Draw Strumpfthing

christinetheastrophysicist: Feynman Diagrams are used to...

Sat, 28 Apr 2012 11:42:46 -0400

a) Quantum Electrodynamics

b) Quantum Chromodynamics

c) Neutral Weak Interactions

d) Charged Weak Interactions for Leptons

e) Charged Weak Interactions for Quarks

christinetheastrophysicist:

Feynman Diagrams are used to represent the fundamental forces by which elementary particles interact. In all interactions, time flows horizontally to the right.

a) Quantum Electrodynamics: An electron converts into an electron, with the emission of a photon (e → e + γ)

b) Quantum Chromodynamics: A quark converts into a quark, with the emission of a gluon (q → q + g)

c) Neutral Weak Interactions: Any lepton or quark converts into the corresponding lepton or quark, with the emission of a Z boson (f → f + Z)

d) Charged Weak Interactions for Leptons: A negative lepton converts into a corresponding neutrino, with the emission of a W^- boson (l^- → ν_l + W^-)

e) Charged Weak Interactions for Quarks: A quark with charge -1/3 converts into the corresponding quark with charge +2/3, with the emission of a W^- boson (q^-1/3 → q^+2/3 + W^-)

cab1729: what particle are you?

Thu, 26 Apr 2012 13:20:08 -0400

cab1729:

what particle are you?

contemplatingmadness: Thomae’s function, named after Carl...

Thu, 26 Apr 2012 13:12:29 -0400

contemplatingmadness:

Thomae’s function, named after Carl Johannes Thomae, also known as the popcorn function, the raindrop function, the countable cloud function, the modified Dirichlet function, the ruler function,^[1] the Riemann function or the Stars over Babylon (by John Horton Conway) is a modification of the Dirichlet function. This real-valued function f(x) is defined as follows:

If x = 0 we take q = 1. It is assumed here that gcd(p, q) = 1 and q > 0 so that the function is well-defined and non-negative.

Discontinuities

The popcorn function is perhaps the simplest example of a function with a complicated set of discontinuities: f is continuous at all irrational numbers and discontinuous at all rational numbers.

Informal Proof

Clearly, f is discontinuous at all rational numbers: since the irrationals are dense in the reals, for any rational x, no matter what ε we select, there is an irrational a even nearer to our x where f(a) = 0 (while f(x) is positive). In other words, f can never get “close” and “stay close” to any positive number because its domain is dense with zeroes.

To show continuity at the irrationals, assume without loss of generality that our ε is rational (for any irrational ε, we can choose a smaller rational ε and the proof is transitive). Since ε is rational, it can be expressed in lowest terms as a/b. We want to show that f(x) is continuous when x is irrational.

Note that f takes a maximum value of 1 at each whole integer, so we may limit our examination to the space between and . Since ε has a finite denominator of b, the only values for which f may return a value greater than ε are those with a reduced denominator no larger than b. There exist only a finite number of values between two integers with denominator no larger than b, so these can be exhaustively listed. Setting δ to be smaller than the nearest distance from x to one of these values guarantees every value within δ of x has f(x) < ε.

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Thu, 26 Apr 2012 02:54:56 -0400

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Thu, 26 Apr 2012 02:38:45 -0400

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Thu, 26 Apr 2012 02:31:51 -0400

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Thu, 26 Apr 2012 02:12:09 -0400

Here’s why this is amazing. e - approximately 2.61, is a...

Wed, 25 Apr 2012 23:40:44 -0400

Here’s why this is amazing.

e - approximately 2.61, is a number that is defined such that when the derivative of e^x is taken, the answer is e^x. It is used in compound interest for finance.

i - The imaginary number. Defined to be the square root of negative 1

pi - the ratio of a circles circumference and its diameter. Comes up in geometry and trigonometry as an important value for sines and cosines.

1 - The multiplicative identity. Multiply any number by 1 and get that number back.

0 - the additive identity, add 0 to any number and get that number back

All of these things seem unrelated, and they all were in their own corners of mathematics having little to do with each other, at least not on this deep of a level.

Also, in this one equation is addition, multiplication, and exponentiation, the three main tools of arithmetic.

This is elegance and beauty at its finest

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Wed, 25 Apr 2012 23:19:59 -0400

fishingboatproceeds: Edit: Drawn by this 15-year-old...

Wed, 25 Apr 2012 23:19:03 -0400

fishingboatproceeds:

Edit: Drawn by this 15-year-old nerdfighter. She’s great!

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Wed, 25 Apr 2012 21:57:42 -0400

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Wed, 25 Apr 2012 18:48:03 -0400

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Wed, 25 Apr 2012 16:31:24 -0400

Today I realized that my little sister is funnier than me.

Wed, 25 Apr 2012 15:07:24 -0400

Today I realized that my little sister is funnier than me.

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Wed, 25 Apr 2012 14:29:16 -0400

"And the heart is hard to translate, It has a language of it’s own, It talks and tongues and..."

Wed, 25 Apr 2012 14:17:13 -0400

“

And the heart is hard to translate,
It has a language of it’s own,
It talks and tongues and quiet sighs and prayers and proclamations,
In the grand days of great men and the smallest of gestures,
In short shallow gasps.

But with all my education,
I can’t seem to commend it,
And the words are all escaping me,
And coming back all damaged,
And I would put them back in poetry,
If I only knew how,
I can’t seem to understand it,

And I would give all this and heaven too,
I would give it all if only for a moment,
That I could just understand the meaning of the word you see,
‘Cause I’ve been scrawling it forever,
But it never makes sense to me at all.

And it talks to me in tiptoes,
And sings to me inside,
It cries out in the darkest night,
And breaks in morning light.

But with all my education,
I can’t seem to commend it,
And the words are all escaping,
And coming back all damaged,
And I would put them back in poetry,
If I only knew how,
I can’t seem to understand it,

No, words are a language,
It doesn’t deserve such treatment,
And all my stumbling phrases,
Never amounted to anything worth this feeling,
All this heaven,
Never could describe such a feeling as I’m having,
Words were never so useful,
So I was screaming out a language that I never knew existed before.

”

- All This and Heavan Too - Florence and the Machine

Poetry is hard to find in popular music. With this group it is abundant.

"Calvin: Isn’t it strange that evolution would give us a sense of humour? When you think about it,..."

Wed, 25 Apr 2012 12:58:23 -0400

“

Calvin: Isn’t it strange that evolution would give us a sense of humour? When you think about it, it’s weird that we have a physiological response to absurdity. We laugh at nonsense. We like it. We think it’s funny. Don’t you think it’s odd that we appreciate absurdity? Why would we develop that way? How does it benefit us?

Hobbes: I suppose if we couldn’t laugh at things that don’t make sense, we couldn’t react to a lot of life.

Calvin: (after a long pause) I can’t tell if that’s funny or really scary.

”

- Calvin and Hobbes, Bill Watterson

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Wed, 25 Apr 2012 12:57:23 -0400

You know, Hobbes, some days even my lucky rocket ship underpants...

Wed, 25 Apr 2012 12:55:24 -0400

You know, Hobbes, some days even my lucky rocket ship underpants don’t help.

"Laughter and tears are both responses to frustration and exhaustion. I myself prefer to laugh, since..."

Wed, 25 Apr 2012 12:51:16 -0400

“Laughter and tears are both responses to frustration and exhaustion. I myself prefer to laugh, since there is less cleaning up to do afterward.”

- Kurt Vonnegut