Ask HN: What scientific phenomenon do you wish someone would explain better?

Proof? Just look at all the replies you got: each one is dozens of pages of complex (imaginary) math, control theory, and statistics.

The hardest part of QC is exactly what you described: how to extract the answer. There is no algorithm, per se. You build the system to solve the problem.

This is why QC is not a general purpose strategy: a quantum computer won't run Ubuntu, but it will be one superfast prime factoring coprocessor, for example (or pathfinder, or root solver). You literally have to build an entire machine to solve just one problem, like factoring.

Look at Shor's algorithm: it has a classical algorithm and then a QC "coprocessor" part (think of that like an FPU looking up a transcendental from a ROM: it appears the FPU is computing sin(), but it is not, it is doing a lookup... just an analogy). The entire QC side is custom built just to do this one task:

https://en.wikipedia.org/wiki/Shor%27s_algorithm

In this example he factors 15 into 5x3, and the QC part requires FFTs and Tensor math. Oy!

Like I said, it will take decades for this to become easier to explain.

For fun, look at the gates we're dealing with, like "square root of not": https://en.wikipedia.org/wiki/Quantum_logic_gate

I'm going to throw out an analogy that gets at what's observed and why it's surprising, but doesn't relate to the physics of spin, momentum, position or anything that's actually under observation in these experiments.

It's as if we have a pair of dice, and I throw my die and you throw your die many times. In a classical world, if I throw a three, it has no influence on what you throw; you're equally likely to throw 1-6. But in the quantum world it's as if when I throw a one, your die still has the expected uniform distribution, but when I happen to throw a three, you're a little bit more likely to throw a three. Your die is fair if I happen to roll a one, but it's weighted if I happen to throw a three.

Back in the real world, this is the strange behavior that is observed in experiment. Schroedinger's equation predicts the probabilities perfectly. But Bell shows that it's far from intuitive.

The other thing you can do is think about what it means for particular types of categories. For a posetal category, it says that an element of a poset is uniquely determined by the set of all elements that come before it in the ordering. For a group, it says that every element is uniquely determined by its action on the group. (This is basically Cayley’s theorem.) See this MSE post for more intuition: https://math.stackexchange.com/questions/37165/can-someone-e...

Now that can either mean that someone bought a share that someone else was selling or that someone was selling a share to someone who was offering to buy.

The shares are listed as a series of buy and sell orders in what's called an order book.

If the price a share was sold at was 100$ and you think it will go a bit lower, you could place a buy order at 90$. Should enough people sell shares to reach your price and order, your order will be filled and you will own the share at 90$.

If someone wants a million shares at 91$, you may not get your single share at 90$.

To go back to your example, if you were to place a buy order at 100$ for a 4$ priced share, how much the price moves depends on how many sell orders are in place from 4$ to 100$ and how much you are buying.

If it's only one for share, your order will probably get filled at something like 4.01$ if the spread is low (the spread being the difference between the highest buy order and the lowest sell order).

If you're buying 1000 shares and it's a low volume stock with a "thin" order book, maybe it could go up a few dollars instead but for it to go up to 100$ you have to buy every single share between 4$ and 100$.