〈 Berger | Dillon 〉 @InertialObservr Twitter profile

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〈 Berger | Dillon 〉

4 years

On an elliptical pool table (with a pocket at one of the foci), you literally can't miss when shooting from the other focus

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Illusion of The Year 2019 Winner It's based on a simple Lissajous curve, but uses clever shading/highlighting to create a 'double-axis' illusion

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Robot that can balance a triple-pendulum

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〈 Berger | Dillon 〉

@InertialObservr

3 years

2010: failed out of college 2021: got my PhD in theoretical physics

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〈 Berger | Dillon 〉

@InertialObservr

4 years

index of refraction of liquid = index of refraction of container

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〈 Berger | Dillon 〉

@InertialObservr

4 years

The reason Pringles fit so nicely in a cylindrical tube is because they're hyperbolic paraboloids plotted over a circular domain

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〈 Berger | Dillon 〉

@InertialObservr

5 years

A straight line may be the shortest 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 between two points, but a "Brachistochrone" curve is the path of least time

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〈 Berger | Dillon 〉

@InertialObservr

5 years

Extremely creative Fourier Series animation

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〈 Berger | Dillon 〉

@InertialObservr

3 years

@amyis_trying @MikeBenchCapon my favorite is when people slap the label "conspiracy theory" on something that definitely has happened

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〈 Berger | Dillon 〉

@InertialObservr

4 years

@marrowing instead of saying "happy holidays" try replacing it with "fuck you idiot" See where that takes you. See how you like it.

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〈 Berger | Dillon 〉

@InertialObservr

4 years

A perfectly square grid (inspired by @DrGBuckingham )

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〈 Berger | Dillon 〉

@InertialObservr

5 years

Any time you pick up a well shuffled deck, you are almost certainly holding an arrangement of cards that has never before existed and will likely never exist again. - Yannay Khaikin

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〈 Berger | Dillon 〉

@InertialObservr

4 years

@marrowing Instead of calling someone "gorgeous", try replacing it with "ugly" See where that takes you. See how you like it.

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〈 Berger | Dillon 〉

@InertialObservr

5 years

the most beautiful equation in mathematics..

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〈 Berger | Dillon 〉

@InertialObservr

4 years

i appreciate the sentiment, but those are not exponential functions

Neil deGrasse Tyson

@neiltyson

4 years

I’m just sayin’

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〈 Berger | Dillon 〉

@InertialObservr

4 years

One of the simplest fluid models is the so-called Trochoidal Wave •It describes each water particle as tracing out a circle whose radius decreases exponentially with depth, & has each particle share the same rotation frequency

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〈 Berger | Dillon 〉

@InertialObservr

5 years

Neat demonstration of magnetic field lines

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Vertically oscillating points whose frequencies are their positions on the x-axis [ i.e. yᵢ = sin(xᵢ t) ]

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〈 Berger | Dillon 〉

@InertialObservr

5 years

the coolest demonstration of frame-rate matching i've ever seen..

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〈 Berger | Dillon 〉

@InertialObservr

4 years

(1) tuning fork vibrates (2) nearby air molecules vibrate (3) this causes other nearby air molecules to vibrate & so on.. (4) vibrating air wiggles other tuning fork (5) ball goes boop

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〈 Berger | Dillon 〉

@InertialObservr

3 years

you've heard of elf on a shelf, now get ready for

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〈 Berger | Dillon 〉

@InertialObservr

4 years

eⁱˣ = cos(x) + i sin(x)

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Coastline Fractal

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〈 Berger | Dillon 〉

@InertialObservr

5 years

Neat example of relative velocities and non-inertial reference frames (GoPro is attached to the hockey stick)

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Feeling stupid is the first part of learning

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〈 Berger | Dillon 〉

@InertialObservr

3 years

😃! = 😃😀🙂...😐😶

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〈 Berger | Dillon 〉

@InertialObservr

3 years

There are 2 methods for solving Partial Differential Equations: (1) Separation of variables (2) Give up

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〈 Berger | Dillon 〉

@InertialObservr

5 years

i joke, i joke..

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Introduction to Physicists' Notation

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〈 Berger | Dillon 〉

@InertialObservr

3 years

i have made the sunk-cost fallacy so many times it'd be a shame if i stopped now

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〈 Berger | Dillon 〉

@InertialObservr

3 years

my fall plans the delta variant

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〈 Berger | Dillon 〉

@InertialObservr

1 year

nah, we need to talk about this

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Faraday Waves are non-linear standing waves •When the container vertically vibrates above its 'critical' frequency, the instability forms standing waves on the initially flat surface

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〈 Berger | Dillon 〉

@InertialObservr

4 years

@SportsCenter

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〈 Berger | Dillon 〉

@InertialObservr

4 years

The Stepping Feet Illusion At first it appears that the 'feet' are stepping & out of sync, but the illusion disappears upon turning down the contrast

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〈 Berger | Dillon 〉

@InertialObservr

4 years

The fastest path between 2 points is along a brachistochrone

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Mathematicians be like ‘i know a place’ but don’t take u there just that the place exists

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〈 Berger | Dillon 〉

@InertialObservr

4 years

My greatest academic achievement

Pringles

@Pringles

4 years

We fixed it for you:

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〈 Berger | Dillon 〉

@InertialObservr

3 years

before getting a PhD i felt dumb.. & at the end of my PhD i still feel dumb, but like in a more advanced way

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〈 Berger | Dillon 〉

@InertialObservr

4 years

This guy stole my animation, posted it, and got 10k more likes .. without giving me a single ounce of credit

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〈 Berger | Dillon 〉

@InertialObservr

4 years

A ball sliding along a 'Lemniscate' curve takes the same time to arrive at a given point as a ball that takes the direct path

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〈 Berger | Dillon 〉

@InertialObservr

4 years

An Ellipse From Circles (inspired by @matthen2 )

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Simple harmonic motion

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Galactic simulations, with and without Dark Matter. Note the stark discrepancy in the rotation curves. No dark matter With dark matter

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Motion along straight lines only (3D)

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Absolutely Amazing Physicists (!) discover a new fundamental and amazing mathematical fact: You can get the Eigenvectors of a matrix using ONLY its Eigenvalues

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〈 Berger | Dillon 〉

@InertialObservr

4 years

bet i made you double-take

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〈 Berger | Dillon 〉

@InertialObservr

5 years

50 double pendulums, whose initial velocities differ only by 1 part in 1000

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〈 Berger | Dillon 〉

@InertialObservr

2 years

Now that computers have feelings i will no longer be able to, in good conscience, ask it to diagonalize a 35x35 matrix for me

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〈 Berger | Dillon 〉

@InertialObservr

3 years

yup, this checks out

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Every circle is the vector sum of two ellipses

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〈 Berger | Dillon 〉

@InertialObservr

3 years

Navier-Goats

Arieh Kovler

@ariehkovler

3 years

Drone photographer Lior Patel followed a herd of sheep for several months, as the herd was shepherded to its summer pasture. Entrancing and relaxing.

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〈 Berger | Dillon 〉

@InertialObservr

4 years

If electrons actually 'orbited' a nucleus, then no atoms could ever form The electron would radiate away all its energy and fall into the nucleus in about 10 𝑡𝑟𝑖𝑙𝑙𝑖𝑜𝑛𝑡𝘩𝑠 of a second

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Mathematics Crash Course For Physics: The Basics On my website are slides i made for Twitter covering: • Fourier Analysis • Function Spaces • Eigenfunctions & Differential Operators • Hermitian Operators • Group Theory & Physics

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〈 Berger | Dillon 〉

@InertialObservr

3 years

theorists in a lab:

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〈 Berger | Dillon 〉

@InertialObservr

4 years

The function x²ⁿ + y²ⁿ = 1 is the unit-circle for n=1, but approaches the unit-square as n→∞

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〈 Berger | Dillon 〉

@InertialObservr

5 years

doggo discovering Newton’s third law

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〈 Berger | Dillon 〉

@InertialObservr

2 years

you ever work all day on something and then realize you're stupid

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Just passed my PhD Advancement to Candidacy via Zoom. Feeling savage.

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〈 Berger | Dillon 〉

@InertialObservr

2 years

Math classes really are like "ok so if we use Euler's method to solve Euler's equation then, by making use of Euler's identity, we can then plug that into Euler's other equation and deduce that Euler's inequality holds so long as the coefficients are Eulerian numbers"

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〈 Berger | Dillon 〉

@InertialObservr

4 years

The curves traced out by the intersection of two lines rotating at different speeds

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〈 Berger | Dillon 〉

@InertialObservr

4 years

25 semi-circular slices whose rotation frequencies are equal to their radii

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〈 Berger | Dillon 〉

@InertialObservr

5 years

This is not a typo.

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〈 Berger | Dillon 〉

@InertialObservr

4 years

if i made a youtube tutorial on making animations in Mathematica, would you all watch it?

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〈 Berger | Dillon 〉

@InertialObservr

4 years

The less-bumpy the road, the rounder the wheel

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〈 Berger | Dillon 〉

@InertialObservr

4 years

dividing by 0 just to feel something

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〈 Berger | Dillon 〉

@InertialObservr

4 years

let's talk about PID stabilization 🔗

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〈 Berger | Dillon 〉

@InertialObservr

5 years

√2 raised to itself infinitely many times is 2

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〈 Berger | Dillon 〉

@InertialObservr

4 years

i feel the time is ripe for me to state my position on this matter: math was invented, not discovered

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〈 Berger | Dillon 〉

@InertialObservr

3 years

non-inertial reference frames are one hell of a drug

cardinal copium

@emotionalpedant

3 years

Jumping on a ship going over large waves

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〈 Berger | Dillon 〉

@InertialObservr

2 years

happy pi day (to scientists), and also happy pi month (to engineers)!

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〈 Berger | Dillon 〉

@InertialObservr

4 years

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〈 Berger | Dillon 〉

@InertialObservr

4 years

You actually 𝑐𝑎𝑛 integrate 1/x using the power rule (with a little help from l'Hôpital)

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〈 Berger | Dillon 〉

@InertialObservr

5 years

At 10k followers, i promised myself would say this so here we go.. My life story is long and complicated, so i'll keep it short and sweet. I'm 27 years old; i failed out of college when i was 19, and the first time i picked up a math/physics textbook was when i was 22.

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〈 Berger | Dillon 〉

@InertialObservr

5 years

41 triple pendulums with 𝑠𝑙𝑖𝑔𝘩𝑡𝑙𝑦 different initial conditions (source:)

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Visualizing the Fourier Series of a sawtooth wave as a "sea" of its Fourier components

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〈 Berger | Dillon 〉

@InertialObservr

5 years

Magician: Pick any number between 1 and 10, and I'll guess it Cantor: A real number? Magician: well, yea.. Cantor: You know what, let's put some money on this

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Electric field of a point charge oscillating between 0% and 80% the speed of light

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〈 Berger | Dillon 〉

@InertialObservr

4 years

if Einstein had a Twitter his comments would be full of people telling him to ‘stick to science’

Paul Halpern

@phalpern

4 years

'I will reside only in a land in which political freedom, tolerance, and equality for all citizens before the law are conserved' -Albert Einstein

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〈 Berger | Dillon 〉

@InertialObservr

5 years

f(z) = zᵐᵒᵘˢᵉ/(z - mouse)

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〈 Berger | Dillon 〉

@InertialObservr

3 years

Here's what a geometric series looks like with complex numbers

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〈 Berger | Dillon 〉

@InertialObservr

4 years

i think it's time to re-indoctrinate the youth

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Area of a Circle

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Pythagorean Theorem (Dudeney's method)

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〈 Berger | Dillon 〉

@InertialObservr

4 years

I mapped the Cosmic Microwave Background (CMB) back onto a sphere

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Did you know? I went to a 2-year community college before university. Now I’m getting my physics PhD.

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Lagrangian Mechanics is an elegant reformulation of Classical Mechanics. It's completely equivalent to Newton's Laws, but is often much simpler and is used constantly in every field of physics.

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〈 Berger | Dillon 〉

@InertialObservr

5 years

The Fine Structure Constant, a thread. (1/137)

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〈 Berger | Dillon 〉

@InertialObservr

4 years

The Physics of glasses 🤓 (far-sightedness)

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〈 Berger | Dillon 〉

@InertialObservr

4 years

CRT televisions operate by shooting electrons at the screen Magnetic fields deflect moving electrons, so placing a magnet near the CRT gives you this neat way to visualize the magnetic field lines

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〈 Berger | Dillon 〉

@InertialObservr

5 years

So, why did you become a mathematician? Mathematician: I don't like working with numbers

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〈 Berger | Dillon 〉

@InertialObservr

5 years

A straight line (y=x) can be written as a sum over sinusoids, known as a Fourier Series.

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〈 Berger | Dillon 〉

@InertialObservr

5 years

Uranium in a cloud chamber: observing the process of radiation emission & decay

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〈 Berger | Dillon 〉

@InertialObservr

5 years

f(z)=z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z^z

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〈 Berger | Dillon 〉

@InertialObservr

3 years

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Time Evolution of Hydrogen in Superposition of Energy Eigenstates (3,2,0 & 4,1,0 states) •The probability density of the electron's position oscillates in time when in a superposition of states of definite energy

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〈 Berger | Dillon 〉

@InertialObservr

4 years

@Gizmodo probably bc no one every asked how it was doing

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〈 Berger | Dillon 〉

@InertialObservr

4 years

Chaotic motion of a magnetic pendulum under the influence of gravity and 3 magnets •The colors indicate which magnet (red, green or blue) the pendulum ultimately ends up at

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