They say only Albert Einstein truly understood the general theory of relativity. In his absence, it may be that no one understands Boston's property tax system.

January is nearly upon us, and with it comes the new tax season. Recent reports that tax assessments have climbed 9.7 percent have put taxpayers in a panic. But increases in tax assessments are not the same thing as increases in taxes. Thanks to Proposition 2½, citywide tax increases themselves are much more sharply circumscribed.

Herein is a brief tutorial on Boston's property tax system. Grab your coffee mugs, fill them full with the real stuff, and let's go. (Should you by chance nod off, I'll understand.)

Proposition 2½ passed in 1980. Lamented by free-spenders and embraced by taxpayers, it put two limits on property tax collections. The first requires that total property tax collections cannot be more than 2.5 percent of a city's assessed value (and by the way, "assessed value" must be fair market value; tax collectors can't play games with that number, either). So, for example, if all of Boston's real property was valued at $100, tax collections could at most be $2.50.

The second limit is that tax increases from year to year can't be more than 2.5 percent. Thus, to continue with the example above, suppose that in year two total assessed values climb by 10 percent, to $110. Taxes themselves, however, can only go up by 2.5 percent, not 10 percent. Thus, taxes in year two would be $2.56 (without the Prop 2½ limit, they would have been $2.75).

This is exactly what is happening this year: assessments are up by nearly ten percent but taxes themselves will go up at most by 2.5 percent.

So, you may ask, "Then how come my taxes went up by 15 percent last year?" Here's where it gets complicated.

The Proposition 2 ½ limits apply citywide. They don't apply to individual pieces of property. In a city as big as Boston, the values of properties from neighborhood to neighborhood, indeed, from block to block, do not all increase or decrease at the same rate.

Go back to the hypothetical above. Suppose that the $100 assessed value in Boston was from two properties, each valued at $50. Suppose in year two, one property increased in value to $70 while the other fell in value to $40. The new value totals to $110 and total tax collections are still limited to a 2.5 percent increase. But the first property will find its taxes going from $1.25 to $1.63 (a 30 percent increase) while the second property finds its taxes going down from $1.25 to $0.93 (a 25 percent decrease). Overall, however, the increase is still only 2.5 percent.

This is what happened to the Back Bay and Beacon Hill over the last several years. Property values in those neighborhoods were climbing while other neighborhoods, like East Boston, were actually seeing declines in value. The result, of course, is that Back Bay and Beacon Hill residents often saw big tax increases.

It gets even more complicated, since Boston also classifies property by whether it's residential, commercial or industrial. We reduce the tax rate on residential building by increasing the rate for commercial and industrial operations — all the while keeping within the Prop 2 ½ cap. Thus, for example, the 1997 residential tax rate was $13.73 for every $1000 in assessed value; the commercial rate meanwhile was more than three times as much at $41.50.

I could go on (and on and on), but I see you're almost out of coffee. One final word — when you get your tax bill, you can appeal it by asking for an abatement. But be careful. Applications for abatements must be filed within thirty days of the mailing of your third quarter tax bill. That tax bill goes out around the end of December which means you have to file your appeal in January. So a word to the wise: don't let the joy of the season make you forget.