One wonders if, given the company's growth since then, Dorsey wishes the first tweet had been more profound.
It's not a question he is prepared to answer though, because on this occasion Twitter is another subject Dorsey declines to take questions on.
While peculiar for a chief executive to deflect questions about his own company, it is one of the dilemmas of Dorsey's dual identity. Twitter is off limits because he is in the UK to promote his other entity, Square. After Dorsey left the microblogging service, he struck up an idea with Jim McKelvey, a software entrepreneur who had run a firm in Dorsey's hometown of St Louis, Missouri, where Dorsey had interned as a 15-year-old.
McKelvey's career had taken an unconventional step into glass blowing, but he was frustrated at his business being unable to accept credit cards.
Two years earlier the iPhone had just launched, but small businesses still need bulky equipment to take card payments. Dorsey and McKelvey hacked together a scanner that plugged into a smartphone's headphone jack, and converted its information into an audio signal that could be decoded by an app. Square was launched in 2010 as a way for small businesses to take credit card payments using a smartphone or tablet.
It takes a 1.75pc fee on transactions, while its software lets businesses manage their finances. In the US, it also offers loans to small businesses that are then paid back by taking a cut of sales, as well as an app for consumers that lets them send money back and forth. Last year it launched its credit card reader in the UK, although other parts of the business are US-only.
Dorsey has been chief executive since, even after taking the reins at Twitter for a second time three years ago. The dual roles have led to tension, most notably in 2015 when Twitter's board demanded he step down from running Square if he wanted the job. Dorsey refused to budge, and Twitter's directors eventually buckled.
The decision seems to have worked out, though. Under Dorsey, Twitter's shares have arrested a lengthy decline since its 2013 flotation. Square, which went public in November 2015, has quadrupled in value since then. For a brief moment in November, its market value surpassed that of Twitter. Today it hovers close to it, worth $18.8bn (£13.3bn) compared to Twitter's $21.4bn. Most of Dorsey's own $3.7bn net worth comes from Square, in which he holds a 15pc stake.
Not that financial gain appears to be Dorsey's main priority. In fact, he ascribes Square's success to taking a different approach to established financial companies, such as banks and payment handling firms. "A lot of the institutions we came across [when starting Square] were optimising profit versus scale," he says.
"We decided that we would include as many people as possible, so we took on a different mindset."
If profit is not the goal, what is? "Our purpose is economic empowerment," Dorsey says. "We saw the financial industry of the past exclude a lot of people, not necessarily intentionally but because they weren't using technology in the right way, they weren't using modern systems and we saw a real opportunity to solve a real problem."
He says when Square started only 30pc of businesses in the US that applied to accept credit cards were accepted. His company's figure was 99pc, because it was willing to take on more risk. "It's just a very different mindset and we had the technology to back it up."
Dorsey is a clear introvert. He rarely gets animated when speaking, seemingly placing a lot more importance on the words he says than the way in which they are delivered. He is almost always dressed in black.
But it would be a mistake to interpret that as evidence of a lack of enthusiasm. Dorsey is known as a compulsive self-improver - his daily routine involves waking early, meditating and walking the five miles to Twitter's San Francisco office listening to a podcast before spending the afternoon at Square, whose office is across the street.
One of his current obsessions is Bitcoin and cryptocurrencies, a topic that many other financial industry executives have dismissed, and which institutions have distanced themselves from. Last year, Square allowed users of its money transfer app to buy up to $10,000 in Bitcoin a week. The service does not exist in the UK, although Dorsey adds a telling "yet". And while the move may have been seen as a cheap attempt to cash in on the surge in Bitcoin's price last year, Dorsey insists otherwise.
"I believe we're the first public company to offer Bitcoin. It's technology that will definitely change our industry and we believe that we will help change it for the positive. Instead of waiting for things to happen to us we wanted to help make them happen."
His other company, Twitter, banned cryptocurrency adverts last week, but Dorsey is far from modest in his expectations for Bitcoin.
He says finance is one of the few areas that remain controlled by a handful of institutions, and that the cryptocurrency, which runs on a "decentralised" network of computers rather than a handful of administrators, will change that.
"I do believe that the world will utilise a global currency and I think the world will utilise one that is decentralised," he says.
"The internet, which represents this unbridled communication network that the whole world can utilise at the same time, is going to require a currency and it likely will be Bitcoin."
It's the sort of statement you are more likely to see on an anarchist's internet forum than from a billionaire. Is there a streak of that in Dorsey?
"I think there's a sometimes healthy and sometimes unhealthy distrust of every institution," he says.
It has been a decade since the world fell out of love with financial institutions. The story of 2018 is that the same is happening to big tech companies, as regulators grow concerned over the influence they have on the information we consume, the data they hold and their effects on our minds.
"I think we should always have questions about anything that we utilise more, or anything that we become dependent upon," Dorsey says, and one senses that he's talking about the technology industry itself here more than just Square.
Dorsey says he is not worried about the threat of regulation for tech companies. "Our role is to help educate regulators around why or how a technology can help and to be very clear when it can't.
"In Square's case, we see our job as constantly having to educate banking regulators around what this technology can do."
Even with a growing backlash against tech companies, Wall Street can still be a bigger enemy, but Dorsey says Silicon Valley has to change too, becoming more democratic and transparent about the decisions it takes. "I think as an industry we probably haven't been great at being that open in the past," he says. "But I'm excited and optimistic that everything is changing towards the positive."
-Telegraph Media Group
