@@blueninja012 Maybe indicators for low height aircrafts like drones? If you could make a stereographic projection for a standardized navigation system and some solar powered LEDs, you could (non-destructively and with no modification to the building) make a pretty cool network of "landmarks" on rooftops for navigation. Swap them out with IR LEDs, and it's completely nonintrusive and doesn't create visible light pollution. :> (However, this *could* have an impact on insects with access to IR ranges of vision. It might not hurt to put them near gardens to attract pollinators.) It's more of a solution looking for an issue outside of the scope of art. The application, for right now, is looking cool... And that's totally fine.
This is cool, illustrates one reason why flat maps distort the globe; shapes that on the sculpture are obviously different sizes appear as equal squares when projected
Fun theory (not fact lol): Some scientists believe in physics similar to this that prove the entire universe itself is a sphere, like planets are. Most physicists consider the "fabric of space" to be a plane. But they feel its planar nature is a projection of sorts, one similar to this. It's far too complex to really explain in a comment, and I can't say I know all the theoretical physics behind it anyway.
I heard it was egg shaped, but not quite and egg, I mean, its all fluid and flowing right? The universe I mean, I want to believe it moves like water in zero g
Saying that it's shaped as a sphere is flat out wrong, since a sphere is a 3d object. The universe is a 4d space-time continuum. The theory is that the universe maps to a _hypersphede,_ not a regular plain 3d sphere. If it's true or not, depends on if spacetime has a positive curvature. This is the part I really don't get about this theory though, since so far all of their measurement methods I've heard about seem like they wouldn't work.
@@henryseg you could have a default mount and a plate that is swappable, but I think a hole for a standard 5mm led would be good enough. (I know this is 6 years old, but the object and customizable piece model is pretty useful to think about imo.)
I was curious why it's "stereographic" (sounds like stereoscopy, but doesn't relate to binocular vision). Wiktionary (en.wiktionary.org/wiki/stereography) describes stereography as "Any technique for representing solid objects in two dimensions". So that's something I learned today :)
This could also be an excellent model to demonstrate Mercator projection in mapmaking. The two lines that are tangent to the plane would be analogous to the equator and prime meridian.
I love how I can open up my computer, type in 'stereographic projection', and immediately get back something like this that illustrates it beautifully (in two dimensions, anyway).
I don't know how you would distinguish between each square unless you count on counting ticks, where a distinction isn't necessary. Also I don't think the projection works if the balls don't touch the ground (which might be what you want to fix when you talk about fresnel, but if you're using a a fresnel lens, it would need to cover the whole area you need positioning on, also you need a direct top down line of sightq.)
John Dee was a renowned mathematician and Mercator frequenter. The scrying tools seem to use projective geometry, and the elemental tables refer to the carnot cycle and the collapse of political regimes. It seems that someone was using these processes to decipher the soyga tables. Abraham Abulafia's combinatorial methods also seem to relate to this.
maybe, but i dont think so (im no mathematician/geographer to know precisely), I believe its not possible because how are you going to project the poles? but a cool fact is: like a cilindrical projection that doesnt show poles correctly, every map is product of the political/cultural predispositions of whoever designs the map
No, there's no projection that makes a perfect map of a sphere. If you look at the grid on the sculpture itself, there aren't really squares on the sphere, but curved lines that intersect at 90° angles. Those curves get distorted into straight lines once you project them into a plane. Tho, scenographic projections are usefull just because they do keep angles the same, which is good
@@arturmizuno in mathematics it's customary to add (negative) infinity to the set of real numbers and set it to be the north pole of the stereographic projection
The squares on the sphere are smaller further from the center, so they project to an exaggerated size on the map. And if you radially transform the map to either preserve distance to center or to preserve areas, then there are no longer squares and the angles become distorted instead.
The other day I was thinking about how light rays from a sphere would distort on when shown on a wall. Then Steven Pinker talks about stereographic projection on the Joe Rogan experience Now this awesome video comes onto my feed.
If you used that method to translate the globe map onto a flat surface, would that flat map be able to be used to accurately navigate without any further translation?
late answer, but that introduces the same problem of stretching the globe area as normal maps. In general it should be possible to use it as a map but as shown in the video the points near the northpole will be displayed with a huge distance in between, also if you want to cross the north pole, you'd leave the map at one side and enter at another. In principle it should be possible to navigate with that, but it seems highly unpractical
@@dw-rh6fb in fact i have not before, so thank you for showing me. I still stand by my opinion of this kind of map being impractical, as the outer rings seem way more apart than they are in reality. If you only need information about the northern hemisphere, then maybe it could be used
@@dw-rh6fb You asked a question, got a good answer, asked a dumb question, got another good answer, and you're saying his opinion doesn't matter? The irony is hilarious. He also never presented any 'flat map', he just analyzed your idea, so there's minus a few points for reading comprehension as well.
Stereographic projection allows you to uniquely assign every point in the sphere a point on the plane (except for one of the poles, which is the light source). Think of it like sailors using maps to traverse the sea. In fact, this type of function is called "chart" because of that. Charts for the sphere are extremely useful in physics and mathematics, since they arise in many calculations.
A more direct application is that you can calculate the surface area of the sphere using charts. Alternatively, you can use something called the "divergence theorem".
Right, the other guy didn't actually answer your question for how you might use this in the real world: maps. Specifically, maps of continental size or greater, especially those of the whole Earth.
every flat map is a projection (you cant draw the information of a sphere precisely on a flat piece of paper, you need to distort form, or distort distance, or distort proportion), as an exaple search the wikipedia list of map projections, each projection is a way to represent the earth (roundish) to a paper/screen (flat on an euclidian plane) this is precisely (or precisely answering your question) a model for visualising the projection (representation) of one specific projection to an audience (like a group of students in a classroom or and educational youtube video) so its like using a string and a pencil to draw a circunference proving what a circunference is what i mean is that it is a tool for teaching
In my engineering class, we learned about stereographic projections to be able to represent layers of minerals and their intersections for later terrain movement (excavating, platform building, extraction of resources). It seemed the best way to do it because it allows you to represent lines with dots and planes with curved lines. It really simplifies everything and you can make yourself an idea of any (underground) terrain by just looking at its stereographic projection
I did something similar for an art project back when I was in school.. I didn't take it to this level of trying to make perfect geometric shapes on the floor, but instead used layering to make unconnected parts look like solid shadow objects.. I wish I had taken it to this level now..
From the thumbnail, I thought that it was a shiny ball (like the ones they use in VFX) and the floor was lit up, like a dance floor, and the ball simply reflected ut. 😅
3d printing is going to help advance human understanding of the physical world by leaps and bounds. Even as a simple teaching aide; these things will bring new understanding to younger generations.
I really wish substance painter got that projection feature. I can already think of soo much application to project tileable textures onto ackward shaped round objects
can't wait for this to get recommended to everybody
lol that do be how it works
It already did
How??????
It begins….
It did.
Also ive never seen “2w ago” it’s always “14d ago”
I’m really late, but this is just so simple but so elegant. Also it looks awesome, and I can actually see there being decent application for it
I got thos recommended to me as well, all of us within 1 day
Yooo you guys too?
Hey! Recommended gang rise up
I'm curious what application it could have
@@blueninja012 Maybe indicators for low height aircrafts like drones? If you could make a stereographic projection for a standardized navigation system and some solar powered LEDs, you could (non-destructively and with no modification to the building) make a pretty cool network of "landmarks" on rooftops for navigation. Swap them out with IR LEDs, and it's completely nonintrusive and doesn't create visible light pollution. :> (However, this *could* have an impact on insects with access to IR ranges of vision. It might not hurt to put them near gardens to attract pollinators.)
It's more of a solution looking for an issue outside of the scope of art. The application, for right now, is looking cool... And that's totally fine.
This is cool, illustrates one reason why flat maps distort the globe; shapes that on the sculpture are obviously different sizes appear as equal squares when projected
It is the Global lie that distorts the maps... It's mostly flat and unmoving! Time to break the spell!
Yeah either the shape has to be changed or the land mass of countries towards either pole is increased (no country really close to the South Pole tho)
@@OmegaGenesisTrueEarth dammit I thought ferfers were laughed into irrelevance.
@@OmegaGenesisTrueEarth Yeah, those darn lizard people turning the frogs gay
@@OmegaGenesisTrueEarth I'm sorry, but the only thing you're breaking is my faith in humanity
Fun theory (not fact lol): Some scientists believe in physics similar to this that prove the entire universe itself is a sphere, like planets are. Most physicists consider the "fabric of space" to be a plane. But they feel its planar nature is a projection of sorts, one similar to this. It's far too complex to really explain in a comment, and I can't say I know all the theoretical physics behind it anyway.
I heard it was egg shaped, but not quite and egg, I mean, its all fluid and flowing right? The universe I mean, I want to believe it moves like water in zero g
Saying that it's shaped as a sphere is flat out wrong, since a sphere is a 3d object. The universe is a 4d space-time continuum.
The theory is that the universe maps to a _hypersphede,_ not a regular plain 3d sphere. If it's true or not, depends on if spacetime has a positive curvature.
This is the part I really don't get about this theory though, since so far all of their measurement methods I've heard about seem like they wouldn't work.
@@Mernom there is the n-sphere
The universe may be just an emergent property of some underlying process.
See also Eric Weinstein talking about E8.
neat! How about a version which actually has space for a single LED in the exact right position?
+Kram1032 The problem is what the mount should look like - it would need a different design for every kind of LED.
@@henryseg you could make one with a hole at the dead centre that you could line up any old light to- phone flashlight, normal flashlight, etc
@@henryseg I could see something that has an LED inbuilt, along with a lil knob that moves the LED up and down to "focus" it
@@henryseg you could have a default mount and a plate that is swappable, but I think a hole for a standard 5mm led would be good enough. (I know this is 6 years old, but the object and customizable piece model is pretty useful to think about imo.)
Ikea sells a usb powered led lamp (halvklart) that has a magnet and a sticky back. It would be an ideal candidate for this
Properly explaining something like this in 1 minute is a talent! Well done 👏
This is really cool! What software/instruments did you use to make the sculptures?
I use the 3d CAD software Rhinoceros.
I’d use the drums and piano.
@@official-obama how about mayonnaise
No Patrick, mayonnaise is not an instrument!
@@diagoleben, it’s just the object you place on an escalator
New thing: Stereographic projection. Using light rays to map from the sphere to the plane.
Amazing Henry Segerman, some wonderful work in your posts.
The math has more impact IMHO because it is happening in the real world. Diagrams or simulations have less of a magical quality. Great concept!
Great work, Henry, excellent use of the medium.
Brilliant, I love it!
I was curious why it's "stereographic" (sounds like stereoscopy, but doesn't relate to binocular vision). Wiktionary (en.wiktionary.org/wiki/stereography) describes stereography as "Any technique for representing solid objects in two dimensions". So that's something I learned today :)
This could also be an excellent model to demonstrate Mercator projection in mapmaking. The two lines that are tangent to the plane would be analogous to the equator and prime meridian.
As a topology tutor, I want a 3d printer so bad.
This would make for a cool demonstration
I love how I can open up my computer, type in 'stereographic projection', and immediately get back something like this that illustrates it beautifully (in two dimensions, anyway).
Here before this blows up in everyone's recommended videos!
This deserves s billion views.
these would be cool to use as lights in public places like car parks and stuff like that
See you in 5 years when the algorithm recommends this to everyone
We're a bit early
Hey Henry, loving your 3D prints and your designs... and this vid is 9 years old! How I wish I'd found your channel earlier 🥲
Thank you. That helped me visualize SPs in my noggin much better.
I thought that was CG for a second! That's awesome!
You've been blessed by the algorithm.
Simple yet elegant, very cool, to the point
Awesome! Straight and simple!
See yall in 3 weeks when this has 1.4 million views
Cool it's like the reverse of the cylindrical mirror pictures.
This has been recommended to me nonstop for at least a week
Yay! You repeatedly fail to disappoint me.
Can one fail something one never tries? :p
Best compliment ever.
I was here 8 years late, but man i cant imagine being that late!
(This is towards all whom see this in their recommended years later)
Excellent simple visual demonstration
this would make a really cool lampshade
Can this be used for indoor positioning systems, in combination with the Fresnel lens effect?
I don't know how you would distinguish between each square unless you count on counting ticks, where a distinction isn't necessary.
Also I don't think the projection works if the balls don't touch the ground (which might be what you want to fix when you talk about fresnel, but if you're using a a fresnel lens, it would need to cover the whole area you need positioning on, also you need a direct top down line of sightq.)
This is awesome! I'd love a lampshade like this
idk why this got recommended to me 8 years later but hey its pretty cool
THANK YOU for not making this 17 min video so you could say all that in the last 1:07 of the video!!
Beautiful, great work.
John Dee was a renowned mathematician and Mercator frequenter. The scrying tools seem to use projective geometry, and the elemental tables refer to the carnot cycle and the collapse of political regimes. It seems that someone was using these processes to decipher the soyga tables. Abraham Abulafia's combinatorial methods also seem to relate to this.
This could make an amazing base for cool coffee table. I actually want that.
I don't quite know why this got into my recommended, but I'm very glad it did!
Huh new reprint of Commander’s Sphere lookin sick
Reccomendations giving us hidden gems once again
That's exactly why I love the witness
This is something I didn’t know that I didn’t know and I enjoyed your quick, educational format. You’ve earned a like from me.
Nice, easy to understand definition that's well-illustrated. Thank you.
This is pretty good for people who don't understand why maps are not 100% acurrate on scales
Thanks for this amazing recommendation youtube.
That looks so beautiful
Finally this was what I was looking for
Such a cool demonstration
This is appearing in everyone's recommended after 8 years.
accidentally watched this with my good headphones. man got the asmr mic
Uzui vs upper 6 looks really good.
That would make a really cool chandelier
Pov :you got this this in your recommendation after 10 years
Not to diminish how cool this is, but... that would make a really nice Candle Holder.
If you do infinity many squares wouldn't that be a perfect map of a sphere?
if you put it on earth then itd be weird but sure you can have a nearly closed sphere
maybe, but i dont think so (im no mathematician/geographer to know precisely), I believe its not possible because how are you going to project the poles?
but a cool fact is: like a cilindrical projection that doesnt show poles correctly, every map is product of the political/cultural predispositions of whoever designs the map
No, there's no projection that makes a perfect map of a sphere.
If you look at the grid on the sculpture itself, there aren't really squares on the sphere, but curved lines that intersect at 90° angles. Those curves get distorted into straight lines once you project them into a plane.
Tho, scenographic projections are usefull just because they do keep angles the same, which is good
@@arturmizuno in mathematics it's customary to add (negative) infinity to the set of real numbers and set it to be the north pole of the stereographic projection
The squares on the sphere are smaller further from the center, so they project to an exaggerated size on the map. And if you radially transform the map to either preserve distance to center or to preserve areas, then there are no longer squares and the angles become distorted instead.
Wow, this makes me understand how universe works.
This is undeniable proof that the earth is flat
That's awesome..... I want a lamp shade like that now. 😁
You made my students happy. Cheers
Incredibly satisfying
Gonna have to leave my mark for when this gets recommended again to me
The other day I was thinking about how light rays from a sphere would distort on when shown on a wall.
Then Steven Pinker talks about stereographic projection on the Joe Rogan experience
Now this awesome video comes onto my feed.
this would be a brilliant candle holder!
very thought provoking
If you used that method to translate the globe map onto a flat surface, would that flat map be able to be used to accurately navigate without any further translation?
late answer, but that introduces the same problem of stretching the globe area as normal maps. In general it should be possible to use it as a map but as shown in the video the points near the northpole will be displayed with a huge distance in between, also if you want to cross the north pole, you'd leave the map at one side and enter at another. In principle it should be possible to navigate with that, but it seems highly unpractical
@@HerrSurIix lol. Have you even seen the Gleason map?
@@dw-rh6fb in fact i have not before, so thank you for showing me. I still stand by my opinion of this kind of map being impractical, as the outer rings seem way more apart than they are in reality. If you only need information about the northern hemisphere, then maybe it could be used
@@HerrSurIix your opinion doesn't matter now like it didnt matter before. Im just letting you know your idea of the flat map was hilarious.
@@dw-rh6fb You asked a question, got a good answer, asked a dumb question, got another good answer, and you're saying his opinion doesn't matter? The irony is hilarious. He also never presented any 'flat map', he just analyzed your idea, so there's minus a few points for reading comprehension as well.
Why does this suddenly recommended to me??
Very cool :)
Holy shit im impressed. I never really thought about this.
Thank you UA-cam recommendations
I'm interested on 4D stereographic projections now.
Cool, learned something new today :)
Cool! What applications is this used for in the real world?
Stereographic projection allows you to uniquely assign every point in the sphere a point on the plane (except for one of the poles, which is the light source). Think of it like sailors using maps to traverse the sea. In fact, this type of function is called "chart" because of that.
Charts for the sphere are extremely useful in physics and mathematics, since they arise in many calculations.
A more direct application is that you can calculate the surface area of the sphere using charts. Alternatively, you can use something called the "divergence theorem".
Right, the other guy didn't actually answer your question for how you might use this in the real world: maps. Specifically, maps of continental size or greater, especially those of the whole Earth.
every flat map is a projection (you cant draw the information of a sphere precisely on a flat piece of paper, you need to distort form, or distort distance, or distort proportion), as an exaple search the wikipedia list of map projections, each projection is a way to represent the earth (roundish) to a paper/screen (flat on an euclidian plane)
this is precisely (or precisely answering your question) a model for visualising the projection (representation) of one specific projection to an audience (like a group of students in a classroom or and educational youtube video)
so its like using a string and a pencil to draw a circunference proving what a circunference is
what i mean is that it is a tool for teaching
In my engineering class, we learned about stereographic projections to be able to represent layers of minerals and their intersections for later terrain movement (excavating, platform building, extraction of resources). It seemed the best way to do it because it allows you to represent lines with dots and planes with curved lines. It really simplifies everything and you can make yourself an idea of any (underground) terrain by just looking at its stereographic projection
I was gonna subscribe, but I realize I'm already subscribed. Sweet!
There are certain voices that are just hypnotizing
Concise demonstration. Good video
why did i get recommended this
thanks now i know whats stereographic projection
I did something similar for an art project back when I was in school..
I didn't take it to this level of trying to make perfect geometric shapes on the floor, but instead used layering to make unconnected parts look like solid shadow objects..
I wish I had taken it to this level now..
This is about to blow up
From the thumbnail, I thought that it was a shiny ball (like the ones they use in VFX) and the floor was lit up, like a dance floor, and the ball simply reflected ut. 😅
Good simple explanation of stereographic projection.
I now know two things: youtube recommendations is a mystery
And light is freaking weird
Good job!!! I would love to have that pencil holder for my desktop 🥰
thank you henry i very much enjoyed this
3d printing is going to help advance human understanding of the physical world by leaps and bounds.
Even as a simple teaching aide; these things will bring new understanding to younger generations.
This is so satisfying THANK YOU for sharing this ! I
i thought this was a 3D model plus really good lighting render.
very nice ray tracing
2D Shadow of a 3D model. Wow!🔥
That was so nice to look at
this gon go viral
excellent board game field
The bg audio in this made me check to see if it was raining outside
8 years!
Is it just me or someone else thinking those shadows look really crisp clear, like dang the rendering of the Matrix really is good huh
Phone flashlights use very small LEDs. The smaller the light source, the sharper the shadows.
What that's so cool I want a lamp like that now.. :D
i feel like this is going to blow up
I really wish substance painter got that projection feature.
I can already think of soo much application to project tileable textures onto ackward shaped round objects
This could be such a cool RGB desk lamp
very nice, I really like this one. it would be fun to make this out of wood.
Thanks for the good video
That's really cool. Thanks.
And how knew that this is a perfect explanation to globe earth and Mercator and similar projection maps of the earth....
Helps me better understand shadows and objects in four dimensions.
Finally! Grid projector