In my opinion, the word "okulo"(it means eye) comes from kabalalah(a jewish mystical tradition). In particular I am talking about the "tree of life". sefirot 8(in esperanto "ok") is the sign of "Binah". that it means "understanding"(mainly by eyes). so probably the word "okulo" could be "ok.ul.o"!. since The doctor was a jewish, I guess my opinion is right. what do you think? does anybody know the root of that word?
If we look at existing works on Esperanto etymology, the root "okul/" comes from Latin "oculus".
This idea is shared by Louis Bastien (Naŭlingva etimologia leksikono de la lingvo esperanto, 1907), Ebbe Vilborg (Etimologia Vortaro de Esperanto, v. 4, 1995), André Cherpillod (Konciza Etimologia Vortaro, 2016) and Seikô Yamasaki (Etimologia Vortareto Pragmata de Esperanto, 1991).
Vilborg compares it to English and Spanish "ocular", French "oculaire", Italian "oculare" and Polish "okular". He adds that the root "ocul" is internationally known with all the words that use it.
About the "ul" part of the Esperanto root, Vilborg proposes that Zamenhof, who was an oculist, was inspired by the Latin word and the name of his job.
In its reform project of 1984, Zamenhof proposed to replace the root "okul/" by "okl/". This proposition was rejected, but some later words were influenced: for example, the word "binoklo" (binocular), officialised by the OA3.
Going with your logic "ok" (to see) + "ul" (person) + "o" (noun) => okulo would rather mean "someone watching, watcher".
There are approaches to reconstruct proto-indo-european language in which the root word is: "oqos" - common in many european languages: oculus (LAT), okulo (EO), ojo (ESP), oko (BOS, BUL, CRO, CZ, POL, SRB, SLK, UKR), øje (DK), вока (BLR), ollo (GAL), окото (MAC), oog (NED), øye (NOR), olho (POR), ochiul (ROM), očesu (SLV), öga (SWE), occhio (ITA), œil (FR), eye (EN). Some of them are quite far away from the original.
Mi pensas, ke "okulo" estas nur prenita el la Latino.
According to dictionaries (e.g. PIV), "okul/" is a root. So the in-Esperanto etymology of "okulo" is trivial: "okul·o", i.e., the root "okul/" with the noun word ending "-o". (Which, as "okul/" is a thing-y root, is in fact the base form of the word.)
As Lepticed's answer layes out, there's consensus among Esperanto etymologists, that "okul/" / "okulo" comes from Latin "okulus", also meaning "eye". But where did "okulus" come from? The entry in Konciza Etimologia Vortaro by André Cherpillod allows us to dig a bit deeper into the exter-Esperanto etymology of the word. It reads
okuloF. L ŏkŭlus ← HE ok. · HE → Sk अक्षि akṣ̂i, Gr ὤψ, Gt augo, Sl око, Li, akis, Arm Աչք aĉk. · L → I òcchio, Ks occhju, F œil, Oc uèlh, H ojo, Kt ull, P olho, Glg ollo, Srd ogu, Rm ochi. Ĝ → G Auge, Jd אויג uyg, Is auga, Nd oog, N øye, Dn øje, Sv öga, Vp Iog. · Sl → R Uk о́ко, Blr Вока, Po Ĉĥ oko, Bg око̀.
So according to Cherpillod, Latin (L) "ŏkŭlus" indeed comes (←) from Indo-European (HE for eo "hindeŭropa") "ok", from which corresponding words (for "eye") in many European and some Asian languages directly or indirectly derive (→). However, he lists no indication of any relation to the Esperanto number word "ok" (8), for which he gives a different etymology also from Indo-European:
okF (8). L octō ← HE okt. HE → Sk aṣ̂ṭan, Gr ὀκτώ, Ga ochto, Ir OĊT, Br eizh, G Nd acht, A eight, Is, átta, Sv åtta, Sl осмь Li aštuoni, Hd आठ āṭh, Pe hǎŝt̀. · L → I òtto, F huit, Oc uèit, Kt vuit, H ocho, P oito, Rm opt.
Kp: He okt «8», ak «pinto»; Gr ὀκτώ, ἄκρα «pinto»; L octō, ăcūtus «akuta»; Sl осмь «8», остръ «akra». Kalkulo sur ok fingropintoj, ne uzante la poleksojn. ☞ naŭ, kvin.
So Cherpillod sees some possible relation (whether causal or not) between the words for 8 and for peak, acute, sharp etc., and probably considers that this might be due to 8 being the maximum one can count on two hands with the fingertips, excluding the thumb (maybe because the thumb was used to touch the "current" finger while counting to keep track).
There's no mention of the Kabbalah, or of Jewish or Israelite languages other than Yiddish (Jd) in either of these entries, though. (If your theory was right, one would probably expect links to ancient or modern Hebrew or similar Semitic languages, which do exist for some other Esperanto words, but aren't known for "okulo" or "ok".) And as "okulo" can be readily explained as being derived from the Latin "okulus", it's very, very unlikely that any such connection would have guided Zamenhof's choice of that word.