NEW YORK >> It was just last summer that the Dow Jones industrial average shed 2,000 points in three terrifying weeks. Investors had a host of things to worry about, including the possibility of another recession.

Now the Dow is within reach of the rarefied 13,000 mark — a level it hasn’t seen since May 2008, four months before the financial system almost came apart.

A strong one-day rally — caused by a deal on bailout money for Greece, perhaps, or an unexpectedly positive economic report — could put it over the top.

What’s more, the average is just a 10 percent rally from an all-time high. And 10 percent rallies can happen fast these days.

The stomach-turning summer is a bad memory. Europe appears to be getting its act together, last summer’s downgrade of the U.S.’ credit rating was quickly forgotten, Washington is mostly behaving, and recession fears are gone.

"There are signs that the economy is getting back on its feet and the market is reacting to that," says John Prestbo, executive director of Dow Jones Indexes. "The mood is just better in this country than it has been for a while."

On Wall Street, too. The Dow traded Tuesday at 12,878, a 21 percent rally from Oct. 3, its low point for last year. In January, the average rose more or less in a straight line and added 3.4 percent, its best start to a year since 1997.

From here, the record is tantalizingly close — 14,164.53, reached Oct. 9, 2007, when the investment houses Bear Stearns and Lehman Brothers still existed and the unemployment rate was 4.7 percent.

A 10 percent surge may seem like a lot, but it’s really not. The Dow has gained almost 15 percent since Nov. 25, just 10 weeks ago.

Though there’s a long way to go to get the country back to economic health, there are pockets of encouragement. Unemployment is still 8.3 percent, but it’s the lowest since February 2009. Economic output grew every quarter last year.

Corporate earnings growth has slowed, but analysts think it will pick up again later this year. Investors, always wary of uncertainty, may even be encouraged by some clarity in the Republican presidential nominating race.

Investors are no longer just trying to stem their losses, says Mark Lehmann, president of JMP Securities in San Francisco: "They’re playing a little offense. Six months ago, they were playing defense."

There’s evidence that the rally has room to run. In a popular measure of how expensive stocks are, the 30 companies that make up the Dow are trading at an average of about 13 times their annual earnings per share.

The last time the Dow was at 13,000, in May 2008, stocks were trading for about 15 times earnings. Stock-market research firm Birinyi Associates estimates Dow stocks have traded at an average of 16 times earnings over the past two decades.

The fire-sale discounts have already come and gone, though. Those were back in early 2009, when the Dow bottomed at 6,547.05, its Great Recession low — a little more than half the level now. Back then, Dow stocks traded at nine times earnings.

Not everyone believes the rally will last. Joe Gordon, managing partner at Gordon Asset Management in North Carolina, is dubious. He cites the unresolved European debt crisis, the U.S.’ historically high national debt and the millions of people who have given up looking for work, part of the so-called underemployed.

"This is like drinking a lot of coffee in the afternoon," says Gordon. "It perks you up, then once it fades 45 minutes later you’re even more tired."

Another wrinkle is that the Dow tracks just 30 companies, so it doesn’t take the full pulse of the market. The Standard & Poor’s 500, with its much larger roster, is still 16 percent away from its all-time high.

"It’s 30 stocks," says Rob Leiphart, an analyst at Birinyi. "It doesn’t give you a representation of anything."

But despite its size, the Dow is the market gauge that penetrates the public consciousness, generating headlines and water cooler buzz more than the less publicized S&P.

That’s important because the stock market, even if it has no direct bearing on the fundamentals of the economy, is a psychological motivator of spending because of something known as the wealth effect.

Even people with no stock investments will let their decisions be influenced by swings in the Dow. When it’s up, we tend to feel richer and spend more. When it’s down — think back to the 500-point daily declines of 2008 — we tend to feel poorer and spend less.

There’s good reason the Dow has pull over the financial mood of the country. Its 30 stocks account for 25 to 30 percent of the market value of all U.S. public companies, and about 40 percent of the dividends, Dow Jones Indexes estimates.

"Nothing of substance can happen in this economy without these companies feeling it," Prestbo says.

A handful of companies have an outsized impact on the index. The Dow is a price-weighted average, which means companies with more expensive stocks have more power to drive the average higher or lower.

If you invest $30 in a mutual fund tracking the Dow, you don’t have a dollar riding on each company. Four times as much of your money would end up on Home Depot, which is trading around $45, than Alcoa, trading around $11.

IBM, the highest-priced stock in the Dow, had a giant influence last year. The Dow rose 5.5 percent in 2011, but without IBM it would have risen only 3.4 percent, according to Leiphart’s calculations.

If you were to cut out the next three stocks on the list, McDonald’s, Chevron and ExxonMobil, then the Dow would have finished down 0.25 percent for the year.

The flip side is that stocks like Chevron, Exxon Mobil, Microsoft and Intel trade well below the 13 times earnings for the full Dow. If they catch up, it could be enough to power the average to a record.