What is a Fourier Series? (Explained by drawing circles) - Smarter Every Day 205

Holy cow, Destin how are you today?

blue brown already explained this long before this video

Paint the Mona Lisa using the Fourier series ;)

Really cool what we can do with fourier :) this is one of the most beautiful structures in science.. thanks for show us different point of view :)

Visualization should be made compulsory before making the undergrads into Maths

uhm so wouldn't that challenge be pretty easy if it was just recursivelydone? That is taking the lines of the image and then simply recursively assigning the mathematical functions?

I sat GIF not Jiff like the peanut butter

Is this like when an electron's linear and angular momentum add up?

I'm from the UK - and I've said 'GIF' (not JIF) for 40 plus years. No one has ever corrected me!

Anytime I'm on a boat I take a picture of the water and Fourier transform it. Fourier transform everything!

Did you really open an academic explanation with "wuddup?"

Just like how he said in the video, “GIF” is pronounced “GIF” and NOT like “GIF”. Argument over.

Fourier mathematics LITERALLY is how the mind (all minds in existence) defined as e^iπ+1=0, project physical reality and it explains how you are able to create matter in your sleep when you dream alone.

-Step One: Nothingness
Our first task is to rationally define “nothing at all”. Only then can we start
to define what “something” is.
“Nothing at all” has no properties of any kind. It has no mass, energy,
speed, extension, dimensionality, location density, weight, colour, smell,
taste, sound, appearance, qualia, consciousness, unconsciousness, or
anything else. Is there anything helpful we can utilise that meets this
definition? There’s only one possible answer: the static mathematical point.
This is “nothing”, “zero”, void, blankness, emptiness. It is nothing and it
does nothing. It has no effects, no consequences. It’s as if it’s not there at
all, and indeed, it isn’t there at all. This is pure zero, abstract zero, unreal
zero, non-ontological zero.
If we can have one nothingness, i.e. one mathematical point, we can have
an infinite number. Nothing can prevent nothing. Where one static point is
possible, infinite static points are possible. But all we are doing is
multiplying nothing. We are merely creating infinite nothingness.
This is the ground state of “reality”. Anyone who wants to explain the
reality we observe must explain why there is more than just this infinite
nothingness. What sufficient reason is there for more than simple nothing?
Leibniz famously asked why there is something rather than nothing.
Mathematically, this equates to asking what could be legitimately, rationally
added to nothing at all, without violating the principle of sufficient reason,
i.e. without creating an arbitrary add on to nothing that we could never
justify.
If nothing is the ground state of reality then anything we add to nothing
cannot violate this ground state, i.e. whatever we add must itself be some
version of nothing at all, while of course not being nothing at all (because
then we could never have “something”)

-Only one thing can be added to static points without defying the principle
of sufficient reason. That thing is motion. If “nothing” = non-existence =
static mathematical points, then “something” = existence = moving
mathematical points. Existence, in other words, is rational, mathematical
motion (🜀).
But why should a mathematical point move? The answer, naturally, is the
principle of sufficient reason itself. If it is possible for a point to move, and
there is no sufficient reason for it not to move, then it must move. The only
thing that would stop a point from moving is if it violated the zero ground
state of the universe.
The principle of sufficient reason does not allow any particular state to be
arbitrarily privileged over any other state that satisfies exactly the same
conditions. Thus, there is no sufficient reason for a static universe of
absolute nothingness if a dynamic universe of somethingness can just as
readily satisfy exactly the same requirement for the universe never to
exceed a ground state energy of precisely zero forever.
There is nothing special about absolute nothingness. It is no more
fundamental than any other state that necessarily obeys the compulsory
ground state energy of zero of the universe.
Every state that satisfies the ground state energy of the universe will and
must exist since there is nothing to prevent it. Moreover it will exist
necessarily and eternally. Every such state is part of the permanent fibre and
fabric of existence. This is the framework of the universe, the inherent
superstructure and substructure. Everything hangs on this. It fills up
existence. There are no gaps at all.
In Leibniz’s system, true substances were “metaphysical” points which,
so Leibniz said, were both real and exact, while physical points were real
but not exact, and mathematical points were exact but not real.
In modern ontological mathematics, static mathematical points are exact
but unreal, while moving mathematical points serve as the basis for both
metaphysical points (concerned with minds) and physical points (concerned
with matter).
===
Ontological Mathematics: How to create the universe. By Mike Hockney.

Great vid but Thais visualisation is Stolen Form 3Blue1Brown

wow !!! marvelous

Tum mera itna prachar mat karo pls my humble request to you

afferim lan. gurur duyulası.

Finally
The video that helps me understand the explanation given by 3Blue1Brown 😂

I learnt Fourier series in 1st semester of my engineering it’s my 2nd semester now and now I finally understand why we did Fourier series.

Love this ... just finished a master's degree and had some of this math in a "controls course" ... this is your best video ever. greetings from Switzerland. Hats off to Doga and your video channel. Daniel

thats hax gimme hacx

This is really awesome!!!

Well done, both of you.

what it sound like

that is nice

Wow, that flip books is creative next level.
You were the first one to come with the idea of geogebra haha

hard G on Gif, i assume he was trolling tho.

Jif is peanut butter

wiper play important role in making different unique waves in electronics
and communication

THE FACE HE MADE when you quoted Steve Wilhite's "it's pronounced Jif" hahahahahaa

In digital signal processing you can add them up in ONE clock cycle.

Probably a really dumb question, so if it's just 'wipers' attached to 'wipers' in a circular motion why do the wipers create a square wave in the 1st illustration and a saw tooth on the 2nd illustration? anybody that can explain please?

Pendulums are not sinusoidal motion. They deviate more and more as the amplitude increases.

soo... we are just functions of functions of circles or rotations of particle waves

Impressing my lawyer girlfriend spitting out the forrier series

Seeing the circles makes the logo reminded me of the cogs of an automaton for the victorian era!

Idk how accurate it is but someone made a cover of a video music using fourier series.. its bad apple

protein folding

It's pronounced GIF!!

Great !

Apply this to Quantum Gravity.

Dude Dude Dude !!!!!!!!!!!!! That is great !!!!!!

BTW: gif with a G ! LOL !

What breaks my brain is how to derive those four functions!