Nowadays, it’s the norm to believe that all events in the universe, even which way a leaf falls in the middle of the forest, is subject to specific Divine Providence (hashgachah peratis — HP in Avodah parlance). However, the Lubavitcher Rebbe says this notion was a chiddush of the Baal Shem Tov’s, and R’ Chaim Friedlander in Sifsei Chaim credits the Vilna Gaon. Given this, it’s unsurprising that we can’t find a rishon who clearly backs the notion. Most teach that the events in all people’s lives are subject to HP. Some, such as the Rambam, say HP is something earned, and that there are people for whom parts of their lives are left to nature or chance. (In fact, in Moreh Nevuchim 3:17 the Rambam says that the position of Chazal is that all people are subject to individualized providence, and in ch. 18 he modifies this by nothing that a given homosapien can be more or less a “person” in this sense — based on how well he understands G-d and His Truth. (More on the various beliefs about HP in another post, someday.)

I actually think this drift in how we see individualized Providence shares a lot with the drift in Western Philosophy since Kant to Existentialism and beyond. There is now little focus on trying to figure out the world as it is, and we instead talk about the world as it is experienced. So, when the rishonim talk about hashgachah they’re having a metaphysical discussion about how G-d relates to the universe. A statement of emunah. Moderns have given up, since such a relationship is inherently unknowable. Instead, it becomes a statement of bitachon (trust [in the Almighty]); everything that happens in my life it the result of my partnership with the Eibershter. It’s not even that we’ve shifted position, we’ve changed topic.

Personally, I feel that the Rambam’s position is hard to defend mathematically, and even the majority opinion that HP includes all events in all people’s lives doesn’t exclude that many other events. This is because of the math that emerged from Chaos Theory.

To explain: The law of large numbers is the idea that if the probability of flipping a coin and getting heads is .5, then if you flip enough fair coins, you are likely to get numbers closer to 1/2 of them coming up heads. That only works for the small minority of aggregates where there are no feedback loops, so that each coin toss is independent. In systems that have such loops, Chaotic results — in which a small, even unmeasurable, change in starting conditions could make large differences in outcome. Thus, the proverbial “Butterfly Effect” — the tiny input of whether or not a butterfly flapped its wings in Africa could change whether or not there is a tornado in Missouri impacting thousands of lives.

All events interact and interplay. The vast majority of systems in the messy real world are chaotic, and nearly everything (if not actually everything) involving humans is. If there were anything whose final outcome wasn’t influenced by HQBH, how could there be anything impacting a person who merited hashgachah peratis whose final outcome was?

(Which is also how I can believe that people have free will in terms of what they do, but can have bitachon that everything that occurs to them is hashgachah. A person has the choice to interject one vector into the mix; weaving them into a total package is Hashem’s orchestration.)

So far my thoughts with respect to classical physics, in which the laws of physics produce deterministic results, even if we can’t get enough information to draw conclusions about the future. But from a Quantum Mechanical (QM) point of view, some things are only statistical. Do the molecules in a gas even have a specific location before a person takes measurements and observes them? Oddly enough, the answer is “no”. This is a different angle then the above. Chaos Theory is about unpredictability because you can’t fully know how things began. Quantum theory deals with true randomness. But it’s another interesting wrinkle anyway.

To explain (somewhat):

If you shine light through a narrow slit onto a wall or some film, it makes a broader line than the slit — the wave expands after leaving the slit. And if you shine it through two such slits that are close enough together, the waves interact leaving a pattern of light and dark stripes on the wall.

But — and here is where QM gets really weird — the same thing is true when you shine less light through the slits. Even down to a single particle. Photons shot at the slit one particle of light at a time will hit the wall in a pattern that over time will create those very same stripes. The light acts like a particle in how it moves, but the probability of where it moves acts like a wave. And while you might be able to dismiss this as a feature of energy, the same experiment can be done with electrons or other things we think of as matter!

And, just to make sure you’re totally bewildered, whether the photon or electron does this weirdness can be turned on or off by choosing whether or not you put a measuring device at one of the slits. If you know which slit the particle went through, the whole wave pattern thing disappears. Until a measurement is done, the particle somehow goes through both paths in a “superposition of states”, in all the places it could have been at once and interacting with the other versions of itself.

Erwin Schroedinger emphasized its weirdness with a famous thought experiment generally called Schroedinger’s Cat. Picture some mad scientist takes a tiny bit of radioactive substance and places it in front of a detector, which in turn has a hammer aimed at a vial of poison gas. This set-up is designed so that there is a 50% chance that enough radiation would be emitted in one hour to set off the detector and release the gas. This being a mad scientist, he takes the whole assembly and a cat and puts them into a sealed box.

It is now an hour later. Whether the cat is alive or dead depends on a quantum event, the amount of radiation. So, like the light passing through two slits, the radiation both and didn’t reach that trigger level until measured. And thus, the vial is both smashed and intact and the cat both alive and dead.

Or is it? There are numerous attempts to explain when a system shifts from the statistical realm of QM and the more deterministic world we live in and how. Here’s a thought that crossed my mind:

Perhaps the line is between nature and HP. Nature is quantum and statistical,but human events are mediated by HP which is deterministic. Which is why observation causes collapse of the wave function — and thus the range of probabilities, it introduces a human being and thus (according to Chazal and most rishonim) individual, non-statistical, Providence. Schroeder’s poor cat wouldn’t merit HP, and therefore his state needn’t be determined until a person opens the box and Providence selects a single outcome.