Buried in a discussion of paternity, the Talmud states that the mechanism of the development of twin brothers is as follows: "דטפה אחת היה ונחלקה לשתים" - "there was one drop of semen that split into two".
Aristotle (384-322 BC) believed that twins were caused by too much seed (which does make a certain intuitive sense I suppose). In the thirteenth century the German theologian Albertus Magnus updated this theory, and suggested that twins were generated when the woman experienced too much sexual pleasure during intercourse. This redistributed the seed throughout the uterus, resulting in twins.
We now know that there are actually only two ways that twins are formed, and neither depends on sperm splitting, too much seed, or an abundance of sexual pleasure. In monozygotic or identical twins (though they are not always literally identical), one sperm fertilizes one egg, and the resulting zygote then divides into two. Since the two offspring zygotes originated from the same "mother" zygote, they are genetically identical - and hence the twins (or triplets, if the zygote splits three ways) are identical and of course of the same sex.
In dizygotic or fraternal twins, two sperm fertilize two eggs and the two resulting zygotes grow together in the same womb at the same time. They are not genetically identical, and are really two siblings who just happen to be sharing a womb at the same time.
That's it. No sperm splits. Sorry.
Fun facts about twins, Israeli and others
For reasons that are not clear, the rate of dizygotic twins varies across the world, (highest in sub-Saharan Africa, lowest in Asia) and varies across women by body habitus (taller women are more likely to have twins - who knew?) and age (older women are four times more likely to have twins) and varies across time (possibly highest when conception is in the summer and fall).
From 1915, when records were first started, through the 1970s, the rate of twin births in the US was a constant 2% of all births. But in the early 1980s the number of twin births in the US more than doubled, and today that rate is over 3%. The cause, as you may have guessed, is the increased use of reproductive technologies.
The states that saw the greatest increase in twin birth rates were Connecticut, Hawaii, Massachusetts, New Jersey and Rhode Island. In these states, the twin birth rate more than doubled!
Finally, although the rate of twin births has increased for women of all ages over the last three decades, in women older than 40 the rate of twin births increased by 200%. There are at least two causes for this dramatic rise. First, as more women postpone childbirth, more are having children later in life, and older women, as we have already seen, are more likely to have (dizygotic) twins. And secondly, more older women are using assisted reproduction techniques, which also increases the rate of twin conceptions.
In Israel, the incidence of twin births increased three fold in the three decades before 2001, a rate even higher than the increase in the US. The authors of a 2004 study on multiple births in Israel concluded that the "increased incidence of multiple births is explained by the special significance attributed to motherhood in Israeli society, which is met by the socio-political milieu and the availability of assisted reproductive technologies". Indeed.
The incidence of twin births in higher in Jewish than it is in Arab Israelis. This is likely explained by their greater use of assisted reproductive technologies (like in-vitro fertilization).
The Talmud wasn't exactly accurate about how twins are formed, but elsewhere it does capture the sense of wonder that so many of us feel as we hold a newborn baby (or two). It's a transcendent moment in which we may, for a fleeting moment, feel the divine.