Shabbos, Mishnah 1. The first four mishnayos of this chapter are actually a digression from the main subject; they follow on from the last mishnah of the previous chapter, which sought sources in the verses - sources in Tanach - for various halachos. Here too we will be occupied with the search for scriptural sources for various halachos.
The source for the tumah of idolatry:
Rabbi Akiva asks: how do we know that an idol conveys tumah by being carried? That is, even if a person does not touch it, the very act of carrying it makes him tamei - exactly like the law of a niddah. A woman who is a niddah, and along with her a number of other sources of tumah in the Torah, have the law that one who carries them becomes tamei even without touching. And where do we learn this from? From the verse in Yeshayah: "tizrem kemo davah" - the verse speaks of idolatry and compares it to a woman who is davah, that is, a niddah. From here we learn: just as a niddah conveys tumah by being carried, even without contact, so too an idol conveys tumah when it is carried.
A more concrete example of tumah through carrying: when the niddah or the idol rests on top of an object, that object beneath them becomes tamei. She sat on the bed - the bed becomes tamei, and so on.
A dissenting view - tumah like a sheretz:
A similar mishnah appears in the third chapter of Maseches Avodah Zarah, and there, alongside this view of Rabbi Akiva, another view is brought as well: an idol does not convey tumah like a niddah, but only like a sheretz. The sheratzim - the eight sheratzim listed in Parshas Shemini, among them the dead mouse - convey tumah only through contact, and do not convey tumah through being carried. According to this view, the halachah is different.
It is worth noting that the very law that an idol conveys tumah is only rabbinic, and even so the Sages provided it with a source from the verses.
A lovely observation on Parshas Vayeitzei:
Let me mention a brilliant insight that a friend of mine raised many years ago, when he learned this mishnah for the first time. At the end of Parshas Vayeitzei, Lavan searches for his terafim, his idols. Rachel had placed them in the camel's cushion, in the saddlebag, sat on them, and apologized for not rising from her place to allow the search - "ki derech nashim li", that she was in the time of her monthly cycle. According to him, it is possible that Lavan sensed the tumah emanating from that spot, focused his attention on it, and thought: here lie my terafim, here are my idols. And Rachel answered him: "derech nashim li" - it is not the tumah of idolatry that you sense, but the tumah of a niddah. And all this is based on our mishnah in Maseches Shabbos, which compares the tumah of idolatry to the tumah of a niddah.