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That's Look at Truck Stop Showers Trucker Rudi 01-24-19 Vlog#1663 - Duration: 16:18.
good morning good morning guys - now welcome welcome to the show
we are just getting going here this morning we had our 10 hour break now
it's time to hit the road again as we like to call it right now we ought to be
super super careful in this parking lot because when I was walking in there
then you have to be careful you don't fall on your house because it is super
super slick in this parking lot but oh well that's just how it goes but anyways
we're getting our day started the Sun is just risen so there is still some
beautiful beautiful colors in the sky which I really really like that but man
did we ever get lucky here last night we only I only managed to see a couple
of spots on that side there and that's where I found me a parking spot and
parked it for tonight but this place got full and I think I showing you guys this
place before we're after that middle section up here is like for paid parking
only you know like you'll see it up here to the right where oldham yellow stakes
are whatever you got the blue reserved sign on it that whole section all the
way to the front is all reserve parking all the way to the end I kid you not
this is like a court at least a quarter of the parking lot that is reserved
reserved parking only but what can I say right that's how they make a lot of
money off of drivers these days then then there's a couple of spots even up
here on the left here too but oh well anyways
we gotta go we had six hundred miles to our customer yet which we should be very
very close to the customer for tonight I'm planning on it anyway so we got a
green light so let's see if we can get that coke out we're not gonna get that
green light nope I kind of figured buddy this other guy was taking it a little
easy there so that's okay I mean it's no sign saying we can't make a right-hand
turn on red so I'm pretty sure we can do that especially since these guys got the
turning lane going right now that's what it looks like I just want to make sure
yeah that guy is turning yet still come on our truck put it in gear sometimes it
takes a second before it actually gets going because it there's got a shift the
ear and it's visit automatically right so here we go
we should be hitting the toll road the i-80 90 they're very very soon we're
only a couple of miles away from finally taking entrance to the ride on i-80 East
I know I'm trying I'm trying RK come on truck shift gears already
sometimes I hate these automatics you know because you're trying to get going
you don't want to be at 2200 rpm and then the truck doesn't want to shift
gears you know and then I got a hit the believer here manually to manually shift
again because then I don't know for some odd reason that just wants to shift two
gears at the same time sometimes and sometimes that's not a good idea
sometimes it's better just to shoot one gear at a time but
yes look at that beautiful beautiful red sky sunshine and all of that stuff that
looks gorgeous I like it anyways I hope you guys do too I know even yesterday it
was gorgeous to there in the morning when I took off but looks nice again
this morning so here we go now we can get into this thing up here I know that
right lane is like sitting on two I 65 Sol's and I don't want to go on that one
I want to stay on this road here
trying to get to the i-89 the toll road that's where we gotta go yeah we'll be
on that pretty much all day I'll be going up to probably prairies perv area
I know they got a he loves up there as well and one of the
reasons I'm going to go up there is because I really need a shower I was
going to take one last night but there wasn't really any parking that the at
the love's there so I kinda had to go over to the Petro who I could have still
gone over there but that would have been a super long walk clothes I would have
to cross that busy busy street right there and I don't really feel like doing
that last night I kind of got tired and pretty much went straight to bed so
didn't even do any editing or anything like that last night so
one day behind kind of so I'm gonna have to get to editing tonight hopefully I
don't feel tired too tired tonight tonight to do it but anyways let's get
down down a road I appreciate you guys tuning in if it's your first time here I
am trucker Rudy I forgot to do that right at the big anchor to say that and
if this is your first time we would love to
have you on board by that subscribe button don't forget to hit that Bell so
that way you'll be notified whenever we upload a new video which is generally
everyday we are we must the our time but you know we need a break to once in a
while all right ready now let's continue cruising here and see what the day will
bring us I have just entered a higher here a little while ago guys and we had
such a nice beautiful clear sky kind of a nice sunrise this morning next thing I
know a couple of minutes later it started to get really cloudy as you guys
can see now and then I checked the weather forecast and they're saying some
winter advisories for this area one to three inches of snow expected at least
up in Indiana and heavy winds 15 to 25 miles an hour possibly gusting up to 35
is what it said so it's like holy moly when are we ever gonna run out of this
weather I guess or just get hammered hard this week even in Steinbach they're
having extreme extreme cold temperatures up there for the next week yet even on
Wednesday it's supposed to be minus 29 just the temperature by itself not even
considering any windshields yeah so put in anyways we just entered into
Ohio and I typed into my GPS there to get me routed to the lovestruck stop up
here by Toledo area Perrysburg I think is the actual name of that area and so
now we're going to go up to that love's truck stop and then we're going to we're
gonna go in there and take this a shower and then of course my phone always has
to ring right and just quickly have to press the button because you're aren't
allowed to press one button on the phone right I just quickly have to press the
button so it's not screaming in our ears I just looks to me like it's a yeah I
don't know some us telemarketer that's pretty much all it is anyway so they can
leave a message if they want to talk to me if it's something important they can
always leave a message right but that's just how it goes I can be driving for a
couple hours as soon as I turn on my camera
somebody's gotta call me right anyhow continue on down to the truck stop we
got about 30 miles to go we'll be there and finally my EZ Pass is working and
had me worried a little bit at the first toll plaza man I got on the 80 because
that one didn't have a gate and the light stayed red so I'm like okay I just
went through anyways because they take a picture of your license plate and it
pulls on your license plate right the company pays for it no big deal right so
then the next one I come up to I figured I'd make sure that I would go up to one
that has a gate and sure enough this time it opened it works so then I went
into Ohio same thing it's working so there's no easy passes finally now I
know for sure it's working I mean up in Chicagoland and all of that they got the
fast lane so you just stay in that if the EZ Pass doesn't work you just take
the picture in your license plate and the company gets charged on that account
because the the EZ Pass is registered with your license plate right so if they
have your registration or your license plate and then okay this EZ Pass belongs
to that truck right so then they charge it to that account but anyways all that
being said that's hammer down and get to the truck stop and take me a shower I
need one bad all right guys here we go we got our
now let's go inside and Tikas that much-needed shower just got here had a
really nice truck driver there beside me because it was kind of tight I couldn't
really make it to the spot so he was nice enough to just pull forward so I
could pull all the way to into the parking spot big fat thumbs up to that
driver I'm telling you but anyways let's go in and take a swig shower I need one
shave and all that good stuff ooh what is
that's almost looking like it's starting to snow man don't be starting to swear
at me here no this is a very very nice shower too look at that nice and big oh
yeah look at that nice table right there brush your teeth and shave and all that
good stuff over there nice and clean too so that's how it's a good shower guys
here we go guys after that very very nice shower we took off again and very
shortly after that somebody called us and next thing I know another guy calls
me and next thing I know we have a big group of people in there and yappin away
there for a good while saw gets me down the road a good while too right but you
know it's fun Navin and that nice little group in there but at the same time I
need to be making some videos too right why we're still still in Ohio but we are
getting very very close to get nada Ohio because we just went through Cleveland
well not really true Cleveland just on the edge of Cleveland so we're actually
east of Cleveland already which that's you know all good ways down already
right but we still have 228 miles to go to get to our customer and I still
haven't gotten the reload offer so I'm not sure what we're gonna be doing
tomorrow but depending on if I get me a reload offer or not here before 4:00 or
at 4:00 o'clock might be depending on all right good tonight originally my
goal was to make it down to its I think it's called in 80 that's just on the
other side of the I 180 but you know very close to our customer right but if
I don't get a reload then I don't really feel the need to really push it so much
to try and get down there right at least that's how I feel about it but we'll see
I might still do it anyways just so that way I'm there you know I don't have to
drive a lot of miles tomorrow morning and if I all the sudden do get me a
reload at least and I can go right starter I see there you go getting close
to the Pennsylvania State Line there's a little bit of Sun every once in a while
being throwing up by other vehicles that's why I'm cleaning the windshields
every so often especially if I want to record right you want to have a nice
clean windshield so you guys can see nicely out of the window right and it's
still kind of very very light flurries all day long but nothing really to worry
about as of yet and they said four o'clock this afternoon it was close to
start hitting and so far it's not doing anything which I'm happy about that
I don't really need it to be doing anything either
I really don't but anyway let's continue on cruising along here and see where we
end up for tonight right we made it yeah we made it to the pin 80
truck stop and I'm only about yeah I would say 15 to 18 miles away from
getting to my customer now the only bad news is I just got my message here this
very late evening from dispatch telling me that my reload is going to be out of
Hazleton Pennsylvania which I kind of suspect it only problem is the load
won't be ready till tomorrow at 6 p.m. they're hoping that will be ready
earlier but the way it looks like it ain't gonna be ready early and it
generally isn't already too much earlier but I figured this load I can deliver it
as long as I deliver it before noon right that's what the load offers said
so guess what I'm gonna do I probably won't be going to deliver this load
until probably 11:00 that's kind of what I'm thinking but in the meantime got
some good news for you the wife had prepared me quite a few goodies here so
let's see we can show you guys on what we're having we got our traditional
peaches a bottle of water and we got some chicken alfredo it looks like yeah
yeah I think we're gonna have us a fantastic fantastic supper what do you
guys think leave me a comment below on what you think what my eating things
that I've been eating here at throughout the week microwaving but you know what
do you think of these ideas are they good ideas or or what I think these are
the best you know home-cooked meals right here in the truck I know they're
frozen and I gotta warm him up but they are very very good meals so and my
opinion anyways and I tried to connect to the penaity Wi-Fi over here and it
ain't working Eddie and working for some odd reason I was kind of hoping I could
upload my videos here but whatever but you know we are going to Canada
and I showed you guys my Wi-Fi system here the other day right so as soon as I
get to Canada I can use that thing and upload a few videos for you guys so but
anyways before my food gets cold here I'm gonna go ahead and have me supper
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DO NOT Destroy My iPHONE in REAL LIFE Challenge! *BOYFRIEND DESTROYS GIRLFRIENDS IPHONE* - Duration: 4:50.
whats good youtube it's nadiyah and josh and today we are back with another videoooooo
We are going to play a game today and it's called don't crash your phone
Don't destroy your phone
So basically we have three boxes
Well, she's going to put her phone under one of these boxes that we have on the table
And I'm not gonna look so I don't know what which box it is, and I'm gonna have to choose
Which one that I think it's not and I don't want to smash her phone. The whole concept is to not smash your phone. So
Now let's flow into
All right
So now we have to omean box, okay
Put in the my course first and then mom move
course first
Feel it twice in a row. So, you know what that means?
It's a really it's the exact same phone same
Rose gold rose gold
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Dynamical Systems And Chaos: The Butterfly Effect Part 5 - Duration: 7:26.
Sensitive dependence on initial conditions is also known as the butterfly effect.
You've probably heard this term before and know the story
but I should mention it briefly
so again the butterfly effect here is this illustration
we have two different initial conditions
this is for the x part of the Lorenz equations
two different initial conditions that differ by tiny tiny tiny amount
we can think of this is 15 meters and this is 15 meters plus 10 nanometers
imperceptible meaninglessly different
and here is the trajectory, the orbit of the two solutions
one we could think of as reality, one is prediction
and hereafter I don't know about 18 minutes or 18 time steps
the two curves go apart
so a tiny change this is idea, like the effects of a butterfly flapping its wings
can make a large difference later on
so maybe speaking somewhat metaphorically
this is somehow the path of a hurricane
and in this version it hits New York city
and this version it hits North Carolina
so the difference, but maybe this is wind speed or something
20 hours ago or 20 days ago who knows
and so this tiny difference could be caused by the flapping of a butterfly's wings
so very small changes in initial circumstances
can lead to very large changes later on
and this is what makes phenomena like this essentially unpredictable
because we can never measure something like this
in fact maybe values this accurate might not even be physically meaningful
James Gleick in his book Chaos has a nice way of thinking about
the butterfly effect in particular the influence or
the effect of butterfly flapping its wings
and he says the following
it's like giving an extra shuffle to a deck of already well shuffled cards
you know that it will change your luck
but there is no way of knowing how it will change it
so that the sort of how I think about the butterfly here
the butterfly might flap its wings
and we know it's going to change something in the future
but we don't know how it will change it
Here is another way to think about the butterfly effect
in our lives we might be accustomed to the idea that
there were particular moments where a small change
in something that we did led to a really big change in the course of our life
so a simple example might be you're burning the toast
and so you are a little bit late leaving the house
and so you catch a train that's one later than the thought,
than the train you thought you were going to take
but the train you had been planning on taking crashed
and a lot of people died
so ok, that's a dramatic example
but we can perhaps think of a number of times in our life
where we were at sort of a key decision point and some very small thing
may be that we didn't know about at the time made a big difference later on
It's sort of like a ball perched on top of the hill
a tiny little change will determine whether or not
the ball rolls down to the right or to the left
So the idea that we have these sort of sudden decision points
is a fairly commonplace one.
But in a system that has sensitive dependence on initial conditions
it's as if every moment is a decision point
at every moment the future trajectory is poised between possible different futures
and the difference between those is a tiny little flap of
gust of wind from a butterfly flapping its wings
that determines which path that will go on
so it's this continuous sensitivity where every point along the journey
a tiny change can make a big change later on
and there is no way to know what those changes will be
finally before moving on to talk about chaos
I should mention that there is a really interesting history to this term the butterfly effect
And I strongly recommend there is a short article by Hilborn in American journal of physics
There is a link to it on the Complexity Explorer page
right down there underneath this video
it's a three page non-technical piece,
if you're interested at all the history of this term
it's a great read I definitely recommend it
Ok, so let me conclude this subunit by defining chaos
We're finally in a position where we can define the chaos in the mathematical sense
So a dynamical system we would say is chaotic
if it meets the following four criteria
First, the dynamical system has to be deterministic
The two types of dynamical systems we have studied so far
in which are the topic of this course
iterated functions and differential equations are most certainly deterministic
as I've stressed throughout the first two units
the dynamical system is just a deterministic rule
if you know the rule and you know the initial condition
that trajectory is unique, it's determined
let me skip over two I'll do these in
well , ok, so let me say this
The system's orbits are bounded
meaning they can't fly off to infinity
So for the logistic equation we've seen that orbits
that start between 0 and 1, remain between 0 and 1
for a system to be chaotic the orbits also have to be aperiodic
ie they never repeat they never follow the exact same path twice
it doesn't go into a cycle
so if the orbits were not bounded
let's say that we had just just the doubling function
then we could have an orbit that would be aperiodic
rigth if you double a number
it just keeps getting bigger and bigger and bigger forever
and it never repeats so that's not so interesting
so this requirement that the orbits be bounded is sort of like fine print
that eliminates the possibility of orbits going off to infinity
so we have bounded orbits that are aperiodic
that are confined to stay in a unit interval
or a square or something and yet nevertheless never repeat
and then the last criteria for something to be chaotic
is that it has to have sensitive dependence on initial conditions
in the sense of we've just been talking about
so if a dynamical system has these four properties
then in physics or math would say it's chaotic.
There's lots more to say about the implications of sensitive dependence
on initial conditions and in general on chaotic dynamical systems
We'll talk about this in the rest of this unit
and in many ways in the rest of the course.
But in the next set of lecture I'd like to explore this idea that
a dynamical system a deterministic dynamical system is capable of producing
random behavior and in order to dig into this idea
we'll need to start by thinking about what even means to call something random
so this will be the topic of the next lecture
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Dynamical Systems And Chaos: The Butterfly Effect Part 2 - Duration: 15:39.
The logistic equation with r equals 4 isn't just aperiodic;
It also has sensitive dependence on initial conditions, the butterfly effect.
In order to illustrate this, I'll need to use a program similar to the one we've already used
to plot logistic equation orbits.
This program is... There is a link to it down here beneath me,
underneath the embedded youtube video on the complexity explorer page
as before, if you click on that, a pop-up window, a new window should appear
and the program will be in it.
I've also made a separate page with links to the two programs
it's over here, somewhere on the navigation bar on the right,
I think it's section 3.7, it might be 3.8, it's called 'logistic equation programs'
there is only one item in this section, and it's a text page with links to these two programs
So, this way you can find them more easily and you don't have to hunt
through the various video pages.
In any event, I will use the second program to illustrate the butterfly effect.
So, here is a program that will let us investigate sensitive dependence on initial conditions.
Before I consider the parameter 4, that is the one we are interested in,
let's go back and I'll consider the value 2.4,
and for this value, I think we have seen before, that there is a stable attracting fixed point.
So, as in the other program, we get to choose the number of iterations displayed.
I'll choose 25.
And now, rather than one initial condition, we can choose 2 initial conditions.
And it will plot two different time series on the same axis.
So, let's choose two, as for 0.2 and 0.45.
Two different initial conditions.
And I click here and make the time series plot.
And, so, let's see: What I call the second initial condition,
that's in green, and the first initial condition at 0.2, that's in purple.
And these two initial conditions start kinda far apart, 0.25 apart,
but very quickly they both get pulled to the same attracting fixed point.
That's what it means to be an attractor, it pulls in your nearby orbits.
OK. So, there is another plot that this makes, and we can see that if we scroll down
here, and, let me see if I can get both of these plots in at the same time.
Ok. So, the blue curve is the difference between the green and the purple curve.
So, it tells us how far apart the two orbits are.
The two orbits start 0.25 apart, or -0.25. I guess it is set up to do purple minus green,
but the sign, if it is positive or negative, it doesn't really matter
for what I am trying to illustrate here.
So, they start 0.25 apart, and then very quickly they are just about 0 apart.
Because the purple and green orbits or itineraries are right on top of each other.
So, again, the blue curve is purple minus green.
It's the difference between the two, the separation between these two orbits.
And, because it's attracting, these two orbits get closer together, this blue curve gets closer to 0
in absolute value.
Lastly, as before, this program will also output some numbers.
So, I call the two time series x and y, so here is x equals 0.2, 0.384 and so on,
and goes to the attracting point at 0.5833,
and y meets a similar fate, it ends up at 0.5833, and this is the difference between these two,
it's x minus y, starts off at -0.25, numbers go positive and negative, but they are getting
closer to zero. And, by the time we get here,
at least with the precision of the computer, the two orbits are exactly the same.
So, this is just another way of seeing that we have an attracting fixed point.
It is another way of visualizing what it means to be an attractor.
Nearby orbits are pulled closer together, and that's what this blue curve is showing.
The blue curve is getting closer and closer to zero.
Let's now try a similar experiment, but for an r value of 4.0
Remember, this was the r value that gave aperiodic, or non-repeating behavior.
So, I'll go back to the top. I'm gonna change this to 4.0
And now, I'll pick the two initial conditions quite close together:
0.2 and 0.21. So, let's make the time series plots
and see what happens. There we go, OK.
So, we have one initial condition, or one itinerary in green, and one in purple.
So, notice that the two itineraries, the two orbits are pretty close for about 4 times
They are pretty far apart here, though, at least by 0.1, and then they start to get very different
by time step 5. And by the time we are at 6, or 7, ot 8,
they seem completely uncorrelated, they are doing their own thing.
And who would have guessed that they started off so close together?
We can see a similar thing if I plot the blue curve, that's the difference between the two,
Let me shrink things down so they fit on the screen.
So, the blue curve is the difference between the purple and the green curves, it is how far apart
these two trajectories are, these two orbits are, as a function of time.
The difference starts off small, initially just 0.01, and it remains small, has a few little bumps,
but around 5 the difference spikes up.
It's actually greater than 0.25, it looks. And then the difference wiggles around.
Sometimes it's positive, that means that purple is larger than green, sometimes is negative,
that means that green is larger than purple. But the main thing is that it starts small, and then becomes
large, either positive or negative, quite quickly.
So, to make this example a little bit more concrete, let's go back to thinking about the logistic equation
as the model for population of rabbits on some island.
And let's imagine that the true population of rabbits on this island is 0.2.
Remember that just means that it's 20% of the way to the apocalypse number, the annihilation number.
And let's imagine, moreover, that the only thing that determines the future of the rabbits
is the logistic equation.
Again, nobody thinks that the logistic equation really controls real rabbit populations,
but, let's just, as a thought experiment, suppose that was the case.
And so, then, the first initial condition, I can interpret that as the reality, what's actually happening,
and what will happen. And the second initial condition,
I will think of that as a measured value. So maybe we send some folks to this island, and they count
all the rabbits, it's not easy to do, and they get a value of 0.21
expressed as a fraction of the annihilation population.
So, this rabbit research team has overcounted the rabbits by a little bit, totally understandable,
rabbits kinda all look alike, they hop around, they have counted some of them a couple of times
instead of just once. No big deal.
So, let's see, so now in this scenario, the first initial condition which is purple, it is the reality,
what actually happens on this island, this very simple island, and the green curve is our prediction.
And we've measured pretty well, we know the rule exactly that determines the rabbit behavior
so, the first couple of years our prediction is pretty good, but then the prediction gets bad here,
even worse by year five, by year five we drastically underestimate the number of rabbits.
Int his context, the blue curve can be thought of as prediction error.
It's the difference between the actual behavior of the rabbits and our predicted behavior of the rabbits
based on the initial condition that we measured.
So, at this point I might ask: this is kinda disappointing, how can we predict the rabbits better?
We would like to be able to say, with more certainty,
what they are doing past 5 or 6 years, or generations, or whatever.
And so, since we know the rule that determines them exactly,
the thing we need to know in order to do better prediction, is to measure the number of rabbits
more accurately. So, we send the team back and we say, alright,
be really really careful this time. We need as precise a measurement of the rabbits
as possible, as close to the true value as possible.
And let's say, let's just imagine, that they come really really close.
So, rather than, they don't quite get 0.2 exactly, they get 0.2000001. I'll put one more zero there.
So there we have, then, a couple of parts in a million.
So, it's easy to just enter those numbers in the computer, but in reality doing a measurement
that accurate is almost impossible, certainly I think,
for any population it's impossible to census to one part in a million. Probably even for people,
most certainly for rabbits. And it's hard to measure things this accurately
even in a physics, or chemistry lab. It's possible, but it's not an easy thing.
OK, so our measurement now is about a million times more accurate.
So, shortly, we'll have better predictions, the predictions that we'll be able to make with
this initial condition in the model will be better.
So, let's see if that's indeed the case.
So I'll click on 'Make the time series plot'
and indeed, the two curves are right on top of each other.
The green curve covers up the purple curve, for quite some time.
We can go, maybe all the way out to almost 20, let's say.
By the time we get to 20, the two curves start to become, to look quite different.
So, our prediction is great for about 18 to 20 generations, but breaks down as wrong after that.
Let me plot a few more iterations, I'll go until 40, see what that looks like.
So, the prediction is great, the green prediction is right on top of purple reality
until about year 20, in which case the two curves, prediction and reality, diverge and appear completely
unrelated to each other. Let's look at the blue plot for this.
So, the blue plot is the prediction error. It's the difference between the two curves,
it's the difference between our prediction and the reality.
So, the difference is very very small, it's near zero, and then around 16 or 17 it starts to grow
just a little bit. And then it explodes near 19, 20, 21,
and becomes very large, and we have huge error.
So, this is a way to visualize the phenomena of sensitive dependence on initial conditions,
often abbreviated as SDIC. This is also known as the butterfly effect.
The idea is that very small differences in initial conditions,
here about one part, a couple of parts in a million, getting magnified and then becomes very large.
So, the blue curve starts at 0 and becomes large, or non-zero, positive or negative,
The blue (green) and purple curves start right at each other, and they spread apart.
The logistic equation is deterministic. It's just an iterated function, an action repeated
again and again and again. So, it ought to be completely predictable.
And, in some sort of sense, it really is. However, in order to make accurate predictions,
one needs an exceedingly accurate value for the initial condition.
So a small error, again as we've seen, a small error, just a difference,
a tiny tiny difference becomes very very large very quickly.
So, it's not the case that it's unpredictable at all, but because it has this property of
sensitive dependence on initial conditions, the starting point matters so much it's...
for all practical purposes, impossible to do long term predictions.
Here's another way to perhaps think about this. Let me go back for a moment to this example.
So, here 0.2 and 0.21. And the prediction that we are able to do here is
out until, well, prediction doesn't last very long; let's be generous and say it lasts for
4 time steps, to the fourth iterate. And after that, the prediction is so bad as to be
completely useless. Actually that sort of sounds like a weather forecast,
not coincidentally. In any event, we can predict out 4 timesteps,
4 days, let's say, or 4 generations. So, if we measure more accurately, we should
be able to make better predictions. And, indeed, that's the case.
So I will go back to this
So, now, I will measure more accurately and we can go out to, again, just for the sake of our --
let's say we can go to 20. And after 20 timesteps, the measurements,
the prediction becomes essentially worthless.
So, on the one hand, yes, more accurate measurements do lead to more accurate
and longer term predictions. However, in order to improve our prediction time
by a factor of only 5 we had to improve our measurement by a factor of a million.
So, we have to work a million times as hard to get a result that is only five times better.
So, yes, it's predictable, but the amount of work we have to do to predict is actually,
increases exponentially with how long we want to do the predictions for.
So, this is another way of seeing or thinking about sensitive dependence on initial conditions.
I'll do another example, or talk through another scenario and then I'll define
sensitive dependence on initial conditions more carefully.
Subtitles by the Amara.org community
-------------------------------------------
Dynamical Systems And Chaos: The Butterfly Effect Part 1 - Duration: 8:06.
In the quiz from the previous section we should have found something kinda weird when r equals 4.
The orbits don't settle in to a periodic cycle, they do something different.
They continue to behave irregularly and, in fact, there is no period at all.
As you probably guessed, this is chaos.
You've seen our first example of a chaotic dynamical system.
So, we have lots to talk about in the next several lectures.
I will be able to define what chaos is, and also what sensitive dependence on initial conditions is,
also known as the butterfly effect.
We'll start by looking more closely at the orbits of the logistic equation when r equals 4.
So, let's look at orbits for the logistic equation when r equals 4.0.
So, I'll change this to 4.0 and let's make the time series plot
and here is what we see;
we can see that the orbit bounces around, gets very close to the apocalypse, or annihilation population
here crashes then grows, and then jumps around again,
and it looks another crash was happening here
but the key thing to note is that we are not seeing any periodic behavior
for hints of it there are some regularities,
a pattern repeats this crash, a growing pattern repeats a little bit
but it never repeats exactly.
Let's look at this for a larger number of iterates
here you see it again, continues to jump around,
it looks like it almost gets stuck here around 0.75, but not exactly
then, again, we see these big falls when it gets close to the apocalypse value
and we can look down on this table of numbers, and perhaps you can look for numbers,
maybe when you did the quiz you looked for numbers that repeat
but you'll keep seeing new numbers, this keeps cycling around
Let's do one more thing, let's try plotting a thousand iterates.
This will look like one big purple blob.
There it is.
And, I guess, the main thing again to know is that we are not seeing
any sort of periodic or regular behavior emerge
if, say, we get back to 3.2, or 3.1, that was an example we studied, that was a periodic value,
you look at the time series plot there, we can see some regularity.
It's a little hard to see, but it's bounding back and forth between these two values.
Whereas if I go to 4, it keeps bounding around.
I think this will go up to 10 thousand... It takes a second to think
It's calculating, it's plotting
Still thinking, still thinking
I am really stressing my computer up by doing this, I feel bad
Now it's getting stressed again
OK, there it is. That was a long time to wait for a big purple rectangle.
So, this is 10 thousand iterates of the logistic equation, it keeps on bouncing around
let me jump all the way down to the bottom of the screen
there it is. The number still haven't hit any sort of cycle
and we keep seeing new numbers all the time.
So we say that this behavior, rather than being periodic, is aperiodic:
The orbit does not repeat.
So, let's summarize the behavior of the logistic equation for r equals 4.0
like we did for other r values.
The difference is that, for this r value, we find that the orbit is aperiodic. It does not possess a period.
The orbit does not repeat, it keeps cycling around irregularly.
So, I have a puzzle: How can we represent that, on a final state diagram?
So, here is the unit (--), the population is always between 0 and 1, remember 1 is the apocalipse
or annihilation population, and 0 is zero.
So, what are the final states for this?
Well, if we iterate it for, say, 10.000 times and then watched it for another 10.000,
we will continue to see the population, which you can think of as a dot on this line, bouncing around.
So, another way to think of this is, iterate for 10.000
and then put a next 10.000, open up a camera for a long exposure photograph as the dot bounces around
and we would see that the dots would fill up this line,
just like in the previous image the purple dots filled up the rectangle
so, it would look something like this
So, there will be so many dots here that they would fill out the entire line, so it would look like a solid line
of these dots. So, the final states is not just 2, or 4 dots because it is periodic, the final states would be
this entire line, because it is aperiodic, and orbit wanders from
very close to 0 to almost 1. So, there is one more thing I should mention before
I am overcome by fumes from this sharpie.
And that is, a little bit about this claim of mine that the orbit is aperiodic
So, this is a result from mathematics that is proven exactly and rigorously for the logistic equation when r equals 4.0
doing so is beyond the scope of this course and requires a good bit of mathematics
it is a standard part of most junior level courses on chaos, or dynamical systems
So, I'm sorry I can't do this proof here, but it is important to mention so that one understands
that this claim is rigorously established.
It is not just a computer result or an experimental result.
It is something one can prove, or deduce, from first principles.
So, this orbit really is aperiodic. There is an infinite number of numbers between
0 and 1, an uncountably infinite number in fact.
And, if you iterate this forever, you will never see the same number twice.
You'll keep seeing new numbers as the orbit moves around.
I think aperiodic behavior in the logistic equation is a somewhat surprising and interesting result.
We make the orbits by iterating a function. We are doing the same thing over and over again.
It is a very repetitious process
But the result is not repetitious at all: it is an orbit that is aperiodic, it never repeats.
So, it's interesting to me, that this very orderly unchanging process produces behavior that
looks so irregular. Moreover, we'll see that the orbits produced by the logistic equation are
in a sense unpredictable. They have the butterfly effect, or sensitive dependence on initial conditions.
And, in a sense, we can even say that the orbits produced by this simple deterministic function are randomness.
So, let's begin digging into these ideas by looking at how two different orbits for the logistic equation behave.
We'll do that in the next lecture.
-------------------------------------------
LUSH Valentine's Day Haul - Duration: 7:41.
Hello home welcome back to my channel if you're new here. My name is Mayra
Thank you guys so much for tuning and I make videos based on beauty health and lifestyle
Video comes out every Thursday for 7:00 p.m. Eastern Time
You can catch more of my day-to-day life up on my Instagram right over here. And here we go
So as you can see by the title of this video today in this video, we are celebrating Valentine's Day
Hence, the cute little red lip for the most part. I tend to keep my lips very nude
But I figured I'd spice things up for this video anyway
So I went to lush and decided I'd pick out some of their Valentine's Day collection. Well, I picked up almost all of them
There's a couple that I did it, but I'm just gonna go through them with you
It smells so good
in my home, I
Love it. So if you go onto their website if you want to order online
They have a section in pink where it says Valentine's Day
Just click that and it will show you all of their Valentine's Day collection
I think they have about eight bath bombs in total for the Valentine's Day stuff
And I think I got six. So I'm going to show you the six that I got some of them are really funny
So the first one I'm going to show you is this unicorn horn. How cute is that?
It's really sparkly - like iridescent and it smells amazing
it's a lot of lavender oil in here and I'm looking at the website and it says that this one is rebalancing and
Calming the next one. I'm going to be showing you and yeah, they actually did this is an eggplant
but look at how cute so if you know about the whole eggplant emoji then you know,
Otherwise you can go and look that up yourself because I'm not going to explain it on here. This one is a bergamot oil
Oh my gosh
It's crumbling on Pournami and the website says it adds shine cleansing and an uplifting fragrance
Which is pretty funny as well. I mean considering it's an eggplant
Another bath bomb that I got. Is this beautiful peach?
Also a little bit of iridescent to it. It smells amazing
It actually does smell like peaches and this one is for cleansing and refreshing that is a really really big bomb
I thought
most of their bath moms are crazy big so you can
Cut them in half save the second portion of it and then use it for next time
I actually have not used any of these before so I'm really excited
Especially with the old theme with Valentine's Day. I think they do a really good job with all of their themes
I know for Halloween, they had when Islam and the stuff was really dope. Hey, this next one is the Love Boat. How cute
with a little heart
Again, all of these smells are so amazing. This is with rose oil, which you can definitely smell the rose
So it says on the site that this one's really fragrant. It's soothing and balancing and here we're not done
I still got more bath bombs. This next one is open your heart bubble bar
It is super sparkly. Oh
It's like oranges let me see what the site says. So it's a Brazilian orange oil again
It's fragrant uplifting and cleansing this smells
This smells like gum. I can't figure out which one from like when I was a kid and like banana medicine
I don't know but it smells so good. It reminds me of some gum
I used to choose a shoe when I was a kid. It's not hubba bubba. It's like juicy fruit me me
I believe for the Valentine's Day collection. They also had like a rose balm that smells really good
But I already had purchased so much that I was like, oh my god. I can't do any more back moms
And then there's another one that looks like a coin and it's called love token
Yeah, it's called love token. And it's all like this gold. It's in the shape of a point. It's all gold like that
I really should have got it
anyways
I was looking at the site and that one is a gardenia
Extract and then they have one more bath bomb for the Valentine's Day collection and that's called the six
There's one that's either blue and yellow or green and yellow and then pink and yellow
So yeah, as you can see I pretty much got all of them except for two
That's bad. That's a lot of bad and I'm not really a bad person
But lately I've been like killing it with the bath bombs
Anyways, those are always a lot of fun and they're great gift ideas for a girlfriend or just your girls
You don't have to be in a relationship to celebrate Valentine's Day. You can get together with your girlfriends go for drinks
Give each other little bath bomb gifts. I think that that's a good. Yeah, I would love to receive gifts like that
So they also have a boxes they're kind of like this, but it's more decorative
Well, you can choose your own bath bombs and put them in the box
Or they have some that are set and I think those go up to like $50
So for this holiday, they do also have a lot of body scrubs
There was a cute one that I saw with like a little island with a little I think it was a time on it
That's not really good and then they also have a lot of body conditioners
There's one that I really wanted to get called American Pie the girl that was helping me out
There was like I can put one aside for you and give you like a little tester that you can take home with you
So it's exactly what she did she gave it to me in this little thing
The smell of this is amazing. So when you're in the shower you use your soul P
lather up this you put after all over your body and then you can rinse it off but it still stays on your skin like
A moisturizer and you don't need to put anything on after you come out of the shower
So I thought that that was really cool. I am a Body Lotion girl. I always put lotion on after the shower
It's just the way I was raised and especially in Canada
You kind of have to or the minute you bend over or a stretch out your arm. It's like crack quite quite quite quick
I know that this has to be used in the shower, but I'm just gonna put the limb right now
Anyways, it's a protective moisturiser. Oh, and it feels exactly like that
It protects you from the cold because it is so rich and moisturizing
And it's like a vanilla strawberry scent and last but not least. I got a shower
Gel, and this is the American cream and this is the naked shower
Gel and by making I mean it doesn't come in any plastic packaging. It doesn't come in the bottle
It's shaped like a bottle, but it's just the whole solid product
so the reason why they're doing this is because
If you've watched a lot of documentaries or you spend a lot of time on Instagram or social media
Then you've seen those plastic waste videos everywhere. So I guess this is a way of lush doing their part
They are now selling a few products that have the bottle like plastic packaging and then this is the naked line
No packaging just the product solid. So this one is strawberry. It's fresh strawberry juice
It's calming and adds shine and it's antioxidant rich
so the girl app is helping me out inside of the lush store was telling
Not to worry about the product because when you see it in a bottle, you're like, yeah
You just use that little bit and then that's it. It stays in the bottle
But when you see it something that's naked like this like the naked brand with no
Packaging you're kind of like, but if I leave that in my shower
So much of it is gonna go to waste and she was telling me that this one actually
Lasts a lot more than the other one
It's because you simply just rub it on your body and then distribute the rest of it as needed
Whereas with the bottle you can squeeze out so much and then that's it
I feel like I'm just gonna put it in a glass container
Just to save it and keep it out of the shower unless I'm using it. I seriously love lush products
I mean I got these last week. I don't know how I haven't dipped into it
I was waiting to film this video in order for me to start using them
I'm sure they'll be gone by next week because I'm obsessed and I cannot wait to try these out
So yeah, and really hope that you guys enjoyed this video
Don't forget to Like share and subscribe right over here and I'll see you guys at the next one
-------------------------------------------
Top 10 Scary Minions Theories - Duration: 11:36.
Hello and welcome back to the most amazing Top 10 Channel on the internet, I am your
host Rebecca Felgate and today we are talking about the Top 10 Scary Minions!
That is right!
Minions!
I went on the minion ride once at Universal and got to experience the whole thing as a
minion which was cool…
I feel like I was inside their mind for a short while….
And what a mind!
Before we get into this video, let me know who your favourite minion or despicable me
character is… mine is of course Gru.
LIKE SHARE.
COMMENTS AT END…..
10 - Minions and the Illuminati Despicable Me is a metaphor for the New World
Order – so says a forum on good old David Icke's Website.
You know David Icke, the guy why came up with the reptilian humanoid theory?
The one about the Babylonian Brotherhood?
Anyway, his fans and fellow conspiracists have concluded Despicable me is all about
dat sweet sweet illuminati takeover.
Firstly the colours of the lettering on Despicable Me are quote un quote luciferian black and
red.
Gru gets a loan from the bank – a reference to the federal reserves ties with the illuminati
and….
Well….
A lot of minions only have one eye.
ONE EYE PEOPLE!
It's a sign!
It's a trap!
It's the illuminati confirmed!
Wait, is that a pyramid they are working on here…….
Suddenly it ALL MAKES SENSE.
9 - Minions Expose The Moon Landing as Fake This theory goes that minions know far more
than they are letting on and that they're trying to tell us something through the movies.
The minions movie is set in 1968, one year before the Moon Landing.
Eagle eyed viewers will have noticed the scene in Minions where they walk across the moon
as two astronauts are planting the American flag, only for the camera to pan out and for
us to realize they are walking across the set of a moon …. are the Minions trying
to tell us the moon landing was faked?
It certainly looks that way to me!
8 - Minions Can't Die The theory goes that Dr Nefario created indestructible
minions.
Youtuber the Theorizer created a video about the immortality of the Minions, saying they
were likely created under water in a process of cell splitting… basically, they're
lab grown.
By their names we assume they are all males… yes… we did just assume the minions gender..at
this point you are going to have to deal with it… so if they are all males they can't
procreate.
The only way new minions are created is if they are… well… created!
But their numbers keep increasing because they cant die.
Or so the theory says….
Think about it….
We see the minions tortured but they never look in any pain - are just stretched and
bent but seem to take it in good spirits.
On minion is seen in space without a space suit on, which for the rest of us would mean
certain death, but for our mate the minion its fine!
He is hit by a rocket and he is still fine!
When El Macho turns them evil he just makes them even more indestructible – which is
scary – something malicious and unkillable!
Minions definitely should never fall into the wrong hands.
I guess the question is – would they survive the apocalypse.
The answer is likely yes.
7 - Minions Are Smooth Like Ken Dolls I don't spend a lot of time thinking about
minion anatomy because…well… tiny evil replicants aren't my jam… but the good
people of reddit, well they are a different story.
We get a few cheeky flashes of minion bum in the movies – they photocopy their butts
and we see some minions nude on the beach.
We never see the front of them, though, which has led people to believe they are smooth
down there.
So….
If they have butts I guess they poop like us….
But as per the theory above they don't seem to procreate….so…well… they wouldn't
need bits would they.
6 - Being a North Korean is a bit Like Being a Minion
What does living in North Korea and being a minion have in common?
5 regime accepted haircuts, that's what.
North Korean Males have strict codes when it comes to their appearance.
They have to abide by what Kim Jong Un says is acceptable.
I wonder who approves the minions hair?
Here are the officially sanctioned male hair cuts in North Korea.
Here are the officially sanctioned minion hair cuts….
TAKE ME TO YOUR LEADER.
5 - Minions Did 9/11 I don't like this theory, I think it is
pretty tasteless, but none the less it became a meme and was circulated around the internet.
The reason this theory even exists in the first place is because we know minions support
the bad guy, the villain, and love a bit of destruction.
We don't know specifically what they were up to in the 2000s but the internet has attributed
the melting of steel beams to minions.
I think maybe the less said about this one the better.
4 - The Antarctica Theory Anyone else think it is weird that the Minions
emerge from voluntary exile in Antarctic in 1968 after over 100 years off the grid?
Well the theory is that this was scripted in in order to avoid linking the minions to
the Nazis.
Minions as we know love to back the villain, they love to back the bad guy and there was
very much one key bad guy during this period of history and that was Adolph Hitler.
Linking Minions to historical baddies was fine, but the creators of the Despicable me
franchise thought that linking them to the leader of the Third Reich was a step too far,
and let's be honest they were right.
Sooo… that is why that weird plot point exists….
THE ONLY THING IS THOUGH… some people think they were actually confirming that the minions
did work for Hitler becauseeee it seems Hitler went on a secret mission for oil in Antarctica
in 1938.
Who was farming that for him?
WAS IT MINIONS?
Actually maybe though.
Some also think he had a secret base in the icy region!
I wonder who could have been running things.
3 - Minions Inspired Were by Jewish Holocaust Child Prisoners.
This is the picture that sparked a sick and wild theory about the beloved kids characters.
The theory accompany the image was that minions were inspired by Jewish Children adopted by
Nazis for the sole purpose of using them in horrifying experiments, including poisonous
gas experiments.
The theory was perpetuated on Facebook and Twitter in 2015 ahead of the minions movie
– with a caption that read - [MINIONS]" was the name with which you called Jewish
children who were adopted by Nazi scientists TO EXPERIMENT WITH THE SAME CYCLON-B gas component
used in gas chambers.
It turns out that this conspiracy theory simply wasn't true and that actually the picture
is of trainee marines in the early 1900s.
Thank goodness… that would have been FAR too twisted.
2 - The White Walkers are OG Minions Look …. I am making this up because finding
ten was REALLY hard …and recently in the Cars theory list I gave you 11 so cut a honey
some slack… also… nobody said I couldn't make up my own theories.
SO… we know that Minions are from an ancient race who feel naturally inclined to support
the bad guy.
We also know that they all look pretty similar…annnd that humans can be turned into minions with
a special ray … because it happens at universal….soo…like… even though White Walkers, the minions of
the Night King, are depicted as undead blueish whiteish menaces….
Do they share a common ancestry with minions… okay… this one is weak… but like maybe
that is the twist we have all been waiting for?
1 - Minions are Actual Minions for the Devil If you are ever browsing Jesususisprecious.org,
which I am sure you all regularly do, you will notice that there are some poisonous
words written about the Despicable Me franchise.
One of my favourite articles… sure…articles… on the site is by one David J Stewart who
claims to be exposing the real motive of minions.
HE says….
Wait let me read a little quote….
He says: Satan is going after the children!!!
Have you ever heard about "the Devil and his minions?"
It's not a mere coincidence that the word "minions" was used.
The message taught by the minionscharacters are really bad for children.
Look at the promotion poster for Despicable Me 2, which reads at the top: "When the
World Needed a Hero, They Called a Villain."
Talk about the Antichrist.
The Illuminati are preparing the world's children to receive the coming SuperVillain, THE BEAST.
Satan is DESENSITIZING children to the idea of a villain being bad.
I could go on, but I don't want to spoil the gem of an article for you!
SO that was the Top 10 Scary Minions Theories…this was a hard one!
I feel like a good few solid theories but then not so many small ones…..
CHARACTER…..
LIKE SHARE.
Comments from scary frozen theories Agustin Bermudez Lopez said
Han reappeared as a statue at ferd mansion.
Wait a second could Fred family is connected to Han family or is it time travel.
Time travel can be so confusing.?
Superiorofturtles said: No joke but what type of people watch a movie and have the time
to make theories about it??
And here I am, watching movies and complementing on how good it was People with more time than
you……superior of turtles!
Kristina Karpf said: Rebecca thank goodness your back please don't leave?
Babeee I didn't go anywhere.
-------------------------------------------
Chợ Hoa Lớn Nhất Hóc Môn Sài Gòn Năm 2019 - Ẩm Thực Việt - Duration: 6:51.
For more infomation >> Chợ Hoa Lớn Nhất Hóc Môn Sài Gòn Năm 2019 - Ẩm Thực Việt - Duration: 6:51. -------------------------------------------
Tổ Quốc Gọi Tên Mình - Nguyễn Văn Diệu [NVD thuychinh] - Duration: 6:14.
For more infomation >> Tổ Quốc Gọi Tên Mình - Nguyễn Văn Diệu [NVD thuychinh] - Duration: 6:14. -------------------------------------------
Goyang Dayung OFFICIAL ~ Putri Zombie feat Vlog DhewaCintA - Duration: 23:50.
Vlog Putrie Zombie +Share &Subscribe welcome
-------------------------------------------
Dynamical Systems And Chaos: The Butterfly Effect Part 1 - Duration: 8:07.
In the quiz from the previous section we should have found something kinda weird when r equals 4.
The orbits don't settle in to a periodic cycle, they do something different.
They continue to behave irregularly and, in fact, there is no period at all.
As you probably guessed, this is chaos.
You've seen our first example of a chaotic dynamical system.
So, we have lots to talk about in the next several lectures.
I will be able to define what chaos is, and also what sensitive dependence on initial conditions is,
also known as the butterfly effect.
We'll start by looking more closely at the orbits of the logistic equation when r equals 4.
So, let's look at orbits for the logistic equation when r equals 4.0.
So, I'll change this to 4.0 and let's make the time series plot
and here is what we see;
we can see that the orbit bounces around, gets very close to the apocalypse, or annihilation population
here crashes then grows, and then jumps around again,
and it looks another crash was happening here
but the key thing to note is that we are not seeing any periodic behavior
for hints of it there are some regularities,
a pattern repeats this crash, a growing pattern repeats a little bit
but it never repeats exactly.
Let's look at this for a larger number of iterates
here you see it again, continues to jump around,
it looks like it almost gets stuck here around 0.75, but not exactly
then, again, we see these big falls when it gets close to the apocalypse value
and we can look down on this table of numbers, and perhaps you can look for numbers,
maybe when you did the quiz you looked for numbers that repeat
but you'll keep seeing new numbers, this keeps cycling around
Let's do one more thing, let's try plotting a thousand iterates.
This will look like one big purple blob.
There it is.
And, I guess, the main thing again to know is that we are not seeing
any sort of periodic or regular behavior emerge
if, say, we get back to 3.2, or 3.1, that was an example we studied, that was a periodic value,
you look at the time series plot there, we can see some regularity.
It's a little hard to see, but it's bounding back and forth between these two values.
Whereas if I go to 4, it keeps bounding around.
I think this will go up to 10 thousand... It takes a second to think
It's calculating, it's plotting
Still thinking, still thinking
I am really stressing my computer up by doing this, I feel bad
Now it's getting stressed again
OK, there it is. That was a long time to wait for a big purple rectangle.
So, this is 10 thousand iterates of the logistic equation, it keeps on bouncing around
let me jump all the way down to the bottom of the screen
there it is. The number still haven't hit any sort of cycle
and we keep seeing new numbers all the time.
So we say that this behavior, rather than being periodic, is aperiodic:
The orbit does not repeat.
So, let's summarize the behavior of the logistic equation for r equals 4.0
like we did for other r values.
The difference is that, for this r value, we find that the orbit is aperiodic. It does not possess a period.
The orbit does not repeat, it keeps cycling around irregularly.
So, I have a puzzle: How can we represent that, on a final state diagram?
So, here is the unit (--), the population is always between 0 and 1, remember 1 is the apocalipse
or annihilation population, and 0 is zero.
So, what are the final states for this?
Well, if we iterate it for, say, 10.000 times and then watched it for another 10.000,
we will continue to see the population, which you can think of as a dot on this line, bouncing around.
So, another way to think of this is, iterate for 10.000
and then put a next 10.000, open up a camera for a long exposure photograph as the dot bounces around
and we would see that the dots would fill up this line,
just like in the previous image the purple dots filled up the rectangle
so, it would look something like this
So, there will be so many dots here that they would fill out the entire line, so it would look like a solid line
of these dots. So, the final states is not just 2, or 4 dots because it is periodic, the final states would be
this entire line, because it is aperiodic, and orbit wanders from
very close to 0 to almost 1. So, there is one more thing I should mention before
I am overcome by fumes from this sharpie.
And that is, a little bit about this claim of mine that the orbit is aperiodic
So, this is a result from mathematics that is proven exactly and rigorously for the logistic equation when r equals 4.0
doing so is beyond the scope of this course and requires a good bit of mathematics
it is a standard part of most junior level courses on chaos, or dynamical systems
So, I'm sorry I can't do this proof here, but it is important to mention so that one understands
that this claim is rigorously established.
It is not just a computer result or an experimental result.
It is something one can prove, or deduce, from first principles.
So, this orbit really is aperiodic. There is an infinite number of numbers between
0 and 1, an uncountably infinite number in fact.
And, if you iterate this forever, you will never see the same number twice.
You'll keep seeing new numbers as the orbit moves around.
I think aperiodic behavior in the logistic equation is a somewhat surprising and interesting result.
We make the orbits by iterating a function. We are doing the same thing over and over again.
It is a very repetitious process
But the result is not repetitious at all: it is an orbit that is aperiodic, it never repeats.
So, it's interesting to me, that this very orderly unchanging process produces behavior that
looks so irregular. Moreover, we'll see that the orbits produced by the logistic equation are
in a sense unpredictable. They have the butterfly effect, or sensitive dependence on initial conditions.
And, in a sense, we can even say that the orbits produced by this simple deterministic function are randomness.
So, let's begin digging into these ideas by looking at how two different orbits for the logistic equation behave.
We'll do that in the next lecture.
-------------------------------------------
S. Korean troops now allowed to leave base twice a month for up to 4 hours - Duration: 0:51.
now great news for soldiers here in South Korea because starting today they
will be allowed to leave base after finishing their daily duties the Defense
Ministry says leaves will be granted twice a month for up to four hours a day
soldiers can go on leave at 5:30 p.m. but must return by 9:30 p.m. for roll
call while off-base they can do more or less
anything they like as long as it doesn't violate the military's strict code of
conduct however the ministry says no more than
35% of troops at a single base should be away at once it added that the new
regulations are being introduced as this system ran smoothly during a trial run
in late August of last year
-------------------------------------------
At least 8 dead in U.S. Midwest deep freeze - Duration: 0:38.
a deadly arctic cold snap that is sweeping through the United States
Midwest has now claimed the lives of at least eight people temperatures are
still lingering between minus 20 and minus 30 degrees Celsius in most parts
with the windchill making it feel more like minus 50 most services and
operations have grinded to a halt in the region including transport and schools
as well as power lines and water pipes freezing over several states have also
declared states of emergency the deep freeze is expected to last for another
day or two before starting to warm up but just slightly
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Trump wants "big deal" with China or he will "postpone" it - Duration: 1:39.
so amid the ongoing trade talks between the US and China in Washington President
Trump has waded in he's saying that he would either strike a very big trade
deal with China or simply postpone it was the word he used for more on this
and other news from around the world let's turn to our know Adam so Adam just
fill us in on the latest piece well mark president Trump has signaled that trade
talks in Washington are going well but he did say the US will not reach any
final trade agreement with China until he sits down again with the president's
is inked ping I think that probably the final deal will be made of it's made
will be made between myself and president chief he also said any deal
made with China would be a big one but added he is willing and to wait for that
to happen a very big deal or it's gonna be a deal that will just postpone for a
little while when asked if he was willing to delay the March 2nd deadline
on imposing tariffs on Chinese imports Trump said he didn't know the president
was MIT was to meet the Chinese trade delegation later Thursday which includes
Beijing's Vice Premier knew her expectations of the world's two biggest
economies reaching any comprehensive deal over the next month on low the US
is essentially demanding China to lowers its economic aspirations and claiming it
is stealing American intellectual property Beijing vehemently denies the
allegations and is unlikely to easily give in to Washington's demands
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Third foot-and-mouth disease case confirmed at cow farm in Chungju - Duration: 0:44.
a third case a foot-and-mouth disease was confirmed on Thursday in
chungcheongbuk-do province where 11 cows were reportedly showing symptoms of the
highly contagious disease the latest case is the first detected outside of
gyeonggi-do province the South Korean government imposed a 48-hour nationwide
ban on animal movement as of 6 p.m. Korea time Thursday in light of the
outbreak the ban will restrict the movement of livestock including pigs and
cows as well as vehicles that carry animal feed the government will release
a statement this morning or measures to prevent the further spread of the
disease
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TAPETES DE BARBANTE PARA SALA FACIL - Duration: 0:55.
For more infomation >> TAPETES DE BARBANTE PARA SALA FACIL - Duration: 0:55. -------------------------------------------
Hello my old Heart | 24 hour warriors MAP - Part 15 - Duration: 0:38.
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