I have had the following idea / opinion in a long time, but I am not sure if it is true.

From what I understand, in a processor, coarsely the voltage U required to operate is proportional to the frequency f at which it is run, and the computing power is proportional to the number N of transistors present and the frequency f.

Therefore, one could:

  • divide the frequency of the processor by k, allowing to divide the voltage by k
  • increase the number of transistors by k^2

This would in turn give a computing power increased by a factor k (increased by k^2 because of the number of transistors, decreased by k because of the frequency), for an electric power unchanged (power is U^2/ R * N where R is the electric resistance, U is divided by k, N is increased by k^2). If Moore law gives more and more transistors for the same price, then you should have no limit to the computing power you achieve (at the cost of reduced frequency and possibly requiring parallel hardware and algorithms).

Is that reasonable (or even true), or is there an underlying error? Naively / loosely, I think about this as an explication of why the brain is so much powerful while using a bit less energy than a CPU (brain is typically 20 watts and 100Hz, CPUs nowadays often from 35 to 130 watts and 3GHz, some people say ).

Edit 1:

  • Yes, I know that the energy consumption / power consumption is the wall that processors are meeting. Here I talk in terms of voltage (before converting to power consumption) because it is what predicts (or so I believe?) which frequency one can run at.

  • The computing power does is proportional to the number of transistors. For example, one can simply build more cores given more transistors. The problem then is power consumption; this is why I consider a decrease of frequency, so that power consumption increase by increasing the number of transistors is zeroed by the power consumption decrease due to running at lower voltage (and, hence, frequency).

  • I know that this will not increase the one thread execution speed, and will require parallel algorithms, but this is not the question. In the same way, architecture is not the question either. I am aware that manufacturers now add more and more transistors to the caches etc to increase one thread execution speed / reduce latency, but this is not what I ask for here. Here I ask only about whether a very general scaling argument is true, then using this scaling with parallel software is another question.

  • By the way, we are getting better at using parallel architectures: Artificial Neural Networks on GPUs are all about it. This is exactly the idea behind the brain also: very slow at one thread operation, but incredibly parallel and powerful computing power. What I want to understand really is: given the silicium technology used on current transistors, can we in theory if Moore law holds (i.e., we get more and more transistors for the same cost) build something as powerful as the brain that does not use megawatts or more. For this, it sounds that the solution is to increase parallelism, and reduce frequency (as in the brain). For example, if my scaling argument holds, you can get the frequency of your chip from 3GHz to 100Hz (i.e. divide frequency by alpha = 30 millions) and by adding a LOT of transistors (alpha^2, but if you expect Moore law to hold, we will get it ultimately), and therefore increase the computing power of the chip by the same 30 millions factor. I agree, this is not that straightforward to pack so many transistors, maybe you would need a 3D chip (like the brain) or another architecture change, but I am just interested about the scaling.

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    \$\begingroup\$ Computing power is proportional to number of transistors? What are the units of "computing power"? And the right term to refer to instead of "tension" (commonly known as "voltage") is power. Nobody cares about voltage alone. \$\endgroup\$ – Eugene Sh. Aug 16 '18 at 21:36
  • \$\begingroup\$ Just a short note. Dr Hennessey spent several days speaking to me, personally, about the MIPS approach with RISC vs CISC, back in 1986 when I visited their facility then. They used TWO ORDERS of magnitude fewer transmission gates and inverters (transistor equivalents) than Intel did, at the time, because neither Mot nor Intel would sell them ANY access to the best FABs of the day. They had to do more, with less. And they did. They nearly scared the pants off of Intel. And there was a huge shift towards RISC. Mot, for example, launched the 88k. Intel fielded its own projects, too. \$\endgroup\$ – jonk Aug 16 '18 at 21:41
  • \$\begingroup\$ In any case, the trend in computer CPUs nowadays is to increase the number of cores, while the clock frequency has stood almost still for several years now. Optimizing the software to take advantage of multiple cores (parallelization) is one of the big challenges. \$\endgroup\$ – Dampmaskin Aug 16 '18 at 21:41
  • \$\begingroup\$ The result at Intel was something I was a part of -- the PPro and P II -- both of which used RISC inside (the re-order buffer) to achieve their CISC behaviors. I think the gist here is that higher clock rates can often trump more done per clock, assuming that the memory systems can feed the pipe. Today, there are superscaler, multicore, parallel pipelines, and more techniques available. So it's "complicated." Things cannot be so simply broken down into just "more transistor equivalents" or "higher clock rates" alone. \$\endgroup\$ – jonk Aug 16 '18 at 21:42
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    \$\begingroup\$ I would strongly advise to get the Hennessy and Patterson classic text, amazon.com/Computer-Architecture-Quantitative-John-Hennessy/dp/… After you read it all and understand 50% of it, come back. For now I politely vote to close this question as "too broad". \$\endgroup\$ – Ale..chenski Aug 16 '18 at 22:09

You cannot lower the voltage indefinitely, at some point transistors simply stop working, regardless the frequency. Current CMOS technology achieved about 500mV threshold voltage, and this is not expected to get better any time soon:

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