic that has nothing to do with your life. Astronomers use a plain running count of days, the same everywhere in the world, so that no calendar argument can touch it. Work it out on paper for the date you were born, then check it against Horizons, the free service NASA runs. When your pencil and a NASA computer agree, the subject stops being a rumour and becomes something you can do.

Two things happen along the way. Around the third month the words all arrive at once and you become briefly insufferable at dinner, because confidence follows vocabulary and judgement is slower. Around the ninth month you meet a disagreement you cannot settle: two programs, two books, two answers. That week is the useful one.

On teachers: a book cannot mark your work, and a wrong idea feels exactly like understanding. Want one who gives you references, teaches the arithmetic and not only the conclusions, and whose course has a stated end. Paying for teaching is ordinary. Paying for secrets released level by level is not.