I have been doing some re-thinking concerning the potency of Moore's Law, one of the underpinnings of the arguments for the likelihood of a Singularity. Moore's Law promises an exponential improvement in the hardware available to us, and it does so at a rate which is fairly predictable (at least for as long as Moore's Law has to run). From this, you can deduce that even if nobody figures out a more clever approach to the most difficult computable problem facing you, if you give it long enough then Moore's Law will provide a "big enough hammer" to solve the problem by brute force alone. Or, at least, that is how I used to look at it.

What is causing my reassessment is the fact that it is not only possible, but actually rather easy to devise problems that are resistant to solving by faster hardware alone. Consider the following example: count from 1 to 2^256. It is easy to state the task, yet completing it would require more energy than the Sun will put out during its lifetime. If this sounds unbelievable, let me demonstrate that it is not.

First, we need to start with a value for the amount of energy the Sun will emit. The estimate I will use is 10^46 joules, which is probably an overestimate, but as we will see, that will not help any. Now I divide the 10^46 joules by 2^256 to get an "energy budget" for each count. The result of this division is 8.63 * 10^-32 joules as the maximum energy that can be expended per count. This is about 10 orders of magnitude more than the ~kT limit needed to erase one bit.

Now there might be those who wish to quibble by pointing out that reversible computing architectures have been proposed that would not be subject to the kT limit. My response is several fold. First off, all the computers that have been built so far require far more than kT per bit changed. Next, you would need a computer at least billions of times more efficient than the most efficient possible non-reversible computer to do any good. Finally, even if you had a computer that efficient, you would need a Dyson Sphere and the willingness to devote the rest of the Sun's energy output to a single problem. Note also that the question of the speed of the computer you are using doesn't even enter the picture; we are just talking about energy usage so that improving the number of FLOPS (FLOating point OPerations per Second) your computer can churn out does absolutely nothing to make the problem more soluble.

The ease with which one could set up a problem that is completely beyond the ability of Moore's Law alone to render tractable suggested to me that there may well be problems in AI (Artificial Intelligence) that simple BF&I (Brute Force & Ignorance) cannot and will not solve by itself. More clever algorithms, either by themselves or in combination with a bigger hammer, could make the problem into one that can be solved, but when (or whether) you will develop such a better approach to the problem is inherently far less predictable than forecasting the availability of more powerful hardware.

Does any of the above prove that there will be no Singularity? Of course not. But it does suggest that it is possible to run into a problem that is, and will continue to be, resistant to all attempts to solve it by more powerful hardware alone. That increases my estimate of the chances that we will run into a "show-stopper" on the way to the Singularity.