Is the "business cycle" an actual economic principle?

Economists tend to view the business cycle as one of the main stylized facts which any theory must account for, rather than a principle in itself.

In terms of statistical evidence, market price movements are definitely not a vanilla random walk - random walks don't have long tails unless you add something else into the theory. The usual baseline model is a random walk in which the variance is also governed by a random walk; a quant trading shop will augment this with occasional jumps and a few small terms to account for higher moments of the distribution. And even that is just the baseline to reasonably model a single asset - modelling multiple assets is far more complicated, since they usually become more correlated during a crash (another phenomenon which wouldn't happen in a vanilla random walk). If you want to learn more about this stuff, look for a mathematical finance class.

Getting back to the economics side, every major class of macroeconomic theories has an answer to the question "What the heck is up with these business cycles? Why do markets sometimes crash way harder than they should with random walks?" Real business cycle (RBC) theory posits that they're the result of shocks to the economy, e.g. hurricanes or wars. Market monetarism attributes crashes to tight money, as measured by NGDP. Keynesianism focuses on variation in aggregate demand. Monetarism focuses on variation in the money supply and/or money velocity. Etc, etc. If you want to see the fancy stuff, pick up a book on "recursive macroeconomic theory".

But to the degree that the business cycle is a separate understandable phenomenon, can't investors use that understanding to place bets which make them money while dampening the effect?

This is part of what the various theories try to explain. Some require irrationality in order for business cycles to exist - usually in the form of "sticky wages", meaning that people don't like wage cuts even if the alternative is getting fired and accepting lower pay elsewhere. In this case, traders can't necessarily counterbalance the whole effect, no matter how clever they are - so markets will crash as soon as the traders know that a sticky wage problem is on the horizon. On the other hand, RBC explains (some) business cycles without any irrationality at all: if a big hurricane significantly lowers GDP this year, then society as a whole will eat into their savings to cover the costs - which means eating into the capital stock, and lowering GDP over the next few years. Traders can't price that in until they know about the damage, at which point there's a market crash.

As johnswentworth notes, recessions are way worse than what you'd get from a random walk. There is something to be explained.

To his list of theories, I would add Austrian business cycle theory (ABCT), which introduces the notion of the temporal structure of capital and explains e.g. why fluctuations in employment are larger in industries further up the capital pipeline/further away from end consumers (mining, refining) than in industries closer to the consumers (retail, hospitality).

According to ABCT, when the central bank lowers interest rates below the natural rate which clears supply (household savings) against demand (businesses seeking loans for investments), this causes overinvestment and undersaving. More specifically, the lower interest rate guides businesses to invest in capital further up the capital pipeline, with longer time to "maturation" (to being useful to the end consumer), e.g. oil tankers. The gap between savings and investment (which no longer matches) is covered by new money being put in circulation by banks.

As the new money keeps pouring in, inflation picks up, the central bank reacts by lifting the interest rates again, this makes the long-term investment projects (which were profitable) unprofitable again, this makes all the capital that was already put into them mis-allocated and much lower in value than before (if you have an unprofitable, half-built oil tanker, it's not easy to convert it to some more useful form of capital, like cellphones).

Thus, real wealth has actually been lost throughout the economy (as opposed to Keynesian theory, where no value is actually lost, everyone is just caught in crowd psychosis, like a murmuration of sparrows following each other down the market).

The central bank reacts by monetary easing, dropping the interest rate to zero, thus preventing the healthy clearance of the built-up misallocation, and a new bubble can build on top of the previous one.

(In reality, I think, each recession will have slightly different causes and many theories will be partly right about particular recessions. There is always some element of the Keynesian "I will sell because everybody else is selling" etc.)

I think you may be confusing the business cycle with market cycles.

Also

anticipate a random walk with an average of 10%/year growth,

I suggest anyone who believes this have a closer look at world wide stock market returns over time. If you cherry pick the most successful of the ~200 markets (ie the US market) and ignore inflation you can maybe get 10% PA returns.

But unless you have evidence that you can pick the most successful market prospectively, then 3-4% after inflation and costs is more like it.

Bear in mind at the start of C20 the US had only recently exited a ruinous civil war, rule of law was limited, there was rampant corruption, etc etc. Which country that (might) looks like this would you pick as the top performer of the next 100 years?

There are a LOT of examples of things that mostly fit this shape, and it's understandable if you add to the random walk theory the fact that the feedback loop takes time, and humans tend to overreact. Many systems with delayed feedback and naive reactions have cyclic rather than static equilibria.

That said, from what I can tell, it's more about explaining past events, and fitting into a theory, than about predicting future events - I haven't seen many great successes in using the theory to make correct decisions.

There are certainly economic theories that account for business cycles. Keynes's General Theory of Employment, Interest, and Money is the go-to book here.

If you expect the market to fall, you would want a short position. If the market continues to rise, that bet will lose lots of money. A bet against the market has to be very well timed, and that's very hard to do. As the saying goes, the market can stay irrational longer than any investor can stay solvent.

But to the degree that the business cycle is a separate understandable phenomenon, can't investors use that understanding to place bets which make them money while dampening the effect?

The theory can tell you that we're headed for a downturn, but when exactly that will happen is unpredictable, because the system is chaotic and the bubble burst can be triggered by any Schelling point that looks like "uh-oh, time to sell". E.g. Lehmann Brothers. E.g. 9/11.

If you don't know whether the recession is coming in a year or three, that's too much ambiguity to make any money off of it.

Lots of the processes in business are nonlinear. And some decisions are "sticky" like investments hiring and sunk costs of all sorts.

Knowing the processes are nonlinear mustn't automatically allow for prediction. It might merely change the distribution, and it will be difficult to predict where you are there.

An illustrative idea is assuming that you can show that the market moves at times in jumps rather than in smooth continuous fashion.

This might not help you actually predict market moves when you do not know where the point happens where it goes into a jump from a continuous walk.

In fact, many are trying to predict markets using all kinds of well proven phenomena. In the vast majority of cases, those predictions don't demonstratively work.

As mentioned the ABCT has some good points in explaining why things might happen. But I also think the coordination problem over time in terms of economic activity will inherently get things wrong, so downturns will occur.

There have also been some evidence that political event, like various elections, can influence.

I don't think any lend themselves to true function precision (echoing the time problem moses mentions).

I would ask if you're inquiring based on financial market fluctuations are if you're asking about real business cycles (recession/depression and expansion/contraction) events. I think characterizing real economic cycles as driven by a random process would be problematic -- even if one might suggest that the sale of any given can of soup might be modeled that way.