Let's take a number like 3 divided by 7.
That would be 0.428571428571428571 with 428571 repeating infinitely.
That would be analogous to periodic tiling.
You put shapes in a certain order and you can tile infinity by just repeating those shapes in that order.
It might not be 1 shape, the arrangement might be quite complicated, but it still repeats.

Now think of a number like Pi.
The first few digits of pi are:
3.141592653589793238462643383279502884197... but it continues on forever.
You will never find a series of digits that's finite in length that makes up Pi by just repeating it infinitely.
This is like aperiodic tiling, you will never find a finite group of shapes that makes up the whole thing by repeating it infinitely.
The arrangement of any part is always at least slightly off.

Now math guys have known about aperiodic tiling for a while, but they found it worked with only a few different shapes put together.
They did more math and didn't find anything that said they couldn't do it with just 1 shape.
That's why the hat is exciting to the math people. Knowing something can exist and actually finding the thing are two very different things in math. So they were really excited when they found that it was a relatively simple shape.
It could have been some monstrous shape that takes up 200 GB, or something that would only be found in the year 2723 or something.
They're just glad we have it in the here and now and on a regular screen.

To complete a stride, Achilles foot would have to move to half way through his stride, and to do that it would need to move half way to that , and so on.
That just shifts the thing down.

The universe having some kind of finite resolution like the planck length would also resolve this.
But it's not necessary, for the reasons stated above.

That's not what an aperiodic tiling means.
The analogy is:
3.141414141414141414141414 with 14 repeating infinitely would kinda be like periodic.

The first few digits of pi are:
3.141592653589793238462643383279502884197... but it continues on forever.
That's closer to aperiodic.

What you've done is point at the two instances of 97 and said, "see it repeats".

Just like you will never find a finite series of digits that if repeated will give you pi exactly. You will never find a group that if repeated infinitely, would tile infinitely.

Or believe in God, take advantage of the structure of organized religion, just not the Catholic Church.
People have been sick of the Catholic Church for centuries and have been doing something about it since 1517.
I'm an atheist, and even being an organized theist has better options.

Full article from u/sneakpeak_sg: > # Not forbidden for anaesthetists to leave surgery to take phone call but surgeons prefer those who don’t

> SINGAPORE – Anaesthesiologists are trained to properly monitor a patient under anaesthesia, said two bodies representing the speciality, responding to queries about how some leave the operating theatre during an operation, for instance to take a phone call, which they are not expressly forbidden to do.

> Noting that Singapore has had very few mishaps related to anaesthesia, the College of Anaesthesiologists and the Singapore Society of Anaesthesiologists said jointly: “Regardless of the level of risk of the surgery, the level of monitoring takes into account the clinical risk and medical complexity for the patient which is within the purview of the professional expertise of the attending anaesthesiologist.”

> Surgeons, however, while acknowledging that anaesthesiologists sometimes do leave the theatre, said they would prefer to work with someone who is present throughout a procedure.

> In January, an anaesthetist was suspended for 2½ years by the Singapore Medical Council (SMC) for repeatedly walking out of an operation at Gleneagles Hospital in 2016 to answer phone calls.

> The 64-year-old cancer patient, who had many other health problems, suffered an embolism on the table and died the following day.

> The SMC said the patient’s already low chances of survival were further reduced by the anaesthetist’s delay in taking action.

> A disciplinary tribunal agreed with the SMC that such behaviour “would shock the public and harm public confidence in the medical profession”.

> Dr Islam Md Towfique had previously been suspended for six months by Parkway Pantai, which owns Gleneagles and reported the incident to the SMC.

> In his defence, Dr Islam said his action “accorded with a common practice among anaesthetists in the private sector” and that “there are no official guidelines or notices regarding the making of phone calls while anaesthetists are taking care of their patients”.

> Though the college and society of anaesthesiologists did not say whether doctors are permitted to leave in the middle of surgery, they noted: “For medical procedures requiring anaesthesia, the attending anaesthesiologist ensures a level of monitoring that is commensurate with the clinical risk and medical complexity for the particular patient. Low-risk procedures have a reduced propensity for intraoperative and postoperative adverse events.”

> Low-risk surgery includes cataract surgery, lump excisions, gastroscopy, colonoscopy, reduction of dislocations, and circumcisions.

> The National University of Singapore Yong Loo Lin School of Medicine did not respond to queries about the issue.

> Several senior surgeons told The Sunday Times that if it were up to them, they would always choose an anaesthesiologist who is present throughout the procedure, whether high or low risk.

> However, it is not always possible to choose, especially after regular hours, when fewer anaesthesiologists are available.

> The surgeons said a number do leave the surgery to answer phone calls from other patients, particularly if they do not have an answering service. Some also spend time reading or playing games on their phones, especially during long procedures, when they are not actively needed for stretches of time.

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Do note. The guy seems to be talking about simple odds using real plane crashes for some reason.
Real world statistics do not work that way.

In the real world plane crashes are not independent events.
In the real world you knowledge of the odds of plane crashes is not complete.
A plane crash will cause the ground crew and flight crew to change their behavior, shifting the odds.
A plane crash is evidence that your assumptions on the safety of a given model of plane might be incorrect.

In the magical world of simple odds, safety audits and groundings wouldn't make a lick of sense. They do in the real world.

And again, see the part about the Boeing 737-800 MAX.
Sometimes its a problem with the whole class of plane.
That's the most recent example I can name off the top of my head.
There are many many examples of this.

You can keep going to see sometimes how changes in process/certification lead to the crashes.
And sometimes that first crash is the sign those problems are starting to come home to roost.

That's defective thinking as well.

Given that one plane crashed, it is much more likely that another plane of the same type will crash.

EG: a design mistake causes undue stress on a part, that part wears out faster that it should. That part breaks mid air and causes a plane crash. It is likely that the parts in all the similar planes has also been under stress, and might be breaking soon as well.

This is why the FAA tends to ground all planes of a certain kind until they figure out it wasn't the plane causing the issue.

See also the Boeing 737-800 MAX

The Air Force General re-defines an infra-red photon emitted by his skin shortly after his 1st year birthday as part of his body.
Statistically at least one was released out into space.
Meaning it is <age - 1> lightyears away.
The precendent was set by the Marine gaining from a lost body part.

Air Force people are more techies/lawyers than soldiers.

Congestion is a huge issue.

A single subway train can carry hundreds of people, nearing a thousand.

Now imagine how much road will be required to get a thousand cars to some place. How wide the roads will need to be, how many people need to be displaced to fit it. How loud it's going to be for those who remain.

Parking is an issue.

Now imagine, how much parking you'll need to house a thousand cars. It's a building that does nothing but house cars. You need to clear land, it's going to block views and take up space.

Equity is an issue.

Now think on those people too poor to afford cars. All those opportunities to get ahead will be lost to them due to their inability to get around. The deck was stacked against them already, now they have an additional disadvantage.

Environmental issues are another issue.
Think of the energy needed to repeatedly move a thousand car weights every day for hours. That isn't coming for nowhere, even green energy like solar or wind has up keep and wilderness habitat displaced. It's far better than fossil fuels, but not zero. Also think of all the manufacturing for a thousand cars, the tons of metal needed for the bodies, the tons of rare-earth elements for the batteries and electronics. That is if we do go green and electric, more likely it will be all fossil fuels for a long time.

Oh and that single train carrying a thousand people. Several of those will be going every hour for rush hour.

The USA has a reputation for creating urban hellscapes thanks to its car centric approach. You do not want that for your country.

Zealand 3: The Return of the Dutch.

1st world infrastructure, 3rd world mentality.
You can't crash build the latter, that takes time.

Maybe a bridge constructed in the 1930s had such limitations.
But modern suspension bridges often are built tall enough for ships to pass under, with ramps that get that high on either end. They don't really care if the height change on the ramp has to be small or large on one or both ends.

The sides of what you're bridging probably are.

It's mainly because most features are relatively level.
We don't really have many problems making a ramp.
We build them to connect surface and elevated highways/roads all the time.

Steam Deck?
Arguably a console or a PC.

It's a cultural thing.
We have 10 fingers, and a lot of people counted that way.
There's another way where you point to a finger bone with a thumb, that way you can count to 12. They mostly lost out to 10, but you still see them all over the place. Most notably the clock. It's 12pm somewhere in the world right now.

Programmers work in powers of 2, and 16 is a convienent power that closely mirrors how we used to set up memory. There are 16 combinations of four 1s/0s in a row and 8 1s/0s in a row make up one computer byte. Hence why you see programmers use numbers like 1F A2 FF

You could count to any number, but these are some of the most common ones.

A bacteria has a lot of stuff that it needs to do in order to remain alive.
It tends to do that stuff differently from how our cells do it.
So if you stop that stuff from happening, the bacteria dies.

A virus on the other hand is arguably not even alive. A virus does so few things on it's own that many scientists seriously say that we shouldn't call that small chunk of genetic material wrapped in protein "life". It is very hard to kill something that isn't even alive.

The medicine we do have concentrates on sticking to the virus or the sticking to the places the virus sticks to so it can't get in.
Targeting the stuff that makes copies of it self doesn't work well because our cells need that to remain alive.