北岡のひとりごと 3
since June 19, 2025
ひとりごとというよりメモ帳
「地平線近くに見える月は天頂付近に見える月よりも1.5%遠い」ということを初めて知りました（NASAのサイトにあるらしい）。意外と地球は大きくて月は近いのですね。今後のネタにしたいと思います。ついでに計算してみました。地球の半径は赤道上では6378km、地球から月までの距離は384400kmとのことですので（ChatGPT調べ。たぶんそんな数値）、天頂に月が見える時の距離を384400kmとすると、地平線近くでは384400+6378=390778kmです。その比、390778/384400=1.01692です。すなわち1.7%遠いです。引用されているNASAの文献では1.5%とのことで、これは赤道上ではなく、アメリカの緯度で計算したので少し値が小さいのでしょう。それでも結構大きいですね。月（ChatGPT調べで半径1737.4km）の目に映る大きさΘを2 arctan(月の半径/距離)で計算すると、天頂では0.517924度、地平線では0.509471度でした。その比は、0.517924/0.509471 = 1.01659 で、天頂の月の方が1.7%大きいです。この数値は距離比の1.7%と同じであることから推定すると、アメリカの緯度すなわち日本の緯度では、天頂の月は地平線の月よりも物理的には1.5%程度大きく見えていると考えられます。大きさの錯視があって1.5%大きく見えたという場合は、そこそこ大きい効果なので、この数値は錯視を考える上で軽視できません。すなわち、月の錯視とは、地平線の月は天空の月より1.5%（1-1/(1+0.015)）網膜像は小さいというのにずいぶん大きく見えるという強力な錯視というわけです。
What color is this dot? New illusion demonstrates weird vision quirk
An optical illusion with nine simple dots reveals a surprising amount about the eye and brain
By Nora Bradford edited by Allison Parshall
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mirror gaze effect
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Gamut relativity: A new computational approach to brightness and lightness perception
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Author Affiliations
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「ＡＩも惑う、脳の勘違い「錯視」…特性生かした商品開発も」（読売）
https://news.yahoo.co.jp/articles/a05853f238d11a85d29feb1902e7b69d5ca5daa3?page=1
日経
https://www.nikkei.com/article/DGXZQOUD131WX0T11C25A0000000/
錯視の研究は、視覚を実験心理学的に研究する領域の一つとして発展してきた。錯視の「錯」には「まじる」などの意味があるが、ここでは「まちがえる」という意味で使われている。英語では錯視は "visual illusion" で、"illusion" は「対象の真の性質（と認識されたもの）とは異なるその対象の知覚」すなわち錯覚のことである。そうはいうものの、錯視は病的なものではなく健常なものである。錯視は「間違った」視覚と表現されていても、視覚としては正常に働いた結果、たまたま対象の性質と知覚が一致しなかった場合に、錯視というラベルが貼られているだけである。もっとも、対象の性質と知覚が一致しない現象なら何でも錯視と呼ばれるかというとそうではなく、おもしろいもの、不思議なもの、美しいものが錯視と呼ばれる傾向にある。すなわち、錯視は芸術と関係がある可能性がある。この関係性は、今後の錯視研究のテーマの一つになるかもしれない。
<November 5, 2025>
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Released on J-STAGE February 24, 2009, Online ISSN 1468-5884, Print ISSN 0021-5368
https://doi.org/10.4992/psycholres1954.37.139
https://www.jstage.jst.go.jp/article/psycholres1954/37/3/37_3_139/_article/-char/en
Abstract: Magnitudes of the apparent depth of eccentric circles and real
cone stimuli were measured as a function of viewing distance when they
were rotated on a circular disc and viewed monocularly. The diameters of
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