Reindexing a blog in Blogshares will cause its total value to be recalculated, and will also cause ideas to be produced, based on industries the blog is voted into. Math 101 gave the basics of outgoing shares values, Math 102 covers reindexing as it relates to shares math.
Reindexing is very straightforward, when this happens, the total values of all incoming links are added, and the blog's base value of B$ 1,000 is added, to give the blog's current valuation, which is then used to calculate the blog's outgoing valuation as outlined in the Math 101 article.
The key point to understand here is when it is appropriate to reindex a blog. The most elementary concept is to only reindex a blog when this will result in an increase in the blog's value. The Stock Broker function in Blogshares is very handy for this, if you own any shares at all in the blogs you are interested in reindexing, as it will tell you exactly how much a blog may gain if reindexed at that particular moment. The second most common way to determine this would be to pull up a blog's page in Blogshares, and add up the incoming values yourself with a calculator.
Ideally, the blog should gain at least 2% in value to be worthwhile to reindex, if a blog is worth B$ 500,000, and will gain B$ 10,000, then reindexing would be good, if it may only gain B$ 5,000, then reindexing may actually harm the blog.
One new change in the shares math is the use of a multiplier that can cause a large boost to a blog's outgoing value, if it has roughly 3x the number of outgoing links as incoming (as detailed in Math 101). The multiplier varies on a daily basis, I hope to have more exact details on this posted soon. There are times in the cycle where a blog can actually lose a small amount of incoming value, but gain outgoing value, but there are other times where a blog may gain a small amount of incoming value, but lose outgoing value. The 2% rule above will generally guarantee that a blog will have more outgoing value, assuming all else stays the same.
The things that are likely to change, of course, are the number of incoming and outgoing links. When reindexing a blog, either your own or someone else's, you should check the blog's page in Blogshares, and see what the current number of incoming links are, and compare that to the value from when the blog was last reindexed. If the outgoing total from the last reindex is still roughly 3x the incoming number, and the blog's value will be going up, then it should be safe to reindex. If the incoming link total is significantly different from the last reindex, reindexing may cause the blog's outgoing value to crash. If you are not the owner of that blog, contact the blog's owner, and advise them that they may need to add (or possibly remove) outgoing links to avoid their value crashing.