Steve Mould - 2023-05-26
Get an exclusive Surfshark deal: enter promo code STEVEMOULD for an extra 3 months free at https://surfshark.deals/stevemould 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: https://youtu.be/fyD1yv-6sTc and be sure to subscribe! And a huge thank you to Andrew Draminski and Michael Barson for the second mirror. My video about caustics: https://youtu.be/wk67eGXtbIw My video about Chinese Magic Mirrors: https://youtu.be/v2yV6IeL-Jw You can buy my books here: https://stevemould.com/books You can support me on Patreon and get access to the exclusive Discord: https://www.patreon.com/stevemould just like these amazing people: Tj Steyn Pavel Dubov John Doe Lizzy and Jack Jeremy Cole Brendan Williams Alan Wilderland Frank Hereford Lukas Biewald Damien Szerszinski Marshall Fitzpatrick Heather Liu Grant Hay John Zelinka Paul Warelis Matthew Cocke Nathan Blubaugh Twitter: http://twitter.com/moulds Instagram: https://www.instagram.com/stevemouldscience/ Facebook: https://www.facebook.com/stevemouldscience/ Buy nerdy maths things: http://mathsgear.co.uk
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.
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.
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.
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
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?
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.
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.
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.
"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 YouTubers 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 .
8:59 even though the result is heavily distorted, the idea of a mirror flipping an image horizontally (well... unflipping...) is pretty damn cool.
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.
Alpha Phoenix is such a good channel; it's great to see him getting more exposure.
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
steve + alphaphoenix collab is something I never knew I needed
I used to play around with makeup mirrors trying to understand where the reflection flipped when i was a kid
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 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!
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 :)
The "parabolic hyperboloid" (saddle) is one of my favorite shapes.
My dad's too
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.
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
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!
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.
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
In theory a fairly cheap alternative to doing wire edm would be to use a hotwire to cut foam into the required shape.
0:41 is top tier content
THATS MY TYPE OF YOUTUBER
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
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.
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.
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.
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)
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.
In terms of making a saddle mirror non-planar 3dprinting might be the easiest way to get accurate shapes
@SteveMould - 2023-05-26
A big thank you to Brian for the first mirror. Check out his channel, it's brilliant: https://www.youtube.com/c/alphaphoenixchannel
And a big thank you to Andrew Draminski and Michael Barson for their mirror too.
The sponsor is Surfshark: enter promo code STEVEMOULD for an extra 3 months free at https://surfshark.deals/stevemould
@Manoplian - 2023-05-26
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)
@2treeman435 - 2023-05-26
@@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.
@ITRMUGENITR - 2023-05-26
I am sure these guys can get the mirror for you https://youtu.be/jJXBBdHOOqY
@Manoplian - 2023-05-26
@@2treeman435 He said "a maxima" and that's not gramatically correct regardless of context.
@Perryman1138 - 2023-05-26
Am I the only one that wants to see the mirror rotating?