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> In reality, eventually, 'the hat' tiling does repeat, but not anywhere near enough for it to be noticeable.

To clarrifiy (for OP): that's only because your photo only shows so much of the thing, and there are is only a finite (but very huge) number of possibilities your photo could show. If your photo zooms out more when needed, every part of the wall would be truly unique.

Just because they're technically from the same plant does not mean they're identical. Just as eating an apple isn't the same thing as eating an apple leaf or the bark of an apple tree, grass and grains have different nutritional values, and affect the quality and flavour of the beef. It's not just marketing.

That's interesting because I have two wireless mouse. One of them requires two AA batteries and the other one requires one AA battery.

So if one mouse can work on 1.5 volt why can't the other one, given its basically the same product.

Although frequently a remix is sold as a remaster, if the intention of the remix is to replicate the original work.

It is a measure of the economic activity (production of goods and services) within a country. It isn't necessarily very precise if a country has a large black market or barter trade. It can be used to gauge the size of an economy and is somewhat indicative of how productive and the potential income levels of the citizens.

Method of calculation is complex - broadly it can be calculated by adding the income of all the participants or alternatively by measuring the expenditure of all the participants - netting out exports and imports.

Is it important - yes as a broad macroeconomic indicator. It is a simple measuring stick but any deep analysis of an economy requires much better economic data (GDP is too broad and simple). But it isn't super important otherwise and certainly not much importance for everyday people doing everyday things.

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The only people who correctly use batteries are Philadelphia Eagles fans who used a barrage of "cells" in their battery.

Voltage is derived from chemistry. There is an electric pressure associated with different reactions, and a battery is a device for creating a lot of this pressure in parallel. The basic reactions tend to produce something in the area of 1.5 volts. This is normal for alkaline batteries, the sort you are used to.

The devices we power with those piles usually need more power than this. My knowledge of this is very dated at present, but it comes down to the kind of transistors in the chips. You get about 3 volts out of 2 batteries... Roughly 5 volts out of 3...

In a periodic tiling you can take a copy of the original tiling and slide it some combination of left/right and up/down such that it will look exactly like the original tiling. The most basic example is to imagine an infinite sheet of grid paper. If you slide it around you wouldn’t be able to tell whether you are looking at the original or the copy. This is called translational symmetry.

In an Aperiodic tiling you can’t do this. Such filings do not have translational symmetry. You might be able to find sub patterns that look like other sub patterns but if you try to map them to each other you’d find that the tiles around them eventually don’t line up. There are many such tilings.

What’s unique about “the hat” is that it’s the first time an aperiodic tiling has been made using a single shape. The first aperiodic tiling used thousands of different shapes. And before now we’d been able to find multiple aperiodic tilings using as few as two shapes. But this is the first one which uses just a single shape. And to make it even more interesting it was found not by a professional mathematician but a hobbyist (though he did work with two universities to prove the shape he used was, in fact, capable of aperiodic tiling).

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My maths teacher used a rather helpful little memorable explanation for my class (honestly that guy was a fucking legend, wish I had the time to pop into my old school for a quick visit with some of those teachers, some really are damn fine at their jobs)

See the positives and negatives as cowboys. It’s a silly thing but it’s the silly stuff that sticks in your head far easier and longer. For below, take a to mean a cowboy and b to mean a town.

A good cowboy visiting town is good: a + + b = positive (or just a + b)

A good cowboy leaving town is bad: a + - b= negative (or just a - b)

A bad cowboy visiting town is also bad: -a + b = negative (shown as a - + b)

But, a bad cowboy leaving town is good: -a - b = positive (shown as a - - b)

Now I’m not a teacher (don’t envy their job at all) and it has been… let’s just say quite a few years since I was at school and leave it at that… if I’ve not explained it clearly then my apologies, but that should hopefully be useful. It’s also good to see positives and negatives as literal mirrors of each other. Zero is the mirror line, but they are the exact same and work the same way… so remove the positive and negative prefixes, you’ve just got numbers… and adding and subtracting then becomes trivial. The + and - complicate the look of it… but ultimately the numbers behave the same regardless if they’re positive or negative so they only way to make add and subtract behave in the exact opposite way to what they typically do… is to use numbers from the opposite side of that mirror line. Otherwise add will always go up, and subtract will always go down…

Studio recordings are usually multi-tracks that are combined into a single stereo mix. The producers and audio technicians did their best to create a master that would give the best result, which prior to about 1980 was vinyl records. Remastering means you go back to the original recordings and create a new master that is created to sound great on modern media and equipment. They might also clean up noise, and make other corrections like dynamic range and equalization.

This is a great comment by another Reddit user:

Remastering explained

It is a true art form and people like Kevin Gray and Bernie Grundman are living legends that need to ensure this craft is shared.

"Mastering" in its original sense is producing a master stamp for pressing vinyl records, the term has extended to recording raw tracks, tuning, mixing and compiling them into finalized tracks to be put on a master disc or tape ready for replication.

Remastering means the raw tracks are mastered again using newest technologies, like hi-res encoding or surround sound/spatial audio .etc.

Ah, so many things vary by state. I guess that's generally a good thing! Thanks for the explanation.

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It is a legal requirement.

If you are a scammer there is another reason, If you us it they do know what mail address it it is from so they knew it is an account that is used and someone did read the mail and it did not just end up in a spam filter.

So they can validate that it is an account that is in use and it the address could be used for som phishing attack or just spam.

Indictment is more the formal process of filing charges. When the prosecutors believe they have sufficient evidence to support them in court. They can enlist a grand jury to decide if there is enough evidence to warrant it before hand, but all the grand jury looks for is if they believe there is enough evidence to go to trial, usually used in what expected to be high profile cases not always used.

Arraignment is the formal procedure for the defendant to enter his plea with the judge.

I saw a video on that. They had arrows pointing right, up and front, and connected them end to end in order to make a new arrow that pointed to the destination. Are quaternions the same as making calculations using x, y and z coordinates?

They also used trigonometry to transform back and forth between coordinates and angles.

They are often used to describe rotations in the 3D world. So when you have a camera drone (multicopter) there is a good change that they are used to process the sensor inputs (gyroscope/accelerometer) and calculate the corrections needed for a stable flight.

Can I press more: I guess we use charge and indictment interchangeably, then, to essentially mean the paper versus the presentation of them? Am I in the ballpark?

They probably use some widely used mailing software to manage sending e-mails to their mailing list/subscribers. Most of these software packages have a setting where you can give the recipient an option to unsubscribe.

Lots of companies that offer e-mail to the standard person (gmail, yahoo) might be more likely to put incoming e-mails without an unsubscribe option on their spam list. If Google puts your company e-mails in the spam box by default, it's much worse (for the advertiser) than giving people the option to unsubscribe.