The problem is not silicone nor limits of whatever physical. A von Nemann computer is a formally deciding machine ( not : system) and is therefore limited pretty much harder.
Most human decision is not formal it is
"intuitive". von Neumann computing lacks "gut feeling" as well as "ideas".
So intelligence is rather non sequitur -
the new idea is not consistent with the problem.
That is human and most possibly animal
solution finding is not logical.
So far there is no such thing as artificial intelligence.
That would require a not formal theory of context.

Well, all the data I could find say that Moore's law is still going on. Of course, nothing can go on exponentially forever - I think we'll see chips growing in power for several years; maybe not exponentially any more, but still getting more powerful. Then, there are innovations that might revolutionize the field and start a new and even faster exponential spike - quantum computing for instance. In the end, however, this is not the point. The point is what we are going to do with all this computing power. I argue in my text that better computers are simply taking us to hell faster. Quantum computers are not going to help much, if this is the case.

Sorry to be anal about this but silicon is the semiconducting metal that makes most of modern computing possible where as silicone is a polymer using a silicon and oxygen backbone most commonly used to seal the edges of baths.

This is why Intel and AMD are not offering any new technology below 0.8 Micron instead launching Dual Core and Quad Core using the the last genuine drop in cricuit size off the PENTIUM 4

Umm, well before we had transistors no-one would have thought you could go beyond some speed in valve switching. Perhaps we will stop using transistors and use some new invention not yet discovered which does not depend on silicon? You may see this as unlikely, but given that is has happened at least once before in this particular field I don't see any evidence for this. Saying nothing can replace silicon is a bit like Lord Kelvin in 1900 making the following statement:

"There is nothing new to be discovered in physics now."

He believed only refinements in measurement were left to be made. This was before relativity, quantum theories, subatomic particles etc.

No new technology is "on the horizon" before it is discovered, if it was, we wouldn't have to discover it!

Seems to me that before making absolute pronouncements on the future of electronics chips, one should learn the difference between silicone (caulking, implants) and silicon (computer chips, etc.)

Distributing units of work amongst parallel CPUs has the same effect as hiring more officials. At a certain point
the administrative effort to share workload exceeds added processing power.
So theoretically the limit of n in n core CPU chips is well established. It is 8.
if one wants more the applications had to be thoroughly re-programmed.

For the performance of normal PCs that most people can afford, this whole discussion is utterly irrelevant and has been for about a decade.

CPU speed might be 2.4MHz or more, and the advertised memory speed might be 833MHz or more, but memory (and even cache) is so awful that the actual effective memory speed will be maybe 150MHz at the sustained very best, and well below 15MHz and as low as 6MHz with certain sequences. The core spends most of its time, as it were, standing in line while the memory is perpetually out to lunch or hiding somewhere, as if the PC were some sort of miniature DMV office.

Added cores may shorten a few operations slightly, but mostly they will be just be sales-pitch gimmicks that just sit there waiting on the memory while consuming electricity. This is why software that actually needs to compute intensively, such as, say FPGA design software, may need ferociously expensive "hardware accelerators" when it's used on a large job. The CPU cores probably could do the job, but the memory trots along leisurely in some bygone era.

The problem is that since, say, 1980, memory access time for normal, affordable chips, has improved from around 80 nanoseconds to around 5 or 7. That's it. (And 32-bit Windows on Intel-style chips does two non-useful "descriptor" fetches for every real fetch; one of those is usually cached, so call that 10 or 14 nanoseconds.) The very high speeds given in data sheets are mainly trickery, so complex that the explanations occupy many dozens of densely filled pages. The tricks work when the memory is accessed in continuous rigid lockstep sequence. That happens in contrived "benchmarks", but not so much in real computing with real software. Once the sequence is broken, the same tricks slow things to a crawl, accounting for the sub-15MHz performance under the right (i.e. wrong) conditions.

What has improved tremendously is the density of dead storage. So you can store lots of songs or videos on your PDA, which is nice (but doesn't address "performance".) Playing back audio is rather undemanding, and even video on a tiny low-res screen is only moderately demanding. The utter lack of improvement in memory speed is not really an obstacle there.