Its easier to understand if you remove color and shades, and just consider a similar black and white image. With this, the screen is just a bunch of dots in a grid. If you have something going diagonally across them, such as a triangle, you have to decide which dots to turn on and which to turn off. This means you end up with a choppy looking pattern:

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If you can also show gray colors, you can render that line at a higher resolution and average the values of each small block, resulting in gray near the line and a much smoother image. The more averaging you do, the better the end result will be, and this is why 8x looks better than 4x and so forth.

This is known as super sample antialiasing (SSAA). There are other methods to achieve similar results with various benefits and drawbacks:

Temporal antialiasing (TAA) which averages between multiple frames with slightly different camera angles. This one was made well known by Unreal Engine 4.

Another is called Fast Approximate Antialiasing (FXAA), which uses some image recognition-style techniques (a severe simplification) to find the jagged lines and blur them.

It’s worth noting that some hybrids will use the engine to break if the battery is full or you want more braking power than the battery can absorb, before engaging the actual breaks. This works as you get some breaking power from engaging the engine without giving it any fuel. - using mechanical force to compress the air in the cylinders. Obviously this does not work in a full electric that lacks an engine.

The key difference is how the two processors function. A GPU is designed to do the same calculation lots of times at once, though with differing values, while a CPU is designed to do lots of different calculations quickly.

A simple way to think about this logic is that a single object on the screen in a game will be on multiple pixels of the screen at once, and each of those pixels will generally need to do the exact same set of calculations with just different input values (think like a*b+c with differing values for a, b, and c). The actual rendering process does the same idea at multiple levels, where you are typically going to position and rotate the points (vertices) of each object in the same way. It also turns out that this same style of calculation is useful for a lot of other stuff: physics calculations*, large math problems*, and artificial intelligence*, to name a few.

However for general program logic you aren't repeating the same calculations over and over with just different data, but instead need to vary the calculations constantly based on what the user is trying to do. This logic often takes the form of "if X do Y else do Z".

Now, modern CPUs will have some hardware designed to function like a GPU, even if you discount any embedded GPU. Using this is very good if you just need to do a small amount of that bulk processing, such that the cost of asking the GPU to do it and receiving the result will be too expensive, however its no where near as fast as the full capabilities of a GPU.

Beyond those design differences which are shared between dedicated and embedded GPUs, a dedicated GPU has the benefit of having its own memory (RAM) and memory bus (the link between the processor and memory). This means both the CPU and GPU can access memory without stepping on each other and slowing each other down. Many uses of a GPU can see massive benefits from this, especially games using what is known as "deferred rendering" which requires a ton of memory.

As a note, there is no reason you couldn't just do everything with one side, and, in fact, older games (eg Doom) did everything on the CPU. In modern computers, both the CPU and GPU are what is known as Turing complete, which means they can theoretically perform every possible calculation. Its just that each is optimized to perform certain types of calculations, at the expense of other kinds.

* As a note, artificial intelligence heavily relies on linear algebra, as does computer rendering. Many other math problems can be described as such, converting the problem into a set of matrix operations, which is specifically the specialization of GPUs.

It does need more elaboration, but using loans with stock as collateral is a way to avoid, or at least minimize, taxes very long term. If the collateral raises in value at least as fast as the interest rate, you can take out more loans to service the initial debt. If the collateral raises faster than the interest rate, this can be extended to add on more debt load in total. Using this is risky, in the same way that margin stock is dangerous: losses are magnified more than gains are, and a stock drop can wipe out many times the amount of wealth from the owner.

The loans will also let them do better timing with sells, delaying payments such that they can liquidate a stock that lost value at the same time as stock that gained value, reducing the taxable liability when they do actually sell. This is presuming they hold any stock that actually lost value.

Most of the rich will have outside sources of income that they can use to service any debts they have. This will include items such as base pay and stock grants from the companies they own.

If they manage to delay the repayment until death, proper estate planning allows other tricks with minimizing tax liability.

A stock buy back is when a company buys some of its own stock. As doing so reduces the amount of shares available, it results in the stock price going up - the whole supply and demand idea.

This is one of two ways a company can distribute cash to its investors, with the other one being to pay a dividend. With this, the company just directly pays the owner of each share of stock some amount of money.

The rich will generally prefer a buy back due to how it affects taxes, at least in the US. Notably, the rich can take loans using the stock as collateral allowing them to defer paying taxes, often permanently as no tax is owed until the stock is actually sold. Dividends get taxed immediately, using the same rate as if you sold stock.

A common complaint is that the same companies performing the buy backs are saying they cannot afford to pay their workers more, despite spending many thousands per year per employee on the buy backs. This is also at the same time the company is trying to get tax breaks or stimulus money so they can stay in business.

"In network" means the doctor or location has a contract with insurance regarding payment rates and other details of coverage. Typically, this contract will also include provisions such as no "balance billing", where the doctor can charge you more than your insurance thinks is acceptable, requiring you to foot the bill.

A doctor or location "accepting" insurance means they are willing to bill the insurance directly. A location not accepting your insurance does not mean your insurance won't cover the work, but merely that you'll need to pay the doctor directly and file a claim with the insurance to be reimbursed.

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Presuming the US: There are also a few specific laws in place, such as insurance having to treat all emergency care as "in network" and balance billing being disallowed for such care. You also cannot be billed as "out of network" if you go to an "in network" facility and are treated, fully or partially, by an out of network provider, unless you are reasonably warned ahead of time that the provider is out of network.

If you managed a perfect inverse of the wave, the two waves will cancel enough other out and there will be no sound at all. This means that, with perfect noise cancelation, you could be sitting right on top of a jet engine and would hear nothing and have no damage occur.

Practically, getting a perfect inverse is impossible. You'd need a speaker perfectly aligned between the source of the sound and your ears, and the source will actually be a bunch of different points inside the engine, meaning you need roughly an infinite number of infinitely small speakers and microphones.

I did find a video that shows how the phasing works. Its worth noting that the antiphase (opposite) sound will sound the same as the original if heard on its own.

A fireplace is heavily a décor element, and thus intended to look pretty, even at the expense of efficiency. Some gas and electric ones will even have speakers built-in to provide the sound of burning wood. Typically, you can adjust the mixture in a gas fireplace to be more efficient, though doing so will sacrifice much of the décor element.

You can also get gas space heaters, which are intended to produce heat without looking pretty, and will generally be adjusted for a high efficiency burn.

>Why can’t port numbers below 49152 act like “Airbnb for applications?” Conversely, why can’t port 49153 and above have, per your analogy, “long-term tenants.” Or can they?

Convention - the same as why a hotel room generally won't have a long-term occupant and an apartment won't have a short-term renter. With that, its also likely somebody else may be using them for their intended purpose, thus causing random failures if an application tries to use them incorrectly.

Firewalls will also frequently block or allow specific ports by number, though they will normally only block incoming connections, not outgoing. This may cause a program using an unexpected port to get incorrectly blocked, requiring users to manually open those ports.

>Furthermore, what event on the server would be equivalent to “evicting” a program from its “apartment?”

Generally, the operating system will have a method of force disconnecting a socket, though such APIs are normally tightly restricted in usage. In most cases, they are restricted to usage by debugging tools.

The order of operations is merely a common standard agreed upon by mathematicians. There is nothing innate with mathematics that requires that standard, though having a standard of some form is a requirement for the common infix notation.

There are other options, such as pre-fix and post-fix notation, also known as Polish and reverse-Polish notation. With pre-fix notation, you'd write `1+2*3` as `+ 1 * 2 3` or `+ * 2 3 1` and `(1+2)*3` as `* 3 + 1 2` or `* + 1 2 3`. With these, you don't even need to define left-to-right or right-to-left as its implied by the definition - though you have to agree whether its pre-fix or post-fix.