When envisioning the computer on the starship Enterprise, did Gene Roddenberry not fathom computers getting more powerful even as they got smaller?

In general yes, the original Star Trek expected computers to continue to be large furniture-sized machines, as well as to be capable of exploding when told semi-witty logic problems, as Kirk and Spock managed to do to several otherwise dangerous computer systems.

But… your question is somewhat impossible to answer, because the Star Trek ship computer also does things we can’t do yet, and don’t know how to do, such as have enough artificial intelligence to solve very complex new science problems very quickly, often by just talking to them or pressing some buttons for a minute or so. Maybe the Handwavium processors required will turn out to be big, use lots of vacuum tubes, and be subject to suicide when presented with paradoxes.

It’s been said though that the computers used by NASA to control a trip to the moon and back, were room-sized, and now could be done with the computers in our “smart” phones. Of course, we’d still need months or research and development by a team of top-rate engineers to really do that, but that computer system had data and speed less than our phones do.

Well, for personal devices, yes.
But even today, the most powerful supercomputers still fill entire warehouses and consume as much power as a small city.
It stands to reason that the flagship of the Federation would not be content with a small box in a corner, when it has a lot more space for a supercomputer, and thus, more computing power. Which it needs, because the Ship’s computer does not just control basic ship operations, but also has to handle and process all the sensor data, tactical computations, transporter calculations and storage and of course the holodeck.
And as you certainly know, they did have small personal devices, like the small flattscreen terminal on Picard’s desk, the PADDs, and even the Tricorder.

*flatscreen
It remains a constant source of amusement to hear trekkies attempt to justify the shite which they honour.

For me, not a “trekkie” but just a guy who never missed an episode of Star Trek, its everything Mr. Roddenberry and his farsighted sci-fi writers did envision, not what they didn’t. Sure, the technology in many ways looks silly and quaint today —but in those slightly less cynical times when TV was churning out brain-numbing (albeit unfanthomly popular) junk like I Dream of Genie and Hee-Haw, ST was quite ahead of its time in both tech ideation and storytelling, and provided a universe of fodder for the raging imaginations of young sci-fi fanatics like me.

I don’t think the Star Trek Computer is as big as the “Super-computer” in War Games. Or even the NORAD computer in Fail-Safe.

Gosh..he introduced cell phones on one of his original series.

Oh, you are harsh. Roddenberry was a great visionary. He did anticipate the tablet computer, along with a bunch of other scientific advances which have come to pass some because of Star Trek’s influence.

They all had tablets,cell phones that could talk without towers plus other neat stuff. Pretty visionary for even then. Having a huge computer like mentioned is not out of the ordinary even for today. The one on the enterprise even had some A.I.

@marinelife Oh, you are harsh.
I am not slamming the guy; I believe Roddenberry was way ahead of his time. I am just reflecting on where computers have come from in my lifetime, from the super large (and primitive by today’s standard) IBM RAMDAC (slightly before my time), the Apple IIe, to today’s tablet PCs. When the Apple IIe came out I thought it was wicked smart, today I am not sure a 4G Smartphone could not out pace it, and easily too. The Apple IIe was as large a briefcase on its side, not counting the monitor, the 4G Smartphone, about the size of a stack of post cards. It seems which each new phone or tablet it can do more and more, faster than its predecessor. I am just thinking if that trend continues, the computer on the Enterprise would be able to do all that it does, but do so in a package around the size of a Yukon Denali, or at worse an ample sized 5th wheeler.

Cut the man some slack! After all, he came up with the concept, but many others wrote scripts and added concepts of their own.

It was fantasy. Seems sort of shitty to judge his view of the future in the present context.
Would you treat Jules Verne the same way?
Do you know who Jules Verne was?

^ It was fantasy. Seems sort of shitty to judge his view of the future in the present context.
If that is how you see it, then I guess you see it that way. The truth is, he missed judged the direction technology would go, in that part. That IS not like it hasn’t happened to others. I am sure there are things believed to be common place in the future today, that when the future get here, won’t be anything like it. I used to think sentient automatons like Data would be common before clones, but man seems to have made bigger gains in clones than robotics (as far as machines that can think on their own in real time).