“Can Machines Think, and How?”

In this post, I will share what I learned from Prof. Cahit Arf’s talk titled “Can Machines Think, and How?”

Prof. Arf was one of the best, if not the best, Turkish mathematics professors. He is known for the Arf invariant, Arf rings, the Hasse-Arf theorem and Arf semigroups. Sadly, my current knowledge of these topics does not go beyond having skimmed the Wikipedia pages, but we will get back to this later. You can refer to Prof. Sertöz’s paper to read about Prof. Arf’s scientific biography. Prof. Arf also appears on the back of the 10 Turkish Lira note.

Prof. Arf’s talk is particularly interesting because it was given in 1959. Let me frame this historically. The concept of neural networks dates back to 1943, where McCulloch & Pitts modeled neurons using electrical circuits. Then, there is Hebbian learning in 1949, which can be summarized as “Neurons wire together if they fire together.” Rosenblatt published the perceptron learning rule in 1958. Widrow & Hoff invented the delta learning rule in 1959. Linnainmaa’s and Rumelhart’s backpropagation works came out in 1970 and 1985 respectively. So, 1959 is early days for neural networks. I didn’t know that a Turkish mathematician was interested in this area, let alone giving a talk on it back then.

The other interesting thing about this talk is its purpose. This talk was part of a series where the goal was to teach basic scientific concepts to the public and to promote university studies. Following Atatürk’s principles on science and education, this series was a great initiative on educating the public. Nevertheless, trying to explain how machines can think to the public in 1959 sounds pretty difficult to me. Note that there is no Internet, no email. Even now, whether machines can think or not is a good topic of debate. Yet, as you read, you see how Prof. Arf explains like you are 5, and everything becomes crystal clear.

Now, the talk itself.

Machines can think

Prof. Arf defines thinking as “giving different reactions to different observations, in your own language.” So, an alarm clock thinks too in this context, because we say -in its own language- “Wake me up at 4am,” and it replies in its own language by beeping. In the same way, you tell the phone who you would like to speak to -in its own language- and it says “Ringing” or “Not available” by beeping in a certain way.

This definition of thinking makes sense to me. When you do not give any reaction -physically or mentally- to any observation, you do nothing. When you give the same reaction to the same observation, your reaction becomes a reflex after some point - there is no thinking. When you give the same reaction to different observations or vice versa… You simply do not know what you are doing, do you?

The machines in Prof. Arf’s examples solve one problem only, and they solve problems that a human can solve. This is not interesting at all, you might say. On the other hand, the human brain is famous for its capability of adapting to new and unseen situations. So, he asks: “Can we make a machine that can mimic human brain in solving unseen problems? And how?” The how part implies we can. Prof. Arf goes on to explain what machines are and how information flows between the memory and the control unit. I will not go into the detail here.

Instead, I would like to take a look at how people solve problems. We put together information to solve problems. How do we learn the necessary information? Nobody is born with the knowledge, that’s for sure. We observe our environment. We take actions and experience new situations. We learn from those experiences and store them in our memory. By the time the same situation arises, we already know it. We can handle it. On the other hand, when we face an unseen situation, we quickly refer to our memory. If nothing is found in there, we refer to the knowledge in books, and then to -memories of- other people. It is all about the memory, isn’t it? When people argue about how large language models (LLMs) memorize information, it comes off a little bit absurd. We do it the same way.

To conclude this section, I should say once more that I agree with Prof. Arf. By looking at the most recent LLMs, we now know that machines can think, or at least mimic human thinking. But still, it all depends on the definition. Moreover, does it really matter? As Edsger Dijkstra said, “The question of whether a computer can think is no more interesting than the question of whether a submarine can swim.” On a related note, you might find John Searle’s Chinese room argument interesting.

Difficult problems

What struck me the most in this talk is how Prof. Arf approaches seemingly difficult problems.

When faced with difficulties, people often escape into ease by saying all the successful people “have this personality trait” or “from this country” and so on. They simply stop working when they find a difference between them.

Prof. Arf put it simply: Anything someone can do, someone else can do better (here is a Formula 1 video from 2007 on Hamilton & Alonso). In fact, complex issues are not that complex. Solving them is like climbing the stairs. One step is easy, but one thousand requires blood, sweat and tears. His advice is to trust your mind, to be patient and to climb one by one. Just show patience so you can understand something thoroughly and keep climbing one by one. Patience and understanding thoroughly is the key.

Maybe I should spend more time on the Arf invariant and write an article on it. No rush though.

Acknowledgments

Thanks to Onuralp Görmez and Arsen Berk Tekdaş for reading the draft and providing valuable suggestions for improving the text.
Last edited: Oct 12, 2024.