For those who do not want to follow the beaten track, and want to follow the beat of a different drum, heres another very exciting path

Jose and Eugene Saletan, Classical Dynamics



I will say more about this later when I write about the Landau-Lifshitz pseudotensor and the Rosenfeld-Belifante pseudotensor

Landau and Lifshitz - Volume 1 Mechanics

V. I. Arnold has said that there are mistakes in Landau's mechanics. I am afraid I have to disagree. This is very difficult to understand. This book is far beyond perfect. It is the most immaculate conception.

A beautiful formula discovered by Feynman

Feynman discovered this formula using Hamiltonian mechanics

The wobbling rate of a top is twice the angular speed of rotation

$$ \dot{\phi} \simeq 2\omega $$

At the Pocono conference Niels Bohr was in attendance. Feynman made the mistake of trying to explain the path integral without showing any formulas. He thought that If he showed formulas they would not believe it.

Show a single formula Bohr said. I will understand. 

Today I was walking near the dust. I sat on the pavement and was thinking of a new formula, something new and interesting. I found this interesting expression

$- \left( \frac{2e^2}{3 \pi \hbar c^3} \right) $

I might say more about this later. For now,

$ \frac{e^2}{\hbar c} $

To understand this movie, watch the forest scene and the car scene at night.




Christ has rejected humanity

This is a very expensive painting by Vasari, that I sometimes hang in the room. I do not remember how I obtained it.

The road to hell is paved by good intentions

Please, don't ever forget this book

https://arxiv.org/abs/quant-ph/0608140

Even though he seemed like an experimental physicist, for some reason he always carries around a copy of Mukhanov's physical Foundations of cosmology

I looked at my Rolex. the time stopped at 9:02

Today I solved the 𝜏-θ puzzle

It is not actually possible for such a thing to exist. It must have been taken a long time ago.

Many times I have seen him carrying a black thin spiral notebook. 

I happen to know there is atleast one drawing in it.

A new chemical element that I discovered - Helio Bordeaux BL

 

One day at tifr-h, a boy came inside [somehow]

why don't you teach me physics
the boy asked

OK. I said.

$\epsilon_{\mu \nu} = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$


$\epsilon_{\mu \nu} \epsilon^{\nu \rho} = g^{\rho}_{ \ \mu}  $

Solving simple problems 4

A sequence $u_n$ is determined by the relations

$u_1 = \alpha + \beta$

$u_n = \alpha + \beta - \frac{\alpha \beta}{u_{n - 1}}$


Show that

$u_n = \frac{\alpha^{n+ 1} - \beta^{n + 1}}{\alpha^n - \beta^n}$

$ = \alpha^n + \beta^n $


solution

u_n = u_{n - 1} + 

$u_1 = \alpha + \beta$

$\alpha + \beta + \left( \alpha + \beta - \frac{\alpha \beta}{\alpha + \beta} \right) + \ ...$

$\alpha + \beta + ( \frac{    (\alpha + \beta)^2 - \alpha \beta    }{\alpha + \beta + \ ...}$

prize for proof

 $\int_M \ f^* \Omega = (deg f) \int_N  \Omega$

acceptable solution -

Whitney number $W(\gamma )$ is equal to either deg f  - 1   or  deg f + 1



"I would like to continue. question : what is a Hopf fibration?"

fiber $S^3$ - Hopf fibration

fun - 
what is a one sided surface?

Möbius strip in $\mathbb{R}^3$

Maryna Viazovska - New mathematicians of the 21st century

 

New

M-theory and a couple of other mathematical physicists were standing on a hill in Edinburgh, talking about modular lie algebras. Some people who were around put a question to M-theory - What do you think about loop quantum gravity? He said "isn't that just lattice gauge theory?"

they say that the 'calculus and sheaf theory' comment was also made here, but no one remembers clearly.

Dil Se

 

It is impossible to figure out this movie

but here's a hint:

555 timer

after a week of walking around tifr-h, I started reading a research monograph by Anastasios Mallios. these are new ideas that are worth looking at for a few nights.

this must never be forgotten.

..and he seemed to believe that, even though he was not.
i do know, but seem to think i cannot remember.

Something so exciting

Abel wrote a monumental work on elliptic functions which, however, was not discovered until after his death. When asked how he developed his mathematical abilities so rapidly, he replied "by studying the masters, not their pupils."


On this note, I did tell the strange people from youth that 90% of the arxiv is nonsense. Let me clarify, I read all kinds of papers. If you want to remember the comment that I only check Bousso and Douglas Stanford and so on, remember Abel's remark.

When I was young, one of the principles close to my heart: everyone except Einstein is a moron. This is probably exactly how Einstein thinks of it, but he might have changed his mind when he found out about Feynman.

I have decided not to buy anymore classic books

This is the last one

I also have a sufficient number of poetry books

What is an automorphic function?

it is a symbolic statement which does not have an answer

$\int {\log z} \  {}^{\square} = M$

$\int {\log z} \  {}^{\square} + f(M)^{\sim } + \ ... $

M is an automorphic function

The Sphere

 

The book is mine, but the movie is yours.

Math Tripos

If x, y, z are unequal, and if

$2d - 3y = \frac{(z - x)^2}{y} $

solution

The answer follows because

$\left( \frac{z}{y} \right)^2 = 1 + \frac{1}{2} + \frac{3}{2} + 1 + \ ... $

$x + y + z = \alpha$

$x = \frac{\alpha}{3}$

$y = 3x$

$z = 3\alpha + 5 + 2$

Solving simple problems 3 - Dieudonne 'Infinitesimal Calculus'

This is not really a simple problem, but still fun.

In the neighborhood of $+\infty$, the function $\frac{\sin x}{\sqrt{x}} + \frac{\sin^2 x}{x}$ has for generalized principal part the function $\frac{\sin x}{\sqrt x}$; but the integral $\int^{+\infty}_1 \frac{\sin t}{\sqrt t} \ dt$ is convergent whereas the integral $\int_{1}^{+\infty} \left( \frac{\sin t}{\sqrt t} + \frac{\sin^2 t}{t} \right) \ dt$ is not convergent.

Solution 

$\int_{1}^{+\infty} \left( \frac{\sin t}{\sqrt t} + \frac{\sin^2 t}{t} \right) \ dt < 0$

$\epsilon > \frac{1}{2} + 1$

$\delta = 1 + \frac{1}{2}$

$ \frac{\sin x}{\sqrt x} > \frac{1}{5} + \frac{1}{2} + 1$

 

volume of cylinder = $\frac{h^3}{1 + a}$

$$ \left( \frac{1}{a} \right)^n \int dr \ d\theta \ dh \ R(r, \theta, h) = n + \frac{1}{2} $$

the 'dimension' of a cylinder is $n = \frac{1}{2}$

How does Niels Bohr view Galois theory?

the profundity cannot be explained

fundamental theorem of algebra

$ (z - a_1)(z - a_2) ...  =  0$

root field

Sapna

This house is for you.

I will show you how to get there.

beyond the scary moor where i picked up a dagger

 

An ith from the moor

Message from Diablo

Do not keep more than 1 Jewel of Freedom in your account.    (Requirements -15%)

this is so far beyond understanding that if you look directly your eyes will fall out

 

I'd Be a Fearless leader - Rahul

https://youtu.be/KswddTB4j8A?list=RDKswddTB4j8A

 

Unknown property 'align-items'/ Declaration dropped.

parsing value   declaration dropped

I am sorry to say, but this book is mine

1960s

William S Burroughs

Hunter S Thomson

Kurt Vonnegut

https://thecrow1989.blogspot.com/

 

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diablo134

natalya_jyu                              new copy

192.168.0.105

red short sword

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The window was closed, and no one ever saw it being opened again.

Diablo rouge encampment to stony field

its perfect

(assassin)

Today I bought this painting.

I will not be buying anymore paintings.

hacked microsoft edge used during diablo hacking operation

 

Now something is about to happen.

Moon from terminator 79

Notes for 'Advanced General Relativity' (Warwick postgraduate course)

Pseudo-Riemannian space

element of a vector space V can be expanded in terms of a basis

For a vector bundle the basis of sections does not exist [probably no one will understand]

p-form valued sections

g_jk,l = Γ_jkl + Γ_kjl

g_ij are not observable like the potentials

g is a transverse wave

Fun - what is 'teleparalellism'?

exercise. GR two-body problem

solution to ‘teleparallelism’ exercise

acceptable solution

- parallel vectors at different points of space

full marks

- h is symmetric and rank n - 1

probably should not try to figure out in full detail

another acceptable solution

g^ij R_ij = R

what is the relationship between R and Λ

R is the Ricci scalar

It is not very difficult to understand the Einstein field equation, but writing them in a form in which they can be manipulated is very hard

How did Hilbert discover the field equations?

think before looking at the answer

g is the Lorentzian metric and $\delta g$ is any symmetric (0, 2)-tensor that vanishes outside a compact set. This allows us to define the variation of the action as 

so we have

we get

[ when Hilbert told Einstein about this, he explained to Hilbert what the christoffel symbols are ]

The power of the Jacobian under transformation is called the weight of the tensor (density)

In order to perform the variation of the action, we need a lagrangian which is a scalar

√g has weight -1

d⁴ x has weight 1

g^{μ ν} has weight -2

so, if

ℒ = - 1/16πG g^{μ ν} R_{μ ν}

(this is 16 instead of 8 because we did not include the speed of light)

-1/16πG ∫ d⁴x √g ( R_{μ ν}  - 1/2 R g_{μ ν} ) 𝛿g^{μ ν}

variation of  ∫ ( L - 1/2κ R ) √g d⁴ x = 0

gives the field equations

Hilbert misunderstood the meaning of integration by parts

what are the Bianchi identities?

you just say that the curl of R^i_{jklm} = 0

 Ich weiss es, widerspruchsfrei ist die Sache schon, aber sie enthalt meines ...

 

the beginning is the end

Sat Chit Anand

Eli vance is indespensable for deliberation

Eli vance is indispensable for deliveration

Eli vance is indespensable for deliveration

Far in the future,                             scrolling message board

displays  string theory transforms as an irreducible representation of Diff(S^1) '

 

something happened here a long long time ago

why does heat flow from hot to cold?

the explanation of the fact that heat flows from hot to cold involves the concept of fluctuations. fluctuations distinguish which particles to absorb energy from and which particles to reflect elastically

it fell from the tree

there were a few people remaining. walked up to the tree, behind which he disappeared. there under the tree was this item.

with a note:

write string theory in the margins

J. V. (P.G.) College, Baraut (Bhagpat) U.P.

persistent instance

non persistent instance - image irretrievable

The time was 1:13

no more, and never more. i shall not return . .