How does keeping the mitzvot make us a wise and understanding people?

In parshat va`etchanan, we have:

ד וְאַתֶּם, הַדְּבֵקִים, בַּה', אֱלֹהֵיכֶם--חַיִּים כֻּלְּכֶם, הַיּוֹם.	4 But ye that did cleave unto the LORD your God are alive every one of you this day.
ה רְאֵה לִמַּדְתִּי אֶתְכֶם, חֻקִּים וּמִשְׁפָּטִים, כַּאֲשֶׁר צִוַּנִי, ה' אֱלֹהָי: לַעֲשׂוֹת כֵּן--בְּקֶרֶב הָאָרֶץ, אֲשֶׁר אַתֶּם בָּאִים שָׁמָּה לְרִשְׁתָּהּ.	5 Behold, I have taught you statutes and ordinances, even as the LORD my God commanded me, that ye should do so in the midst of the land whither ye go in to possess it.
ו וּשְׁמַרְתֶּם, וַעֲשִׂיתֶם--כִּי הִוא חָכְמַתְכֶם וּבִינַתְכֶם, לְעֵינֵי הָעַמִּים: אֲשֶׁר יִשְׁמְעוּן, אֵת כָּל-הַחֻקִּים הָאֵלֶּה, וְאָמְרוּ רַק עַם-חָכָם וְנָבוֹן, הַגּוֹי הַגָּדוֹל הַזֶּה.	6 Observe therefore and do them; for this is your wisdom and your understanding in the sight of the peoples, that, when they hear all these statutes, shall say: 'Surely this great nation is a wise and understanding people.'
ז כִּי מִי-גוֹי גָּדוֹל, אֲשֶׁר-לוֹ אֱלֹהִים קְרֹבִים אֵלָיו, כַּה' אֱלֹהֵינוּ, בְּכָל-קָרְאֵנוּ אֵלָיו.	7 For what great nation is there, that hath God so nigh unto them, as the LORD our God is whensoever we call upon Him?
ח וּמִי גּוֹי גָּדוֹל, אֲשֶׁר-לוֹ חֻקִּים וּמִשְׁפָּטִים צַדִּיקִם, כְּכֹל הַתּוֹרָה הַזֹּאת, אֲשֶׁר אָנֹכִי נֹתֵן לִפְנֵיכֶם הַיּוֹם.	8 And what great nation is there, that hath statutes and ordinances so righteous as all this law, which I set before you this day?

Why should the nations think us so smart, because we keep the mitzvot? I think one can answer in a straightforward manner, that you cannot argue with success. It is not that the mitzvot all are all readily apparent to the nations as brilliant, ethical, and correct. But by keeping these commandments, we maintain this relationship with God which the nations can witness and appreciate. Thus, it must be that our laws and practices are good ones, and so we are a wise and understand people to keep and maintain such customs and such a relationship.

Alternatively, and more fitting with certain aspects of the text, there is something to the practices themselves that the nations can appreciate and respect, perhaps as more just and righteous than their own. Are these two concepts linked or not? I can see it either way. It could be two reasons for learning and keeping these mitzvot. First, to maintain the relationship with God, and second, because they are intrinsically wise, fair, and righteous. Both of these things are Israel's glory. Not necessarily that we should define ourselves by how others look at us, but sometimes a perspective from outside helps us appreciate just what it is we have.

Ibn Ezra on this:

[ד, ה]
וטעם למדתי אתכם –
אחר שאמר אשר אנכי מלמד אתכם, להוסיף כאשר צוני ה', כי המצות הם מצותיו שתעשו בארץ שיתן לכם השם לירושה.
ועוד: כי יש לכם תפארת במצותיו על כל הגוים.
והטעם: כי עיקר כל המצות יבינם המשכיל וידע למה נתנו.

[ד, ז]
כי מי גוי גדול -
שיש לו אלהים שיהיה קרוב אליו שיענהו תמיד בכל אשר יבקש ממנו בחכמה, גם אין גוי גדול אשר לו חקים ומשפטים צדיקים בשקול הדעת, כמו ישראל.

וטעם גוי גדול –
בעבור חכמי לב יראי ה

'.

So the intelligent person will perceive and appreciate the wisdom at the root of the mitzvot, and know why they were given. And there are two points here, one maintaining our relationship with Hashem following the mitzvot pertaining to the land; and secondly because it is our glory because they are intrinsically good and and wise laws.

Avi Ezer cites this bit that there will be glory to them in His commandments, and takes off on it. See here in Mikraos Gedolos, and here in a stand-alone sefer. Though neither is a very good image, so see in your own Mikraos Gedolos:

Behold, one who sees this will be astonished at the words of the pasuk that וּשְׁמַרְתֶּם, וַעֲשִׂיתֶם--כִּי הִוא חָכְמַתְכֶם וּבִינַתְכֶם, לְעֵינֵי הָעַמִּים: אֲשֶׁר יִשְׁמְעוּן, אֵת כָּל-הַחֻקִּים הָאֵלֶּה, וְאָמְרוּ רַק עַם-חָכָם וְנָבוֹן, הַגּוֹי הַגָּדוֹל הַזֶּה.
Is he really saying to learn well in order that you be wise in your ways, and you will have glory over your fellows and your peers, such that they will accept you in honor as a master and teacher?! Isn't this notice not pleasant for an intelligent person, that the learning should be on account of the glory and grandeur, and all the more so for a complete nation?

And what is correct in this is that great things are hinted at in these verses. For it is known that in days of old, in which the Jews were for prey and spoil in the cities of the nations, they thought to find favor by going in their statutes and in adornments {?} of gold and silver. And they already were answered {?} by a patron, that in time of dire straights for their, from their exiles and from moving about because of the jealousy of the nations, because of their going about loftily, with clothing of silk and embroidery, they should tear their clothing from upon their hearts.

And afterwards, many of our brothers thought to find favor in the eyes of the nations by learning their language and statutes {/customs}, in order to find favor in their eyes, while our statutes and our Torah: Scripture, Talmud, and Poskim were set aside in the corner with none to gather. And even this did not work for them. For the nations laughed at them.

But set your heart upon the days of old, in which Hashem answered us whenever we called Him; and every one

of us knew the names of the angels and among us were prophets, and among us were sages and righteous people!

And even in the days of the Tannaim, they made use of the bat kol, and all their words were like fiery coals; with the breath of their mouths they put a wicked man to death, and with the gaze of their eyes they cast down corpses.

This was our glory, and all knew that there was not withheld from them the science of nature and geometry, and the language of the nations and their writing. However, the primary aspect of their glory was only in the divine knowledge. For in this it was apparent within them great providence and influence more than any nation. For they intend by performance of the commandments the lofty aspect of them, and their entire direction is to delve into the greatness of the Creator until they receive the providence and influence, and they

do not perform the commandments like those who perform them by rote.

And behold, the Torah reveals to us, as a reminder to inform us, that if the spirit of {desiring} glory comes upon you, to find favor in the eyes of the nations, and to become beautiful in their eyes such that they will say about you that you are a wise and discerning person, and you think to seek {?} honor in writing and speech, and you cast away the commandments of Hashem over your back, you are making yourself "beautiful" for nothing. And this is what the Scripture is saying: Behold, I have taught you statutes and ordinances... However, observe the

commandments in a fitting way, such that you are not "redeemed" {?} in the pas bag {food; another text: pas bagei} of the times {perhaps zeitgeist?}. For is it not so that then the nations will laugh at your commandments and your statutes, when they see your degraded stature, which of old had been similar to a date-palm. Rather, perform them in a proper manner, as I have written, and then it will be that your wisdom and your wisdom will be extremely great in the eyes of the nations when they see the great religious knowledge and also see the great success of the people, in that Hashem is close to them whenever they call {to Him}. For the wisdom of a person illuminates his face, and whoever sees our people in their tranquility will certainly know that our statutes are good and that Hashem is our beloved and our friend. And this is what the Scripture states {pasuk 9}: However, take heed and watch your soul, lest you forget, etc., and it be to you like an antiquated edict {see Rashi on Vaetchanan, Devarim 6:6, citing Sifrei}, a command fulfilled by people by rote, to come to Him as a nation {?} comes, while their hearts are distant from Him. Is it not the case that then, you will not find favor in the eyes of the nations. And also this will not help them, for they will say that Hashem forgot us, because

we walked despondently. This is the gist of the words of these pesukim; once you set them upon your heard, you will return and see the words of mussar which come out of these pesukim.

And now, know for yourself how deep were the words of the mekonen {author of Eicha}.

{Eicha 3:17-18}

יז וַתִּזְנַח מִשָּׁלוֹם נַפְשִׁי, נָשִׁיתִי טוֹבָה.	17 And my soul is removed far off from peace, I forgot prosperity.
יח וָאֹמַר אָבַד נִצְחִי, וְתוֹחַלְתִּי מֵה'. {ס}	18 And I said: 'My strength is perished, and mine expectation from the LORD.' {S}

To say that for the multitudes of good and peace that You granted me in my soul. And this is vatiznach {is removed far off}, You have caused to forget my soul and spirit, from the great peace which You have showered me; {nashiti tova} I forget prosperity -- this is the goodness of the existing world. וָאֹמַר אָבַד נִצְחִי -- "And I said: 'My strength is perished'" for we have strayed from believing in eternality; וְתוֹחַלְתִּי מֵה' -- "and mine expectation from the LORD {is also gone}" for the future, for we have said that we have been decreed upon, and there is no Judgement or Judge, and the same thing occurs to the righteous and the evildoer, and {channeling the next pasuk} You Hashem recall my affliction and my anguish, to grant atonememt for all that we have perverted. And the mekonen speaks as if Hashem is opposite him, and in bitterness he wails saying in second person and third person at an upper degree almost all the blessings: Hashem is good to those who hope for him, and to the righteous. And do not be astonished about that which we see, that what impacts the righteous is like that of the incidents of the wicked, for You Hashem, seek the soul.

{All this an interpretation of:

כה טוֹב ה' לְקֹוָו, לְנֶפֶשׁ תִּדְרְשֶׁנּוּ.

25 The LORD is good unto them that wait for Him, to the soul that seeketh Him.

}

That Your main aim is to seek out and improve the soul of the righteous person, while the body is incidental, and the Torah does not speak about the dead. And I have gone on at length to speak regarding the words of Chachmeinu za"l in perek BaMeh Madlikin upon the pasuk

יז וַתִּזְנַח מִשָּׁלוֹם נַפְשִׁי, נָשִׁיתִי טוֹבָה.

17 And my soul is removed far off from peace, I forgot prosperity.

and here is not the place for me to extend.

End quote. It is interesting how Rabbi Shlomo Hakohen of Lissa, Avi Ezer, turns the message of this pasuk into an argument against Haskalah, which was flourishing at this point, in the 18th century. Another interesting statement is that:

This was our glory, and all knew that there was not withheld from them the science of nature and geometry, and the language of the nations and their writing. However, the primary aspect of their glory was only in the divine knowledge.

Does he mean that they knew all their was to know about science via tradition or Divine guidance, or that they studied the current-science and mathematics of their day? I am not sure.