Except that while it's very hard to get it exactly right, it's really easy to get close.

Getting to 360ish days is relatively trivial - as best as we can tell, a 12-month, 360 (+- 10) day year was developed independently in at least India, China, Mesopotamia, and Mesoamerica - and that's a minimum: there's reason to believe that northern Europe, Mediterranean Europe and/or North Africa, Southeast Asia/Polynesia, South America, North America, and southern Africa also independently developed calendars that were not far off from 360 days. From a 360-day calendar, all you have to do is throw in a few non-year Holy Days before New Year (which, for many calendars, happens at one of the four main days - the solstices and equinoxes) until it's the right time, and move on. Alternatively, if your calendar is lunisolar, you add a month if New Year is too early.

Yes, getting things exact is really hard - even the Julian Calendar is off by a little bit, and technically the Gregorian Calendar is off by a little bit (it's off by .0003 days per year - or about one day in 3000 years). But I think you're selling human intelligence short saying it's not trivial to get a working calendar - as long as you understand the calendar isn't perfect, being a few days off isn't a problem. And both ancient calendars still in use (Chinese, Hebrew) understood that, and had rules to make sure that the calendar was not off by more than one month - and it's safe to assume they weren't the only ones like that.

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> the lunar schedule of 13 months of 28 days which is 364 days

Except that synodic months actually last 30 days, not 28, and there are nearer 12 of them per year than 13.

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Excellent point about the importance of measuring time to determine longitude. Probably the main driver for more accurate time keeping during the Era of Exploration.

>However, the probability of rolling 6 6s in a row varies based on the prior events.

I mean, sort of, but that's not what you're actually calculating.

>After 5 6s are rolled, the final roll is still a 1/6 event, but after, say, 3 6s, the probability is (1/6)3.

Yes, but no. That's still just the odds of rolling 3 in a row. That calculation does not care about or consider the previous 3 rolls at all. It's indistinguishable from just checking the probability of 3 rolls, because that's all it's doing.

You're not wrong in removing the previous 3 rolls from the calculation, but that's exactly what they mean by "only looking forward." You literally need to ignore the earlier rolls to calculate the future outcome. You don't look back.

if you're circumnavigating the globe, eventually you will care, at least a little bit.

A small bit of trivia that isn't worth a top-level comment: according to wikipedia, when Magellan's sailors returned from the first circumnavigation of the globe, they were off by a day and surprised by this.

(Also according to wikipedia, the loss/gain of a day by circumnavigators had been predicted a few hundred years earlier by Abulfeda, a geographer/historian/prince)

As I said, the probability of any single roll being a 6 is 1/6, because each roll is a fully independent event.

However, the probability of rolling 6 6s in a row varies based on the prior events. After 5 6s are rolled, the final roll is still a 1/6 event, but after, say, 3 6s, the probability is (1/6)^3. P(6 6s) ≠ P(6 6s given 5 6s). The given part is the piece that looks backwards.

Yeah very surprised at all the top comments explaining how the ancients had it all figured out! Even at the end of the Roman Republic they had the seasons and the calendars all out of synch until the Julian Calender figured out how to have it work out with leap years and such. And of course even that wasn’t quite right… getting a working calendar was absolutely not a trivial task (and figuring out why it worked wasn’t trivial either!)

Astronomy is very ancient. Certainly older than civilization itself. They didn’t know anything about the Earth orbiting the sun, but they did notice a cycle of the sun tracing a lower to higher path in the sky over the course of a year. It is trivial to set up a line of stones to mark when the sun rises at its lowest and highest points and that gives a way to detect the winter and summer solstices.

Humans, like other animals, are not adapted to a world with ready access to abundant macro-nutrients. How your body reacts to a 32 ounce big-gulp and a large fries is not something that evolution has had an opportunity to apply selective pressure to.

Straight up overeating whilst keto doesn’t make me lethargic as shit like overeating pasta would

Crops that require high concentrations of nitrogen, are usually the most treated with fertilizer.

For example, sugar cane fields in Florida are fertilized several times during the growing season. The fields are in south central Florida in or near the basin that drains into Lake Okeechobee. This causes blooms of blue-green algae. This is a highly toxic mess. It makes the lake unusable for boaters and outdoors people. This also aversely affects the St Lucie River which drains out of the lake to the east and the Caloosahatchee River to the west....These waterways and tributaries often become odoriferous nightmares. Anyone with allergies, asthma or other respiratory issues have to stay away from the water until such time as the blooms disappear.

Video games are very "noisy" in terms of image output, tons and tons of approximations and high precision but limited "accurate" solutions are used to render out the result and as such tons of factors to consider, too many to really give you an "exact" one thing but a very very simple one is a natural anti-aliasing as a result of downsampling.

Much of this has to do with the fact that we are rendering out to "pixels" and geometry doesn't always fit perfectly and as such filtering is needed to clean up the artifacts.

If your game is running at say Full-HD (1920x1080) and you have absolutely nothing else being done to the image (no anti-aliasing, no mip-mapping, no anisotropic-filtering, etc.) you'll have a bit of a pixel soup of a scene (some textures will be blurry, others will be pixelated, and you'll have "jaggies" across most non-transparent objects in the game).

You can easily solve a lot of these problems by simply using a buffer that is 4x larger than your target output resolution, drawing your game scene to this and then sampling it down to the target resolution.

This is usually what we call "super-sampling" and there are several ways to do this when you downsample down you merge or exclude information downwards and much of the sub-pixel information from the source information is transformed.

If you have a camera at your home you can effectively do this yourself in the real-world; take a photo, open said photo in say photoshop, resize photo down 33% and you'll notice image quality on the resized photo is usually improved (this is also for a variety of reasons, mostly ISO noise though is reduced heavily).

It's just not widely utilized because it's computationally expensive and it isn't always the case that all of a games shaders scale with the increased resolution (or in rarer cases, certain targets can't be created because some shaders could already be overdrawing).

If you want just overall a... "glimpse" into how complicated it is to render a game scene I highly recommend this post by Adrian Courrèges which will give you a deep but IMHO high level explanation from a semi-modern game: https://www.adriancourreges.com/blog/2015/11/02/gta-v-graphics-study/

Asking for a friend

Digestion takes energy. While you're digesting, you're tired. Once you've digested, you have energy.

Finally a good answer!

Cool AF! Didn’t know that they were able to track and measure they solar altitude! How did they do this with their rudimentary tools?

I want to add just as a point of (possible) interest that although you may have only heard this terminology in reference to car engines, there are also major implications (or at least used to be) in aviation.

As a plane gains altitude, the air becomes thinner. In a plane driven by a piston engine or engines turning propellers, this means you have to adjust the mixture of fuel and air in the cylinders to compensate, but it also means that even if you adjust the mixture optimally engine power inevitably drops off the higher you go. However, this can be to some extent alleviated by using forced induction.

For jet aircraft (including turboprops, which use a turbine engine to turn a propeller rather than a piston engine) this isn't a concern, and the piston-engined aircraft that still exist usually no longer operate at a high enough altitude to make forced induction necessary.

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Just to add some detail.

A supercharger is normally driven by a belt/chain/gear attached to the crankshaft (central spinning part) of the engine.

A turbocharger is driven by the outgoing exhaust gases from the engine. For this reason, there can be a little delay between pushing on the accelerator and actually getting the boost in power.

Both of these may be used in a frugal sense to get more *efficiency* from the engine, or in a performance sense to get more *power* output (or a little of both).

Your body releases a chemical called cholecystokinin that aids with digestion and gives you the feeling of being satiated. It's also found in the central nervous system and some believe that it may give you that sleepy feeling after eating.

It makes sense that your body would want to slow down to digest too because blood flow is being directed from your muscles and to your digestive tract.

Also after eating you have just started digesting the food but it hasn't been broken down enough to be utilized immediately. Simple sugars are broken down first, then the complex carbohydrates followed by proteins then fats.

If you ask “what is the chance I roll a 6 on this one die roll?” That never changes at 16.7%.

But if you were to ask ‘what if I roll twice and get at least one 6?” That’s 30%

Chance on 3 rolls? 42%

6 rolls? 67%

But if you rolled 5 times and didn’t get a 6 yet, the chance your last roll is a 6 remains 16.7%.

Digestion requires energy. More eating = more energy. Your stomach focuses on digestion and the rest of you feels tired.