“Now please convey my respects to the supreme protector of the world. Circling him to your right, dedicate my religious donation.”
In what sense is buddha the supreme protector of the world? which world is being referred to? the earthly world? the heavenly world? all worlds? i don't feel protected. protecting dhamma? only good people?
The term used in Thig 13.3 is lokanātha.
According to the PTS Pali-English dictionary entry on "nātha":
Nātha Nātha [Ved. nātha, nāth, to which Goth. nipan (to support), Ohg. gināda (grace)] protector, refuge, help A v.23, 89; Dh 160 (attā hi attano n.), 380; Sn 1131 (Nd2 has nāga); DhA iv.117; PvA 1. lokanātha Saviour of the world (Ep. of the Buddha) Sn 995; PvA 42. — anātha helpless, unprotected, poor J i.6 (nāthânāthā rich & poor); PvA 3 (˚sālā poor house) 65. Cp. nādhati.
Nātha means saviour, protector. Anātha, the opposite of nātha, means helpless, unprotected, poor.
lokanātha means "saviour of the world".
The Buddha is saviour of the world in the sense that he brings teachings to the world to liberate the helpless from suffering i.e. "supreme guide for those who wish to train".
‘That Blessed One is perfected, a fully awakened Buddha, accomplished in knowledge and conduct, holy, knower of the world, supreme guide for those who wish to train, teacher of gods and humans, awakened, blessed.’ He has realized with his own insight this world—with its gods, Māras and Brahmās, this population with its ascetics and brahmins, gods and humans—and he makes it known to others. He proclaims a teaching that is good in the beginning, good in the middle, and good in the end, with the right meaning and phrasing. He reveals an entirely full and pure spiritual life.
MN 41
Read it from the author's perspective -- she has taken "refuge" in the Buddha, the Sangha, the Dhamma.
See also SN 6.2 which says that monks must "dwell in dependence on" someone, more consummate than themselves (in this case the Buddha).
Lastly note the concise dictionary:
a protector, patron, lord; a husband; a prop, support; ~ especially the lord, the Buddha
Their dialog is about marriage (the wife being under the husband's control, the man being "trapped", their having "followers").
Now think of the "support" (and "husband") meanings -- the Buddha has social authority, creates the Sangha, defines the rules they live by, told people to allow the bhikkhuni order to exist and to not harass the nuns, etc.
The central word here is lokanāthaṁ, which a dictionary says means the lord of the world.
If we search for this & similar terms (here, here & here), they appear found in later texts, including Sanskrit & early Mahayana texts.
Notably, the suffix nātha is found in the Dhammapada, where Sujato translates nātho here different to as he translates nātho in Thig 13.3.
Self is indeed the lord of self,
Attā hi attano nātho,
for who else would be one’s lord?
ko hi nātho paro siyā;
When one’s self is well-tamed,
Attanā hi sudantena,
one gains a lord that’s rare indeed.
nāthaṁ labhati dullabhaṁ.
In the suttas, it seems, the most common word translated as protector is rakkha
Dhamma surely protects one who practices Dhamma;
Dhammo have rakkhati dhammacāriṁ
Looking after yourself, you look after others; and looking after others, you look after yourself.
Attānaṁ, bhikkhave, rakkhanto paraṁ rakkhati, paraṁ rakkhanto attānaṁ rakkhati.
And how does a mendicant protect?
Kathañca, bhikkhave, bhikkhu rakkhitā hoti?
When a mendicant sees a sight with the eyes, they don’t get caught up in the features and details.
Idha, bhikkhave, bhikkhu cakkhunā rūpaṁ disvā na nimittaggāhī hoti nānubyañjanaggāhī.
All of the above said, there are two suttas AN 10.17 & AN 10.18 using the term 'nātha' found in Thig 13.3.
Mendicants, you should live with a protector, not without one.
Sanāthā, bhikkhave, viharatha, mā anāthā.
Living without a protector is suffering.
Dukkhaṁ, bhikkhave, anātho viharati.
There are ten qualities that serve as protector.
Dasayime, bhikkhave, nāthakaraṇā dhammā.
What ten?
Katame dasa?
Firstly, a mendicant is ethical, restrained in the monastic code, conducting themselves well and seeking alms in suitable places. Seeing danger in the slightest fault, they keep the rules they’ve undertaken.
New Concise Pali English Dictionary
nātha
masculine
a protector,patron, lord; a husband; a prop, support; ~ especially the lord, the Buddha
PTS Pali English Dictionary
nātha protector, refuge, help AN.v.23, AN.v.89; Dhp.160 (attā hi attano n.), Dhp.380; Snp verse 1131 (Nd ii.has nāga) Dhp-a.iv.117; Pv-a.1. lokanātha Saviour of the world (Ep. of the Buddha) Snp verse 995; Pv-a.42 ■ anātha helpless, unprotected, poor Ja.i.6 (nāthânāthā rich poor); Pv-a.3 (˚sālā poor house) Pv-a.65 Cp. nādhati.
Ved. nātha, nāth, to which Goth. nipan (to support), Ohg. gināda (grace)
Personally, I am inclined towards the translation of 'Lord of the World', which means the Buddha is unaffected by or governs the world around him via governance of mindfulness & wisdom. However, as originally said, Thig 13.3 appears to be a later text using early Mahayana language therefore 'Protector or Saviour of the World' may be more accurate in this context.
Also, the term 'lokanāthaṁ' is found in the later Manorathapūraṇī commentary attributed to Buddhaghosa, here.
duve saccāni akkhāsi sambuddho vadataṃ varo sammutiṃ paramatthañca tatiyaṃ nupalabbhati
The Awakened One, best of speakers, Spoke two kinds of truths: The conventional and the ultimate. A third truth does not obtain.
tattha: saṅketavacanaṃ saccaṃ lokasammutikāraṇaṃ paramatthavacanaṃ saccaṃ dhammānaṃ tathalakkhaṇan ti
Therein: The speech wherewith the world converses is true On account of its being agreed upon by the world. The speech which describes what is ultimate is also true, Through characterizing dhammas as they really are.
tasmā vohārakusalassa lokanāthassa satthuno sammutiṃ voharantassa musāvādo na jāyatī ti
Therefore, being skilled in common usage, False speech does not arise in the Teacher, Who is Lord of the World, When he speaks according to conventions.
(Mn. i. 95)
