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Nefillat Apayim
Who is Gad? What is the context of David’s statement at the beginning of Tachnun?

(א) וַיֹּ֙סֶף֙ אַף־יְהוָ֔ה לַחֲר֖וֹת בְּיִשְׂרָאֵ֑ל וַיָּ֨סֶת אֶת־דָּוִ֤ד בָּהֶם֙ לֵאמֹ֔ר לֵ֛ךְ מְנֵ֥ה אֶת־יִשְׂרָאֵ֖ל וְאֶת־יְהוּדָֽה׃ (ב) וַיֹּ֨אמֶר הַמֶּ֜לֶךְ אֶל־יוֹאָ֣ב ׀ שַׂר־הַחַ֣יִל אֲשֶׁר־אִתּ֗וֹ שֽׁוּט־נָ֞א בְּכָל־שִׁבְטֵ֤י יִשְׂרָאֵל֙ מִדָּן֙ וְעַד־בְּאֵ֣ר שֶׁ֔בַע וּפִקְד֖וּ אֶת־הָעָ֑ם וְיָ֣דַעְתִּ֔י אֵ֖ת מִסְפַּ֥ר הָעָֽם׃ (ס) (ג) וַיֹּ֨אמֶר יוֹאָ֜ב אֶל־הַמֶּ֗לֶךְ וְיוֹסֵ֣ף יְהוָה֩ אֱלֹהֶ֨יךָ אֶל־הָעָ֜ם כָּהֵ֤ם ׀ וְכָהֵם֙ מֵאָ֣ה פְעָמִ֔ים וְעֵינֵ֥י אֲדֹנִֽי־הַמֶּ֖לֶךְ רֹא֑וֹת וַאדֹנִ֣י הַמֶּ֔לֶךְ לָ֥מָּה חָפֵ֖ץ בַּדָּבָ֥ר הַזֶּֽה׃ (ד) וַיֶּחֱזַ֤ק דְּבַר־הַמֶּ֙לֶךְ֙ אֶל־יוֹאָ֔ב וְעַ֖ל שָׂרֵ֣י הֶחָ֑יִל וַיֵּצֵ֨א יוֹאָ֜ב וְשָׂרֵ֤י הַחַ֙יִל֙ לִפְנֵ֣י הַמֶּ֔לֶךְ לִפְקֹ֥ד אֶת־הָעָ֖ם אֶת־יִשְׂרָאֵֽל׃ (ה) וַיַּעַבְר֖וּ אֶת־הַיַּרְדֵּ֑ן וַיַּחֲנ֣וּ בַעֲרוֹעֵ֗ר יְמִ֥ין הָעִ֛יר אֲשֶׁ֛ר בְּתוֹךְ־הַנַּ֥חַל הַגָּ֖ד וְאֶל־יַעְזֵֽר׃ (ו) וַיָּבֹ֙אוּ֙ הַגִּלְעָ֔דָה וְאֶל־אֶ֥רֶץ תַּחְתִּ֖ים חָדְשִׁ֑י וַיָּבֹ֙אוּ֙ דָּ֣נָה יַּ֔עַן וְסָבִ֖יב אֶל־צִידֽוֹן׃ (ז) וַיָּבֹ֙אוּ֙ מִבְצַר־צֹ֔ר וְכָל־עָרֵ֥י הַחִוִּ֖י וְהַֽכְּנַעֲנִ֑י וַיֵּֽצְא֛וּ אֶל־נֶ֥גֶב יְהוּדָ֖ה בְּאֵ֥ר שָֽׁבַע׃ (ח) וַיָּשֻׁ֖טוּ בְּכָל־הָאָ֑רֶץ וַיָּבֹ֜אוּ מִקְצֵ֨ה תִשְׁעָ֧ה חֳדָשִׁ֛ים וְעֶשְׂרִ֥ים י֖וֹם יְרוּשָׁלִָֽם׃ (ט) וַיִּתֵּ֥ן יוֹאָ֛ב אֶת־מִסְפַּ֥ר מִפְקַד־הָעָ֖ם אֶל־הַמֶּ֑לֶךְ וַתְּהִ֣י יִשְׂרָאֵ֡ל שְׁמֹנֶה֩ מֵא֨וֹת אֶ֤לֶף אִֽישׁ־חַ֙יִל֙ שֹׁ֣לֵֽף חֶ֔רֶב וְאִ֣ישׁ יְהוּדָ֔ה חֲמֵשׁ־מֵא֥וֹת אֶ֖לֶף אִֽישׁ׃ (י) וַיַּ֤ךְ לֵב־דָּוִד֙ אֹת֔וֹ אַחֲרֵי־כֵ֖ן סָפַ֣ר אֶת־הָעָ֑ם (ס) וַיֹּ֨אמֶר דָּוִ֜ד אֶל־יְהוָ֗ה חָטָ֤אתִי מְאֹד֙ אֲשֶׁ֣ר עָשִׂ֔יתִי וְעַתָּ֣ה יְהוָ֔ה הַֽעֲבֶר־נָא֙ אֶת־עֲוֺ֣ן עַבְדְּךָ֔ כִּ֥י נִסְכַּ֖לְתִּי מְאֹֽד׃ (יא) וַיָּ֥קָם דָּוִ֖ד בַּבֹּ֑קֶר (פ) וּדְבַר־יְהוָ֗ה הָיָה֙ אֶל־גָּ֣ד הַנָּבִ֔יא חֹזֵ֥ה דָוִ֖ד לֵאמֹֽר׃ (יב) הָל֞וֹךְ וְדִבַּרְתָּ֣ אֶל־דָּוִ֗ד כֹּ֚ה אָמַ֣ר יְהוָ֔ה שָׁלֹ֕שׁ אָנֹכִ֖י נוֹטֵ֣ל עָלֶ֑יךָ בְּחַר־לְךָ֥ אַֽחַת־מֵהֶ֖ם וְאֶֽעֱשֶׂה־לָּֽךְ׃ (יג) וַיָּבֹא־גָ֥ד אֶל־דָּוִ֖ד וַיַּגֶּד־ל֑וֹ וַיֹּ֣אמֶר ל֡וֹ הֲתָב֣וֹא לְךָ֣ שֶֽׁבַע שָׁנִ֣ים ׀ רָעָ֣ב ׀ בְּאַרְצֶ֡ךָ אִם־שְׁלֹשָׁ֣ה חֳ֠דָשִׁים נֻסְךָ֨ לִפְנֵֽי־צָרֶ֜יךָ וְה֣וּא רֹדְפֶ֗ךָ וְאִם־הֱ֠יוֹת שְׁלֹ֨שֶׁת יָמִ֥ים דֶּ֙בֶר֙ בְּאַרְצֶ֔ךָ עַתָּה֙ דַּ֣ע וּרְאֵ֔ה מָה־אָשִׁ֥יב שֹׁלְחִ֖י דָּבָֽר׃ (ס) (יד) וַיֹּ֧אמֶר דָּוִ֛ד אֶל־גָּ֖ד צַר־לִ֣י מְאֹ֑ד נִפְּלָה־נָּ֤א בְיַד־יְהוָה֙ כִּֽי־רַבִּ֣ים רחמו [רַֽחֲמָ֔יו] וּבְיַד־אָדָ֖ם אַל־אֶפֹּֽלָה׃ (טו) וַיִּתֵּ֨ן יְהוָ֥ה דֶּ֙בֶר֙ בְּיִשְׂרָאֵ֔ל מֵהַבֹּ֖קֶר וְעַד־עֵ֣ת מוֹעֵ֑ד וַיָּ֣מָת מִן־הָעָ֗ם מִדָּן֙ וְעַד־בְּאֵ֣ר שֶׁ֔בַע שִׁבְעִ֥ים אֶ֖לֶף אִֽישׁ׃ (טז) וַיִּשְׁלַח֩ יָד֨וֹ הַמַּלְאָ֥ךְ ׀ יְרֽוּשָׁלִַם֮ לְשַׁחֲתָהּ֒ וַיִּנָּ֤חֶם יְהוָה֙ אֶל־הָ֣רָעָ֔ה וַ֠יֹּאמֶר לַמַּלְאָ֞ךְ הַמַּשְׁחִ֤ית בָּעָם֙ רַ֔ב עַתָּ֖ה הֶ֣רֶף יָדֶ֑ךָ וּמַלְאַ֤ךְ יְהוָה֙ הָיָ֔ה עִם־גֹּ֖רֶן האורנה [הָאֲרַ֥וְנָה] הַיְבֻסִֽי׃ (ס) (יז) וַיֹּאמֶר֩ דָּוִ֨ד אֶל־יְהוָ֜ה בִּרְאֹת֣וֹ ׀ אֶֽת־הַמַּלְאָ֣ךְ ׀ הַמַּכֶּ֣ה בָעָ֗ם וַיֹּ֙אמֶר֙ הִנֵּ֨ה אָנֹכִ֤י חָטָ֙אתִי֙ וְאָנֹכִ֣י הֶעֱוֵ֔יתִי וְאֵ֥לֶּה הַצֹּ֖אן מֶ֣ה עָשׂ֑וּ תְּהִ֨י נָ֥א יָדְךָ֛ בִּ֖י וּבְבֵ֥ית אָבִֽי׃ (פ) (יח) וַיָּבֹא־גָ֥ד אֶל־דָּוִ֖ד בַּיּ֣וֹם הַה֑וּא וַיֹּ֣אמֶר ל֗וֹ עֲלֵה֙ הָקֵ֤ם לַֽיהוָה֙ מִזְבֵּ֔חַ בְּגֹ֖רֶן ארניה [אֲרַ֥וְנָה] הַיְבֻסִֽי׃ (יט) וַיַּ֤עַל דָּוִד֙ כִּדְבַר־גָּ֔ד כַּאֲשֶׁ֖ר צִוָּ֥ה יְהוָֽה׃ (כ) וַיַּשְׁקֵ֣ף אֲרַ֗וְנָה וַיַּ֤רְא אֶת־הַמֶּ֙לֶךְ֙ וְאֶת־עֲבָדָ֔יו עֹבְרִ֖ים עָלָ֑יו וַיֵּצֵ֣א אֲרַ֔וְנָה וַיִּשְׁתַּ֧חוּ לַמֶּ֛לֶךְ אַפָּ֖יו אָֽרְצָה׃ (כא) וַיֹּ֣אמֶר אֲרַ֔וְנָה מַדּ֛וּעַ בָּ֥א אֲדֹנִֽי־הַמֶּ֖לֶךְ אֶל־עַבְדּ֑וֹ וַיֹּ֨אמֶר דָּוִ֜ד לִקְנ֧וֹת מֵעִמְּךָ֣ אֶת־הַגֹּ֗רֶן לִבְנ֤וֹת מִזְבֵּ֙חַ֙ לַֽיהוָ֔ה וְתֵעָצַ֥ר הַמַּגֵּפָ֖ה מֵעַ֥ל הָעָֽם׃ (כב) וַיֹּ֤אמֶר אֲרַ֙וְנָה֙ אֶל־דָּוִ֔ד יִקַּ֥ח וְיַ֛עַל אֲדֹנִ֥י הַמֶּ֖לֶךְ הַטּ֣וֹב בעינו [בְּעֵינָ֑יו] רְאֵה֙ הַבָּקָ֣ר לָעֹלָ֔ה וְהַמֹּרִגִּ֛ים וּכְלֵ֥י הַבָּקָ֖ר לָעֵצִֽים׃ (כג) הַכֹּ֗ל נָתַ֛ן אֲרַ֥וְנָה הַמֶּ֖לֶךְ לַמֶּ֑לֶךְ (ס) וַיֹּ֤אמֶר אֲרַ֙וְנָה֙ אֶל־הַמֶּ֔לֶךְ יְהוָ֥ה אֱלֹהֶ֖יךָ יִרְצֶֽךָ׃ (כד) וַיֹּ֨אמֶר הַמֶּ֜לֶךְ אֶל־אֲרַ֗וְנָה לֹ֚א כִּֽי־קָנ֨וֹ אֶקְנֶ֤ה מֵאֽוֹתְךָ֙ בִּמְחִ֔יר וְלֹ֧א אַעֲלֶ֛ה לַיהוָ֥ה אֱלֹהַ֖י עֹל֣וֹת חִנָּ֑ם וַיִּ֨קֶן דָּוִ֤ד אֶת־הַגֹּ֙רֶן֙ וְאֶת־הַבָּקָ֔ר בְּכֶ֖סֶף שְׁקָלִ֥ים חֲמִשִּֽׁים׃ (כה) וַיִּבֶן֩ שָׁ֨ם דָּוִ֤ד מִזְבֵּ֙חַ֙ לַֽיהוָ֔ה וַיַּ֥עַל עֹל֖וֹת וּשְׁלָמִ֑ים וַיֵּעָתֵ֤ר יְהוָה֙ לָאָ֔רֶץ וַתֵּעָצַ֥ר הַמַּגֵּפָ֖ה מֵעַ֥ל יִשְׂרָאֵֽל׃

(1) The anger of the LORD again flared up against Israel; and He incited David against them, saying, “Go and number Israel and Judah.” (2) The king said to Joab, -his army commander, “Make the rounds of all the tribes of Israel, from Dan to Beer-sheba, and take a census of the people, so that I may know the size of the population.” (3) Joab answered the king, “May the LORD your God increase the number of the people a hundredfold, while your own eyes see it! But why should my lord king want this?” (4) However, the king’s command to Joab and to the officers of the army remained firm; and Joab and the officers of the army set out, at the instance of the king, to take a census of the people of Israel. (5) They crossed the Jordan and encamped at Aroer, on the right side of the town, which is in the middle of the wadi of Gad, and [went on] to Jazer. (6) They continued to Gilead and to the region of Tahtim-hodshi, and they came to Dan-jaan and around to Sidon. (7) They went onto the fortress of Tyre and all the towns of the Hivites and Canaanites, and finished at Beer-sheba in southern Judah. (8) They traversed the whole country, and then they came back to Jerusalem at the end of nine months and twenty days. (9) Joab reported to the king the number of the people that had been recorded: in Israel there were 800,000 soldiers ready to draw the sword, and the men of Judah numbered 500,000. (10) But afterward David reproached himself for having numbered the people. And David said to the LORD, “I have sinned grievously in what I have done. Please, O LORD, remit the guilt of Your servant, for I have acted foolishly.” (11) When David rose in the morning, the word of the LORD had come to the prophet Gad, David’s seer: (12) “Go and tell David, ‘Thus said the LORD: I hold three things over you; choose one of them, and I will bring it upon you.’” (13) Gad came to David and told him; he asked, “Shall a seven-year famine come upon you in the land, or shall you be in flight from your adversaries for three months while they pursue you, or shall there be three days of pestilence in your land? Now consider carefully what reply I shall take back to Him who sent me.” (14) David said to Gad, “I am in great distress. Let us fall into the hands of the LORD, for His compassion is great; and let me not fall into the hands of men.” (15) The LORD sent a pestilence upon Israel from morning until the set time; and 70,000 of the people died, from Dan to Beer-sheba. (16) But when the angel extended his hand against Jerusalem to destroy it, the LORD renounced further punishment and said to the angel who was destroying the people, “Enough! Stay your hand!” The angel of the LORD was then by the threshing floor of Araunah the Jebusite. (17) When David saw the angel who was striking down the people, he said to the LORD, “I alone am guilty, I alone have done wrong; but these poor sheep, what have they done? Let Your hand fall upon me and my father’s house!” (18) Gad came to David the same day and said to him, “Go and set up an altar to the LORD on the threshing floor of Araunah the Jebusite.” (19) David went up, following Gad’s instructions, as the LORD had commanded. (20) Araunah looked out and saw the king and his courtiers approaching him. So Araunah went out and bowed low to the king, with his face to the ground. (21) And Araunah asked, “Why has my lord the king come to his servant?” David replied, “To buy the threshing floor from you, that I may build an altar to the LORD and that the plague against the people may be checked.” (22) And Araunah said to David, “Let my lord the king take it and offer up whatever he sees fit. Here are oxen for a burnt offering, and the threshing boards and the gear of the oxen for wood. (23) All this, O king, Araunah gives to Your Majesty. And may the LORD your God,” Araunah added, “respond to you with favor!” (24) But the king replied to Araunah, “No, I will buy them from you at a price. I cannot sacrifice to the LORD my God burnt offerings that have cost me nothing.” So David bought the threshing floor and the oxen for fifty shekels of silver. (25) And David built there an altar to the LORD and sacrificed burnt offerings and offerings of well-being. The LORD responded to the plea for the land, and the plague against Israel was checked.

In this statement, God has offered David three choices: to be chased by enemies, suffer a famine, or suffer a disease. David responds that he chooses a plague, because he would rather suffer at the hand of God than by other people because God is great and merciful.
Context for Gemara: We have just learnt the story of וזה התנור של עכנאי. Basically, two Rabbis get into a fight- Rabbi Yehoshua supports the majority opinion, and Rabbi Eliezer supports the minority opinion. They fight back and forth, and a Rabbi Eliezer proves through a multitude of miraculous events that God is in his side. However, Rabbi Yehoshua quotes the famous line ״לא בשמים היא״ to establish that we need a majority of humans- at this stage, divine intervention is not how we establish laws. Rabban Gamliel ostracized Rabbi Eliezer, and he was so upset it is said that his eyes burned whatever they saw.

אימא שלום דביתהו דר"א אחתיה דר"ג הואי מההוא מעשה ואילך לא הוה שבקה ליה לר"א למיפל על אפיה ההוא יומא ריש ירחא הוה ואיחלף לה בין מלא לחסר איכא דאמרי אתא עניא וקאי אבבא אפיקא ליה ריפתא

The Gemara further relates: Imma Shalom, the wife of Rabbi Eliezer, was the sister of Rabban Gamliel. From that incident forward, she would not allow Rabbi Eliezer to lower his head and recite the taḥanun prayer, which includes supplication and entreaties. She feared that were her husband to bemoan his fate and pray at that moment, her brother would be punished. A certain day was around the day of the New Moon, and she inadvertently substituted a full thirty-day month for a deficient twenty-nine-day month, i.e., she thought that it was the New Moon, when one does not lower his head in supplication, but it was not. Some say that a pauper came and stood at the door, and she took bread out to him. The result was that she left her husband momentarily unsupervised.

אשכחתיה דנפל על אנפיה אמרה ליה קום קטלית לאחי אדהכי נפק שיפורא מבית רבן גמליאל דשכיב אמר לה מנא ידעת אמרה ליה כך מקובלני מבית אבי אבא כל השערים ננעלים חוץ משערי אונאה

When she returned, she found him and saw that he had lowered his head in prayer. She said to him: Arise, you already killed my brother. Meanwhile,the sound of a shofar emerged from the house of Rabban Gamliel to announce that the Nasi had died. Rabbi Eliezer said to her: From where did you know that your brother would die? She said to him: This is the tradition that I received from the house of the father of my father: All the gates of Heaven are apt to be locked, except for the gates of prayer for victims of verbal mistreatment.

It is customary to cover one's face during Nefilat Appayim. The Magen Avraham (131:2), consistent with his view above, explains that the cover serves to separate between one's face and the ground, serving as a barrier, thereby permitting one to perform Nefilat Appayim. Therefore, he claims, one may not lean upon one's arm without a sleeve or another type of separation, as one's body cannot serve as a separation between the face and the floor.
According to the Magen Avraham, it seems that those who merely cover their foreheads, but leave the majority of their head and face exposed to the ground, are not performing Nefilat Appayim correctly. Rather, one should cover one's entire face with one's sleeve, or recite the Tachanun over a table or bench, which serve as a separation.
The custom to cover one's face may also simply be an expression of shame and humility, consistent with the theme of Tachanun, especially according to the opinion of the Mishna Berura cited above, which fundamentally rejects the need to lean or to separate one's face from the floor.
We understand the more technical opinion cited by the Magen Avraham. In contrast, the Mishna Berura is much more emotional. Sometimes it can be hard for us to emotionally connect to davening. By doing a physical motion, we are able to enter a natural state of mind to say Tachnun.
There is an unspoken agreement in society to do our best in circumstances and not to complain. Granted, this is beneficial for a meaningful and productive life. However, this attitude can also leave us with little time to reflect over conflicts or struggles which we face each day.
There are many days in which we omit Tachnun because they are days of joy, and therefore saying Tachnun would be contradictory. On those days, we don’t make ourselves small and simply appreciate God and all his glory. The Tachnun mindset is not always appropriate- that’s why we have a specific time to say it.
מורשה לנו - ולא להם ואיכא משום גזל כדמפרש: