If I had a bitcoin for every person I've met in the past six months who told me that bitcoin is a scam then I'd be a rich man. Or a poor one, depending in which day of the week we're talking about. Watching the exchange rate for bitcoins over the past month is like seeing the outline of a rollercoaster on the horizon. On 7 January, for example, a bitcoin was trading at $934; by 27 February it was down to $528; and on 5 March it was $678. So I guess that if you were "investing" (ie speculating) in the things, you'd feel as sick as any Alton Towers customer on a bad day.

But here's the really strange thing: while "normal" people – and many mainstream journalists – seem to think that this bitcoin stuff must be some kind of racket, some of the computer scientists and hackers of my acquaintance think it's the most interesting idea to have come along in ages. And in a way that discrepancy may be the key to understanding the phenomenon.

Jonathan Swift famously observed that "when a true genius appears, you can know him by this sign: that all the dunces are in a confederacy against him". This is a bit unkind to my friends and relations, but it contains the germ of a truth. Could it be that the reason bitcoin stirs up such hostility and controversy is that it flies so brazenly in the face of what we have always assumed to be an incontrovertible truth – which in this case is the belief that credible currencies have to be issued and controlled by central banks?

Pause for brief technical intermission. Wikipedia has a useful entry on bitcoin, describing it as "a peer-to-peer payment system and currency". It was created in 2009 by a fiendishly clever, pseudonymous individual calling himself Satoshi Nakamoto. (Sounds sinister already, doesn't it? One can almost imagine this Nakamoto cove reclining in an Eames chair, stroking a white cat.) It's a "cryptocurrency", so called because it uses cryptography to control the creation and transfer of bitcoins. (Cryptography, eh? The plot thickens. Where is 007?) Bitcoins are created by a computational process called mining, in which participants verify and record payments into a public ledger in exchange for transaction fees and newly minted bitcoins. Users send and receive bitcoins using wallet software on a PC, mobile phone, or a web application. Bitcoins can be obtained by mining or in exchange for products, services or other currencies. And some businesses now accept payment in them.

In the public mind, however, an air of rackety seediness surrounds the currency. It was, for example, the favoured dosh of the shady characters who bought and sold illicit stuff on the (now closed) Silk Road online marketplace. And last week, MtGox, one of the leading bitcoin currency exchanges, filed for bankruptcy, saying that it was "highly likely" that a bug in its computer systems had enabled a person or persons unknown to steal 750,000 of its users' bitcoins. That's about $500m in old money, and since there's no such thing as deposit insurance in the cryptocurrency world, a lot of folks are suddenly finding themselves much poorer and are mightily pissed off.

These, er, setbacks have prompted an orgy of I-told-you-so commentary, which is fair enough. But in the heat of battle, an important point may have been missed. Money serves three functions: as a medium of exchange, a unit of account and a store of value. Recent history shows that bitcoin performs the second and third of those functions badly: its volatility makes it useless as a hedge against risk. But there remains the first function – as a medium of exchange.

And here things get really interesting because bitcoin seems to perform well in this role by making small online payments very cheap and easy. Ever since the web took off, one of the things that has stopped online commerce, publishing, etc, from realising their full potential is the high cost of secure online transactions. Typically, credit cards exact fees of between 2.5% and 5%, which makes "micropayments" (fractions of a penny per transaction) impossible. But it turns out that bitcoin does micropayments rather well, in which case it could be a real game-changer. And that may be what lies at the root of the geeky excitement about cryptocurrencies. Bitcoin may or may not endure. But the idea underpinning it might just be one whose time has come.