Alexander I. Poltorak

Curses, Blessings, and Semiconductors

Mount Gerizim (photograph circa 1900 from the Jewish Encyclopedia, Public Domain,

Ki Tavo

And it shall come to pass, when the Lord thy God shall bring thee into the land whither thou goest to possess it, that thou shalt set the blessing upon mount Gerizim, and the curse upon mount Ebal. (Deuteronomy 11:29) These shall stand upon mount Gerizim to bless the people, when ye are passed over the Jordan: Simeon, and Levi, and Judah, and Issachar, and Joseph, and Benjamin; and these shall stand upon mount Ebal for the curse: Reuben, Gad, and Asher, and Zebulun, Dan, and Naphtali. And the Levites shall speak, and say unto all the men of Israel with a loud voice: Cursed be the man that maketh a graven or molten image, an abomination unto the LORD, the work of the hands of the craftsman, and setteth it up in secret. And all the people shall answer and say: Amen. (Deuteronomy 27:12-15)


In last week’s Torah Portion, Ki Tavo, Moses gives instructions on carrying out the injunction already given earlier in the Torah portions Re’eh. He instructs his people, upon crossing over the Jordan, to place six tribes on mount Gerizim to bless and six tribes on mount Ebal to curse. What follows are curses for idolatry and other sins of immorality and injustice. But where are the blessings? They seem to be conspicuously missing.[1] Rashi (quoting the Gemara in Sotah 32a) says that while the blessings are not written explicitly, each curse was preceded by the blessing, which was the inverse of the following curse. For example, the first blessing was, “Blessed be the man who does not make a graven or molten image,” followed by the curse, “Cursed be the man that makes a graven or molten image,” etc.

Nevertheless, Rabbis still saw a lingering question—Why blessings are not written explicitly? Maharal asks this very question, “If you will say, ‘Why are the curses written in the verse? On the contrary – the blessings should be written!’”[2] In another place, Maharal answers that now that the curses are said explicitly, we understand that the blessings were certainly said explicitly, since the verse says “the blessing and the curse,” placing the blessing first.[3]

I find a curious parallel with this approach in a quantum phenomenon related to semiconductors.

As far as electrical conductivity is concerned, there are three types of materials: conductors that conduct electric current, insulators that do not conduct electricity, and semiconductors that are in between—under certain circumstances, they can conduct small currents.

As some may remember from high school physics, the electric current is the orderly flow of electrons. Conductors are able to easily and efficiently conduct electricity, because they have a lot of free electrons. When an electromagnetic field is applied, these free electrons turn into a river that flows in one direction, carrying on the electric charge. In insulators, there are no free electrons—all electrons are locked in place in the atoms of the insulator—thus, they do not conduct electric current. Semiconductors are in the middle.[4] Although they don’t have free electrons, even a weak electromagnetic field can knock some electrons from their positions in the atoms creating a small current.

What is interesting about semiconductors is that when electrons are knocked out of their position in the (valence band of the) atom, they leave a hole. However, this hole is not just a simple hole but a whole lot more. A “hole” usually means just an absence of something. A hole left by an electron is not just an absence of the electron, it is an entity that acquires properties of a particle and behaves like one. A hole becomes a carrier of electric charge—specifically positive charge—the same in magnitude but opposite in polarity of the electron’s charge.[5]  The amazing thing about semiconductor holes is that they behave like particles themselves, able to travel, acquire energy, and collide with electrons. Moreover, they have properties of a particle—effective mass, charge, and energy, even though there is nothing there besides the void. Thanks to these properties, holes are called quasiparticles. And, of course, each such quasiparticle has a wave functions associated with it.


When an electron leaves a helium atom, it leaves an electron hole in its place. This causes the helium atom to become positively charged (Wikipedia–public domain).

Returning to our Torah portion, we have the instructions given by Moses that both blessings and curses be said. Yet only curses are explicitly listed in the Torah. How do we know that the blessings were said first? A curse may be seen as the opposite of a blessing, or a void in the blessing if you will. Indeed, all those who are not worshiping graven or molten images are blessed. However, those few who do worship graven or molten images are excluded from the blessing—they are cursed. A curse, therefore, may be seen in this parallel as a “hole” created by exclusion from the blessing. A curse is the flipside of a blessing. Just as with electrons and holes in semiconductors that have the opposite electrical charge, the blessing and the curse have the opposite “spiritual charge.” Just as with semiconductors, electrons and holes are equally effective in conducting electricity (albeit to opposite poles), a blessing and a curse are equally effective (albeit to opposite ends). Since the hole, by definition, is a void in a blessing (just as in semiconductors, a hole is a void made by a missing electron in the valence band of the atom), seeing the voids, we can be certain that there the blessings came first.

Notably, we find a similar concept in Sifrei, where it is stated, “from the positive, I understand the negative.”[6] It is interesting to find a structural parallel between classical biblical hermeneutics and quantum phenomena in solid-state physics.


[1] According to the Book of Joshua (Joshua 8:30-35) and the Talmud (Sotah 32a), the blessings were also explicitly pronounced. So the question is not, Why the blessing were not pronounced? They were! The question is rather, Why are blessings are not listed in the Torah?

[2] Rabbi Judah Loew ben Bezalel (“Maharal,” 1526 – 1609), Gur Aryeh supercommentary on Rashi on Deuteronomy 27:12.

[3] Maharal, Gur Aryeh on Deuteronomy 11:29.

[4] Technically speaking, all materials could be turned into a conductor, given strong enough electromagnetic field. The resistance to conducting electric current is called resistivity and materials are classified based on the value of their resistivity. Conductors have very low electrical resistivity of 10-8 to 10-4 Ωcm; insulators have very high resistivity of 108 to 1018 Ωcm; and semiconductors have a resistivity between conductors and insulators—10-4 to 108 Ωcm.

[5] To be precise, electrons orbit the nucleus forming bands or shells defined by their energy levels. When an electron moves from the valence band (the shell outside the closed shells) into the conduction band (the outer cloud, from which electrons most easily escape from the atom), a hole is created. In other words, holes are the electron voids in the valence band. Electrons have a negative charge and holes have a positive charge. Consequently, electrons flow from minus to plus, and holes flow from plus to minus.

[6] Sifrei on Deuteronomy 11:18. Originally published on on September 18, 2022.

About the Author
Dr. Alexander Poltorak is Chairman and CEO of General Patent Corporation. He is also an Adjunct Professor of Physics at The City College of New York. In the past, he served as Assistant Professor of Physics at Touro College, Assistant Professor of Biomathematics at Cornell University Medical College, and Adjunct Professor of Law at the Globe Institute for Technology. He holds a Ph.D. in theoretical physics.
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