Human intelligence vs artificial intelligence
Source: "11+ Maths, 10 minute tests", OUP, 2015

Human intelligence vs artificial intelligence

Consider this math problem for 11-12 year olds. Now, taking into account what an 11-year old knows about functions, one can more or less limit the space of possible solutions to linear, maybe at most quadratic functions, in any case something continuous and differentiable (I don't mean that the 11-year old would know what that means, I just mean no weird functions). As I was looking for a solution, I was at the same time thinking what a machine would do in this case and how what I was doing is really very different from what a machine would do. Apart from considering the context (a problem for an 11-year old), I definitely did not set up a loss function and did not set up a neural network with 2 hidden layers and one node each which I then optimized using gradient descent (and I am almost certain that that's not what my brain subconsciously did). In fact, the way (I guess) a student can argue is that the inputs have a difference of 3 which translates to a difference of 1 in the output, so you could hypothesize that the second function is something like g(x) = x/3. From there, working backwards, it is easy to arrive at the first function being f(x) = x + 7. What would a computer need to do? If you actually start by just the visual information contained in the image above and the audio input "This is a problem for an 11-year old", a computer would need to carry out the following tasks:

  1. use some sort of image recognition software to recognize the words and the overall problem from the image,
  2. use speech recognition to understand the audio input,
  3. browse the web to figure out what 11-year olds are expected to know,
  4. figure out what the image actually means, i.e., that we are looking for two functions f(x) and g(x), so that g(f(5)) = 4, g(f(8)) = 5 and g(f(11)) = 6,
  5. set up a model (e.g., 2-hidden layer, single node neural network, among other possibilities),
  6. minimize the loss function,
  7. (ponder what a human would do ;)

Even after all these steps, I wonder if with the 3 data points at hand the solution would be exact. Also, I wonder if there is a computer somewhere in the world that has the capability without any additional programming (so completely unsupervised, just given the visual and audio input) to solve this problem in about 1 minute (which is what was expected of an 11-year old, since this was one of 10 questions in a 10-minute test, that being quite ambitious in my opinion).

As much as I am amazed by the advances in AI, it is these kinds of simple problems which I think exemplify how far and how different computer "thinking" is from human cognition.

Thanks Valeri for sharing your thoughts - In addition to your great points, I would like to add even after all the steps 1-7, we will face sort of "Causality" problem- Now with our "human thinking" we could "explain" how the function g(f(x)) works in this case, but I doubt anybody could explain "how" the Neural Network probably with thousands of parameters give 4, if the input is 5 :)

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