Man, having to adjust your clock one second every few million years is so inconvenient.

@ShauryamAkhoury

4 жыл бұрын

Ikr!! It's soooo annoying

@yououtuber4176

3 жыл бұрын

I hope that I will still live in the same time zone.

@la33s18

3 жыл бұрын

@Anant Tiwari its okey you will someone to interact with some day

@v4v819

3 жыл бұрын

It's more inconvenient then resetting your regular clock every year... How do you set a reminder for every few million years... What do you set a reminder on, for every few million years... In 10 thousand years, everything presently including our bones will be dust...

@56independent42

3 жыл бұрын

this is why i ise a wifi clock. someone else adjusts it for me.

"I'm going to show you how the first atomic clock worked. I'll start with jello."

@MrArchDelux

5 жыл бұрын

Thanks, I have got speakers & sight you know.

@ProctorsGamble

5 жыл бұрын

dry. very dry. like good martini.

@siukslessiuksles1894

4 жыл бұрын

Who does that?

@MrVosh-nj2lc

3 жыл бұрын

Editing is great until you start cutting through the bone.

@pennise

3 жыл бұрын

There's always room for Jello.

These are hidden gems hiding in youtube

@sandeepr1253

6 жыл бұрын

Trippie Redd autistic shoota #iwillslap6ix9ine Great .....

@sunilsoni3310

5 жыл бұрын

Those hidden gems were all there was on youtube a few years ago. Those gems that are now hidden are what made youtube big.

@marionem6163

3 жыл бұрын

If they weren’t hiding they wouldn’t be hidden

@michaelknight2342

3 жыл бұрын

More hidden gems: Ben Krasnow, Sam Zeloof, Jacob Collier, Apartment Sessions, Adam Neely, Technology Connections, Strange Parts, Styropyro, Michael Reeves, Marc Rober, SeanHodgins, Explosions&Fire, Tech Ingredients, SmarterEveryDay, AlphaPhoenix, Nighthawkinlight, ElementalMaker, Abroad in Japan, tesla500, Usagi Electric, Daniel Schiffer, Tom Scott, The Thought Emporium, Charles Cornell, Christian Jackson, Casually Explained, mikeselectricstuff, Medlife Crisis, Jacob Mann, Jeremy Fielding, muteFPV, Bob Reynolds, Carl Bugeja, DOMi & JD Beck, MIT OpenCourseWare, Tom Stanton, NileRed, Flavor Lab, :3ildcat, Stuff Made Here, JYMV

@BudgiePanic

3 жыл бұрын

@@michaelknight2342 I recognize about half of these :) You should add Ben Eater to the list, former Khan Academy contributor, now making the best videos about low level computer operation I've ever seen.

It seems so simple after somebody already invented it... I guess that's the catch. The best engineers are the ones who know their science but who also are slightly on the creative side.

@Listoric

7 жыл бұрын

John England j

@rhettorical

Жыл бұрын

There's an old tale of some detractors who were razzing Christopher Columbus at a party, claiming that his accomplishments were of no special note since "Everyone was visiting the New World these days, it's easy." He challenged them to stand an egg on end. They naturally failed to do so, and asked him how he would do it. He proceeded to smack the egg's end on the table so it deformed enough to stand upright. "You think it easy, now that I have shown you," he said.

@jakobhayden3976

10 ай бұрын

Cesium atom ions existing in different forms being separated by magnets only to be reenergized by radiation to oscillate a piece of quartz utilizing the piezoelectric effect. Ah so simple

@alphabeta3528

10 ай бұрын

@@jakobhayden3976 ye. That's why inventors are very precious

@troll2637

8 ай бұрын

​@@ListoricRichard America k

I'm a high school science teacher, and I'm very impressed with how clearly you narrate your videos. You also pick some of my favorite physics subjects to explain!

@flat-earther

9 ай бұрын

hi wiscgaloot, have you become a flat earther yet?

"I'll tell you how an Atomic Clock works." "Lets look at some Jello." the timing on that was perfect lmao

@tompycz2225

5 жыл бұрын

The timing was as perfect as the atomic clock's

I don't know what you're talking about. But it sounds smart, so here's my like

@madingahmar4420

4 жыл бұрын

mangaka08 lol

@this_is_patrick

4 жыл бұрын

@@mangaka08 bruh that's a pretty hood way of explaining things lmao

@mothhunter2337

3 жыл бұрын

is your pfp fry em up?

@melody3741

3 жыл бұрын

I hate when people do this. If you actually bothered to watch the entire video, it’s only five minutes, he will literally explain it to you piece by piece and you will understand it and can stop making these stupid comments.

@-se

3 жыл бұрын

@@melody3741 it's just a dumb joke, don't read too much into it. Loosen up that butthole and have fun a little bit with your life, ❄️.

Explaining it is the easy part. Someone had to figure all that out. Insane.

you lost me after, the jello but I loved the vid. LOL

@injusticeanywherethreatens4810

7 жыл бұрын

Take a high school chemistry and physics class, then come back to it.

@grahaminatorca85

6 жыл бұрын

+ThatOneEngineeringStudent You come off as someone with their nose up in the air talking like that. Yes I took high school chemistry and physics.

@V0YAG3R

6 жыл бұрын

ThatOneEngineeringStudent Walk the talk! Make your own atomic clock then come back to us and show the world how, with your high school level alone of chemistry and physics, you really grasped it all 👌🏻

@Phoenix-dh6ct

4 жыл бұрын

Put video on quantum

not where I expected to him start "The way that atomic clocks works amazes me, let me explain how the very first one worked. I'll start with Jello"

How do people figure this shit out?! Blows my fucking mind.

@byronwilliams7977

9 жыл бұрын

u just got scienced :D

@loupax

9 жыл бұрын

domjubgwefer they were not screaming "I'm never going to use this stuff in real life" in school for once. Probably helped

@megakeenbeen

9 жыл бұрын

domjubgwefer Yeah, Science

@puncheex2

9 жыл бұрын

megakeenbeen Yeah. And engineering.

@dirkwalker9686

7 жыл бұрын

Tiny advancements and discoveries really stack up. One person couldn't do it, but together the global scientific community can do mind blowing things over time.

The background music for this channel always reminds me of a Legend of Zelda game. It just adds to the awesomeness of it

@jackmanhardt9909

5 жыл бұрын

I'm pretty sure that music is from one of the Pokemon Mystery Dungeon games

Nothing better than starting your day with an Engineer Guy video! I really enjoyed the look back at how atomic clocks were originally designed. I bet that had to be a feat during their era, I assume they had to use a lot of analog electronics to keep their detector circuit going. Also a great tie-in to a ubiquitous piece of technology, GPS.

The mark of a great, nay brilliant teacher, ..taking complex subjects and making them both easily understandable , and entertaining. Thank you , once again Bill. :)

@petergreenwald9639

10 ай бұрын

Makes Bill Nye look like the slacker guy. This guy is obviously a skilled and knowledgeable engineer who knows his stuff and stays out of camps he isn't qualified to prance around in.

I love your appreciation for other's ingenuity. I'm humbled by your humility.

Thank you for this very well done explanation , i was always curious as to how atomic clocks worked and i had a completely wrong idea about how they did , again thank you for clearing things up

I just wanna say I LOVE your videos!! Thank you for putting these out for the world to learn... I love the engineering perspective you give on things, you've made me look at a cell phone differently ever since I'd seen that video. Keep up the good work!!

"The way that atomic clock amazes me... let me explain with how the very first one worked... I'll start with Jello." - You sir are a comedian and a scholar.

I love how you presented the concept! Nice animations and analogies. Thanks for the quality content:)

its satisfying to see such an idea being so perfectly explained

"About the size of a quarter" is taken very broadly I see XD Nice vid, as always.

@FanboyFilms

3 жыл бұрын

I was gonna say a half dollar would have been closer. But those aren't very common these days.

Bill, you are an amazing presenter! You make science so much interesting and fun = )

Your videos are always concise and inspiring. Great job as always.

I'm so happy to see the new EG video.

GPS calculations also have to factor in general relativity for accuracy. 1) The velocity of the satellites slows down their clocks AND 2) Their position within Earth's gravitation field speeds up their clock. Without these corrections the results would be off by a hundred meters laterally and thousands of feet vertically.

@samtzam3774

8 жыл бұрын

This happens because the physic laws is related to the frame of observation. (General relativity) The error actually with not correction is some cm/sec.

@ayeshakhan796

4 жыл бұрын

Did Einstein consider the atomic clock (or analog clock) in his relativistic time dilation because of gravitational distance? How do these two devices are differentiated against gravity?

Bill Hammack I bought your book a few years back. I love it so much. In fact it was the only book I ever so cling to it. I hope you will make more books. I will buy them.

@carolynmmitchell2240

6 жыл бұрын

Gary Yong Kah Joon he does, he has a few.. he has one on a blimp

Ideas can be really beautiful. Thank you for the video!

I LOVE THESE VIDEOS! This one was the best one yet! Hope for more to come!

A cesium atom in an atomic clock beats 9,192,631,770 times a second.

@happmacdonald

7 жыл бұрын

Yup, thank you for pointing that out, Elizabeth. And for the readers at home that number is not rounded or an average. It is *absolutely exact* because we actually define the time interval we call a "second" to be precisely that many oscillations of Cs133. Even when the theory of relativity predicts that spacetime distorts, dilating time relative to another observer, both the standard unit Second and the frequency of Cs133 are dilated in kind so you simply wind up with more or fewer seconds (and Cs oscillations) measured by the out of sync observer per unit of their own time. :3

@cheongziyong8871

7 жыл бұрын

+Happ MacDonald Isn't time defined by the speed of light? Or is that distance I'm thinking of?

@cheongziyong8871

7 жыл бұрын

+Happ MacDonald Isn't time defined by the speed of light? Or is that distance I'm thinking of?

@happmacdonald

7 жыл бұрын

Actually, you'd be surprised but time is better defined by the causal propagation of a process having the capacity to move *slower* than light (that is, slower than uninterrupted causality) through space. Nonetheless, the question of "what is time made out of" (answer: it's made out of the opportunity for systems to causally evolve, and it dilates in different circumstances because the opportunities for systems to evolve are impacted by relative velocities and warped spacetime geometry) is different from "how do we humans choose to standardize our measurement of it" (answer: in units such as Plank Time, and seconds which are exact multiples of vibrations of Cs133). :3

@xImBeaST12321x

7 жыл бұрын

the speed of light establishes the distance in SI... i dont remember the exact number but yeah a meter is the distance that light travels in a couple billionths of a second.

Ya, well, that's just like, your opinion, man.

@ilovemykitties84

7 жыл бұрын

lol the dude!

@oneminutefixed5003

7 жыл бұрын

Adam R that jello really tied the lesson together

@furryz666

7 жыл бұрын

OneMinuteFixed "theres always room for jello"

@fernandaabreu5625

6 жыл бұрын

Furryz "Grandma's chicken salad" I'm sorry, I just couldn't help myself.

@TestTheAcid

6 жыл бұрын

sad

This was great. I love the random trivial facts you put into the videos.

This is becoming one of my favorite channels. Thanks alot!

"I'll start with jello." I like the way this is going, Bill!

Are there different types of atomic clocks? I've heard elsewhere that atomic clocks work by directly measuring the oscillations of cesium atoms to define a second (9192631770 per second). The method described here is only using the cesium to regulate a quartz crystal clock.

@podgemcgrath

9 жыл бұрын

The Caesium-133 atom is used for the definition of the second so you would think that most atomic clocks use the Caesium atom for time keeping when in fact they don't because of the high cost associated with it. The most common atomic clock is the Rubidium atomic clock because it is significantly cheaper to make.

@brettshook9915

9 жыл бұрын

The clock described in this video actually does measure the oscillation period of cesium atoms in two different states. The first magnet ensures that only cesium atoms in the the lower energy state flow into the microwave chamber. Some electronics (think microwave emitter of some sort) excite this chamber with a particular frequency. The goal of the electronics is to 'tune' in to that particular frequency which causes cesium to jump to the correct energy state (the higher one). Once it has hit the right frequency, higher energy atoms will begin to flow out of the chamber thus striking the detector. This forms the feedback loop. If the electronics have the frequency wrong, atoms don't strike the detector. So the analog electronics adjust automatically (based on detector output). Now you have a hyper fine time reference. I think the piece of quartz is used as the generator of the high frequency signal. If you apply a voltage to the quartz you can 'tune' the frequency at which it oscillates. So the electronics only have to adjust a voltage across the quartz to finally arrive at the correct output frequency. en.wikipedia.org/wiki/Caesium_standard en.wikipedia.org/wiki/Negative_feedback

Glad you are back. Watched the first series and enjoyed it. Keep up the good work!

Still, the most interesting channel on yt. This guy's voice can turn my head in his direction.

you look like luke skywalker does now

@batfan1939

7 жыл бұрын

So it's not just me? BTW, Mark Hamill is also the voice of the Joker. Has been for twenty years. Batman: The Animated Series (and any cartoons, films and games related to it), the first few "Batman: Arkham…" games, and DC Universe Online to name a few.

@linkinparkfan0459

6 жыл бұрын

JREADY and i thought i was the only one..

"About the size of a quarter" *is about the size of an Eisenhower dollar*

@ralanham76

3 жыл бұрын

"ABOUT"

@cherrypepsi2815

3 жыл бұрын

@@ralanham76 "about"

@hindugoat2302

3 жыл бұрын

@@cherrypepsi2815 if engineer guy is so smart, why cant he engineer himself a decent haircut ?

@cherrypepsi2815

3 жыл бұрын

@@hindugoat2302 ouch that's gotta hurt

This series is getting so good I might just buy the book!

Great presentation, simple but to the point.

I was doing fine until about the 3 second mark then it was all downhill from there.

@tactknightgaming2066

3 жыл бұрын

Similar to a JRPG. Game starts off with you looking for your neighbor's missing cat only to end up with having to kill god by the end lol.

music is a bit too loud compared to the speaker

I love these videos! This one I actually understood best since I work with electronics and a lot of my equipment has quartz oscillators.

I just found you like Thursday, and oh man, I'm in love!!!

I'll start with Jello.

I'm a bit tired and I am not sure if I got everything immediately, but I'd like to ask how long it lasts before you're going to need to change a part for maintenance of such a device.

@Nosirrbro

7 жыл бұрын

No moving parts and no exposure to outside air combined with microscopic scales means that, discluding being shoved into the center of a brick of C4, the atomic clock never needs any fixing.

@Tarik360

7 жыл бұрын

+Nosirrbro That's amazing! Are they also waterproof?

@Nosirrbro

7 жыл бұрын

Tarik360 Uhm, I wouldn't think so, but I guess you could waterproof the casing of it.

@Tarik360

7 жыл бұрын

+Nosirrbro That is an even better way of doing it! Good night!

I had no idea this is how the atomic clock worked. I always thought it had something to do with decay rate/half life of an ion. This makes so much sense.

Phenomenal explanation!!

But then how is this related ot the SI definition of a second or the caesium standard? From Wikipedia: "A caesium standard or caesium atomic clock is a primary frequency standard in which electronic transitions between the two hyperfine ground states of caesium-133 atoms are used to control the output frequency." It also says that a second is defined as exactly 9,192,631,770 transitions of those two states. I don't see how that number of transitions between the low energy state and the high energy state is important for the functioning of this atomic clock.

@davidbeyondplus2587

8 жыл бұрын

From what I remember from physics class is that the SI units is determine by the time light takes to travel a certain distance. Since light is a constant, a frequency or pulse using light can keep a measure of change which is time. A long time ago Galileo measured time using his heart pulse.

@shanmugavallielangovan7928

6 жыл бұрын

never believe wiki.its wrong on one way or the other

@MC-mx1mt

6 жыл бұрын

David Beyondplus but my reference book mentions the caesium atom's one.

@danav3387

5 жыл бұрын

Wikipedia is NOT a recognized nor reliable source for correct information about anything...

Great video, but i was wondering: why is a Cesium atom with a higher energy electron deflected by a magnetic field?

@puncheex2

9 жыл бұрын

Matt Philips AKA Percival The higher energy cesium is ionized more - i.e.. it has lost more electrons, giving it a more positive charge.

@subh1

8 жыл бұрын

puncheex2 I think the ionization is the same (they don't lose electrons, but the electrons only jump to higher energy level). In the different energy levels it's the magnetic moment of the electrons in the two states that are different though (a quantum mechanical property, because the electrons are not point particles, and are instead wave functions).

@donantoniodilampedeusa259

6 жыл бұрын

No - the magnetic moment of the electron in the lower state is antialigned with the nuclear magnetic moment, ie N lines up with S, in the upper state the electron's N pole is aligned with the N pole of the nucleus making an overall bigger magnetic moment for the upper state.

Great easy clear explanation (specially the feedback system that controls the cesium/ quartz fork). Thanks.

Perfect video, thanks! Best explanation I found so far.

Mam : Ok students please write your exams. Question, how atomic clock works? Me : I can't write my exam I am sick

You say "the most accurate of atomic clocks", and though I know this is pedantic, you'd really rather say "the most *precise..." Accuracy of a clock is in how you set it. Precision is its timekeeping abilities, that it will stay perfectly consistent. If you don't reset your clock over Daylight Savings, it'll be inaccurate by 1 hour, but it could still be perfectly precise for thousands of years.

@micahphilson

6 жыл бұрын

For instance, my clocks and watches are mostly very imprecise (especially my watches; they're super cheap, but fun), but they're all set very accurately, because I'll wait upwards of a minute just to set them exactly to the second from my computer or phone, so that they're all withing a couple seconds of eachother. Insofar as the source time I get from those is accurate, so are the rest, though some may veer off time after awhile.

@robertromero8692

6 жыл бұрын

If it's not very precise, it won't be very accurate. So it's valid to say that it's losing accuracy.

As always, a superb explanation.

Brilliant video, thanks for the upload!

Fascinating. But don't we need to use an even more accurate clock to know that we calibrated this one correctly? Wouldn't we need one that loses 0s in a quintillion years to determine that this one loses 1s in 138,000,000 years?

@2006mct42

9 жыл бұрын

That's a good question. I think that is done theoretically. The definition of one second is theoretical. So error of the practical clock is estimated compared the theoretical definition of one second.

@johnnytremp

9 жыл бұрын

2006mct42 no, the definition of a second is defined by the amount a cesium atom oscillates.

@2006mct42

9 жыл бұрын

johnnytremp Yeah I know that definition is about counting the oscillation of the atomic states of cesium but the practical problem is about error that builds up over time in the clock. So what I wanted to say is that a perfectly accurate clock is not needed to estimate the accuracy of another clock. We should just know the definition of the second. They just do the math and calculate the probable error.

@arooobine

5 жыл бұрын

I think what they do is compare a bunch of cesium clocks against each other and statistically calculate the error.

My fucking brain!!!

@fex144

7 жыл бұрын

you brain is fucking?

@Nosirrbro

7 жыл бұрын

He has two brains: His brain for fucking And his normal brain He has exclaimed, for no particular reason, the existence of his brain for sexual intercourse.

@mikakorhonen5715

7 жыл бұрын

CrazyCow500 Einstein's fault! BTW Einstein liked fucking.

Thanks Bill. Another amazing video, as always. :)

Always short sweet and full of knowledge

It's Like a Phase Lock Loop !!

Also thanks to special and general relativity

@stevencp

7 жыл бұрын

yeah, notice he skipped over the time difference of satellites because of relativity... that would have lost to many people!

it amazes me that the signals travel so fast. Simply amazing.

not sure how people don't follow this guy, he's explaining the stuff incredibly clear and as simple as possible, i mean, i'm from finland i understand everythign he's saying..., i went to school tho, did u? ;)

you lost me at 1:35

@user-wq9mw2xz3j

3 жыл бұрын

you should understand that with just normal high school atomic physics

You need to make move videos. I command it..

Best explanation I've found on YT.

This guy has the most amazing voice for an engineer. His videos are too awsome.

"About the size of a quarter" The chip is at least twice the size of that quarter he held up.

Ok I'm sorry but that thing is a good bit bigger than a quarter.

@ChaiSuBin

6 жыл бұрын

Hey man, don't refer to your genitalia as 'that thing'.

@carolynmmitchell2240

6 жыл бұрын

The Odd Strategical Gamer he can call it whatever he wishes man, who are you to tell him what he can and cannot call his pecker.

Just started watching this channel and I love the content

I LOVE your channel, keep it up!

For ever 1 of these videos you have 100 flat earth and global warming conspiracies

@carolynmmitchell2240

6 жыл бұрын

Jamie Jr DeFelice the earth is warming(and cooling in other places) but it's not a result of the populations but a result of weather manipulation tactics involving dropping atomized alumimum on us and particle accellerators.. look into the artwork of the scientists at the accelerator in Chicago, they want to melt the south pole for some reason.

Yeah that's nice but I'm still proud of my 3rd grade baking soda and vinegar volcano.

Great illustration.

Great presentation and nice music.

A GPS receiver needs *THREE*, not "at least four" satellites to locate its positron on the Earth. And the "one satellite to correct the time of the receiver, three to locate its position" is utter BS - time is deduced from the location solution even with only three satellites available. If four satellites are available, a 3D location + time will be computed (latitude, longitude, altitude, time). If only three satellites are available, the solution will be 2D so altitude will not be computed - but the location and time will (latitude, longitude, time). This is basic stuff widely available in books and online for many years, there is no excuse for spreading wrong information on a presumably technically-oriented KZread channel.

@cultpony

8 жыл бұрын

corisco tupi You need four satellites for accurate measurements of position. Of course, you can get a position with only three satellites and possibly only two, but do you know why? Three satellites will result with two points and you have to choose which one is probably the right one. You make assumptions. You can, for example assume that you are, on average, about 6371 km from the center of the earth and take that as basic altitude. But that isn't always true. This is an average value that will be wrong most of the time, for example when you are on a mountain. When you are closer to the poles you will be 6357 km from the center of the earth and near the equator it will be 6378 km. If you have some cheap GPS receiver it will, of course, make that assumption and probably get a result that is somewhat right but still off by a bit. But if you are in a plane you need precise results and assumptions of altitude won't work. You need all four sats visible to calculate position, altitude and time. The fourth sat increases the accuracy of your position and gives additional data about it, with only three you are just making a wild guess and hope it's right. Technically you can also make a good guess where you are with only two sats in the sky but it will be horribly inaccurate. TL;DR You are wrong. You can't get a position out of three satellites. You either need a fourth satellite or make an assumption of your height.

@coriscotupi

8 жыл бұрын

MrEyecikjou Sorry, you are wrong. First off, you *CANNOT*get a position fix with two satellites, the minimum is three. Also, the difference from a position fix from 3 satellites to 4 is that the former gives a 2D position (no altitude information so the fix will be on the geoid surface, approximately sea level - but latitude and longitude WILL be acurately given), while with 4 satellites you get 3D (lat, long, alt). Of course, the more satellites, the better the accuracy but this holds true for any increase, not just from 3 to 4 satellites. I.e., 5 satellites gives a better accuracy than 4, 8 is better than 7, etc, assuming the satellite geometry at the moment and receiver location is adequate.

@cultpony

8 жыл бұрын

corisco tupi If you make a few more assumptions you can work out a position with only 2 sats, it's just VERY inaccurate. And you always will need an altitude when calculating with 3 satellites, as 3 sats resolve to 2 possible positions, additionally the position itself is less accurate.

@coriscotupi

8 жыл бұрын

MrEyecikjou 3 satellites resolves to ONE position on 2D.

@cultpony

8 жыл бұрын

corisco tupi 1 sat gives you a sphere, 2 give a circle, 3 give 2 points and 4 1 point, look up the math.

@0:23 This statement blew me away. This level of engineering and accuracy is nothing short of a miracle.

I would just like to thank you for your ability to 1. Teach us the watcher's of your show just how stuff works but 2. Show how complex our daily lifes truly are. So once again thanks.

I use these videos to further my knowledge of physics and they sure work. Thanks a lot

man you're awesome in explaining the stuff

Okay, I'm sold, I'm buying your book. lol. Amazing stuff.

Excellent video, thanks for posting, much appreciated. A+

Man you're awesome. Keep doing this videos.

I watched Some of ur vids recently and i love them all ......... i wish u never stop making vids .... god bless u

Thanks for the video! Well done!

Wonderful design, thanks for the good explanation.

I love these videos, thanks Bill!!

I like that how the oscillator readjusts the feedback loop. I sort of understand the combining of the high energy frequency to disrupt the timing pattern on itself, which is quite a clever way for self adjusting. 🙂

Very very informative .. This video deserve more viewers

I absolutely love your ending theme music.

Such an Awesome informative video! Thank you!

Great explanation

Easy to listen to. Great presentation. More please.

I def plan on using some of these in my classroom! Keep up the good work!

Very informative video! Thank you!

This guy is fascinating , good stuff man.

@engineerguyvideo

6 жыл бұрын

Thank you

Love it! Keep up good work.

YES! New Engineeringguy vid

Love these and very well explained too!☘️👍