וידעתם היום כי לא את בניכם אשר לא ידעו, "and you will know this day, that not with your children who did not know, etc.⁠" This verse tells that all the wonderful deeds performed by the Lord which Moses speaks about are not events which will happen in the future [like the promises of prosperity in the land of Canaan he had told them about. Ed.] Rather, "you yourselves have seen all this with your own eyes.⁠" Everything we read here is an introduction to verse 7: "for you have seen.⁠" Moses recalls that the people (or most of them, those 40 years and over) have been witnesses to what he is describing. If we find Moses relating to Datan and Aviram and what happened to them while omitting mention of Korach who was the leader of that rebellion, the reason may well be that he felt ashamed that a member of his own family had become guilty of such a sin. Or, he may have singled out Datan and Aviram as they had exceeded everyone else in their demagoguery and their effrontery, strutting around cursing, etc. (compare Tanchuma Korach 8).

You are already aware that the "hidden" miracles are performed by the attribute Shaddai, the attribute which God employed in His dealings with the patriarchs. That attribute is referred to here as the שם הנכבד והנורא הזה, את ה' אלו-היך in Deut. 28,58. The "manifest" miracles are the ones orchestrated by God's attribute Hashem, the tetragram. This is the attribute of God which manifested itself to Moses all the time. This is why you find at the beginning of this passage when Moses refers to all the miracles which affected the bodies of the people, i.e. "hidden miracles,⁠" not dramatic changes in the laws of nature, that Moses employs the attribute ה' אלו-היך for the God who had performed them, just as Moses had done since the beginning of the Book of Deuteronomy. When he switches to recalling "manifest" miracles, the ones which changed the laws of nature, such as the descent of people into the bowels of the earth after this event had been announced in advance, suddenly Moses mentions only י-ה-ו-ה, the attribute Hashem as orchestrating that event.

את גדלו ואת ידו החזקה וזרועו הנטויה, "His greatness, His powerful hand and His outstretched arm" Every intelligent person knows that terms such as "hand,⁠" "arm,⁠" "mouth,⁠" "nose,⁠" etc., cannot be applied to God in the literal sense of these words. They merely represent celestial equivalents of extensions of the essence of God just as these parts of the body are extensions of the essence of people on earth, extensions which enable the essence to carry out its will. Every such term used by the Torah in connection with God describes a specific function such an extension performs. Just as we do not call a "hand" once "a hand,⁠" and another time "a foot,⁠" the same is true of these terms when used in connection with God. We do not lump "arm" and hand together when describing these organs as part of a human being. Similarly, we do not do so when we describe them as extensions of the essence of God.
The definition of יד, "hand,⁠" includes the surface of the hand up until the beginning of the fingers. The part from the wrist to the elbow is known as קנה, whereas the part from the elbow up is known as זרוע. This is the part of the arm on which we put the phylacteries. On occasion this is known as the higher region of the hand, the part on the same level as the heart. Concerning this arm the sages in Menachot 43 said that proof that Israel is beloved of the Lord is that He assigned this part of the arm for them to place the phylacteries of the hand, and the head to place the phylacteries of the head. The proof that the part of the arm above the elbow is called זרוע is found in Job 31,22 כתפי משכמי תפול ואזרועי מקנה תשבר, "may my arm drop off my shoulder; my forearm break off at the elbow.⁠" Job enumerated parts of the arm beginning with his shoulder, followed by זרוע, continuing with קנה, the arm below the elbow, the part which links up with the hand.
We find similar terminology in the Mishnah in Oholot 1,8 where 248 limbs (bones) of man are enumerated, thirty of them being considered part of the פסת היד, 'the hand;' 6 of these bones of the hand are attributed to each of the fingers. The Mishnah enumerates 2 bones as being part of the forearm (below the elbow) and 2 more as part of the elbow, one in the upper arm and four in the shoulder. This Mishnah is proof that the part called קנה are the bones linking the hand to the elbow. The term עציל is a word found in the Baraitha describing the word מרפק in the Mishnah (elbow). In Biblical language the עציל of the Baraitha is identical with אציל as described in Ezekiel 13,18 על כל אצילי ידי, "upon all my elbows.⁠" Targum Yonathan clearly translates the word אצילי as "my elbows,⁠" [in contrast to Rashi who considers it as "my armpits". Ed.]
In Massechet Sofrim 3,15 we find the halachah "a man is not to place a Torah scroll upon his knees and hold it down with his elbows (so it does not fall) as it is unseemly (to place one's weight upon the Torah scroll).⁠" Having explained the difference between יד and זרוע, the author of Masechet Sofrim continues: "it is a well known fact that the זרוע is "greater" (more powerful) than the יד, seeing the power of the hand is derived from the arm and not vice versa.⁠" This makes it clear that whenever the Torah speaks of both hand and arm, the arm is always considered as describing something even more forceful than the hand.

Both the mention of God's "hand" and mention of God's "arm" are references to the attribute of Justice at work. The attribute of Justice operates on different levels of intensity, however. Just as red wine comes in different shades of red so the attribute of Justice becomes manifest in different degrees of severity. The manifestation of a weak form of the attribute of Justice presupposes that there must be a stronger form from which the weaker form derives its input. I have explained this in connection with the two letters ה in מי כמוכה in Exodus 15,11. This is also the meaning of Isaiah 53,1: וזרוע ה' על מי נגלתה, "against whom has the "arm" of the Lord become manifest?⁠" When David (Psalms 44,4) speaks of כי ימינך וזרועך, "Your right hand and Your arm,⁠" he also refers to God employing His power against the Canaanites as first relatively mildly, ימינך, followed by a stronger dose, i.e. זרועך. I have alluded to all this in my commentary on Exodus 14,31 "Israel saw the great hand, etc.⁠"

When the Torah speaks here of God's "greatness, גדלו,⁠" followed by His "strong hand, ידו החזקה,⁠" and "His outstretched arm וזרועו הנטויה,⁠" this is similar to what we read in 5,21. הן הראנו ה' אלו-הינו את כבודו ואת גדלו ואת ידו החזקה וזרועו הנטויה describes "His strong hand and outstretched arm, The word כבדו describes the "weak" manifestation of the attribute of Justice, a manifestation containing also part of the attribute of Mercy. This fact is underscored by use of the tetragrammaton for God in that verse. It is as if the Torah had written 'כי בי-ה ה' a combination of Justice, i.e. י-ה,and Hashem, i.e. Mercy. Solomon used similar terms when he prayed at the dedication of the Temple (Kings I 8,42) asking God to respond when the people would first hear God's attribute of Mercy mentioned,שמך הגדול followed by the attribute of Justice, i.e. את ידך החזקה וזרועך הנטויה.