# Ryabko, Reznikova, the Use of Ideas of Information Theory for Studying 'Language' and Intelligence in Ants

The actual reading of the paper and the writing of this note took place in March 4th of 2023. It became too long for being an entry of Short Notes on Various Papers, 2023.

URL. The paper was read so that I can see how ideas in information theory can be utilized in a practical manner outside the field of coding and communication. A remarkable phenomenon, ubiquitous in Nature, is the emergence of "seemingly" intelligent systems out of "mindless" individuals. The behavior of insect societies, in particular that of bees and ants, is an example of significance. In the abstract, it was claim that, via information theoretic tools, one can show that

- Ants are able to
*grasp*regularities and to use them for "compression" of information, - Ants are able to transfer to each other
*the information about the number*of objects, - Ants
*can*add and subtract small numbers.

Emphases are my own, since their meaning are ambiguous, for

- In what sense can ants grasp regularities?
- What is the information about the number of objects?
- What is really doing the addition and subtraction of small numbers?

## 1st experiment, number as information

The approach taken is to investigate the process of information transmission by measuring time duration which the animals spend on transmitting messages of definite lengths and complexities, not that of signal deciphering (trying to map certain behavior to a linguistic entity that bears meaning). "The messages of definite lengths and complexities" here is abstractly just finite binary sequences $0100100111$ etc., implmented by binary tree mazes: each fork corresponds to a $0$(left) or an $1$(right), a path from the root to a leaf is then coded uniquely by a finite sequence of $0,1$s. All except for one leaf are empty, and the one nonempty leaf has food in it. All paths are designed to be of equal length. Every fork corresponds to a binary choice, which in turn corresponds to one bit of information to be transmitted. Example: in a $Y$-shaped maze, one bit of information should be transmitted by a scout to other individuals.

Highly motivated (by starvation and such) ants are placed in an arena which was divided into two sections, one containing the nest (with colonies each of about 2000 individuals), and the other with an experimental system (a binary tree maze). The colonies were found to include teams of constant membership, consisting of one scout and 3-8 foragers; the scout mobilized only members of its team to the food.

In trials, one of the scouts that were moving on the experimental arena was placed on a leaf of the binary tree that contained the food, and the scout returned to the nest by itself. Other possibilities that could help the ants to find the food except for information contact with the scout is eliminated, including the use of an odor track (the maze was replaced by an identical one when the scout returned and was contacting its team). Briefly speaking, the scouts needed to really remember the path they traversed in the maze.

It was found that, when the scout touched the forager ants after returning, some foragers will leave the nest for the maze, and the duration of this kind of contact is far longer than other contacts (made for the exchange of food); more than 30s vs 5s. Statistically the hypothesis that forager ants, upon contact with a scount that returned, find the leaf containing the food by chance is rejected by comparing the time used to find the food when the individuals are informed or not. Surprizingly, the mean time for uninformed ants to find the food after following the sequence of turns `LRRL`

is far shorter than `RLLR`

(`RRRR`

shorter than `LLLL`

but not that radical), and it seems that informed ants are more likely to find the food faster when the required sequence is `RLLR`

or `LRRL`

instead of `LLLL`

and `RRRR`

. However since the amounts of sampling is small these can be by chances.

Under the assumption that for length $i$ informations, the duration of the contacts between the scouts and foragers $t=ai+b$, the rate of infformation transmission, $a$, is found to be approx. 1 bit per minute. The contact was considered to begin when the scout touched the first forager ant and to end when the first two foragers left the nest for the maze, so even if the ants are starved and highly motivated, the rate is an effective one (but whats the difference anyhow, when you don't do anything upon hearing a bad message, it amounts to the fact that no information was transmitted to you).

## 2nd experiment, Regularities

Of interest is that for sequences "of low Kolmogorov complexities", it took less time for the information to be transmitted. The simpler the text the less time for information transmission. But here the notion of Kolmogorov complexities is dubitable (or I simply don't understand Kolmogorov complexity that well): which universal Turing machine is computing the sequences? Kolmogorov complexities for different universal Turing machines for an equivalence class defined by equivalent iff
$$
C_{T_1}(s) - C_{T_2}(s) < C_{T_1,T_2}
$$
so there is an integer shift that makes some sequences simpler for $T_1$ and some simpler for $T_2$, in particular for simple sequences, and Kolmogorov complexities work well only for complex sequences (it works asymptotically). In addition to assuming that ants can be seen as possessing abilities approximating to universal Turing machines, one needs to assume that the same universal Turing machine is computing really simple sequences like `010100`

. Human intuition *might* suggest that `010101`

is more regular than `011010`

, but this corresponds to a class of specific implementation of universal Turing machines. Which one should be the specific implementation class is unclear, and the notion of intuitive regularity that classifies `011010`

to be less regular than `010101`

might not exist at all. The comparison data of mean durations also don't look that significant so that one can suggest that ants can "use simple forms of rule extraction in order to optimize their messages".

## 3rd experiment, number per se

### Information about the number of objects

New experiments. Given a comb-like trunk with 25+ branches. Each branch ending with an empty trough except for one filled with food. Ants come to the initial point of the trunk over a bridge, and hence might need to count the number of branches that need to be passed in order to reach the correct trunk. The trunk can be circular. The spacing between branches in a trunk are equal, and different trunks with different spacings are used. Again, when the scout returned to the nest, the trunks are replaced by an identical one, so that odor tracking methods cannot be utilized.

Assuming the duration of the contact is $t = ai+b$ where $i$ is the numbering of the branch with food, it turned out that $a$ and $b$ are close for different shapes, distances between the branches and lengths of the branches and the choice of the branches. In modern human languages the code word of a number $i$ is approximately proportional to $\log i$, while here the code word is simply identified with the number. Again the statistics are not that well, but it is somehow convincing.

### "Arithmetic" skills

First, recall that *Zipf's law of abbreviation* states that the more frequently a word is used, the shorter that word tends to be, and vice versa; the less frequently a word is used, the longer it tends to be. Keeping the same setup as above (the trunk setup), a similar experiment testing whether regularity makes the representation of a number shorter is carried out, and it was found that contact duration for familiarized numbers are lowered. The experiment is divided into three stages,

- Equal probabilities for all branches
- High and equal probability for branches $k,l$, low for others.
- Equal probabilities for all branches.

In the third stage when the food is found to be in the $k,l$ and *nearby branches*, the contact duration is reduced more significantly. There is an overall reduction, and the reduction is significant especially for large numbering branches, while not to the level of $k,l$.

The fact that there are reductions for nearby branches is interesting. This can mean that for numbers closer to $k$ and $l$, their description became also shorter. This reduction in the length of description is similar to the fact that the Roman numeral X is shorter than IIIIIIIIII, and subsequently XII is shorter than IIIIIIIIIIII. The authors claim that this means ants have arithmetic skills. This is debatable, but what is clear is that the *notion of regularity in ants' "minds" is changed*, somehow contradicting the conclusion given by considering the Kolmogorov complexity of binary sequences.