Do we not find that idolatry is more stringent than murder or any other Aveirah in the Torah? So why did Aharon conclude that is better that they worship the Golden Calf rather than kill him?

Toras Chaim: The punishment for idolatry is worse, as if one worships an idol, it is as if he has denied the entire Torah. However, after idolatry, it is possible to fully repent. But if they would have murdered Aharon haKohen, there would have been no way to repair the sin.

Rav Hamnuna says that the beginning of a person's judgment in the World to Come is about Torah study. But does the Gemara in Shabbos 31a not teach that when a person passes away, the first question he asked is 'Nasasa Venasata b'Emunah' - 'did you do business honestly' and only the second question is whether he had fixed times for learning? (Tosfos)

Tosfos Answer #1: That Gemara is speaking about someone who studied Torah, but who did not fix times to learn. Here, it is referring to someone who did not study Torah at all.

Tosfos Answer #2: Everybody is first questioned about his business dealings, but a person is punished first for his laxness in Torah-study.

Ein Eliyahu: Our Gemara is referring to the judgment 'L'Asid Lavo' - in the future, at the end of days. The Gemara in Shabbos is referring to each individual, after their death.

Iyun Yaakov (Kidushin 40b): He is first judged for his Torah study. However, he could make a valid claim that he was busy earning a livelihood. But this is only legitimate if he was honest in business. If he was dishonest and stole, he cannot then claim that he was busy earning a livelihood. So, in order to make the final judgment about his Torah study, his honesty must be evaluated.

Ben Yehoyada: The phrase 'Nasasa Venasata b'Emunah' also refers to the study of the Oral Torah (rather than to business), as Chazal use the same phrase of 'Noseh veNosen' - 'give and take' in reference to Torah study.

Maharatz Chayos (Shabbos 31a): 'Nasasa Venasata b'Emunah' refers to the study of Seder Zeraim (the first Seder of Mishnah), as Reish Lakish expounds (Shabbos 31a) from the word 'Emunah' in the Pasuk in Yeshayah (33:6).

Why is there specifically a maximum of three sins before being punished?

Peirush haRosh Al haTorah (Devarim 30:2): The Maharam of Rotenberg explained that there are three partitions before Hash-m. The first is called 'Ra'ash', the second is called 'Eish' and the third is called 'Ruach'. After that, there is 'Kol Demamah Dakah' (see Melachim I 19:11-12, where these phrases occur), where Hash-m's Divine Presence rests. There are angels appointed for each partition and when a person sins, it comes to the first partition and the angels stop it and he is forgiven. The second sin comes to the second partition and the same thing happens; and the same with the third sin. But after that, when he sins a fourth time, the sin comes to the section of Hash-m and is not forgiven.

What are the seven pits alluding to?

Maharsha: They allude to the seven planets. Even if all of the planets and constellations, (meaning his Mazal - his fate based on the stars) are against the righteous Jew; Hash-m changes his Mazal and does not allow them to damage him. In contrast, an evil person will be lost because of his evil, and no planets and constellations can save him.

What is this idea of singing when he comes out of court?

Ben Yehoyada: It is common that when a person loses in court, on his way home (or to his store) he shouts and complains against the Dayanim who found him liable. This is foolish as on the contrary, at that time, he should be singing and praising the Dayanim for saving him from theft.

What is the purpose of Shmuel sourcing all of these sayings from Pesukim?

Iyun Yaakov: He is teaching that these sayings are not just common speech. Since they are learned from Pesukim, one may not say them (even as common speech, without the Pesukim) in an unclean place, such as a bathroom.

If the original statement was a parable, what was it alluding to?

Ben Yehoyada: If there is brotherly love between Jews, even if the sword (of war) is in the world, the Jews will still live peacefully. But if there is no brotherly love, even if the 60 Masechtos of Shas are being studied, they will not live peacefully.

Pesach Einayim (Chida): If a person's love for Hash-m is strong, he could be in the same bed as a prohibited woman and not sin. A sword would be enough to separate them, as we find in the case of Palti ben Layish and Michal bas Shaul (as the Gemara discusses later on 19b). But if his love for Hash-m is not strong, even a very wide bed will not help.

Why are all three Pesukim needed to explain the term 'Lo Saguru'?

MDC: Each verse highlights a different type of fear that a Dayan might face when making decisions in court. The Pasuk in Devarim 28:39 teaches about fear of personal damage. The Pasuk in Mishlei 6:8 encourages a Dayan to act diligently, just as the ant works without fear of consequences. The Pasuk in Mishlei 10:5 teaches about fear of choosing the wrong time to make a decision. Rather, the Dayan must act at the right moment and not delay.

What is the meaning of 'אמת לאמיתו' - 'an absolutely true judgment'? Is a true judgment not enough?

Tosfos (Megilah 15b dh Zeh): 'Emes' excludes a 'Din Merumeh' - a case where a Dayan suspects that there is deception (either by a litigant or by his witnesses), even after the testimony of the witnesses, the Dayanim should not yet make a ruling. Rather, they must thoroughly cross-examine the witnesses, until the truth comes out. Then, they will come to the absolute truth. (Such cross-examination is usually only done in capital cases.)

Beis Yosef (Choshen Mishpat Siman 1): Even if the Dayan judges truthfully, if he combines with it a great love of the innocent or hatred of the guilty, it is not absolute truth. (The Taz there explains that even if on this occasion, the Dayan ruled correctly, his feelings might lead him to judge incorrectly next time.)

Why does an absolutely true judgment bring the Shechina to dwell in Yisrael?

Maharsha (Bava Basra 8b): The Gemara compares it to the sky. Even though it might appear as different colors, its true color is that of Saphir. Hash-m sees the truth even when things are unclear. Similarly, if a Dayan reaches absolute truth, he can be compared (Kiveyachol) to the Shechina which brings the Shechina to dwell.

Why does the Gemara give two things to bear in mind - a sword and Gehinom? Is the threat of Gehinom not enough to instill fear in a Dayan?

Ben Yehoyada: A Dayan might corrupt a ruling because of a desire for money. Money is related to 'legs', as Chazal say (in Pesachim 129a) on the Pasuk (Devarim 11:6), "and all the possessions at their feet" - this refers to a man's person, as it stands him on his feet. Hence, a Dayan who wishes to corrupt the judgement in order to strengthen his legs through money, should view himself as if a sword is resting between his thighs.

Iyun Yaakov: The two fears refer to punishment in this world (the sword) and the next world (Gehinom). This could explain Chazal's words on the Pasuk (Devarim 16:20), "Justice justice you shall pursue". The Gemara later on teaches (Sanhedrin 32b) that we learn from that Pasuk that one should pursue the best Beis Din. The Pasuk then continues, "that you may live and possess the land". So the result of pursuing the best Beis Din is that you will live (in this world) and possess the land (in the next world, as Chazal expound).

Why is the required clarity of the judges compared to both the morning light and one's sister?

Vilna Gaon (Aderes Eliyahu, Devarim 16:19): There are two different types of clarity needed in order to making a ruling - the facts and the Halacha. The facts of the case must be as clear to the judge as the morning light. The Halacha must be as clear as the law that one's sister is prohibited to him.

If ten sat in judgment and, for example, seven ruled wrongly and three ruled correctly; would the three share the responsibility for the wrong ruling?

Birkas Avraham: They are also responsible, since they were part of the Beis Din that ruled wrongly.

Aruch LaNer: They do not bear responsibility as there was nothing that they could do to avoid the wrong ruling.

Why did Chazal choose to describe that 'the chain hangs around the neck of every one of them'?

Mishnas Moshe (Horayos p. 33): The Gemara earlier (7a) stated that 'a judge should always view himself as if a sword is resting between his thighs, and Gehinom is open under him'. In order to view himself in this way, he should be looking downwards. This is achieved by viewing himself as if he is wearing a chain, as its weight would lower his head.

Why is appointing an improper Dayan where Torah scholars are found, compared to planting an Asherah next to the altar?

Maharsha: The Gemara teaches (Shabbos 10a) that when a Dayan judges truthfully, he becomes like a partner with Hash-m in the creation of the universe. But a person who appoints an improper judge when there is a proper judge to appoint, it is like putting fake gods 'next to' Hash-m.

Aruch LaNer: The prohibition of planting an Asheirah applies even before it has been worshipped. Similarly, it is a sin to appoint an improper Dayan, even before he has issued a wrong ruling.

Rav Chaim of Brisk (cited in MiShulchan Gavo'ah Devarim p. 138): Although a regular idol is apparent to all, an Asheirah looks like any other tree and its nature is not visible from its external appearance. So too an improper Dayan, his external features do not indicate his true nature. This causes the public to be misled.

Why was Rav concerned that he would come home empty-handed, meaning liable to pay for ruling wrong in Beis Din? An expert Dayan is exempt from payment, even if he makes a mistake? Furthermore, why was he complaining about coming home without financial gain when it is prohibited for a Dayan to accept a bribe? (Maharsha)

Sefer Sama D'Chayei (cited in Anaf Yosef): Rav's phrases can be understood as follows - 'He goes of his own free will to meet death' - he views even financial disputes like capital cases and deliberates in judgment. 'And he makes no arrangements for his household's needs' - he does not allow family connections of litigants to affect his judgment as a Dayan. 'He will return home empty-handed' - he gains no personal benefit from the judgment. 'If it would only be that he comes back like he left' - he is does not trust himself not to make a mistake and he prays to Hash-m to given him Divine assistance.

If, as Rashi explained, a speaker should not come last to the Drasha after everyone is sitting, as it will look as if he is stepping on their heads, why does the Gemara specifically apply it to a Dayan? It should apply to anyone..? (Benayahu)

Rashi: It applies 'even' to a Dayan. (Since a Dayan is supposed to be respected and revered by the people, one might have thought it does not apply to him.)

Why do Chazal specifically mention resolving a dispute about a stove and an oven?

Maharal (Gur Aryeh, Devarim 1:17): For example, two people (brothers or neighbors) divided a house that contains an oven and a stove. They had not made their claims on those items, but rather, on the house itself. One might have thought that since there is no way to actually split the item, one should simply give the oven to one and the stove to the other. Therefore, the Pasuk teaches that one make a reckoning even on those items and the one who received the oven must reimburse the other, since an oven is worth more than a stove.