The other day in the supermarket, as I leaned to grab a pack of birthday candles, the woman next to me asked my soon-to-be 4-year-old if it was his cake that we were decorating.

Yes, he replied. His birthday was tomorrow.

She turned to me and wistfully said, “Enjoy it. These years raising your kids will go by so quickly. In a second you’ll blink and they’ll be over.”

I must confess that normally I have no patience for unsolicited advice or commentary, particularly from strangers regarding parenting issues. But when this woman spoke, much to my own dismay, my eyes welled up with tears. It was a reminder that I needed to hear.

While the hours between dinner and bedtime seem to crawl along at a snail’s pace, I am becoming more and more aware of just how quickly time is moving. It feels like my youngest child, soon to be 2 years old, was just born. And friends of mine with teenagers echo the same sentiment; just yesterday their children were beginning to walk and talk. But that yesterday was really 15 years ago.

We all know that there is a subjective element to the way time is experienced. What happened to those dog days of summer that seemed neverending? Time does indeed fly when we are having fun, and conversely, seems to slow down when we are engaged in less-than-enjoyable tasks.

And when you drive somewhere for the first time, closely following directions,it seems to take much longer than it does when you return. Several studies have confirmed this perceptual bias, and explained that when we are engaged in a task that involves problem-solving, time seems to slow down.

“When your mind is focused on something other than the passage of time, you are fooled into thinking that less time has passed,” writes Jay Ingram, in “The Velocity of Honey: And More Science of Everyday Life” (Penguin).

Nothing marks the passage of time more quickly for parents than the growth of other people’s children.There are some friends who my husband and I don’t see more than three or four times a year. And each season I am astounded by their children’s growth. When did he get taller than his father? She is getting curvy. Is that peach fuzz? When did his voice get so low? Is she wearing a bra?

But it’s easy to lose sight with our own children. We see them every day. We bathe them and feed them and answer their many questions. We hurry them out the door each morning. We fight with them each night to go to bed. We help them with homework and ferry them from one activity to another. We break up their fights and console their shattered egos and broken hearts. It is difficult to appreciate their growth.

And then there are those unexpected moments: They return from sleepaway camp.We overhear a conversation they are having with friends.They handle a defeat with grace. Their math homework no longer includes numbers. They speak a language that we don’t know. Where did the time go? we wonder. And we’re back to that “It seems like just yesterday” refrain.

There is no doubt that time does seem to speed up the older you get. A study by psychologists at Goldsmith’s College in London confirms as much. And even more worrisome are the several studies that try to attach a logarithmic equation to the subjective experience of time. According to one set of calculations I found on a Web site, Marginal Revolution, if you plan on living until you’re 80, your perception of time will speed up so much as you get older that by the time you are 40, your life as it is subjectively perceived will be 71% over. Apparently, the years from 60 to 80 will feel like no more than 13% of your life.

And if that isn’t disturbing enough, there is another set of equations found on that same Web site that puts the age of 17 1 /2 as the midpoint of your subjectively experienced life. I guess that the hours and days and winters and summers during your childhood seem to last for so long that the years 18 to 80 will feel as if they lasted as long as the first 17.

I’m sure those equations don’t factor in the hours between 6 p.m. and 8 p.m., in my house at least. But the truth is that even as much as some of the hours can drag, the days do fly by. And there is no magic pill to counter this speeding up of time, even if it isn’t as dramatic as those logarithms.

The only answer is to listen to the woman at the supermarket, and all those who have commented along the same lines to a harried mother or father, who looks more capable of collapsing from exhaustion than treasuring the moment. Even those witching hours will someday seem like they passed too quickly. Hard to believe, but true.