cauchi

The ‘I Am Heath Ledger’ Trailer Is Out and Our Hearts Are Broken All Over Again
Heath Ledger in footage from the upcoming documentary “I Am Heath Ledger.” (Photo: YouTube)

The death of Heath Ledger hit harder than most. While, at 28, he was still sorting out things in his personal life, he seemed to be hitting his stride professionally. We had such high hopes.

Seeing the first trailer for the I Am Heath Ledger documentary, which premieres at the Tribeca Film Festival on April 23 and will air on Spike on May 17, is a punch in the gut. The Australian actor from Brokeback Mountain, 10 Things I Hate About You, and The Patriot seems so alive again in the unseen footage and the stories told by his family (his sister Kate Ledger), friends (musician Ben Harper), lovers (model Christina Cauchi), and colleagues (director Ang Lee). It makes us sad to know that while there may be new documentaries about him, there will be no new footage of him ever again.

Because of this, we thought we’d capture some of his best smiles from the doc trailer to fully appreciate them. There were many.

Heath Ledger in “I Am Heath Ledger.” (Image: YouTube)
Heath Ledger in “I Am Heath Ledger.” (Image: YouTube)
Heath Ledger in “I Am Heath Ledger.” (Image: YouTube)
Heath Ledger in “I Am Heath Ledger.” (Image: YouTube)
Heath Ledger in “I Am Heath Ledger.” (Image: YouTube)
Heath Ledger in “I Am Heath Ledger.” (Image: YouTube)
Heath Ledger in “I Am Heath Ledger.” (Image: YouTube)

Spike’s I Am documentary series is a look inside look the lives of extraordinary people told by their inner-circles. Naomi Watts, another ex (she dated him four years before his 2008 death from accidental overdose), will also appear in it, but she was omitted from the trailer.

This trailer does feature Ben Harper, who wrote his song “Happily Ever After in Your Eyes” for Heath when he welcomed daughter Matilda with Michelle Williams in 2005, talking about how Heath was “the most alive human.” He lived without abandon. “If it wasn’t on the edge, it didn’t interest him.”

Christina Cauchi, the Australian model who dated him from 2000 to 2002, remembered Heath’s love of filmmaking. “There were always cameras around — a video camera or a Polaroid camera or the film camera,” she said. “That’s the only way I think of him. With the camera in the hand.”

Brokeback helmer Ang Lee described Ledger as the kind of actor who would “steal the whole show,” adding, “That’s the power of Heath Ledger.”

But there was angst. His agent, Steve Alexander, talked about how it was never a dull moment working with the star. “He kind of almost pulled out of every movie he ended up doing,” he said.

And Heath’s friend Matt Amato spoke about his struggle with celebrity — and how it was a double-edged sword. “He wanted fame,” he said of his pal, “and then when he got it he didn’t want it.”

Heath would have been 38 today.


Read more from Yahoo Celebrity:

Emmanuel Cauchy on the Traversee de la Lune (ED+), the first complete traverse of the Grand Ross (1850m) and Petit Ross (1721m) on the isolated Kerguelen Islands in the southern Indian Ocean. The Kerguelens are about 2000 miles away from the next populated island, and so this may be one of the most remote climbs on earth. [Photo] Lionel Daudet.

mediumhadroncollider  asked:

why in every math and physics class I've taken in college must we always derive or prove the cauchy schwartz inequality? does it ever end?

no

and i hope you like vectors buddy because the first week of every physics and math class ever is “review”

and by “review” i mean only of vectors. its all vectors. forever. you cannot escape the vectors. they can smell fear

Advanced Math Pickuplines
  • I’m proving the existence of love at nth sight by induction, and you’re my base case. 
  • Are you a ring theorist? Cause dat ass is a maximal ideal.
  • I could extend integrally and show you my going-down-property
  • “I believe you’ll find my Hardy-Littlewood quite maximal.”
  • Are you a compact set? Cause I’d love to get you under my finite covers
  • Is your contravariant hom-functor left exact? Cause I’d like to inject into you.
  • I wish I were the first N terms of your convergent Taylor polynomial expansion so I could get close to you.
  • Our love is like the topology on A and B {{},{A,B},{A}}: it’s not discrete, and everything else is trivial (down to homeomorphism).
  • I wanna simplify the square root of -u squared so u and i can be together.
  • I feel that you and I can’t be described as the union of two disjoint open sets whose complement is empty.
  • “My Cox-Zucker algorithm implementation is quite optimal.”
  • I’ve got an orthogonal non-linear operator that’d I’d love to integrate over your entire surface.
  • I think our Collatz Conjecture holds: wherever we start, we should end up being one.
  • You make me NP-hard, but I have an algorithm for you to approach me.
  • My legs are separable if you’re doing the splitting.
  • Hey babe, are you an inverse function? Because you make my natural log rise exponentially.
  • I’d do you like the squeeze theorem - that way I could take you to the limit and hit it from both ends.
  • Are you an equivalence relation on Cauchy sequences? Because you complete me!
  • Let’s make a bijective function and get one-to-one and onto.
  • You and I must be inverse logical functions. Because I could compliment you all day! 

Now i only need to find a cute math nerd to use them on. Any volunteers?

Taken from: this subreddit

anonymous asked:

Could you explain this tfw no ZF joke? I really dont get it... :D

Get ready for a long explanation! For everyone’s reference, the joke (supplied by @awesomepus​) was:

Q: What did the mathematician say when he encountered the paradoxes of naive set theory?
A: tfw no ZF

You probably already know the ‘tfw no gf’ (that feel when no girlfriend) meme, which dates to 2010. I’m assuming you’re asking about the ZF part.

Mathematically, ZF is a reference to Zermelo-Fraenkel set theory, which is a set of axioms commonly accepted by mathematicians as the foundation of modern mathematics. As you probably know if you’ve taken geometry, axioms are super important: they are basic assumptions we make about the world we’re working in, and they have serious implications for what we can and can’t do in that world. 

For example, if you don’t assume the Parallel Postulate (that consecutive interior angle measures between two parallel lines and a transversal sum to 180°, or twice the size of a right angle), you can’t prove the Triangle Angle Sum Theorem (that the sum of the angle measures in any triangle is also 180°). It’s not that the Triangle Angle Sum Theorem theorem is not true without the Parallel Postulate — simply that it is unprovable, or put differently, neither true nor false, without that Postulate. Asking whether the Triangle Angle Sum Theorem is true without the Parallel Postulate is really a meaningless question, mathematically. But we understand that, in Euclidean geometry (not in curved geometries), both the postulate and the theorem are “true” in the sense that we have good reason to believe them (e.g., measuring lots of angles in physical parallel lines and triangles). Clearly, the axioms we choose are important.

Now, in the late 19th and early 20th century, mathematicians and logicians were interested in understanding the underpinnings of the basic structures we use in math — sets, or “collections,” being one of them, and arithmetic being another. In short, they were trying to come up with an axiomatic set theory. Cantor and Frege were doing a lot of this work, and made good progress using everyday language. They said that a set is any definable collection of elements, where “definable” means to provide a comprehension (a term you’re familiar with if you program in Python), or rule by which the set is constructed.

But along came Bertrand Russell. He pointed out a big problem in Cantor and Frege’s work, which is now called Russell’s paradox. Essentially, he made the following argument:

Y’all are saying any definable collection is a set. Well, how about this set: R, the set of all sets not contained within themselves. This is, according to you, a valid set, because I gave that comprehension. Now, R is not contained within itself, naturally: if it is contained within itself, then it being an element is a violation of my construction of R in the first place. But R must be contained within itself: if it’s not an element of itself, then it is a set that does not contain itself, and therefore it is an element of itself. So we have that R ∈ R and also R ∉ R. This is a contradiction! Obviously, your theory is seriously messed up.

This paradox is inherently a part of Cantor and Frege’s set theory — it shows that their system was inconsistent (with itself). As Qiaochu Yuan explains over at Quora, the problem is exactly what Russell pointed out: unrestricted comprehension — the idea that you can get away with defining any set you like simply by giving a comprehension. Zermelo and Fraenkel then came along and offered up a system of axioms that formalizes Cantor and Frege’s work logically, and restricts comprehension. This is called Zermelo-Fraenkel set theory (or ZF), and it is consistent (with itself). Cantor and Frege’s work was then retroactively called naive set theory, because it was, of course, pretty childish:

There are two more things worth knowing about axiomatic systems in mathematics. First, some people combine Zermelo-Fraenkel set theory with the Axiom of Choice¹, resulting in a set theory called ZFC. This is widely used as a standard by mathematicians today. Second, Gödel proved in 1931 that no system of axioms for arithmetic can be both consistent and complete — in every consistent axiomatization, there are “true” statements that are unprovable. Or put another way: in every consistent axiomatic system, there are statements which you can neither prove nor disprove. For example, in ZF, the Axiom of Choice is unprovable — you can’t prove it from the axioms in ZF. And in both ZF and ZFC, the continuum hypothesis² is unprovable.³ Gödel’s result is called the incompleteness theorem, and it’s a little depressing, because it means you can’t have any good logical basis for all of mathematics (but don’t tell anyone that, or we might all be out of a job). Luckily, ZF or ZFC has been good enough for virtually all of the mathematics we as a species have done so far!

The joke is that, when confronted with Russell’s paradox in naive set theory, the mathematician despairs, and wishes he could use Zermelo-Fraenkel set theory instead — ‘that feel when no ZF.’

I thought the joke was incredibly funny, specifically because of the reference to ‘tfw no gf’ and the implication that mathematicians romanticize ZF (which we totally do). I’ve definitely borrowed the joke to impress friends and faculty in the math department…a sort of fringe benefit of having a math blog.

– CJH

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inkblottedsoul  asked:

So I read your tags on the "calculus" thing about Leibniz or Newton, and wasn't Archimedes also hugely involved? Like, I know he was killed before he could finish it and I'm unsure if his work was actually used later as far as it went, but I think I remember my teacher saying he was one of the first.

Ok, it’s time for a bit of a trip, because people always say shit like “Newton invented calculus” or they swap out Leibniz, and MAYBE, sometimes they’ll mention Archimedes.  Science, including math, doesn’t work that way.  It’s incremental.  The bits and pieces of what we now call “calculus” were developed over a LONG period of time by many different people.

So before we begin, calculus is the study of a thing called a “limit” which is a way of doing infinitely many things.  There’s two main parts of calculus: differential calculus, which uses limits to talk about rates of change, and integral calculus, which uses limits to talk about areas and volumes.

Ok, now, to Archimedes.  He developed what was called the “method of exhaustion.”  You want to know how much area is in a circle? First, fit a triangle inside the circle.  You can figure out it’s area.  Then a square.  Then a pentagon, and take the number of sides bigger and bigger, and the more you have, the closer it is to being the whole circle.  In modern terms, you compute those areas, and then you take the limit as the number of sides goes to infinity, and BAM, area of a circle (which is also a way to calculate pi, and there’s fun history there, too)

Now, we jump a thousand or so years, because Archimedes got stabbed and, frankly, people had to figure out polynomials, modular arithmetic, and geometry a bit more before the next part of calculus was really popular.  We come back to the story with Descartes.  He said “We can describe the plane by pairs of numbers!” and it was AMAZING.  Suddenly, geometry was freed from Euclid and was dominated by numbers.

So what’s the first thing you do in that case? You try to compute the lengths of some shit.  Like spirals, parabolas, etc.  Descartes came up with some tricks, but he declared that no one would be able to do it for cubics, WAY too hard.  Never ever.

So of course, not long after he died, Fermat did it.  Fermat figured out how to compute the rates of change (slopes of tangent lines) for any curve that was defined by polynomials.  Any at all.  And how to use that to figure out the length, though some lengths couldn’t be computed cleanly, he could still calculate them pretty damn well.

This is actually about 60-70% of what you need to get through a calc course.  All thanks to Fermat, who often gets no credit for it.

So then, a BUNCH of people start working on area inside of curves, and Isaac Barrow (Newton’s teacher) figures out that rates of change and areas are closely related: there’s a thing called the Fundamental Theorem of Calculus that is the details, and it’s REALLY important.  But of course, he can only do things for polynomials, really.

And now Newton comes along, and he systematizes it, and says “Well, not all functions are polynomials…OR ARE THEY?!” and declares that all functions are just polynomials with infinitely many terms, and you can just treat them the same way.  Neither of these statements is true, but they’re not the worst things you could say.  So now, Newton could handle all the functions that show up in classical physics…and BOOM, physics revolution, though he hides the calculus for various reasons.

Leibniz, possibly unaware of how Newton got his results, figures out how to do things more generally, treating functions as just things, not as big polynomials.  He developed the product rule (also called the Leibniz rule) and his notation was WAAAAAY better, and then, the shit hit the fan when Newton found out.

It’s one of the nastiest academic disputes ever (take into account that Newton was basically a supervillain and in charge of England’s money supply), but it’s a bit off topic.

So, we’re now at about 80-90% of a calc course, and the rest was filled in by the other European mathematicians and physicists of the time, with a LOT of work replicated in England and on the Continent because of this dispute.  We tend to remember the Brits, because, well, we’re Americans, but also because Britain was getting more powerful at the time.  So we have Maclaurin and Taylor who cleaned up the “infinite polynomial” business standing out particularly.

The Continent had its revent in the 19th century, when people found out “Oh, shit, these proofs, they all have holes in them” and it was Cauchy (French) and Weierstrass (German) among others who fixed it all up.

So, hope you enjoyed this lesson in history of math, next, ask me about the Jewish woman who made her father (who was one of the great 19th century mathematicians) a completely forgotten name whose work is often attributed to her by accident, and who completely revolutionized our understanding of physics, and who is, honestly, one of my favorite historical people ever (bonus point if you know who it is)

silverheartcat replied to your post “i’m psychically compelled to explain 0.999… = 1 to everyone i see…”

pls explain

@silverheartcat basically most people who haven’t studied math don’t know what a number actually is. it depends on the type of number, but real numbers can be seen either as dedekind cuts or equivalence classes of cauchy sequences, which is the construction i like better. the cauchy sequence construction also helps to understand what decimal representation actually is: 0.999… is basically the sequence 0, 9/10, 99/100, 999/1000, …, which is in the same equivalence class as the sequence 1, 10/10, 100/100, 1000/1000, …, because the sequence 0-1, 9/10 - 10/10, 99/100 - 100/100, … converges to 0 in the rationals. here both sequences converge in Q to the same number so you don’t have to take the difference, but sometimes the limit isn’t in Q eg. sqrt(2)