Saddle shaped mirrors are really weird to look in
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- čas přidán 25. 05. 2023
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A saddle point is a point that is concave and convex at the same time, so what's it like to look into a mirror like that?
A huge thank you to Brian at AlphaPhoenix for the first mirror. Check out his brilliant video showing how it was made: • Two ways to make asymm... and be sure to subscribe!
And a huge thank you to Andrew Draminski and Michael Barson for the second mirror.
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A big thank you to Brian for the first mirror. Check out his channel, it's brilliant: czcams.com/users/alphaphoenixchannel
And a big thank you to Andrew Draminski and Michael Barson for their mirror too.
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Not a big deal, but as someone who values knowledge, you might want to know that maxima and minima are plurals, if you have a single point then that point is a maximum or minimum (or as is the case for saddles, both)
@@Manoplian I think the plural is used in reference to the fact that there are multiple maxima/minima on the curve. The point being that the saddle point is both maximum and minimum in orthogonal directions.
I am sure these guys can get the mirror for you czcams.com/video/jJXBBdHOOqY/video.html
@@2treeman435 He said "a maxima" and that's not gramatically correct regardless of context.
Am I the only one that wants to see the mirror rotating?
I appreciate that you demonstrated that a Pringle, while saddle shaped, cannot be used as a saddle.
My equestrian aspirations shattered.
I guess we’ll never see usable saddles made of pressed potato sweepings. Oh well, more Pringles for me
I'm bothered by how many pringles were wasted in this video.
Absolutely lost my shit when he said that
countless lives may have been saved
You could not have possibly found a worse mask to use, but it's absolutely hilarious.
I think you mean you couldn't find a *better* one.
I think Michael Myers might have been worse lol
@@insouciantFox ¿Por qué no los dos?
My first thought when I saw it was that obviously it was a Reagan mask and he was making some obscure joke... Looks nothing like Arnie, lmao.
I don't know, pretty much ANY clown mask is creepier.
I wonder what happens if you have 2 of these kind of mirrors facing each other?
Like with 2 concave mirrors, they act like a lens and you can make a telescope.
Maybe depending on what angle they have with each other it could yield some interesting behaviour?
Yes please that would be awesome. Not sure how you would record it you'd be probably need to drill a small hole in the middle of one to get a good perspective
@@argeniside1015 it might be simpler with a simulation.
You could make one of the two saddles only half-silvered so you could see through it and record a hall of saddle mirrors.
I'd imagine you'd just be applying different levels of stretch effect in different directions, which means two saddle shapes 90 degrees apart would in theory just yield a zoomed in image, or possibly a normal image.
Crazy how Arnold Schwarzenegger sees Richard Nixon when he’s looking in the mirror 🧐
I’m 99% positive this was the old viral “say something obviously wrong to get comments” trick. And it’s working
@@tallguynow yeah I kinda felt the bait when he repeated his name so many times lol.
@@tallguynow dammit, I knew this tactic and I still fell for it.
@@amonynous9041 I don’t mind it when the content is still good. I respect good creators who also play the game well
Thank goodness someone said it...& that I didn't have a mild stroke or something.
Wait...9:30- I can tell it's A.S. now.
11/10, really made me feel like Arnold Schwarzenegger looking into a saddle-shaped mirror
Soon we will be able to be Arnold too!
WE ARE LIVING IN THE FUTUUREEH
What's it like to be Arnold Schwarzenegger watching this video?
I felt more like Richard Nixon
@@_BangDroid_😂 Thank god wasn't the only one, I could see some resemblance to Arnold at the last minutes of the video when squinting and repeating a mantra "Schwarzenegger, Shwar...". Most of the time I was mumbling in my mind "...that is Richard Nixon..." 😵😵
@@_BangDroid_ HA HAAAaa 🤣 nixon CONFIRMED !
It bothers me that the digital version of the mirror didn't come with a digital version of Arnold Schwarzenegger.
The bad mask version of Arnold Schwarzenegger.
That omission reflects poorly on the channel, for sure.
The thing I find fascinating about tiny flat-surfaced hand-held makeup mirrors is that they make your face look thinner than it truly is.
It took me a while to figure out how that works: it's just parallax plus the small size of the mirror.
there is actually a pretty common type of ornamental mirror where you can do something similar:
a helical mirror! - There are lots of helical reflective garden ornaments. They also have the turn-picture-sideways property.
i was just going to mention helical mirrors! what's really cool is that you rotate the helix by 45 degrees, so that your reflection looks right side up - NOW: if you wave your right hand, the image waves its right hand too (unlike ordinary flat mirrors). so you can use it see yourself as others see you.
Wow
Okay, being honest, the laser and fog are making such an intuitive 3-dimensional view of what is going on and I love that!
2D is harder to grasp and conceptualise, but this? That's really good
Agreed. The laser made everything click much easier to grog. While also looking cool!
I remember this being used to illustrate other concepts before and having the same intuitive impact. Looks like laser-and-fog is a fantastic tool for explaining geometry, especially for higher dimensions.
Would love to see more videos of this (laser + fog + bent mirrors) if someone has links to share.
@@ittixen cloud chambers helped lots in early nuclear physics.
The Ken doll riding the Pringle saddle is way more funny than it has any right to be
But only in a mathematical sense.
Yee haw! 🤠
Ride it, big boy!
That must've saddled down humanities' hardest physics debate for centuries
Ken rode that Pringle saddle way harder than he ever rode Barbie YEEHAW
I don't see it anywhere. Timestamp?
The rotation reminds me of how they used to rotate images quickly in computer graphics: use a shear transform (like turning a square into a rhombus) on the x axis, followed by a shear transform on the y axis, and then the result is a rotation around the center. Back then this could be implemented a lot more efficiently because instead of multiplying lots of points with a matrix using floating point arithmetic you could just shift rows of pixels a few times.
I love the shout out to AlphaPhoenix! I've been a fan of him for like 5 years now, super underrated science youtuber. One of those channels that even if I think I won't like the video because I don't care about the topic, I watch anyway and I always am happy I did.
"Maximum" and "minimum" are the singular form you should have used. "Maxima" and "Minima" are plural.
I hope you liked this pedantry.
Came here to write the same comment. It’s a bit of a pet peeve.
@@germansnowman Same here
I liked this pedantry
I could believe what I heard. Surely, he did that only to evoke comments to appease The Algorithm. Or does anyone ever really say that? Never heard it like that from anyone, let alone a "teacher"...
I liked this pedantry. Other peeves: cappucinos (it's cappucini), graffitis (already plural), vacuums, conundrums, mediums, tamale (it's tamal).
What flavour was the Pringle used? My guess is cheese and onion
It was! Damn, that's some good Pringle knowledge
@@SteveMould it looked like there were cheese+onion particles on your fingers
geoguessr but instead of places it's pringles flavors
@@embolysm I agree, but I looked at the pringle itself. Cheese and onion tends to have more flavouring particles I find
We need toknow... FOR SCIENCE!!!
One of these mirrors would be great in a science museum. Mounted on a big wheel on the wall, with the focal point around eye height while standing, and you can turn the wheel to get the different distortion effects.
Steve: "Hi there, could I please have an adjustable saddle-shaped mirror?"
Everyone: "No."
Brian: "Uhh... Sure!"
I'm waiting for Thought Emporium to sputter silver coat a pringle now
I like how you use Excel as a 3d graphing calculator
Fantastic collaboration! Love to see two of my favorite CZcamsrs working together
Yeah. I've never expected Steve Mould to collab with Arnold Schwarzenegger.
In her garden, my mother has some decorations that basically consist of shiny strips of metal that have been twisted into a helical shape, and they have that effect of turning the reflection of their surroundings sideways. It always puzzled me how that works.
The Cloudgate sculpture in Chicago, or The Bean as it’s known, is mirrored. You can walk underneath it and experience this. It’s very peculiar.
@6:32 so anxious seeing the laser hitting the camera sensor lol
Here's a question, can you make a saddle shaped lens that does something similar? Or will you just get a blurry image all throughout?
A thin saddle shaped lens should behave exactly the same way, but would be much more difficult to make. For one thing, you need to finish two precise surfaces rather than one; for another, since it's concave in one direction and convex in the other, it will need to be quite thick, so the "thin lens" approximation might break down.
nice idea, maybe it could work with 2 cylindrical lenses; 1 positive and 1 negative in the orthogonal direction. The problem with both lenses having to be at the same location might be avoided using a normal (2d) lens in between for re-imaging or maybe 2 lenses in a so called 4f configuration. Anyway that only requires standard lenses, no specials
Maybe you could get two sheets of plastic, warp them into a saddle frame, close in the sides like an aquarium and fill it with water .
Alpha Phoenix is such a good channel; it's great to see him getting more exposure.
I was wondering why the simulation looked so familiar, and realized that it looks very similar to the reflection from the bell of a brass instrument! The “flare” of the bell vs the circumference of the bell cause a similar saddle point shape. Awesome video as always!
I would love to see someone 5-axis mill (and then sand down to a good finish) two wooden blocks that sandwich together and act as the moulds for the PETG (or similar). This way the parabaloid is almost perfect as you can bring in a 3D model for CAM. By heating up the PETG and having it compressed between the two blocks, I would think there would be little, if any, warping as seen here. Also, I said wood as I believe it would be the easiest to get the required finish after the machining, but if another material is better (possibly nylon...?), then that would work too - just something that could be machined well with a small lolipop cutter or similar.
Anyway, great video Steve, and I look forward to your next ones!
Honestly as a machinist this feels like a three-axis thing to me. The curvatures and slopes are not that great, so I'd just do a bajillion passes with a ball endmill, probably from at least two directions.
@@seth094978 I was thinking that also, but I feel 5-axis would just help that bit extra for surface finish. But I’m not stopping doing it in 3-axis though, and have a billion G02s haha…
@@TheUnluckyLee ha ha. I remember the fist time I wrote a G18 G02. It was kind of terrifying to see the Z axis move like that. Also, I would probably use aluminum because it's so easy to polish and cut, and way more consistent than wood. 1145 steel would work easily too, and paper-filled phenolic resin would be great if heat transfer needed to be lower. I used to get like 32 microinch finishes on phenolic using a f#$%ing table saw.
This sounds like a collaboration project for Titans of CNC.. He has everything; 9 Axis turning and milling, EDM wire, EDM shape milling, Grind turning, multi-axis grind milling, 3D printed metal and a host of other equipment... If anyone can cut and polish a complex shape first surface mirror to micron accuracy it would be his crew
The humor in your recent videos has brought me such immense happiness and enjoyment.. I love your content, and can't wait to see what comes next :)
In my laser physics class we talked about how sometimes laser cavities are purposefully made unstable so that you can pump them harder. It made me wonder if a saddle mirror could find some use for something like that. Cool to see someone actually make one!
As someone who works in the ophthalmic optics industry, this all makes sense. It would be interesting to see the perspective of a lens lab, particularly when they have to deal with a high power mixed astigmatism (so front curve > back on one meridian and back > front 90' to that with a large difference between the two and both having a strong refractive power). It's based on transmission rather than reflection, but it should work out the same. If nothing else I can guarantee they have experience making very specific surface geometries.
The "parabolic hyperboloid" (saddle) is one of my favorite shapes.
My dad's too
4:17 did he just draw a graph with Excel?
Yeah its optimal
What about Fresnel mirrors that have normals that don't correspond to a 3d surface? You could build one where each microfacet points at 90 degrees to its position from the centre, so on the left-hand side it points upwards, at the top it points right, on the right it points downwards and at the bottom it points left and so on. I don't know what this would look like without simulating it but I think it would both scale and rotate your reflection.
I guess its possible but its just as complicated to build as what's been shown already
1:37 I felt like that pringle is rotated differently and I had a brainlag
Same
Same
I just love how you'll provide several ways to conceptualise a thing, if i dont understand one diagram ill understand another
This is one of the very rare instances where I knew the answer before I clicked the video
When I was young I had a plastic mirror square which was flexible
I have no idea where it came from or how it got it, but it was definitely part of something larger that had since been broken and lost
I ended up playing around with it a bunch which is when I figured out how it worked
Thank you for the memories as well as the details explanation! There's a lot of things in here that I had no idea about as well
That Arnold Schwarzenegger mask looks a lot like Ronald Reagan 🧐
I thought it looked like nixon 🤣🤣
It is Ronald Reagan
mixing up 2 evils is easily excused
It would be cool to have a video covering how macro lenses work.
Suggested alternative method of creating a smooth hyperbolic paraboloid mirror: 3D print polycarbonate hyperbolic paraboloid with a high resolution 3D printer, then use a vapor treatment method for polishing to an optical grade surface, then vacuum metalization process with silver or aluminum (silver offers a better reflectivity, but aluminum is generally more available at a production level while being less expensive and still offering a high quality mirror with slightly less reflectivity). There are dozens of viable ways to make this shape mirror, but in terms of material holding shape/cost/ability to make multiple iterations (can program and 3D print many different focal points/curve eccentricities)/ability to achieve the desired shape without "wobbly bits", this method offers many advantages.
Thanks for another fantastic video. I have seen this effect before though. Some fun house mirrors (though not many) more than just being alternatively convex and concave along some axis, are genuinely negatively curved albeit slightly. I wonder how they get made.
One thing did surprise me. In the UK Pringles chips are still saddle shaped. Here in Australia the situation is sad. Presumably due to cost cutting the chip is curved but only in one direction and definitely not a saddle. Nice to see they are making them properly somewhere
Having the different types of mirrors, each with their own pros and cons, made it even more interesting than just having a perfect mirror.
I used to play around with makeup mirrors trying to understand where the reflection flipped when i was a kid
I believe that having a non-symmetric face may provide some more insight into which sides are being twisted/flipped.
5:55 Ever so often I drive by an art object. A kind of mirror with a 90-degree rotated reflection. As I also need to attend to traffic I never had time t look at it more than a glance. I tried to find it a few times on Google but not knowing the name of the object I could find nothing.
Now I recognize the shape is much like your mirror. Thank you for solving a long-lasting mystery.
Tried it in Blender. The physics there are awesome. A plane turned into a saddle-mirror also reflects at 90 degrees.
7:51 I think that the horizontal stretching is puzzleing you because the face is horizontally fliped at the beggining but we can not see the difference due to it being symmetric. It would be interesting to do the animation with a non symmetric face, for example a pirate with an eye patch. Thanks for the video
8:59 even though the result is heavily distorted, the idea of a mirror flipping an image horizontally (well... unflipping...) is pretty damn cool.
the attention to detail is impressive! (I'm of course referring to the sponsor segment, where the phone has an Arnie wallpaper and the netflix profiles next to Steve are all Arnie characters)
I'm here because Alpha Phoenix's Brian Haidet has some of the best explanations of high level physics in a, "explain like I'm 5 and was dropped on my head when I was 2" type of way. His explanations rival Applied Science's Ben Krasnow, and Veritasium's Derek Muller. Brian's video on CO2 lasers is 10/10.
Amazing stuff.
0:41 is top tier content
THATS MY TYPE OF CZcamsR
In terms of making a saddle mirror non-planar 3dprinting might be the easiest way to get accurate shapes
steve + alphaphoenix collab is something I never knew I needed
9:00 "…the ultimate way to make a physical saddle-shaped mirror…"
There's an interesting construction method I saw for this many years ago. *Literal* construction as it turns out. Some people wanted to use this shape in building construction, because it can be extremely strong. You make a frame of 4 equal sides, but skewed like your adjustable mirror. Then you stretch thin strips of a material across it along those straight lines you mentioned early in the video, in both directions. They used a gauze or wire mesh. as the strips are much longer than wide, they deform easily. Once you have formed the basic surface this way, you coat it with something that can stick to the mesh (concrete in their case). A think layer would smooth out any issues, then you could spray on a mirror coating. Back then, they called the shape "hypar" (for hyperbolic paraboloid) but a quick google shows that has been re-approriated.
Oh, for Arnold movies, Total Recall is worth it.
I would say that the truly mathematical way to make a saddle is to play with soap water.
On this note: if you can make an elastic surface stiffen while in tension (drench in epoxy? ), you should be able to make a nice saddle shape.
I'm surprised you didn't mention chirality! A flat mirror shows the image flipped across the plane, so that front becomes back. But adding a concavity to the mirror in one direction also lets it flip the image along that plane, which flips the chirality back (the mirror z=x^2 reflects in the xy and yz planes). So, when you look at your mirror from far away, you're seeing (a distorted version of) how others see you! The combined result of two reflections is a rotation about twice the angle, so z=x^2 shows objects rotated 180° along the y-axis, and when you spin the mirror your reflection rotates twice as fast.
Coooool!!! (My reaction to all Steve mould videos ever). This actually reminded me of a question my friends and I came up with whilst procrastinating work. We took a Pringle, drew a triangle on it and then we’re like…what do the angles inside this triangle sum to? Because it has concave and convex axes, two angles will presumably be in spherical coordinates or hyperbolic depending on orientation.
I noticed this effect once when camping at a festival. Someone had decorated their gazebo with those dangling reflective helical plastic strips that spin in the breeze. I was fascinated by the fact that the reflection was inverted left to right if you held it at the right angle. I never could figure it out.
So maybe the easiest way to make these is to get a long strip of reflective plastic and twist it along its length.
In theory a fairly cheap alternative to doing wire edm would be to use a hotwire to cut foam into the required shape.
1:07 i want pringl(
Great video! You could also have explored similar image effects in transitioning from concave to convex with the Bean in Chicago
Love the subtle humour in your videos, Steve
The didactic quality of your videos is amazing. So many cool tricks to demonstrate physics in a comprehensible and fun way.
7:00 21st century humor scene
I litterally have an exam on exactly these types of points on curves in maths tomorrow morning (yes, 8am on a Saturday, french engineering is messed up). Thanks for reminding me to go revise! ;)
Hi Steve. An easier technque to make the mirror by hand would be using a leather hard clay slab and the wooden mats as a base. The leather hard clay will not get textured as much and when glazed and fired will have a very smooth finish. That can be easily coated in mirror surface with alpha Phoenix's machine. I'm pretty sure there will be a lot of potters in the UK glad to collab with you and make some saddle mirrors.
Friend: can I borrow your homework?
Me: 7:53
2:50 "science diagrams that look like shitposts"
2:58 agreed
Hi Steve a good but expensive source of saddle shaped mirrors is the bell of brass instruments (even better if they’re silver plated). I noticed many years ago that if you look at your reflection you don’t seem ‘reflected’ horizontally like you do in plane mirrors.
That stop after T2 just made my day, Sir. Thank you. That bit is most appreciated.
The saddlepoint is a maximUM, not maximA.
@@booty_mcscooty But you can't have a A minima or A maxima, because mini/maxima are both plurals. That would be like saying "Here are a tunas and a crackers for a snack".
7:06 Just your average Oblivion NPC texture
Those simulations are so cool. I'd immediately want to change the properties to try and simulate gravitational effects on light
I've got these self-sealing ice cube bags: you can pour water in but somehow it can't get out
i'd love to see a video explaining how that mechanism works, it still looks like black magic to me
1:13 HEY!? I was gonna eat that!!! y u drawin' on my pringle?
Nooo 😭
Isn't that similar to astigmatism? Have you looked into Zernike polynomials and optical aberrations? I think it would be a good follow up topic to this
I have astigmatism and that didn't look at all like it
@@axelprino The wavefront of astigmatism is a hyperbolic paraboloid. Did you see how the image would slant like turning a square into a parallelogram? That's part of what a cylindrical lens (to correct astigmatism) does when you give it an angle. Also, one meridian has more dioptric power than the other, making some light converge at let's say the retina, and other portion before the retina if it is myopic ot behind the retina if it is hyperopic astigmatism. That's that causes the blurrynes of astigmatism. And also the squeezing in one direction and stretching in the orthogonal direction to the previous.
I used to have natural astigmatism, then laser refractive surgery (worst mistake of my life) and now I have even more astigmatism and a bunch of higher order aberrations that can't be corrected with glasses or soft contacts.
Draminski is a cool guy!! He’s super passionate about this shape. Awesome to see his work finally on the channel!
Wow. That focal point twist got me!
And lazer light demo was the cherry on top
It feels you could be able to answer a question I've posted to many of my artist)engeneer friends: what do you see standing in a mirror sphere?
The best answer so far has been "a magnification of your eye", but i still can't imagine it.
So, what you'd see changes depending on a fair few different variables, such as the material of the sphere, the light source, and your position in the sphere.
What you would generally see is the emanation of the light source in combination with the distortions of your physical appearance. Think of a true 360 degree funhouse mirror bouncing the light/images around to create a sort of fractalized droste effect which is smeared over every curvature (which are effectively infinite because any new line can be drawn between two coordinates with infintessimally smaller ratios of difference). It would basically be a big mess of you + shine, with the reflections becoming less distorted the closer they are to you/object. So your shoes, for instance, would appear more distinct directly underneath where you're standing, before fractalizing outwards away from the object/observer.
@@EmberLung we realized that the light source would be a big issue, and also the position. I'd love to see it though. I've tried to come up with a way to build a sphere, but I definitely don't have the space.
There is a Vsauce video from 9 years ago "inside a spherical mirror"
@@Deus_Almighty I've seen it, it seems obvious something interesting will happen, but i find it hard visualizing it
@@MartinTedder I'm sure you can make it in a rendering engine
0:46 Ahh, yes, it's the famous Richard Nixon / Gary Busey version of Arnold Schwarzenegger. lol
Here from AlphaPhoenix. Nice collab u did there and good visualizations for ur explanations. :)
Another great video, Steve. Love your work.
4:10 When you said z=x*y boy did I think you were going to show video of Graphing Calculator.
It's quite interesting that 5 minutes after the release of this video, Numberphile released a video about parabolic mirrors: czcams.com/video/oSXVmuNIfRI/video.html
It is because today (May 26th) is Mirror Day in Canada
Hey Steve, I'm in Australia and just saw you on QI! Excellent work mate. 👍😎🇦🇺
Great stuff! Thanks for your content Steve!
This is in fact trivial to make, use reflective mylar foil and stretch it to square frame. The more rickety frame is used, the easier it will deform into saddle shaped mirror.
Awesome as always! Has anyone mentioned Titans of CNC as a possible manufacturer for your mirror? They love to do projects that showcase their capabilities and this kind of thing totally seems like they might have some ideas or be interested. I had recently watched their video on EDM when yours came out and had already thought your channels might do well to collab. This vid cements that suspicion! 😁
I have wondered for soooo long why only some reflections flip, thanks for quenching my brain thirst!
Is that...
Spoontrioc?
9:29 must use to be out of context
That looks like 2 Birkeland currents wrapping around each other 6:21/ 7:29 but love to see a mirror by making it more focused with the rays of light I'd love to see that in slowmotion twisting
It seems like you could have made the setup with the physical mask work if you had something like a very long bar clamp to allow you to adjust the distance and there are probably a few ways to attach something that rotates to the clamp.
i don't think that mask is arnold my dude
After he ate a Pringle he's allergic to perhaps
Isn't that Nixon?
I think so
Arniex
It reminds me a lot of playing around with a funhouse mirror. I always found it interesting when I ended up with legs at the top and bottom and no head.
The best way to understand the higher dimensions.
Things that move through the visible layer are seemingly floating, and somewhere between energy and matter where it cuts off. When shifting, it causes distortion of the physical form and likely its properties.
1:32 you are constantly saying maxima and minima while referring to a single point. Am I wrong or should it be maximum and minimum? I see this happening at my university a lot, too, is this just the classic epidemic of errors that becomes the standard because everybody adopts the error?
You're completely right. I thought it was common knowledge, especially for people with university-level intelligence.
Great! Thinking is needed in our future. My concept of this requires some deep thought. Thanks for encouraging people to think abstractly ❤️💕. Godspeed to our future generations ❤️💕
I know a trumpet player who saw this video and said the distorted reflections looked really familiar. His trumpet is silver plated, so he can see his own reflection in the back of the "bell" (the wide end) while playing. Being a tube, the trumpet is a convex mirror, but as it flares out at the bell end it concaves in the opposite direction.
Congrats Steve, you invented a new way to create cursed images. I am impressed.
I subbed because you actually went out of your way (one way or another) to subtitle this video!