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Greeting other with Genuine Joy
A SMILE
It cost nothing, but creates much.
It enriches those who receive, without impoverishing those who give.
It happens in a flash and the memory of it lasts forever.
None are so rich they can get along without it and none so poor but are richer for its benefits.
It creates happiness in the home, fosters good will in a business, and is the countersign of friends.
It is rest to the weary, daylight to the discouraged, sunshine to the sad, and nature’s best antidote for trouble.
Yet it cannot be bought, begged, borrowed, or stolen, for it is something that is no earthly good to anybody till it is given away!
If someone is to tired to give you a smile, leave one of yours.
For, nobody needs a smile so much as those who have none to give.

Part 1: The Torah Sources for greeting other's with greeting and a joyous smile:

Part 2: Psychological Gains of Smiles:

Part 3: Greeting Gentiles

Part 4: It'll Save your life!

Part 1: The Torah Obligation

(ח) יְהוּדָ֗ה אַתָּה֙ יוֹד֣וּךָ אַחֶ֔יךָ יָדְךָ֖ בְּעֹ֣רֶף אֹיְבֶ֑יךָ ...(יב) חַכְלִילִ֥י עֵינַ֖יִם מִיָּ֑יִן וּלְבֶן־שִׁנַּ֖יִם מֵחָלָֽב׃ (פ)

(8) You, O Judah, your brothers shall praise; Your hand shall be on the nape of your foes...(12) His eyes are darker than wine; His teeth are whiter than milk.

אמר ר' יוחנן טוב המלבין שינים לחבירו יותר ממשקהו חלב שנאמר ולבן שנים מחלב אל תקרי לבן שינים אלא לבון שינים.

Rabbi Yoḥanan said: One who whitens his teeth to his friend by smiling at him is better than one who gives him milk to drink, as it is stated: “And his teeth white [leven shinayim] with milk” (Genesis 49:12). Do not read this expression as leven shinayim; rather, read it as libbun shinayim, the whitening of teeth. Likewise, the phrase: With milk, can be read as: Than milk.

(טו) ס֣וּר מֵ֭רָע וַעֲשֵׂה־ט֑וֹב בַּקֵּ֖שׁ שָׁל֣וֹם וְרָדְפֵֽהוּ׃

(15) Shun evil and do good, seek amity and pursue it.

The Altar of Slobodka gave a parable:

Imagine that a man came to Yeshiva every morning and stood by the door each morning holding a jug of milk and cups. As each person existed, the man offered him a cupful of sweet, refreshing milk! You can perform an even greater mitzvah by greeting your friends with a smile!"

R’ Avrohom Grodzinski (1883-1944) embodied this teaching. He spent hours practicing his smile in front of a mirror and worked for two years on greeting others pleasantly, even during the darkest days of the Holocaust.

(כה) יָאֵ֨ר ה' ׀ פָּנָ֛יו אֵלֶ֖יךָ וִֽיחֻנֶּֽךָּ׃ (ס)
(25) The LORD deal kindly and graciously with you!
(יח) לֹֽא־תִקֹּ֤ם וְלֹֽא־תִטֹּר֙ אֶת־בְּנֵ֣י עַמֶּ֔ךָ וְאָֽהַבְתָּ֥ לְרֵעֲךָ֖ כָּמ֑וֹךָ אֲנִ֖י ה'׃
(18) You shall not take vengeance or bear a grudge against your countrymen. Love your fellow as yourself: I am the LORD.
(לב) וְלֹ֤א תְחַלְּלוּ֙ אֶת־שֵׁ֣ם קָדְשִׁ֔י וְנִ֨קְדַּשְׁתִּ֔י בְּת֖וֹךְ בְּנֵ֣י יִשְׂרָאֵ֑ל אֲנִ֥י ה' מְקַדִּשְׁכֶֽם׃
(32) You shall not profane My holy name, that I may be sanctified in the midst of the Israelite people—I the LORD who sanctify you,
(ג) וַאֲבָֽרֲכָה֙ מְבָ֣רְכֶ֔יךָ וּמְקַלֶּלְךָ֖ אָאֹ֑ר וְנִבְרְכ֣וּ בְךָ֔ כֹּ֖ל מִשְׁפְּחֹ֥ת הָאֲדָמָֽה׃
(3) I will bless those who bless you And curse him that curses you; And all the families of the earth Shall bless themselves by you.”

(טו) שַׁמַּאי אוֹמֵר, עֲשֵׂה תוֹרָתְךָ קֶבַע. אֱמֹר מְעַט וַעֲשֵׂה הַרְבֵּה, וֶהֱוֵי מְקַבֵּל אֶת כָּל הָאָדָם בְּסֵבֶר פָּנִים יָפוֹת:

(15) Shammai used to say: make your [study of the] Torah a fixed practice; speak little, but do much; and receive all men with a pleasant countenance.

Brachot 7a: It's a Mitzvah to greet someone using the name of G-d.
Shalom is in fact one of the names of G-d.
We learn this out from Boaz-who goes and greets others with the name of G-d.

ואמר רבי חלבו אמר רב הונא כל שיודע בחברו שהוא רגיל ליתן לו שלום יקדים לו שלום שנאמר בקש שלום ורדפהו ואם נתן לו ולא החזיר נקרא גזלן שנאמר ואתם בערתם הכרם גזלת העני בבתיכם:

And Rabbi Ḥelbo said that Rav Huna said: One who is aware that another person is accustomed to greet him is not only obligated to return his greeting, but he must greet him first, as it is stated: “Seek peace and pursue it” (Psalms 34:15). If the other person extended his greeting to him and he did not respond, he is called a robber, as it is stated: “It is you who have eaten up the vineyard, the spoils of the poor is in your houses” (Isaiah 3:14). The only way to steal from a pauper who owns nothing is to rob him of his dignity by refusing to return his greeting.
The Pelle Yoetz: When greeting someone with a Shalom Aleichem one should have in mind that one is praying for him to be blessed with peace.
When we open our mouths and smile at someone we are communicating the following message: "I want to show you what is inside of me." When we smile and display our teeth, we are showing others that there's a lot inside that we want to share.

R Yisrael Salanter used to say that during the Ten Days of repentance a person has to be very careful to deal pleasantly with others,

Part 2: How Smiling makes you and the whole world smile with you!

1. Smiling improves health.
The very act of smiling can make us happy. That’s the surprising finding of two psychological scientists, Tara Kraft and Sarah Pressman, of the University of Kansas, in a groundbreaking 2012 study. They divided people into groups and asked them to complete a series of stressful tasks; some were asked to smile while others were not.
The results were striking. Participants who smiled experienced markedly lower levels of stress. “The next time you are stuck in traffic or are experiencing some other type of stress, you might try to hold your face in a smile for a moment” explains Dr. Pressman; “Not only will it help you ‘grin and bear it’ psychologically, but it might actually help your heart health as well!”
2. Smiling is contagious.
Smiling at someone is the surest way to put a grin on their face – and make them feel happy. People subconsciously mimic the facial expressions of the people around them. When we see a smile, we often can’t help but follow suit. “Smiling will change our body’s nervous system in a way that fits with happiness,” explains Adrienne Wood, a researcher at the University of Wisconsin.
Your smile affects everyone around you.
Your face is in the public domain. The expression you wear affects everyone around you. The Chazon Ish noted that smiling is not just a personal matter. Exuding happiness has a profound influence on everyone around us.
3 Smiling makes us more attractive.
Smiling makes us more attractive than being healthier, losing weight and wearing makeup. That’s the surprising finding of a 2017 study at Swansea University in England. People judging the attractiveness of men and women in photos consistently rated those who were smiling as more beautiful. The effects of having a smiling expression were as powerful as being slim, wearing makeup, and being young, researchers found.
4 Smiling helps us to see the world as a better place.
"Judge everyone favorably” (Pirkei Avot 1:6). According to a 2015 study at University College London, smiling might help us to achieve this.
Researchers asked participants to look at various photos while they underwent MRIs. Some of the subjects were asked to smile while they did, others to frown and others were asked to have neutral expressions on their face. Those people who smiled during the experiment were more likely to perceive other people favorably. It seems that the very act of smiling makes us more magnanimous and conditioned to like other people more.
In a 2010 Wayne State University Study
(יט) כַּ֭מַּיִם הַפָּנִ֣ים לַפָּנִ֑ים כֵּ֤ן לֵֽב־הָ֝אָדָ֗ם לָאָדָֽם׃
(19) As face answers to face in water, So does one man’s heart to another.
The Messilat Yesharim Chapter 7 and Rabbeinu Bachyeh speak of how our external actions effect our internal feelings:
Thich Nan High
Sometimes your joy is the source of your smile, but sometimes your smile can be the source of your joy-
-Facial Feedback Hypothesis
We can effect our mood through our facial expressions
Part 3: Greeting Gentiles

אמרו עליו על רבן יוחנן בן זכאי שלא הקדימו אדם שלום מעולם ואפילו גוי בשוק.

Tangentially, the Gemara mentions that they said about Rabban Yoḥanan ben Zakkai that no one ever preceded him in issuing a greeting, not even a non-Jew in the marketplace, as Rabban Yoḥanan would always greet him first.

(ז) תַּלְמִיד חָכָם לֹא יְהֵא צוֹעֵק וְצוֹוֵחַ בִּשְׁעַת דִּבּוּרוֹ כִּבְהֵמוֹת וְחַיּוֹת וּמַקְדִּים שָׁלוֹם לְכָל הָאָדָם כְּדֵי שֶׁתְּהֵא רוּחָן נוֹחָה הֵימֶנּוּ.

(7) A disciple of the wise should not be noisy and loud like cattle and animals when talking, nor even raise his voice overmuch, but converse calmly with all people; nevertheless, in speaking calmly he should not overdo it lest he resemble the overpoliteness of the arrogant. He should be first to greet every person, so that their spirit be pleased with him He should judge every person favorably, telling the praiseworthy things about his friend and not at all about the blameworthy things; love peace and pursue it.

Good Morning Sister
One day, the residents of Monsey were surprised to see the mother Superior of the nearby convent stop the venerable Rav Yaakov Kaminetzky during his daily walk and speak to him. He explained afterwards that the woman wanted to knows why all the other people in town shunned the nuns whenever they saw one another in the street, while Rav Yaakov himself always greeted the nuns with a hearty smile and a "good morning".
Smiles will Mamash Save your life
Rav Shmuel Shapira, the rav of Prochnik, Poland, in the years before World War 2, had a habit of taking long walks in the forests near his town. Rav Shapira was known for his pleasant demeanour and benevolent disposition. As he walked he gave a warm greeting to everyone he passed, Jew or non-Jew. Every morning as he passed by the farm just outside the city, he would greet its owner: 'Good Morning Mr. Mueller." At first the man ignored the rabbi and looked away, but in time, as Rav Shapira greeted him consistently in a friendly manner, the man began to nod his head in recognition. Eventually Mr. Mueller began to tip his cap in response tot he rabbi's greeting, and the edges of his lips would turn up in a wan smile.
All this came to an abrupt stop with the nazi's blitzkrieg conquest of Poland. The Jewish residents won the township, including Rav Shapira an this family, were shipped off to concentration camps. Rav Shapira and his family, were shipped off to concentratration camps. Rav Shapiro was transferred from one camp to another until he was brought to his final destination-Auschwitz. He stumbled out of his cattle car and stood in line for selection. As the line moved forward he became filled with apprehension.-he had a pretty good idea of what the selection meant. judging by those he saw being sent to each side, he realised that anyone who was sent to the left would be taken immediately to the gas chambers.
There were two people in line in from of Rav Shapira: then there was one; he stood face to face with the officer in whose hands his fate rested. He glanced up at the man's face and their eyes met. Suddenly Rav Shapira took a step forward and said "Good Morning mr. Mueller."
The officer's steely eyes opened wide for a split moment. Then he said: "Good Morning rabbi," and waved him to the right,
Rav Shapira survived the war to tell the story.
An Amazing True Story about the Power of a Smile
In his book, Reflections of the Maggid, Rabbi Paysach Krohn tells the following story:
In Argentina there was a ritual slaughter complex, comprised of several buildings. There was a building where the animals were fed, a building where they were slaughtered and the meat packed and loaded onto trucks, and an office building with dressing rooms for the shochtim (ritual slaughterers). The entire area was surrounded by a tall chain link fence and everyone entered through a wrought iron gate in the front, near the parking lot.
The owner, Yisrael (Izzy) Nachmal, was a workaholic. He was the first one in every morning and the last one out every evening. He oversaw every aspect of his company, Ultimate Meats, and made it a point to know every worker. The guard at the front gate, Domingo, knew that when Izzy left in the evening, he could lock the gate and go home.
One evening as Izzy was leaving, he called out to the guard, “Good night, Domingo, you can lock up and go.” “No,” Domingo called back, “not everyone has left yet.” “What are you talking about,” Izzy said, “everyone left two hours ago!” “It is not so,” Domingo said, “One of the shochtim, Rabbi Berkowitz, hasn’t left yet.” “But he goes home every day with the other shochtim, maybe you just didn’t see him,” Izzy said. “Believe me, I am positive he didn’t leave yet,” the guard insisted. “We better go look for him.”
Izzy knew that Domingo was reliable and conscientious. He decided not to argue, but instead got out of his car and rushed back to the office building with Domingo. They searched the dressing room thinking that perhaps Rabbi Berkowitz had fainted and was debilitated. He wasn’t there.
They ran to where the animals were slaughtered, but he wasn’t there either. They searched the truck dock, the packing house, going from room to room. Finally they came to the huge walk-in refrigeration room where the large slabs of meat were kept frozen.
They opened the door and to their shock and horror they saw Rabbi Berkowitz rolling on the floor, trying desperately to keep himself warm. They ran over to him, lifted him off the floor and helped him out of the refrigerated room, past the thick heavy wooden door that had locked behind him. They wrapped blankets around him and made sure he was warm and comfortable.
Izzy Nachmal was incredulous. “Domingo,” he asked, “how did you know Rabbi Berkowitz hadn’t left? There are over two hundred workers here every day. Don’t tell me you know the comings and goings of every one of them?”
The guard’s answer is worth remembering. “Every morning when that rabbi comes in, he greets me and says hello. He makes me feel like a person. And every single night when he leaves he tells me, ‘Have a pleasant evening.’ He never misses a night – and to tell you the truth, I wait for his kind words. Dozens and dozens of workers pass me every day – morning and night, and they don’t say a word to me. To them I am a nothing. To him, I am a somebody. “I knew he came in this morning and I was sure he hadn’t left yet, because I was waiting for his friendly good-bye for the evening!”