"Why have expensive machines rippling with applications on every desk," they said, "when we can stick one super machine in the basement and connect cheap terminals to it throughout the building?"
Bill Gates won the argument for the intelligent device, but after 15 years or so, the game is moving forward again. Because now, all that wizzy software can live in monster data centres, frankly anywhere, and be accessed by the internet - so-called "Cloud computing".
Our e-mail is already handled this way - by servers located centrally and accessed online. Google Apps as well as smaller players like Zoho and ThinkFree also provide web-based word processing, spreadsheets, presentations. And perhaps, surprisingly, not least for its investors, Amazon is now a supplier of web-based computing power.
The shoulders pushing this bandwagon are already powerful, but last week, among a number of significant strategic innovations, Microsoft announced its own plunge into Cloud computing with Microsoft Azure.
Such a strategic shift is of real consequence for our business. The earliest providers of Cloud-based services, including Google, have driven the pace of adoption with the provision of attractive free services, creating a vast new source of advertising inventory.
Developing work from multiple locations on different machines - writing the presentation at work, refining it on the mobile, presenting it on the client's system - will be reflected in entertainment. We'll use our mobile to tell our home systems to download a movie for us to watch later. And take last night's unfinished TV programme to work in our pocket.
Cloud users can access just the software feature they need, as opposed to buying up a suite of marvellous technology much of which they never use. Such selectivity will spread. Media owners will have to learn how to make money without being aggregators. Some people won't want the whole paper or a subscription to the whole channel as Really Simple Syndication (RSS) becomes Really Popular too.
Finally, the location of powerful software in the Cloud rather than in devices will make mobile consumption of media much more widely accessible, since the phone no longer has to be all that "smart".
Cloud computing is not just the next new thing in the internet story. This is a chapter change that will affect us all.
Richard Eyre is chairman of the Internet Advertising Bureau; firstname.lastname@example.org