ChatGPT-4o:
44+58+88=190
So, Oliver has a total of 190 kiwis. The five smaller kiwis on Sunday are still included in the total count, so they don't change the final sum.
3,995 karma · joined July 17, 2016
44+58+88=190
So, Oliver has a total of 190 kiwis. The five smaller kiwis on Sunday are still included in the total count, so they don't change the final sum.
Passive damping may be smart, but stupid always wins.
Volume is base x height. Height is a linear function in the vector that rises above the base; the usual properties of the determinant follow from this.
Sheldon's book is more suitable for a second course in linear algebra. It's an excellent book, that my more advanced students have enjoyed.
Sheldon, however, approaches the subject with some rigid dogma: Determinants are evil. His view is they're not practical to compute at scale. It can be good to learn theory with one's determinant hand tied behind one's back, just as it can be good to learn "constructive" mathematics, but this should not be one's only approach.
I used to attend an academic sponsor's day at the math institute MSRI (now SLMath). Afternoons reached to keep us busy. One year Sheldon's wife demonstrated some academic teaching software, and my group was tasked to solve a linear algebra problem that Sheldon had provided. Unaware that everyone was watching us on the big screen, I solved it instantly, using determinants. I still don't understand Sheldon's longer solution.
That test was just multivariate calculus I'd already aced, with funny names. I got one of the top scores in the class. So I decided to study an extra hour next time, just to be responsible. Oops! I flunked a test that was differential equations with funny names.
I didn't really learn ODE's till Columbia assigned me to teach them as an assistant professor.
(You know you're on to something when so many people misquote and misinterpret your result, and say it sucks!)
Of the many formulations of Gilbert-Shannon-Reeds, an easy one to generalize is running the shuffle in reverse. One could flip a fair coin for each card, to decide if it flies up to the right or left hand. Equivalently, let heads fly up to the same hand as before, and let tails fly up to the other hand. As an unfair coin approaches always tails, the inverse shuffle becomes smoother, approaching a perfect shuffle, which Persi can easily do.
One way to measure how smoothly one shuffles is to flip one hand's packet over before shuffling, then count face up / face down runs. For a perfect shuffle, there will be 52 singleton runs: up, down, up, down... For GSR shuffles there will be 26 1/2 runs on average. Experienced human shuffles tend to exhibit 30 to 40 runs. While only GSR can be solved in closed form, one can run simulations to see what happens with smoother shuffles. As a somewhat surprising coincidence, one approaches randomness most quickly with shuffles corresponding to 30 to 40 runs.
I had no idea she was trans. When I figured this out, it became part of my spiel to students: If being different doesn't destroy you, it'll make you stronger. It's not simply that one can be just as good a scientist while being gay, for example. No, we live in a country so stupid it may reelect Trump, and there are still issues with being different. If the experience can teach you that many people are crippled by convention and full of shit, that revelation can liberate you to do more original work.
I don't trust 'Passwords'.
I found this post title "Italian streets that don't exist on any map" misleading, given my experiences there. The article describes fictitious streets.
It stunned me recently by remembering I had an argon tank, something I had only mentioned in a thread days earlier.
I asked it to recall which conversations these were, for sharing on HN. That conversation was comically stupid (REALLY bad, like "Perplexity" bad) and went nowhere.
I rejected cursive after one year, reverting to printing despite all pressures. I couldn't see any upside to cursive. It was harder to read, a concession to lazy adults with poor motor control. A few years later I won a penmanship contest.
What I want to do with these ideas is automate turning computer-generated animation into animation with a hand-drawn life, using machine learning to tune the parameters to express my tastes.
This is all connected: My brother and I were fascinated when we learned how animation worked. I then found myself deathly bored in an hour of school penmanship printing practice, so I worked on animating letter F's turning into letter G's, and so forth. The teacher left me alone until other kids asked what I was doing, and I taught them. She swiftly collected all papers, went to get a primitive projector that barely escaped incinerating our work, and praised various students' penmanship. My collaborators were trembling that they'd be chosen next. We didn't yet understand that one attempts to stop a revolution by cutting off the head.
I was stunned to realize that the ridicule didn't hurt. These experiences helped me learn to think independently as a mathematician.
Flame King Refillable 1LB Empty Propane Cylinder Tank
https://www.amazon.com/gp/product/B00MM3GCVO/
It offers some nuanced controls e.g. to avoid overfilling.
Around 1962, there was an open house evening, the first time I set eyes on a computer. I briefly got to play this exact game.
Later that year, I busted up a bunch of spring clothespins, to use as toggles to work out binary arithmetic from a book our grandfather had given us. The look on my Dad's face was priceless.
type ShowS = String -> String
I've survived in math partly by attempting to catalog how others think. I sense a divide in Haskell, between people who prefer to view the compiler as a hermetically sealed abstraction, and those of us who try exploit what we think the compiler is doing. To view `ShowS` as a rope one needs to consider how the compiler handles lazy evaluation.
Struggling through mathematical notation, or learning technical material in school, can be brutal. Never confuse the medium with the message.
When VR gets more comfortable to wear, it will represent a more dramatic shift than moving from terminals to graphical user interfaces.
For now, the Vision Pro very accurately tracks your eyes, but waits for an explicit finger gesture to act. Future interfaces with deep learning will take the form of very sophisticated visual autocomplete, guided by observations of our reactions that would destroy us at poker.
The Vision Pro is the camel's nose under the tent.
My potential use case is to better understand 3-dimensional topology. I'm not concerned about "popular" uses other than how that affects the viability of the product.
There's a potential for some astounding abstract art, when visual artists catch up with musicians who master their own digital tools. This thing is capable of inducing drug-free hallucinations. And of course one recalls the killer app for VCRs...
https://adam.math.hhu.de/#/g/leanprover-community/NNG4
I recall the feeling, being one of many who "rediscovered" Gröbner bases. This is why one studies history, to recognize the taste when one is a turn away from new history:
There was a leap needed, to generalize Gaussian elimination and the Euclidean algorithm to their common ground of arbitrary polynomials. There's a further leap to noncommuting strings, and then there's typed trees, the "algebraic datatypes" foundation of languages like Haskell and Lean 4. To see term rewriting in these settings as a continuum, one needs to incorporate recursion, to understand how Schützenberger's notions of rational and algebraic languages apply.
The idea of a term ordering is too gnarly here (well past the interstellar frontier of "decideability") for anything besides human intuition or deep learning.
Nevertheless, one sees that term rewriting on typed trees can be the foundation of human thought. Deep learning, while impressive, struggles to simulate recursion using multiple layers. We are discovering exactly how fundamental recursion is to thought. A version of neural nets more closely based on a probability substrate of typed trees might more adeptly model thought.
My first viewings were indeed from the balcony of the Brattle Theatre, where one could get books of ten tickets cheap as a grad student. My last viewing was just before the pandemic, in the Stanford Theatre.
I vowed to let go of all inhibitions, and let the movie guide my emotions. That's how Casablanca deserves to be seen.
Spotify's best quality is 320kbps (Ogg Vorbis).
My interest has reawakened in deliberate listening to music as organized by the artist.
I once sat next to a friend of Steve Jobs, on a flight. He appreciated my admiration, and took a drawing of a "current mirror" iPod charging circuit to show Steve. The conversation became uncomfortable when I asked if Jobs wanted his legacy to be the death of the album.
Jazz is the higher mathematics of music. With Tidal or Qobuz, it's easier than ever to begin an exploration of this world.