A friend mentioned the "yellow pages" to me today, and it occurred to me that I haven't used "The Yellow Pages" for at least five years. I can't remember when I last even saw a copy of the Yellow Pages (until today when I dug out a copy from under a desk). For many years, whenever I've needed a phone number or other information regarding a business, I've used Internet tools. It didn't happen all at once that I stopped relying on Yellow Pages, so I didn't notice any particular date when when it happened. Imagine that the phone companies announced five years ago that there wouldn't be any more Yellow Pages--we might have noticed our discontinued use. But human cognition is often blind to incremental changes. I posted on this topic earlier, using the example of tigers. There are very few tigers living in the wild. Almost all of the tigers of the world are now living in captivity. Very few people were conscious of this change, because it was gradual, but it undeniably happened. If it had happened all at once (with a headline screaming "95% of the wild tigers are gone!") we would have noticed and perhaps reacted. This reminds me of a book by Howard Kurtz (Media Circus), where he suggested that the biggest story of the 20th Century was that millions of African Americans were moving from the rural South to the Urban North, but no one noticed because no one faxed a press release to the news media. In fact, studies show that we are not even able to notice relatively fast moving gradual changes. Because of this human cognitive limitation, important things constantly fall beneath our human attentional radar. Yes, we do notice when an airplane crashes and kills 100 people because headlines are blasted at us and we can perceive the crash site from a single vantage point. But we don't react to drawn out disasters of much greater magnitude. For instance, where are the headlines announcing that 40,000 Americans needlessly die of colon cancer every year because they don't get colonoscopies? That's 110 people who die every day. But they don't die at the same place and there is no crash site to provide dramatic video for news shows. How much else of importance gets entirely ignored because there aren't dramatic photos? Trends are often invisible, whether they are good trends or bad trends. Whether there is a decrease in the standard of living or whether many of us dramatically increase the amounts of corn fructose we eat, many trends are difficult to notice without mathematics and graphs. Most important trends are invisible unless we are vigilant and comfortable with mathematics. Perhaps this should be a word of caution for a society that is heavily afflicted with innumeracy; bad things can happen on our watch yet we might be oblivious. Things like the deterioration of our education system, the increase in xenophobia, the fact that many of us seem to operate burdened with attention deficits, the skyrocketing rate of diabetes, stagnation of wages for several decades, and who knows what else. We face many huge challenges as individuals and as a society. Are we trying to shake a bad personal habit such as overeating? Are we trying to lessen our dependence on oil? Being cognizant of our obliviousness to incremental change can help us by reminding us that we shouldn't be discouraged with tiny sporadic steps of progress when that is all we can muster. It doesn't necessarily take a sprinter to make significant progress. as long as we're going in the right direction. We should keep up our efforts even when it seems like we're not getting much of anywhere, because small steps in the right direction always eventually prevail, even though our progress is often invisible until we've almost arrived.