Synesthesia

Synesthesia is a perceptual phenomenon in which different types of sensations occur automatically in response to a single stimulus in addition to the usual sensations (from Wikipedia).

(1) chromatic synesthesia, in which colors are perceived based on visual features such as letters or dates;
(2) color-auditory synesthesia, in which colors are perceived based on auditory features such as high/low pitch sounds or instrumental sounds;
(3) synesthesia, in which colors are perceived based on features other than visual perception such as touch, smell or concepts;
(4) synesthesia, in which sounds are perceived as smells or shapes as smells;
(5) spatial series synesthesia, in which numbers or dates are perceived as spatial arrangements;
(6) mirror touch synaesthesia, which is the perception of tactile sensations from visual sensations, and
(7) ordinal number personification synaesthesia, which is the perception of personality in numbers.

Synesthesia is based on an individual's subjective sensations and cannot be objectively confirmed by a third party. In addition, the definition of what constitutes synesthesia and what does not has not been settled, so it is possible that there are others besides those mentioned above [1].

I thought it was very rare, but there is a 4.4% chance that someone has synaesthesia, regardless of category. That is, about 1 in 23 people have synesthesia. There are cases where one person has more than one form of synaesthesia, and the number of synaesthesia is correlated with the strength of the synaesthesia and the strength of the cognitive trait (attention to local information, similar to that of the autistic spectrum). While there are individual differences in the way people feel, there is also a curious coincidence, and it is not a "disease" or "genius superpower" [1].

In the book "Boku ni mita numeri ga fukei ga shimaikei" (Daniel Tammet, translated by Mitori Furuya, Kodansha, 2007), London-born Daniel Tammet, a math and language genius, describes his world and allows readers to imagine how it differs from their own senses. For example, here is what pi to 100 decimal places looks like to him.

The most famous part of the number pi is called "Feynman Point," where there are six 9s in a row, from 762 to 767 decimal places, "...99999999.... It is Feynman's favorite place." The scenery at Feynman Point is beautiful. You can see a thick fringe of dark blue light," Daniel said. Incidentally, his own favorite place is where 11 9s appear intermittently four times, from 19437 to 19453 decimal places.

In other books, I wonder if the sense in which the shape of the protagonist's head is compared to the symbol for the root in "The Dr.'s Beloved Equation"[3] is another example of ordinal-number anthropomorphic synesthesia. In "Blue Mathematics" [4], the conversation between high school students who are aiming for the Mathematical Olympiad is another interesting example of the richness of synesthesia expressed through numbers.

A long time ago, I no longer remember where I saw this sentence, but when an 18th century mathematical genius discovered a theorem, he said, "When I think of 0000, I see a landscape of a series of numbers. I see a lack in the smooth ridges of those numbers. It was written that he said something like, "If I fill in that missing piece, it will follow neatly ahead, so I just filled in that missing piece" as the reason for his discovery. I was struck by the fact that someone could see a landscape of numbers when thinking about a mathematical puzzle that has yet to be solved, and find it beautiful or lacking. I also felt a sense of awe, thinking that the person must have just tweaked it a bit to make it more beautiful. I've been fascinated by this feeling ever since I learned that it is called "number sense" or "synesthesia. It's very cool to be able to see in your mind that the answer to math is here somewhere.

Recently (December 2023) a tool has been proposed to visualize sound and color synaesthesia.
Xue Mao, Jie Xu, Jiahong Lang, Shangshu Zhang. Visualization of isomorphism-synesthesia of colour and music. Visual Informatics. Vol7(4).  2023. 110-114

There have also been reports that some people have become aware of latent synaesthesia after experiments in which non-synaesthetes were forced to choose colors for letters and notes as if they were synaesthetes.
Kosuke Itoh. Induced awareness of synesthetic sensations in synesthetically predisposed “Borderline Non-synesthetes”. Consciousness and Cognition. Vol 118. 2024. https://doi.org/10.1016/j.concog.2024.103650.

I've heard that some people don't even realize they have synaesthesia, and in Japan, being "normal" tends to be a good thing, and since it can't be objectively proven, it can affect trust relationships. Because of this background, some people may not say anything about it, so I think that few people are actually aware of it.

References
[1] R. Asano, K. Yokosawa. Series of Integrated Cognition, 6th sense, Synesthesia, Diversity of Integration, Keiso Shobo, 2020
[2] Daniel Tammet, translated by Mitori Furuya, Born on a Blue Day: A Memoir of Asperger's and an Extraordinary Mind by Daniel Tammet, Kodansha, 2007
[3] Yoko Ogawa, The Dr.'s Beloved Equation (博士の愛した数式), Shinchosha, 2005
[4] Yuki Ojo, Blue Mathematics (青の数学), Shinchosha, 2016