Bitcoin with one of the virtual currency community's slogans

There is a future when the City of London really doesn't sleep:

Trading still stops on the Stock Exchange at five sharp, but the banker doesn't stop. He just switches kit. He checks his bespoke Bitcoin miner humming away on the corner of his desk. 0.6 coins mined this year, not bad. Then he opens up his Bitcoin exchange apps, along with the Google Maps plugin that shows Bitcoin exchange rules for local pubs. The game is on: it's Bitcoin Hour.

He runs from bar to bar, prodding live trades of Bitcoins into a touchscreen wrapped round his wrist. He chooses where to go by balancing live prices with the risks of each pub's rules. If he gets stuck at the back of a scrum at a temporarily underpriced bar, the 10-minute rate will revert to something less favourable, and he'll be left drinking slower and at a higher price than the others. Underground dives always offer better rates, but he risks losing enough 3G signal to make a last-minute trade before the bill comes in. Drinking in the City is no longer about overpriced champagne, it's about a personal rating on the Per-Pint futures index.

I was shocked at recent online survey results: 69% of UK respondents had heard of the online currency Bitcoin, and of those 32% trusted the currency. The survey was a quick piece of work done partly to promote the first Bitcoin London conference this week, and I worry that the sampling is biased towards super-hip kids with tablet devices. But even so, that's pretty amazing.

Bitcoins are nothing more than strings of computer code – just like all the other packages of data uploaded and downloaded across the internet. They have value because it's hard to create these particular sequences of code; they are solutions to an ever-changing maths problem, modified to make sure – at the moment – that approximately 150 coins are produced an hour. No more than 21 million coins will ever exist. If you want to understand why, the Bitcoin Foundation has a good wiki explaining the basics.

No bank certifies Bitcoins and no treasury has declared it legal tender. They are worth only as much as other people's desire to use them. A recent profile of Bitcoin entrepreneurs argued that "to be a Bitcoin user is to be a Bitcoin evangelist". They are traded on a shared belief that these sequences of numbers and letters are worth something. It is a technology created completely by faith.

So why are people willing to trust an unregulated technology that poses immediate financial risk? It seems odd given that public trust in science and technology depends directly on the organisations that develop that technology. In the latest Public Attitudes to Science Survey in the UK, 84% of respondents trusted university scientists. 56% trusted industry scientists.

One of my crib sheets for this type of issue is a short paper put together by two Cambridge philosophers for a government advisory group that looked at science and trust. They start from the idea that we always trust someone to do something. Trust is not some kind of wholehearted love-in. It's much more specific than that. I tried to pull apart the different organisations producing, trading and investing in Bitcoin, and work out who is being trusted to do what – and whether I would give them my money.

Trust to do what? Algorithms, market traders and nightclub owners

Trusting the maths of Bitcoin makes sense. Most of the computer code behind it is publicly available, meaning it has been checked over by lots of programmers. The algorithm that limits the supply of coins also verifies transactions between anonymous users. So there is a record of when the coins are bought and sold.

To get Bitcoins from cash, you need to go via a Bitcoin exchange. Mt. Gox is by far the most popular. I got a bit uneasy using their site: wiring money to a branch of a random Japanese bank, with annoying overseas payment fees attached; waiting two to five days with no guarantee that funds will turn up in my account with the exchange (they haven't yet). Once the money clears, I can buy Bitcoins at the current market rate. Although, be warned, the market is much more volatile than, say, stocks and shares. One Bitcoin was worth £65 on Monday and now only £48. But at least using Mt. Gox is safer than meeting up in Union Square in New York where you can trade $50 dollar notes for Bitcoins exchanged via Android smartphone apps.

After I have my coins, I can then transfer them to my virtual wallet on my iPhone. (Apple has disabled apps with a live link to a virtual currency exchange). And I can choose when to spend them. Not that there is much choice in the UK just yet. There is only one pub that accepts them. Luckily it's near my house.

Getting involved with companies that have sprung up around the currency is a much riskier bet. These are the online currency equivalent of nightclubs; daring investments that survive on only their hype. Private exchanges like Coinsetter manage your purchase of Bitcoins for you. The Winkelvoss twins, who once sued Mark Zuckerberg over the ownership of Facebook, have registered a Bitcoin Trust, which will invest in Bitcoins. They hope to operate in the same way commodity–based funds invest in precious metals. And just to mess up metaphor and reality, one New York nightclub owner also runs one of the first Bitcoin payment processing software companies.

Venture capitalists are very excited about these companies. Over $10m were invested in Bitcoin start-ups in the past three months. But it's still very early days – there are more investors than there are companies. I find this all a bit strange when it's not clear exactly why Bitcoins are valuable. I have no idea whether I would be investing in a nightclub or gold bars.

Being your own bank

Putting my faith in Bitcoin is much easier than nanotechnology or nuclear power. So far, I have not trusted the currency to do anything much. It doesn't raise fears about tiny robots taking over the world, or debilitating illness from radioactive exposure. Nor do I have to hand over much control to anyone else – this is an algorithm not a bank. The Bitcoin founders' hands-off approach makes the public's usual questions about how a technology is created less relevant.

However, if the private Bitcoin exchanges and investment companies take off, there will be a different story. This would attract the attention of regulators. Crowdfunding peer-to-peer lending platforms went through this when they began to compete with banks' small business loans. UK crowdfunders are now pushing hard for self-regulation, setting out a code of conduct.

US regulators already have a tense relationship with the Bitcoin Foundation. A similar online exchange was recently shut down in the US after it was used for largescale money laundering. There is an opportunity for a more cooperative approach in Europe. The UK government chose crowdfunding as one of six areas of business where it wants to remove red tape, signalling a willingness to support alternative finance systems.

For some, Bitcoin stands for something much bigger. It is a statement of distrust in banks, and the desire to find an alternative – any alternative. This is certainly the motivation behind Freicoin, an alternative to Bitcoins used by the Occupy movement. It devalues over time, reducing the incentive to save. Switzerland has had an alternative currency system to aid local trade since 1934.

Other technologies that bypass the bank are popping up all over the place – peer-to-peer foreign exchange, open source software to analyse financial market risks or an interplanetary payment system for the space tourists of the future. But Bitcoin is today's flag-waver for distributed, accessible finance. I hope it's around for a while. It's an interesting experiment in negotiating how to trust digital technology. And if technology can help us do anything, broadening the financial powerbase is not a bad place to start.