When Verifone went primal on Square a couple of weeks ago with a no-holds-barred negative PR campaign, I wondered why Verifone was wasting its brand goodwill with such an attack. Sure, Square‘s doing OK, but it appears to be little more than a payments app for artists and vagabond merchants.

But after hearing Jack Dorsey, Square’s founder, speak at Columbia Journalism School today, I know why Verifone went ape-shit. Square just might smoke ALL payments companies, not just Verifone.

I couldn’t help but be terribly impressed with Dorsey. He seems like a quiet, exacting, pedantic man with a programmer’s mind, but a businessman’s upright back. He speaks in such a monotone that I wondered how he attracts any VC funds at all. There doesn’t seem to be much passion behind the precision. But, of course, that is not true at all. He sits atop two remarkably vibrant startups as founder of both Twitter and Square. (Yesterday, he announced that he was returning to Twitter as CEO, while maintaining his role at Square.)

Dorsey sees Twitter and Square in a similar light. They are both, he says, “utilities, like energy or water.” They allow others to build applications on top of them and can be used in various manners. You want to tweet that you are eating Wheaties? Use Twitter. You want to tweet that there should be a revolution in Egypt? Use Twitter. Same for Square. It’s nothing more than a tool for commerce, he says.

“Commerce” is the key word here. “Commerce” goes beyond “payments,” and Dorsey knows it. PayPal, for example, resides in the virtual world. Square, however, is starting from both the virtual world, in that it offers smartphone and tablet interfaces, and the physical world — where the volume of transactions far, far exceeds the volume of virtual transactions. Square is also starting from the other end of the transactions, from the merchant side. When Dorsey says, as he did today, that the team at Square, which now numbers 99, is looking at all use cases, he means it. And he knows that “commerce” and “payments” do not end with the little do-dat that he is giving out to roaming merchants selling at street fairs. Dorsey was asked whether Square might consider European chip-and-PIN or tap-and-pay technology, and his answer was effectively why not? “Let’s make Square available,” is the mantra at the company, he said. “We are not paying attention to one use case. We are going to serve all of them.” Dorsey understands that the pricing model for Square does not allow it to move easily to other payment channels, such as P2P payments, “but it will evolve,” he said.

Now you know why Verifone is freaking out.

Can Square become the dominant payments player? Certainly, there is a need for a Square. If you haven’t read the Federal Reserve’s recently released report on mobile payments, you should. The Fed, which has been convening the presumptive players in mobile payments for meetings over the last several months, spells out what is needed to make mobile payments fly in this nation:

1. The proposed environment is best defined by the concept of an “open mobile wallet.”

2. The mobile infrastructure would likely be based on Near Field Communications (NFC contactless technology resident in a smart phone and merchant terminals).

3. Ubiquitous platforms for mobile should leverage existing rails, including the ACH network for non-card payments, and support new payment types that meet emerging needs. 

4. Some form of dynamic data authentication would be at the heart of a layered mobile payment security and fraud mitigation program. 

5. Standards would be designed, adopted, and compiled through an industry certification program to ensure both domestic and global interoperability, including a standard to ensure that devices used to facilitate mobile payments do not create any electronic interference problems. 

6. A better understanding of a regulatory oversight model should be developed in concert with bank and non-bank regulators early in the effort to clarify compliance responsibilities. 

7. Trusted Service Managers should oversee the provision of interoperable and shared security elements used in the mobile phone.

That’s seven items, for those of you keeping score. Seven various elements that need to come together in order to make mobile payments work. To me, it is obvious that the likelihood of widespread adoption for mobile payments will advance significantly, if one party took care of these seven variables.

That’s why the market needs a Square, but what about Square makes it better suited to become the dominant player beyond the fact that it is already situated in both the virtual and physical worlds? A few factors. One, Square takes a remarkably simple approach to interchange. Square charges just one, flat interchange fee of 2.75%. Not the lowest rate out there, but not the highest either. Dorsey points out that the current merchant account setup taxes the average small business. Because interchange varies and is not paid immediately, small businesses face cash flow problems. Square takes on the interchange/cash flow risk for the business, and that is a substantial benefit to the merchant-user.

Second, Square is simple. As others have said, “simple” is not easy. Financial services “is not easy to design for,” Dorsey said. And that couldn’t be truer. Just its simplicity and cross-platform design give it a leg up.

Third, I didn’t know that Square current geo-tags every transaction. That geo-tagging reduces Square’s risk/interchange. Additionally, Square feeds that information back to the merchant, which adds a whole other feature to Square: data. I have argued that analytics today matters far more than absolute dollar returns, because data and analytics allow for greater revenue realization tomorrow. Square is dead-set on providing that.

When you pull it all together, you’ve got an a) easy to use; b) affordable; c) data-rich; d) interoperable payments option for merchants that can be easily extended well beyond merchants. Now consider what Dorsey has planned for Square:

* Within two years Square will be international;

* Square will add PFM capabilities soon;

* Square plans to extend its reach beyond just merchant card transactions to other channels of payments; and

* Square will further enhance analytics for merchants.

That’s called a play to take over payments.

“Square is growing more rapidly in its first two years than Twitter did,” he said today. “It has the potential to have just as much impact, if not greater, than Twitter.”

After this morning’s presentation, I believe him.