I've got a problem with that video that starts at 4:15. He seems to jump to the conclusion that for every midpoint there is only 1 distance. But that midpoint is formed by picking 2 points on the edge, and one could easily pick two other points on the edge that have the same midpoint (but have a different distance). He did not address that point at that point in the video, and for the next 2 minutes I kept raising that point in my mind. After he continued down that path not addressing that point, I felt that I must have missed something, or that more intelligent math viewers would have solved that open question in the mind in seconds and I am not mathematically inclined enough to be the target audience. And I stopped watching that video.
I think good educational videos are the result of a process where a trial audience raises such points and the video gets constantly refined, so that the end video is even good for people who question every point.
He addresses this at 9:00 in the video. You're thinking of a function graph, but he never made a function. He just sets up a visualization of a set of 3D points.
this is not a conclusion that he jumps to! all that is stated is that there is a mapping from every pair of points on a curve to a set of 3D coordinates specified by their midpoints and distances. there is no requirement for uniqueness here. in fact, the whole point of this is to turn the search for an inscribed rectangle into the search for two pairs of points on the curve that have the same midpoint and distance --- this is stated just 1 min 15 seconds after the timestamp that you point out.
The function defined in the video is "Given a pair of points A and B on the curve, output (x, y, z), where (x, y) is the midpoint and z is the length of the segment connecting A and B", and the pictures are of its image, not its graph. But if you define it visually, then it's very natural to misunderstand it the way you did, since the picture looks a lot like a function graph of a function which takes midpoints (instead of pairs of points) and returns the distance corresponding to that midpoint (which is not well-defined, as you pointed out). If this happens, the viewer is then completely lost, since the rest of the video is dedicated to explaining that the domain of this function is a Möbius strip when you consider it to consist of unordered pairs of points {A, B} (as one should).
Ultimately, if you don't have a 100% formal version of a given statement, some people will find a interpretation different from the intended one (and this is independent of how clever the audience is!). I think 3Blue1Brown knows this and is experimenting with alternate formats; the video is also available as an interactive blog post (https://www.3blue1brown.com/lessons/inscribed-rect-v2) which explicitly defines the function as "f(A, B) = (x, y, z)" and explains what the variables are.
The fact that "given a large enough audience (even of very smart people), there will be different interpretations of any given informal explanation" is a key challenge in teaching mathematics, since it is very unpredictable. In interactive contexts it is possible to interrupt a lecture and ask questions, but it still provides an incentive to focus on formalism, which can leave less time for explaining visualizations and intuition.
> I think good educational videos are the result of a process where a trial audience raises such points and the video gets constantly refined, so that the end video is even good for people who question every point.
It would be at least as long as a one-semester course in typical math major then.
To address your specific question: he doesn't assume each midpoint has only one distance at all. He doesn't say it and the visualization doesn't show it as so.
he maps two points (by using their midpoint) and a distance to the (x,y,foo) if it was two different points with the same midpoint but different distance it would map to (x,y,bar)
Be aware that for global NCAP, safety ratings are dependent on the vehicle class. If a subcompact car receives 5 stars, this does not mean it has the same probability of survivability in full frontal crash as a large executive luxury sedan that received 5 stars.
In fact, if there was a head-on crash between this car and Mercedes E-Class, and you're planning to be in one of the cars, I would advise you to chose the Mercedes.
Yes. Anyone who has worked on conservation of momentum problems in high school physics should recognize this. Even at low collision speeds if there is a large disparity in mass between the vehicles then the lighter one experiences a lot of acceleration.
For an extreme case think of a low speed collision between a bowling ball and a ping pong ball.
In a mismatched collision, the smaller vehicle needs to withstand a higher delta-V than the larger vehicle.
Also, in many cases the bumper heights are mismatched so the larger vehicle's strong structure runs into higher, weaker parts of the small vehicle, further exacerbating the problem.
There are several things you can do to dramatically reduce your risk. Cycle during the day, while sober, with bright colors, with a helmet, and avoiding multi-lane roads. If you do these things you've statistical eliminated most of the risk.
> victim blaming
It's an exercise in reducing risk, not assigning blame.
> the law says I can cycle on those roads
The law can't bring you back to life, but if you want to take the risk that's your decision.
We need to think more game theoretically. Since our courageous cyclist must already have a deathwish to be on the same roads as these vehicles, he should go all in with a vest packed with C4 and ball bearings so that, in the event of a crash (which will cripple him anyway), at least he takes out Starbucks Mom on his way to Paradise.
If you do as I suggest then you eliminate a lot more than 90% of the risk. 62% of cyclist fatalities weren't wearing a helmet, so that alone is a huge thing you can do to improve your odds. 22% are drunk. 50% are on major roads. https://www.iihs.org/topics/fatality-statistics/detail/bicyc...
I knew I would get responses about "why don't cars just..." e.g. why should I change, they're the ones who suck. I'm not suggesting or opposing public policy changes here. I'm giving practical advice which makes cycling much safer than the statistical average.
If you do all of what I say, it's a reasonably safe and healthy pastime.
People who bike for transportation, not just fun, sometimes need to bike at night, on less bike-friendly roads, or without high-visibility clothing. It doesn’t seem to me that the sentence for that should be death.
Please, try to get some high-visibility clothing.
The difference in visibility is between hundreds of meters with high-visibility clothing and meters without.
> It doesn’t seem to me that the sentence for that should be death.
Maybe not death but severe injuries.
Being visiblevin the night is a game changer.
"You" is singular as a cyclist. Wearing appropriate gear can drastically improve your (again, singular) safety.
"You" is plural for motorists. A single motorist deciding to own and operate a soft-and-safe-mobile will not affect your (singular or plural are interchangeable here) risk appreciably.
It doesn't mean you're wrong, and you (singular) can pick your battles, but I think I'd prefer to be alive than correct.
With electric bikes there is the possibility of adding safety gear to bicycles since the extra drag can be offset by motor power. Even just the simple example of allowing the rider to wear better, motorcycle-style protective gear would be a massive improvement - since they aren't pedalling so hard. Such gear could be actively heated/cooled as well.
Since the heavier vehicle has higher momentum, it would decelerate slower when hitting a semi-static-object, which decreases the forces on your body. The smaller vehicle would stop much quicker and you would jerk forward. So a heavier vehicle at the same speed would probably be better, all else being equal. And that's neglecting the additional material a larger vehicle typically has that deforms over longer distance than with a shorter car.
So many are and some aren't. So in many cases it doesn't matter which car you're in, and in some cases the heavy car is better. That means the heavy car is still net better.
I still haven't seen a single argument why a smaller car would be better in a collision.
But a small car doesn’t perform better, why would it? Surely a large car is better when driving into an electrical pole than a small car. What advantage does the small car have?
Also, just to clarify, how did I change the problem? The problem with car crashes is rapid deceleration which injures you, and lighter cars are worse in that aspect compared to heavier cars.
And can you explain why less momentum is better for the passengers? The thing that injures you in an accident is acceleration (or more accurately deceleration), so you actually want more momentum.
Imagine sitting in a large truck vs a kei car and driving into a brick wall. One has the chance to deform the wall which decreases the speed comparatively slowly. The other one abruptly stops when hitting the wall.
Unless the collision target doesn't deform at all, the higher momentum is better. And if the target is completely solid, a larger typically has a larger crumple zone which is better, too.
I cant come up with any reason to prefer the smaller car/momentum, except in very constructed scenarios (driving over a cliff with a weak fence for example).
If the object is completely fixed and effectively inelastic, the main determinant in survival is the distance over which the deceleration of the occupant occurs, assuming a lack of cabin intrusion.
So the mass of the vehicle is ideally fixed in relation to its rigidity, and it’s not better to have less, or more, mass except as the ideal ratio to the rigidity of the vehicle.
What you want is a vehicle that decelerates as slowly as possible over the greatest possible time/distance.
A light vehicle that is very rigid is equally terrible as a heavy vehicle that is very rigid. What matters is how many millimeters it takes for each vehicle to come to a complete stop after colliding with the immovable object.
There are a lot of combinations of vehicle mass and rigidity that meet the ideal here, and it is not sensible to assert that a massive or a lightweight vehicle will be ideal in this case.
What you want is a vehicle that, at the speed of the collision, deforms the most completely and to the longest distance possible without incursions into the passenger compartment.
Ideally, the vehicle would have a very long and well engineered crumple zone in front of the occupants. Here, assuming similar material engineering of the impact absorbing structure, length is king. All things being equal, a car with a stubby front profile will expose its occupants to twice the acceleration as one with a 2x longer hood.
Still, the vehicle must have enough mass that the crumple zone is fully compressed at the speed of the collision. If it’s too light, it will decelerate before the impact absorbing distance if fully used.
If it’s to heavy, it will still be moving when the crumple zone is fully exhausted, and either a sudden peak of acceleration or a cabin intrusion will occur when the passenger cage becomes involved in the deformation zone.
I’m going to guess that on average, you’re still better off in a full sized SUV than In a more sensibly sized vehicle, hitting an unmovable object at speed.
You say you have a background in vehicle safety, so maybe you know something I don’t. Please explain where I’m going wrong here?
All things being equal, this is generally a little bit true, even for collisions with rigid, fixed obstacles - but vehicle design is critical here. For instance, a cab forward truck with no real crumple space does not benefit from mass, as the deformation of the pax compartment is the primary concern. A very lightweight vehicle that is very deformable and has a long crumple zone might outperform a heavier vehicle in terms of the acceleration imparted to the passengers.
The problem is that a “fixed” solid object has effectively infinite mass. This applies when the collision displacement of the obstacle can be measured in fractions of a millimeter. In these cases, the ratio of the lightweight vehicle to the effective mass of the obstacle is effectively the same as with the heavier vehicle vs the obstacle. Here, mass pays no dividends. Only the distance / time covered during the sudden deceleration, and the integrity of the passenger compartment. Of course, the efficiency and extent of restraint systems will also play a major role. But it’s not an automatic win for heavier vehicles in this case.
Notably, most collisions are not with immovable objects, but with other vehicles. In that case, mass is going to win almost every time, since the acceleration experienced by a subcompact vs a full sized SUV is about 2x, which means the forces imparted on the passengers in terms of static loads on their bodies and bones will be 4x.
For passenger survivability in most accidents, the incentives fall heavily towards using the heaviest well constructed vehicle that you can afford.
Crumple zones have been a thing for almost a century.
Momentum doesn't matter. It matters in a vehicle on vehicle collision, but since the pole is essentially infinite I'm not sure why you're bringing it up. Acceleration is what impacts the human body, and it's determined by speed and distance. For the same speed, a larger car will have a longer distance to stop, therefore lower acceleration, and less force on the body.
Even if you assume that the pole doesn't move at all, having less momentum doesn't help you. A smaller car isn't better, in the best case it is equal. But a larger car probably also has a larger crumple zone so it is still better. You still haven't given a single reason why a smaller car would have an advantage.
awesome, i will only buy ford f150s from now on so i can have the most mass during any collision and thus will never be on the worse end of a collision. is it really american if you aren't screwing over your peers?
I was curious (but also lazy) so I went and checked Wikipedia. According to that source, the newest model of Ford F-150 is the fourteenth generation one, so let's look at the numbers for the top-of-the-line Raptor (or what I assume is the top, I'm not a pickup person). Assuming largest manufactured dimensions in all cases for the truck and smallest for the tank:
Just a thought process.. how bad would a f150 <~> f150 collision be, compared to say VW Golf <~> VW Golf?
If everybody went with f150, and the chances of colliding with another heavy one increases right? In the end, the edge is only short lived right?
I guess this means "vehicle safety ratings" only take into account the safety of those inside the vehicle? In a better world the safety of those outside of the vehicle would not only be taken into account but weighted more heavily, which would mean small cars that are safe for the occupants would get the highest ratings. Sadly we not live in that world.
relative rating or not, it has been successful at pushing car manufacturers to make safer cars, at least in the region the article talks about.
recently it has become a selling point to have a 5 star safety rating for cars in the market, which has finally made basic aspects like airbags part of the cheaper trims.
This seems like a clear case for government regulation over libertarianism, because who else holds the interest of this sort of social good at the scale of all cars driving the roads?
The personal moral dilemma here is crazy. Are you willing to risk your own life and the lives of anyone else in your car over the lives of the people in the other car? It's so terrible but you also can't fault anyone individually for choosing a larger car for safety reasons. (Those reasons being, I would prefer to kill someone else than kill myself or others in my car.)
I recently downloaded it from GOG and tried to play it on a 5K studio display. I wasn't able to get a result that did not blur those beautiful pixels, which is such a shame. Yes, I did go into all those setting menus.
Question: Most docks have ample space around the phone to grip it and remove it from the dock easily. Your design encases the phone on every side. How do you get the phone out in the morning?
I think the interesting part is that either this software was able to access the biometric scan feature and inject their own data into it (which third party software should not be able to access or inject at all, only the OS should be able to access, and injecting should be impossible), or was able to access the Secure Enclave directly (which would be a really big deal and a major breach).
According to the article, the Vision Pro will not play common side by side videos. It has its own standard ("WebXR clips"), but nobody distributes these, and videos from that standard are also not playing correctly on the device.
Most likely there won't be any app that plays porn videos because Apple will not allow them. From the article:
> Steve Jobs notoriously believed that the company had a “moral responsibility” to block porn and suggested that “folks who want porn can buy an Android.”
And general movie playing apps might also be required to implement a porn filter. Remember Apple insisted that all Reddit and Tumblr apps have such a filter, otherwise they wouldn't be allowed in the Apps Store, the only way to distribute apps.
If you believe tech battles are decided whether there is access to porn (VHS vs Beta comes to mind), the Apple Vision Pro currently doesn't look like a winner.
> If you believe tech battles are decided whether there is access to porn (VHS vs Beta comes to mind)...
That didn't really happen, to quote from a post from the host of Technology Connections:
> "I didn't include a section on "how lack of porn killed Beta" because _this is a myth_. Many people have heard tales that Sony didn't allow porn to be released on Beta, and that's nothing but an urban legend. There was indeed "back-room" content available on Beta, but far far less of it simply because fewer people had Beta machines than VHS. Porn represented a small percentage of sales on both VHS and Beta, so it's unlikely many people based their decision on what format to buy based on availability of adult content."
There are already apps in the (non AVP) App Store that support playing porn, such as PLAYA. They will come to AVP soon, and the current VR porn sites will no doubt get their act together on WebXR as well...
Peter Gabriel's 2023 album "i/o" has some quite inspired Atmos mixing going on. The track "The Court" is particularly nice. Make sure you pick the "In-Side Mix" version of the album.
Nice Atmos tracks by other artists imho:
- Jaguar by Victoria Monét
- get well soon by Ariana Grande
- Heroes (feat. Mindy Jones) by Moby, Album "Reprise"
The i/o album really blew up the usability of Apple Music. Three mixes per song, one of which (in-side) is an Atmos mix, unless you don’t have Spatial Audio active, when you silently get one of the other two. And they released it one song at a time throughout the year, so it was just a bag of unrelated singles. At the end of the year, the album came out with duplicate tracks for the two stereo mixes, and I don’t even know for sure how to get the in-side mix.
In general, the situation with Spatial Audio mixes is confusing, and it is really annoying for back catalog tracks where instead of the established (sometimes iconic) stereo version you silently get an Atmos version that the label commissioned without input from the original artist/producer/engineer.
In the linked keynote, Jesse Lyu mentions that LLM won't help us actually do tasks - there are currently no so-called "agents" that do something simple like book a flight - the best way to do it is still to click the buttons yourself.
Rabbit means to solve that by creating a "LAM", a "Large Action model", which is a service by Rabbit that will click interfaces for you. I'm not sure this is the right approach - if it is successful, it will lead to more centralisation around Rabbit.
I agree this is a problem, but I feel a better approach would be to have a market of agents that for a small fee actually handle the whole transaction for you. So there might be multiple parties that say they can buy Delta Flight DL101 tomorrow 21:10 for various prices - some might be a service like the Rabbit LAM, others might be booking platforms, and there might even be airlines themselves. And now an agent-concierge that you choose once at the start will look at all the parties, and then pick and buy the right flight for you. This will make the problem a problem of an open market, where good speedy service is promoted, and prices get ever lower. And if the Rabbit LAM gets outcompeted by an ever better speedier solution, that would be a good thing. (This will also allow us to move away from our current dreaded attention-based economy where e.g. a booking websites tries to exploit your required presence during waiting times, which the LAMs would also solve, but, like I said, let's not move towards more centralisation.)
> Rabbit means to solve that by creating a "LAM", a "Large Action model", which is a service by Rabbit that will click interfaces for you. I'm not sure this is the right approach - if it is successful, it will lead to more centralisation around Rabbit.
The LAM is a genius hack to get around the thousands of closed gardens that apps have created.
It also may have been easier than teaching an LLM how to make tons of API calls, and if done right I presume their LAM adapts to UI changes, vs writing integrations against breaking / deprecating APIs.
90% of use cases will be covered by an official API.
They’ll cover the other 10% with “teaching”. Essentially you telling the AI what the lazily written markup actually means. Then they save it into an automation template. QA teams have only been doing that for the better part of 3 decades.
I know a company that employs a building of a 1,000 people doing nothing but performing 1 click. So they put a human in the scraping
/automation loop so they don’t violate the site/services TOS.
Uber wants people in its app, they want to show ads for their subscription membership services, and they want to upsell you on services, and they want you to see sponsored restaurants first when you order food. Uber wants to own the relationship with customers, so they can ~exploit the customers more~ extract more value.
VC backed and publicly listed companies need endless growth, user-centric systems like what Rabbit is offering break those business models apart. Which is why I predict everyone is going to be fighting super hard against making UIs that just get shit done.
Watching the keynote, I found myself thinking how unhappy Uber would be with skipping over interacting with them entirely: there's no "Uber experience" you have when you're in the car, so what do you get from Uber that any random company with a tie in to Rabbit can't get you?
Option 1: a shift in devices/model like Rabbit pull the magic carpet out from under companies like Uber, and everything becomes purely transactional.
Option 2: rabbit-like market creates exclusivity-based need, to ensure Uber is the number-one (or only) rideshare choice, so it doesn't matter that customers aren't "experiencing" Uber. Uber relinquishes the experience to the agent (unlikely).
Option 3: Uber et al wage war against agents and make their use impossible
But if we're not careful this will circle back to apps/silos.
What I'd like to see is the Smalltalk approach: data providers that are able to send/receive messages, and can be connected together to achieve a goal. Even better if the connecting is done by the "machine" after I issue a command.
its been such a long year, I still remember the month of gpt...what was it, not gpt4all...gpt...ah whatever. The "running an LLM in a loop will solve it" approach. I'm not a big fan, I'd need to see something truly transformative.
This seems to be a Langchain wrapper, where the Langchain is a prompt + retrieval based on a few documents.
> Rabbit means to solve that by creating a "LAM", a "Large Action model", which is a service by Rabbit that will click interfaces for you.
https://openadapt.ai is an open source app that runs on your local machine that clicks interfaces for you -— but only for repetitive tasks that you show it how to do.
QA teams have been doing this sort of stuff for decades. With a little know how and an hour you could record a user doing something in the DOM and play it back. There’s no magic here.
I think good educational videos are the result of a process where a trial audience raises such points and the video gets constantly refined, so that the end video is even good for people who question every point.