Can a brain think a finite or infinite number of thoughts?

Iris van Rooij

A few weeks ago, my son Ilaij asked me to post the following poll to twitter:

Part of the story was covered by Vox. But several people asked about Ilaij’s own answer and motivations. He really wants to share his thoughts, so I decided to write this blog. Let me start with a recap of the background story. 

How did you come up with the idea of the poll?

The question came up in conversation1 and Ilaij was instantaneously convinced the answer is ‘infinite’. Given the controversial nature of the question for researchers in my field (i.e., cognitive science), I said: “I also think it is infinite, but I know that many people think otherwise.” This fascinated Ilaij. He asked me to post the poll to find out what other people thought. He carefully designed the response options to include not only ‘finite’ and ‘infinite’, but also ‘I don’t understand the question’ and ‘both’. Reasons for the latter will be disclosed shortly. Read on. 

Together, Ilaij and I carefully drafted the tweet with the hope that people would retweet it and that we’d get at least 100 votes or so. We posted the poll to twitter and went to bed. In the morning we saw that it had been retweeted a few hundred times. And before we knew it, the poll went viral. After 5 days, when the poll closed, it had reached >50K votes2 and received more than a thousand replies.

Clearly the question was non-trivial and of interest to a wide variety of scholars.3 In my mentions, I could enjoy long convos with heated discussion between philosophers, linguists, computer scientists, neuroscientists and cognitive scientists. Even physicists chipped in at times.

What gave Ilaij great joy was that even Harvard’s Human Evolutionary Biology department had retweeted his poll.

Some non-scientists seemed concerned that the twitter poll would not be scientific enough and that I should be teaching better. But I wasn’t that worried and clearly the many scientists in my mentions thought the question was as fascinating as an 11 year old (as did several kids, e.g. here and here). 

What did you think the answer was?

Ilaij’s answer: “Ik denk dat we oneindig veel verschillende dingen kunnen denken. Ik kan bijvoorbeeld ook fantasiegedachten hebben en dingen denken die ik nooit eerder heb gedacht. Bijvoorbeeld, een ‘groene koe’ of ‘gele kip’. Waar houdt het dan op?” (English translation: “I think we can think an infinite number of thoughts. I can think fantasy thoughts and have thoughts about things I have never thought about before. For instance, a ‘green cow’ or a ‘yellow chicken’. Then where does it end?“).

With this intuition, he seems in good company. Linguistics, philosophers and cognitive scientists like Noam Chomsky, Jerry Fodor and Zenon Pylyshyn have long argued that cognition displays a property called productivity. A hilarious illustration is given in this sketch (sent by Judith van Stegeren). 


The neuroscientists and physicists in my mentions more often believed this intuition was mistaken. Interestingly, they argued not from the productivity of thought (mind), but from the finite nature of the `stuff’ that supposedly implements our thinking abilities (brain).4 Physicists added that these limits not only apply to brains, but even to the entire universe. Since the universe is finite and time is ultimately as well, we can think at most a finite number of thoughts; so the argument went. 

There were also people who argued that brains do not think at all. Some believed this for religious reasons, some because they thought that only persons can think not brains (cf. category error), while yet others believed that thoughts arise from the senses instead of the brain. This puzzled Ilaij, as he could not imagine how that all would work. Ultimately, none of the alternative perspectives convinced Ilaij to change his mind about his answer. He still believes that he can think in principle an infinite number of thoughts.  

Why did you include the options ‘both’ and ‘do not understand’?

Ilaij added these response options on purpose. He wanted to test the meta-cognitive abilities of the respondents. (Seriously, I’m not making this up.)3

He reasoned as follows: “Het is niet mogelijk dat het antwoord zowel ‘eindig’ als ‘oneindig’ is. Dat kan niet, dat is tegenstrijdig. Als iemand zegt ‘allebei’ dan hebben ze de vraag niet begrepen. Maar ze weten dat dan niet. Mensen die ‘ik begrijp de vraag niet’ weten dat ze de vraag niet begrepen hebben, maar de mensen die ‘allebei’ zeggen weten dat zelf niet. (English translation: “It is not possible that the answer is both ‘finite’ and ‘infinite’. That is impossible, a contradiction. If someone answers ‘both’ then they did not understand the question. But they don’t know they don’t. People who answer ‘I do not understand the question’ know that they do not understand the question, but the people answering ‘both’ don’t know it.”) Ilaij had a lot of fun coming up with this indirect way of measuring meta-cognition and was content with his solution. 

To his surprise, 9% (approx. 4508) people voted ‘both’. Ilaij: “Ik had niet gedacht dat zo veel mensen ‘allebei’ zouden antwoorden” (Translation: “I hadn’t expected so many people to answer ‘both'”).

Yet, it seemed that many people had less incoherent reasons to pick ‘both’. Most commonly, people opted for the ‘both’ option because on the one hand they believed it is in principle possible to think infinitely many different thoughts, but on the other hand, since our lives are finite, any brain would only ever be able think a finite number of thoughts in its life time.

What was the outcome of the poll for my son? He had great fun and learned a lot from it; including that one can track twitter statistics and that a viral event looks like this (exponential growth followed by extinction? 🤔)

Inspired by the whole experience, he and his sister Zinzi have now also created their own twitter account: @Inquiminds. On their account they will be posting more fascinating questions, intermixed with Zinzi’s colourful drawings and updates on experiences that both of them like to share with the world. I warmly recommend to go follow them there! And RT if you feel like it. It for sure would make them very happy.

Footnotes

1 Being a cognitive scientist, I may inadvertently bring up such questions in conversation. My kids are used to it, though as we realized by this poll going viral, I seldom tell them about my research directly. Both have told me that I should tell them more from now on. 

2 We actually got stuck on 49,930 votes about 2 hours before the poll would close. Even though getting thousands of votes was exhilarating, being only 70 votes short of 50K felt as such a pity. Therefore, Ilaij and I devised a plan to give the poll one last boost. It worked.  

3 If fact, the entire poll was driven by an interest in meta-cognition. Several people had mistakenly thought the goal was to find the answer to the question, “Can a brain think a finite or an infinite number of thoughts?”. But Ilaij already believed he knew the answer. He posted the poll because he wanted to know what others thought about that question. Note that the question was posed “Do you think a human brain …..?”, and this was no coincidence. 

4 This made me realize that the word ‘brein’ in Dutch, which Ilaij used, can mean both ‘brain’ and ‘mind’. It seems that in Dutch there is no good word for ‘mind’ other than ‘brein’. One could use ‘psyche’ or ‘geest’, but I guess these would be considered old-fashioned and/or have much stronger dualist connotation than the English word ‘mind’. Also, if one would want to refer to the physical stuff of the brain (not its functioning) then, more likely, one would use the word ‘hersenen’. All in all, Ilaij probably meant ‘mind’ at least as much as ‘brain’ when using the word ‘brein’ in the Dutch version of the question.