Hiroyuki Nishimoto
AI Data Seminar, May 17, 2024, Center for Mathematical Modeling and Data Science, Osaka University Invited
Sakushi no mekanizumu o akiraka ni shita toki, heringu sakushi ga shisa suru yō ni shikūkan wa kyūtaideatta. Shiten kara shōshitsu-ten made no fuka-sa ga hankei no kyūtaidearu. Koko de shikūkan o tan'ikyū to suru to, nin'i no ten ni okeru sukēru no kansoku-sei wa, shisen to no henkaku th no bibun hōteishiki de arawasa reru. Kono shikūkan moderu ni yori, chokusen-teki ni ugoku roketto no dandō ga daendearu koto ya, ninchi kyori (kyori-kan) no henka o kakuritsu to shite shimesu koto ga dekiru. Kono shikūkan moderu wa, rīman-kyū to kotonari sanjigen hōkō ni mugen'en-ten (shōshitsu-ten) ga sonzai suru fukuso shaei kūkan to naru. Kono kenkyū no mochibēshon wa, sakushi gazō o mochiite kōrei-sha no gazō ninshiki nōryoku o sokutei suru kotodearuga, senmō no risuku kara rinshō kenkyū no ritsuan ni wa itatte inai. Ko no yō ni rinshō shiken wa itsu demo jikkō dekiru wakede wa naku, rinri-tekina kanten kara shiken dezain ga henkei sa reru koto mo mezurashiku wanai. Iryō tōkei-ka wa, kono yō ni shite shūshū sa reru herusukeadēta no tokusei o rikai shi, inga kankei o shinchō ni giron suruhitsuyōgāru.
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When the mechanism of the optical illusion was clarified, visual space was a sphere, as suggested by the Hering illusion. It is a sphere with a radius equal to the depth from the viewpoint to the vanishing point. If visual space is considered to be a unit sphere, the observability of scale at any point is expressed by a differential equation with the deviation angle θ with the line of sight. This visual space model makes it possible to show that the trajectory of a rocket moving in a straight line is an ellipse, and to show changes in cognitive distance (sense of distance) as a probability. Unlike a Riemann sphere, this visual space model is a complex projective space in which a point at infinity (vanishing point) exists in three dimensions.