By DAVID POGUE

It’s always thrilling when somebody looks at the Way Things Have Always Been Done, and then asks: Why?

And then goes on to change the world forever.

1967: Why is it necessary to wait in line for a human teller if all you want to do is withdraw cash?

1974: Why shouldn’t your document on the computer screen look the same way it will when it’s printed?

1991: If shampoo always settles to the bottom of the bottle, why is the cap on top?

Recently, a San Francisco company has been asking an equally groundshaking question: Why can’t everyone accept credit cards?

Look, credit cards are great. There’s a paper trail, there’s fraud protection, there’s incredible convenience — just swipe and go. But why is it that only companies accept them?

Why can’t we use them to pay the piano teacher, the baby sitter, the lawn-mowing teenager, even first graders at their lemonade stand? Why aren’t credit cards accepted at garage sales, food carts and PTA bake sales? Heck, when your tipsy buddy wants to borrow $20 for a cab home, why can’t you eliminate the awkwardness and future conflict by just running his Visa card on the spot?

“Well,” you’re surely spluttering, “because — well, just because! That’s just how it is. Only actual companies take credit cards, everyone knows that!”

Yeah, but why?

The company asking that question is called Square. Its chief executive is Jack Dorsey, who co-founded Twitter — heard of it? Square is not only asking why, it’s proposing to change that rule for good.

There are actually some good reasons individuals don’t accept credit cards; the whole system is a nightmare of fees and red tape.

To become a credit card merchant, you have to buy the card-reading equipment, which costs several hundred dollars. You generally pay a setup fee, and you commit to a one- or two-year contract with the processing company. You pay $15 to $25 a month, and minimum transaction fees of $25 a month, even if you had no sales at all.

The Square Up system, on the other hand, eliminates that stuff. All of it. It makes the barrier to entry into the credit card world so low, there’s virtually nothing to stop you, the little guy, from taking the leap.

First, the equipment: you need an iPhone, iPad, iPod Touch or an Android phone. Why buy a fancy authorizing machine, when you already have a computer in your pocket?

Unfortunately, Apple steadfastly refuses to add a card-swiping slot to the iPhone. So Square provides you with a tiny half-inch reader attachment that snaps into, of all things, your phone’s headphone jack. The reader has a slot where you can swipe a credit card.

(The name Square, of course, refers both to the shape of the little reader and to what it does — as in, “are we square?” Cute.)

The Square plug is free. In other words, not only are you spared the contracts, the minimums and the monthly fees, but your equipment cost is zero. For all Square cares, you can keep your reader in a drawer somewhere and use it once a year.

For each transaction, Square charges you 2.75 percent of the total, plus 15 cents. That’s a lot simpler, and usually cheaper, than actual merchant accounts, where you might pay 3 or 4 percent, depending on the kind of card, plus 30 cents a transaction.

So let’s say someone from Craigslist comes over to buy your old junk. You snap the Square reader into your phone or tablet. You tap in the amount of the purchase; it could be $1 for a yo-yo, $25 for a box of old records or $12,000 for a used car (there’s no maximum amount). You type a description if you like, and maybe even take a photo of what you’re selling.

Now you swipe the customer’s card, which may take you a couple of tries. Your happy customer signs the phone’s touch screen with a finger (a coming software revision will make this step optional). If you like, you can tap in the customer’s e-mail address; the receipt is then sent automatically, complete with a little map showing exactly where the transaction took place.

The software is beautiful and dog-simple. To sign your name, you scrawl with your finger where it says “sign here.” Think you can handle this?

You can add a tip, when that’s appropriate. You can accept and track cash payments. And you can accept credit card payments without the card itself — over the phone, for example. You just need the card number, expiration date and security code, although these transactions cost you more (3.5 percent).

The iPad software is even nicer. It features a “shelf” depicting the kinds of things you sell the most often, with prices included, which is great if you run a small store.

Anyway, that’s the entire thing. Your phone connects to Square, authorizes the purchase, sends the receipt by e-mail and logs the transaction on your personal Square Web page. There, a tidy table reports your income for the day. You can download it as a spreadsheet if you like.

You’ve just accepted payment the way they do it at Apple stores: wirelessly, without a cash register, using a hand-held Internet-connected gizmo. Your biggest problem may be overcoming your customers’ skittishness; people don’t trust what they don’t understand.

Signing up for Square involves supplying your bank routing and account numbers, so Square can deposit your money. Only the first $1,000 of each week’s charges lands in your bank account immediately. Anything over that is reviewed by the company’s auditors; it can take as long as 30 days before you see the rest of the money. That could be a downside if you sell a lot of used cars.

Then again, that’s just for first-timers. The more you use the service without incident, the higher the company will raise that $1,000 threshold. In fact, if you’re willing to share more details about your business with Square upfront, they’ll raise that threshold from the start.

It’s easy to imagine that a concept this disruptive, brilliant and irresistible will take off, but its runway has been bumpy. The initial batches of readers were delayed. Even when they arrived, there were long waiting lists and not enough status reports.

As an antifraud measure, Square originally imposed a $100-a-transaction maximum, making the system far less useful. The original readers were finicky about reading card swipes — and didn’t work with the iPhone 4’s external metal antenna band. (Early Square adopters turned to humiliating workarounds like wedging a scrap of paper between the reader and the phone.)

The company says all of these problems have been fixed. Mass quantities of a redesigned, more reliable, iPhone 4-proof Square reader arrive this week (it’s the one I tested). Within a couple of weeks all backorders will be filled, everybody who got the old one will get the new one automatically, and new orders will be filled promptly.

Let’s hope that’s true. Because the Square system is beautiful, simple and a joy to use. It saves money, red tape, worry and lost sales.

Now let’s just hope more smart people keep asking why. As in, “Why is Wi-Fi free at cheap hotels, but $17 a night at expensive ones?” “Why don’t public sinks have foot pedals?” And “why can’t we just pay for the cable channels we actually want?”