6 min and 59 sec to read, 1748 words

Can you become better at guessing? At a first glance the answer may seem an obvious yes – some people guess badly, others better – but exactly how would you go about that? What are the subskills that make you a better guesser, and can you practice them in some interesting way? Could their be courses in guessing better? If so, what would they teach and would we put them on a resumé?

A few distinctions seem in order — how does a guess differ from a prediction, for example? We know that some of the skills that go into predicting future events also are important for guessing (such as the ability to break a problem into component parts and assess those component parts, as well as respecting baselines in making estimates) – but does this mean that guessing and predicting is the same thing? One possible distinction seems to be that guesses can be about the past and the present as well as the future – but you could argue that a guess is just a prediction of what we will find when we check something more thoroughly. A guess also seems closely related to an estimate – but maybe an estimate is more numerical? A guess seems broader — the etymology of the word is uncertain, but could be traced back to “to take”, and in that sense guessing is to take something as a given, perhaps.

What is the size or nature of a guess? What is it that we guess about? We have some of the same problems with predictions – but we seem to say that we predict events rather than anything else. If that is the case, then maybe a guess is about the way the world is – a state of the world overall? Or is a guess more tightly connected with story and narrative? When we guess, we sort of assume or take a state of the world as a given and act on that assumed state, and the guess informs our understanding of the whole of our world?

That might be reading much too much into the word guess, however. It seems likely that guesses may be both narrow and oriented around facts (patterns!) or broad and essentially represent world states. Are guesses more primitive than predictions and estimates? Is there less precision in a guess?

And, so, to the point: can a guess be scientific?

You could imagine an argument that essentially says that science has its origin in guessing, and that guessing is about how we think the world works. As guesses got more robust and rigorous and we developed guessing as a skill, it morphed into prediction and estimation. Guessing, in this telling, is more primitive and animalistic than any of the other practices we have mentioned.

So, do animals guess? This turns out to be the subject of an interesting set of experiments – the guesser knower tests – and something that is used to discuss whether animals have a theory of mind. ¹ Povinelli, D.J., Nelson, K.E. and Boysen, S.T., 1990. Inferences about guessing and knowing by chimpanzees (Pan troglodytes). Journal of Comparative Psychology, 104(3), p.203.

Povinelli et al describe an experiment investigating whether chimpanzees can understand the difference between someone who has seen an event occur (the “knower”) versus someone who has not (the “guesser”). Four chimpanzees were tested using an apparatus where food was hidden in one of four cups. One experimenter (the knower) observed the hiding, while another (the guesser) did not. Both then pointed to cups, with only the knower pointing to the correct one. Three of the four chimpanzees consistently chose the knower’s cup, even when the procedure was altered so the guesser remained in the room but covered their head during hiding. The authors interpret these results as evidence that chimpanzees may understand that seeing leads to knowing, and can distinguish between someone guessing versus someone who actually knows information. This ability is compared to perspective-taking and theory of mind capacities that develop in human children around age 3-4. The study provides preliminary support for the idea that chimpanzees have some level of attributional abilities regarding others’ mental states, though further research is needed to fully characterize the extent of these capabilities.

The challenge with this is that guessing in the experiment is essentially reduced to being forced to choose at random — the guesser can not, in this experiment, become better at guessing in any way – can they? And what we wanted to figure out was if guessing could be a skill, and if guesses can be scientific — the answer, based on this framing, seems a clear know.

A guess does not feel like a random pick, though. It feels like something more, based on something else. But on what? Previous experience? Narrative understanding? Intuition? This is where it gets tricky — if a guess is based on something we have to be able to define that something to some extent — and we could then start to think about the limits of a guess, when a guess is clearly not a guess anymore. If you ask me how many coins I think you have in your pocket, and I answer “ten geese”, well, I am not guessing at all. A guess delimits the set of answers we will accept at least in some dimensions (at least the famous educated guess does).

And this turns out to be interesting – since there is some connection between the guess and us as organisms – we project ourselves into our guesses in ways that make them more than random. An interesting recent paper by Myer and Madrid highlights this:² Myers, J.M. and Madrid, H., 2024. Synchronizing Rhythms of Logic. arXiv preprint arXiv:2405.20788.

Although quantum states nicely express interference effects, the outcomes of experiments are not states. Instead, outcomes correspond to probability distributions. Twenty years ago we proved categorically that probability distributions leave open a choice of quantum states to explain experiments that is resolvable only by a move beyond logic, which, inspired or not, can be characterized as a guess. Guesses link the inner lives of investigators to their explanations of experimental results. Recognizing the inescapability of guesswork in physics leads to avenues of investigation, one of which is presented here.

We invert the quest for the logical foundations of physics to reveal a physical foundation of logic and calculation, and we represent this foundation mathematically, in such a way as to show the shaping and re-shaping of calculations by guesswork. We draw on the interplay between guessing and computation in digital contexts that, perhaps surprisingly, include living organisms. Digital computation and communication depend on a type of synchronization that coordinates transitions among physically distinct conditions represented by “digits.” This logical synchronization, known to engineers but neglected in physics, requires guesswork for its maintenance. By abstracting digital hardware, we model the structure of human thinking as logically synchronized computation, punctuated by guesses.

We adapt marked graphs to mathematically represent computation and represent guesses by unpredictable changes in these marked graphs. The marked graphs reveal a logical substructure to spatial and temporal navigation, with implications across physics and its biological applications. By limiting our model to the logical aspect of communications and computations—leaving out energy, weight, shape, etc.—we unveil logical structure in relation to guesswork, applicable not just to electronics but also to the functioning of living organisms.

This idea, that guesses link the inner lives of investigators to their explanations is really intriguing. A guess is directed, limited, based on something — it is a sense of sorts. Guessing as a particular sense, like hearing, may be a fruitful path forward in exploring the nature of guesses as well. This may also explain what we could call the “unreasonable effectiveness” of guessing.

The same authors also claimed to have proven that guesses are necessary in some kinds of scientific work — see the notes below. That is also quite intriguing!

And of course, and this is the perhaps bigger thing here, this all leads us to the question of the role of abduction overall in science, thinking and reasoning. But that is a much longer discussion – and one for the future. The relationship between abduction and guessing is key here – and one we will come back to.

Finally, a connection to my day to day work: can artificial intelligence help us guess better? And can an AI guess at all? What would it mean for it to guess, and how would you implement a guessing algorithm?

The question of how you would design a guessing AI allows us to approach the question in a slightly different, design-oriented way. There is a wider point to this, the idea that maybe we need to be able to design something to understand it, that I think is undervalued in cognitive science, philosophy and psychology. The question of how to build a guessing computer forces us to think about how we would design the data, algorithms and interactions of that software in order to enable it to guess — and we also have to decide if we believe that there is a difference between guessing and predicting — or to put a point on it: do we believe that LLMs are really just large guessing engines? If we do – and we may well want to do that – we also realize that they are not information retrieval mechanisms; they are something very different — but not necessarily less valuable. The ability of an economy to collectively and collaboratively guess may well be key to its growth and expansions — and the role of guessing in the economy also becomes fascinating here!

So much more to do and think about – let me know any thoughts in comments!

Other papers I want to look more closely at:

Allison, J., Riggs., Jack, E., Riggs. (2004). (2) “Guessing it right,” John A. Simpson, and myasthenia gravis: The role of analogy in science. Neurology, Available from: 10.1212/01.WNL.0000106936.27018.EC

Mark, Tschaepe. (2013). (1) Gradations of Guessing: Preliminary Sketches and Suggestions. Contemporary Pragmatism, Available from: 10.1163/18758185-90000263

Enric, Trillas. (2023). (5) A Discourse on Guessing and Reasoning. Lecture Notes in Computer Science, Available from: 10.1007/978-3-031-31476-6_14

John, Myers., F., Hadi, Madjid. (2000). (11) A proof that measured data and equations of quantum mechanics can be linked only by guesswork. arXiv: Quantum Physics.

Tadeg, Quillien., Neil, R, Bramley., Christopher, Lucas. (2023). (15) Guesses as compressed probability distributions. Available from: 10.31234/osf.io/gy2fv

Footnotes and references

• 1
  Povinelli, D.J., Nelson, K.E. and Boysen, S.T., 1990. Inferences about guessing and knowing by chimpanzees (Pan troglodytes). Journal of Comparative Psychology, 104(3), p.203.
• 2
  Myers, J.M. and Madrid, H., 2024. Synchronizing Rhythms of Logic. arXiv preprint arXiv:2405.20788.