trying on a metaphor

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Origami Around
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todays bird

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if i look back, i am lost

祝日 / Permanent Vacation
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@coolmathstuff
everyone who wants that sweet sweet 10-20k of student loan debt relief: you have to apply for it by the end of the year, and while the application isnt live yet u can learn when it is by signing up for a reminder here: https://www.ed.gov/subscriptions
countability
“Some Taylor series, like the Taylor series for e^x and sin(x), converge to the function very rapidly. You might call them Taylor Swift series.”
— Calculus professor
New alignment chart
What to say instead of "trivially"
This comes from a very long list of alternative phrases and words that was used to create “a program that will insert condescending adverbial phrases before any statement in a math proof”. But use it where you will - I’m sure other fields can benefit. Tag yourself, I’m “By abstract nonsense“.
By circular reasoning we see that
There is a marvellous proof (which is too long to write here) that
Figure 2 (not shown here) makes it clear that
It is beyond the scope of this course to prove that
Only idealogues and sycophants would debate whether
The Math Gods demand that
For legal reasons I am required to disclose that
Remember the basic laws of common sense:
Life is too short to prove that
All the cool kids know that
Wherefore said He unto them,
With God as my witness,
As a great man once told me,
Galois died in order to show us that
It pleases the symmetry of the world that
Mama always told me
By Euler
By Fermat
I know it, you know it, everybody knows that
You of all people should realize that
The proof is left to the reader that
We need not waste ink in proving that
It would be an insult to my time and yours to prove that
I shudder to think of the poor soul who denies that
We don’t want to deprive the reader of the joy of discovering for themselves why,
Barring causality breakdown, clearly
Through the careful use of common sense,
According to prophecy,
This won’t be on the test, but
When one stares at the equations they immediately rearrange themselves to show that
If I’ve said it once I’ve said it a thousand times,
Our forefathers built this country on the proposition that
By abstract nonsense,
My father told me, and his father before that, and his before that, that
The burden of proof is on my opponents to disprove that
The voices insist that
Assuming an arbitrary alignment of planets, astrology tells us
a quine is any piece of code that generates itself as output and this guy on github made a 100-piece quine relay that generates itself as output after iterating over 100 different programming languages, a quine that works even if you delete one character from anywhere in the code, and a 3d-printed cylinder engraved with ruby code to generate a .obj file of itself
i havent been able to stop thinking about this
them, wrong: a venn diagram is just when you shove a bunch of circles together, see like this them, wrong:
me: ABSOLUTELY FUCKING WRONG. ABSOLUTELY INCREDIBLE I’M TIRED OF THIS. IF YOUR ALLEGED VENN DIAGRAM IS SO RIGHT THEN WHY ISN’T THERE AN INTERSECTION OF ONLY ENVY AND GREED AND NOTHING ELSE
me: MAYBE IT’S BECAUSE THIS ISNT HOW VENN DIAGRAMS WORK
me: U WANNA SEE A VENN DIAGRAM OF SEVEN? I’LL GIVE U A VENN DIAGRAM OF SEVEN
me:
me: i’m just so tired of the lies.
If you’re the kind of pedant who cares about this the correct term for the first thing is a Euler diagram. Venn diagrams have to represent every possible combination of all the sets involved which is why the highest order one we have today is only like 11 or 13 or something.
Ah yes I remember now, HERE is the 11th order venn diagram. Do you like this? no, of course you don’t. This is a bad image.
love this lil bad boy.
everyone else on this site: bold and big-ego showing off all their skills and bragging about everything as loud as a thunderstorm
me: staying quiet as a church mouse while i calmly display my perfect knowledge of times tables
What’s 9 X 8, genius?…
*doesn’t say anything because i am staying quiet*
ummmmmmmmm
yikes
These are called Dolphin Attacks, here’s a research paper on them: https://arxiv.org/pdf/1708.09537.pdf if you want the specifics.
aye can i get uh………determinants of my matrices
you want -2?
you want fucking -2?
determinance
aye can i get uh………determinants of my matrices
When algorithms surprise us
Machine learning algorithms are not like other computer programs. In the usual sort of programming, a human programmer tells the computer exactly what to do. In machine learning, the human programmer merely gives the algorithm the problem to be solved, and through trial-and-error the algorithm has to figure out how to solve it.
This often works really well - machine learning algorithms are widely used for facial recognition, language translation, financial modeling, image recognition, and ad delivery. If you’ve been online today, you’ve probably interacted with a machine learning algorithm.
But it doesn’t always work well. Sometimes the programmer will think the algorithm is doing really well, only to look closer and discover it’s solved an entirely different problem from the one the programmer intended. For example, I looked earlier at an image recognition algorithm that was supposed to recognize sheep but learned to recognize grass instead, and kept labeling empty green fields as containing sheep.
When machine learning algorithms solve problems in unexpected ways, programmers find them, okay yes, annoying sometimes, but often purely delightful.
So delightful, in fact, that in 2018 a group of researchers wrote a fascinating paper that collected dozens of anecdotes that “elicited surprise and wonder from the researchers studying them”. The paper is well worth reading, as are the original references, but here are several of my favorite examples.
Bending the rules to win
First, there’s a long tradition of using simulated creatures to study how different forms of locomotion might have evolved, or to come up with new ways for robots to walk.
Why walk when you can flop? In one example, a simulated robot was supposed to evolve to travel as quickly as possible. But rather than evolve legs, it simply assembled itself into a tall tower, then fell over. Some of these robots even learned to turn their falling motion into a somersault, adding extra distance.
[Image: Robot is simply a tower that falls over.]
Why jump when you can can-can? Another set of simulated robots were supposed to evolve into a form that could jump. But the programmer had originally defined jumping height as the height of the tallest block so - once again - the robots evolved to be very tall. The programmer tried to solve this by defining jumping height as the height of the block that was originally the *lowest*. In response, the robot developed a long skinny leg that it could kick high into the air in a sort of robot can-can.
[Image: Tall robot flinging a leg into the air instead of jumping]
Hacking the Matrix for superpowers
Potential energy is not the only energy source these simulated robots learned to exploit. It turns out that, like in real life, if an energy source is available, something will evolve to use it.
Floating-point rounding errors as an energy source: In one simulation, robots learned that small rounding errors in the math that calculated forces meant that they got a tiny bit of extra energy with motion. They learned to twitch rapidly, generating lots of free energy that they could harness. The programmer noticed the problem when the robots started swimming extraordinarily fast.
Harvesting energy from crashing into the floor: Another simulation had some problems with its collision detection math that robots learned to use. If they managed to glitch themselves into the floor (they first learned to manipulate time to make this possible), the collision detection would realize they weren’t supposed to be in the floor and would shoot them upward. The robots learned to vibrate rapidly against the floor, colliding repeatedly with it to generate extra energy.
[Image: robot moving by vibrating into the floor]
Clap to fly: In another simulation, jumping bots learned to harness a different collision-detection bug that would propel them high into the air every time they crashed two of their own body parts together. Commercial flight would look a lot different if this worked in real life.
Discovering secret moves: Computer game-playing algorithms are really good at discovering the kind of Matrix glitches that humans usually learn to exploit for speed-running. An algorithm playing the old Atari game Q*bert discovered a previously-unknown bug where it could perform a very specific series of moves at the end of one level and instead of moving to the next level, all the platforms would begin blinking rapidly and the player would start accumulating huge numbers of points.
A Doom-playing algorithm also figured out a special combination of movements that would stop enemies from firing fireballs - but it only works in the algorithm’s hallucinated dream-version of Doom. Delightfully, you can play the dream-version here
[Image: Q*bert player is accumulating a suspicious number of points, considering that it’s not doing much of anything]
Shooting the moon: In one of the more chilling examples, there was an algorithm that was supposed to figure out how to apply a minimum force to a plane landing on an aircraft carrier. Instead, it discovered that if it applied a *huge* force, it would overflow the program’s memory and would register instead as a very *small* force. The pilot would die but, hey, perfect score.
Destructive problem-solving
Something as apparently benign as a list-sorting algorithm could also solve problems in rather innocently sinister ways.
Well, it’s not unsorted: For example, there was an algorithm that was supposed to sort a list of numbers. Instead, it learned to delete the list, so that it was no longer technically unsorted.
Solving the Kobayashi Maru test: Another algorithm was supposed to minimize the difference between its own answers and the correct answers. It found where the answers were stored and deleted them, so it would get a perfect score.
How to win at tic-tac-toe: In another beautiful example, in 1997 some programmers built algorithms that could play tic-tac-toe remotely against each other on an infinitely large board. One programmer, rather than designing their algorithm’s strategy, let it evolve its own approach. Surprisingly, the algorithm suddenly began winning all its games. It turned out that the algorithm’s strategy was to place its move very, very far away, so that when its opponent’s computer tried to simulate the new greatly-expanded board, the huge gameboard would cause it to run out of memory and crash, forfeiting the game.
In conclusion
When machine learning solves problems, it can come up with solutions that range from clever to downright uncanny.
Biological evolution works this way, too - as any biologist will tell you, living organisms find the strangest solutions to problems, and the strangest energy sources to exploit. Sometimes I think the surest sign that we’re not living in a computer simulation is that if we were, some microbe would have learned to exploit its flaws.
So as programmers we have to be very very careful that our algorithms are solving the problems that we meant for them to solve, not exploiting shortcuts. If there’s another, easier route toward solving a given problem, machine learning will likely find it.
Fortunately for us, “kill all humans” is really really hard. If “bake an unbelievably delicious cake” also solves the problem and is easier than “kill all humans”, then machine learning will go with cake.
Mailing list plug
If you enter your email, there will be cake!
@glasperlenspielerin
Space filling curve, five generation. Inspired by the awesome http://robertfathauer.com/IterationArt.html
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If one remembers this particular episode from the popular sitcom ‘Friends’ where Ross is trying to carry a sofa to his apartment, it seems that moving a sofa up the stairs is ridiculously hard.
But life shouldn’t be that hard now should it?
The mathematician Leo Moser posed in 1966 the following curious mathematical problem: what is the shape of largest area in the plane that can be moved around a right-angled corner in a two-dimensional hallway of width 1? This question became known as the moving sofa problem, and is still unsolved fifty years after it was first asked.
The most common shape to move around a tight right angled corner is a square.
And another common shape that would satisfy this criterion is a semi-circle.
But what is the largest area that can be moved around?
Well, it has been conjectured that the shape with the largest area that one can move around a corner is known as “Gerver’s sofa”. And it looks like so:
Wait.. Hang on a second
This sofa would only be effective for right handed turns. One can clearly see that if we have to turn left somewhere we would be kind of in a tough spot.
Prof.Romik from the University of California, Davis has proposed this shape popularly know as Romik’s ambidextrous sofa that solves this problem.
Although Prof.Romik’s sofa may/may not be the not the optimal solution, it is definitely is a breakthrough since this can pave the way for more complex ideas in mathematical analysis and more importantly sofa design.
Have a good one!
Over The Years I Have Patented Many Things….
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One™… You Must Pay Me Royalties…
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