That mundane service — harnessing Bitcoin’s workaday utility — is what so excites some investors and entrepreneurs about Argentina. Banks everywhere hold money and move it around; they help make it possible for money to function as both a store of value and a medium of exchange. But thanks in large part to their country’s history of financial instability, a small yet growing number of Argentines are now using Bitcoin instead to fill those roles. They keep the currency in their Bitcoin “wallets,” digital accounts they access with a password, and use its network when they need to send or spend money, because even with Castiglione or one of his competitors serving as middlemen between the traditional economy and the Bitcoin marketplace, Bitcoin can be cheaper and more convenient than Argentina’s financial establishment. In effect, Argentines are conducting an ambitious experiment, one that threatens ultimately to spread to the United States and disrupt some of the most basic services its banks have to offer.

Bitcoin first appeared in early 2009, introduced by a shadowy figure known as Satoshi Nakamoto. The software underlying its creation established that Bitcoins would be released slowly and steadily until there are 21 million of them; at that point, more than 12 decades from now, no more Bitcoins will be generated. These rules produced two somewhat predictable results, especially coming in the immediate wake of the financial crisis and the government bailouts of the big banks. The limited and regular release of Bitcoins appealed to libertarians, who have been skeptical of currencies that governments can print in unlimited quantities. (When Rand Paul announced his candidacy for president last month, his campaign’s website began accepting donations in Bitcoin.) The built-in sense of scarcity also led people to regard Bitcoin as a kind of digital gold, its value likely to increase over time — in other words, something to buy and sell as a speculative investment. The millions of traders, many of them in China, who have bet on the price of the virtual currency have kept the cumulative value of all outstanding Bitcoins well above $2 billion since late 2013. At the same time, that speculative activity has left much of the general public wondering why these virtual coins should be worth anything at all.

But the wild fluctuations in price — the value of a Bitcoin has bounced between $70 and $1,200 over the last two years — have obscured a significant aspect of the currency’s broader potential. Bitcoin digital tokens are part of a new kind of online financial network, which runs on the computers of those who use the virtual currency. People who join and support the network — hosting its open-source software, serving as record-keepers of sorts — receive new Bitcoins as they are released in a kind of recurring lottery, thus encouraging user participation. The details of how the network operates can be mind-numbingly complicated, involving lots of advanced math and cryptography, but at the most basic level, the network makes it possible for the first time to send valuable digital money around the world almost instantly, without moving through an intermediary like a bank or credit-card company or a service like PayPal. In a sense, the Bitcoin network was designed to be a financial version of email, which enables messages to be delivered without passing through a national postal service, or like the broader Internet itself, which allows people to publish news and essays without going through a media company. Instead of just delivering words, though, the Bitcoin network makes it possible to deliver money from New York to Shanghai in a matter of minutes without paying any financial institution.

The number of Bitcoin users in Argentina is relatively small; it barely registers on most charts of global Bitcoin usage. But Argentina has been quietly gaining renown in technology circles as the first, and almost only, place where Bitcoins are being regularly used by ordinary people for real commercial transactions. A number of large American companies have started accepting Bitcoin payments, but so far there has been little economic incentive for their customers to pay with Bitcoins.

In contrast, the best-known Bitcoin start-up in Argentina, BitPagos, is helping more than 200 hotels, both cheap and boutique, take credit-card payments from foreign tourists. The money brought to Argentina using Bitcoin circumvents the onerous government restrictions on receiving money from abroad. Castiglione has some hotel clients, but he says that many of his 800 or so registered customers are freelancers who use Bitcoin to get paid by overseas clients, or companies that want to move money in and out of Argentina. A popular new online retailer, Avalancha, began accepting Bitcoin last summer and has seen the volume of Bitcoin transactions grow steadily since then. Avalancha offers customers a 10 percent discount when they use the virtual currency, because accepting credit cards generally ends up costing Avalancha more than 10 percent as a result of the vagaries of the Argentine financial system. The Bitcoin community in Buenos Aires has been vibrant enough to produce what’s known as the Bitcoin Embassy in the center of the city, a four-story building that serves as the home to eight start-ups whose businesses depends on the Bitcoin network.