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In another world I did get to ride in a 1933 Rolls Royce Woodie. We drove the old girl for about a 35 mile round trip. Oz, picked up the Car in England in the 1970's, had her shipped home to America. He thought it was a good investment at the time...and I believe he was right. However my favorite automotive strut about was his was a convertible Packard with a golf club port behind the front seat and a vacation box which attached to the back. All fricking original down to the top....restored by a guy who worked for packard......then there was the Model T Ford Farm Truck , with an oak flat bed and canopy with mica windows inserted into a leather arrangement covering the flat bed. He said people always wanted him to paint it something other than the flat black...and he said no because that is the way Mr. Ford wanted it so it will stay that way.
Oh by the way I grew up in a family of the Automotive mechanically inclined....me however was the designated flashlight holder or the automotive light holder so me dad could see what the hell he was doing in the middle of winter on a dark night. This was usually so my mum would have a car to drive to the University the next morning. Ya my ma went back to school when she had six kids in elementary and secondary school....To this day I loath working on automotive problems, but I know I'm capable so I do it....but I always double the amount of time it is going to take to resolve the problem. I do the basics... leave the real work to the professionals....but every time I see the cost per hour....it makes me think twice.
The following is what I want:
A. Morphosis to break up/fail
B. Thom Mayne to live in new york city.
I want this in six years. Make it happen, people.
You live in NY and want Thom to enter your local dating pool, in other words?
I love Mobius strips. Always have, always will.
I am. I week an counting for vacation/roadtrip to CO and back. Can't wait. Any tips for places to visit in KC, Denver, ST. Louis or Chatanooga?
Donna, I just mentioned Mobius strips in the "paper modeling" thread. What made you think of them? (did I miss something in TC?)
Nam, have you ever been to Colorado before? Microbreweries are quite abundant here.
City Museum in St Louis is a must-see. http://citymuseum.org/site/
Anything by El Dorado in Kansas City.
Any event that Bread! KC is doing (also in Kansas City).
The condo building across the street from the Denver Art Museum - one of only two Libeskind projects in which I can find any merit.
Boulder. And outside of Boulder, I.M.Pei's National Center for Atmospheric Research.
there is no there, I watched a little video explaining how the universe can be both infinite and bounded, and it mentioned Mobius strips, which are, in two dimensions, both infinite and bounded.
A Mobius strip can only exist in three dimensions. Every point on a Mobius strip has an x,y,z, coordinate. It is not two dimensional.
Not exactly how I would define "infinite".
A möbius strip is simply a single sided surface, at least in theory. A single-sided 3D shape is known as a Klein bottle, and unlike a möbius strip it has no edge boundaries.
Donna, see also tesseracts. Isn't that a great word?
@there is no there
been to CO but not for about 15 yrs. wasn't drinking at time, can't wait to try out the various beers etc...
Lived in St. Louis when i was younger for a few years and so am quite familiar with City Museum, awesome place!
Sarah, no power steering? Do you have strong arms?
Nam, if you want to do some hiking, there are some fabulous trails around I.M. Pei's laboratory that Donna mentioned. For tea time, try the http://www.boulderteahouse.com/ . Also near Denver, is the Red Rocks Amphitheatre and they have a nice visitor's center too. In Denver, check out the arts district on Santa Fe Ave. For brew pubs, try Vine Street Pub in Denver or Mountain Sun or their other location Southern Sun in Boulder.
Oh, and personally, I think the toroid is a good model for expressing bounded infinity.
As for your "valoor" interior, are you sure it isn't maroon instead of red? They're not rolling bordellos. Close, but not quite. Two cars ago, the one that went to almost 300,000 (yes, GM) had a maroon "valoor" interior ... and my hand-me down, three cars ago, had the plump blue "valoor" interior, sort of like taking your living room for long road trips. That one was the most comfortable car I've ever owned, and those days are gone. We have capitulated to the Europeans and Japanese. We had no choice. When I got the brochure for my current car, it was gray or tan inside, and that was it.
In St. Louis, you'll want to go to the top of the Gateway Arch, the Science Center, Union Station (less interesting than when it was just redone), and "the Hill," if you like Italian food. I no longer remember the names of the restaurants, but most are reasonably priced.
In Kansas City, you'll want to see the Seville inspired Plaza, the Sprint Arena, the general planning of the city with its fountains and traffic nodes which earned it the name "the Paris of the Plains," and take in the BBQ (barbeque, not Brooklyn-Bronx-Queens). Curt should rattle off a few places.
In Denver, the downtown core itself sucks, but the skyscraper that looks like an electric razor at the top is worth a picture. You should do the loop trip that takes you to granola infested Boulder (the original architecture of UCo-Boulder is beautiful), Estes Park, and then down the mountains to Idaho Springs, where you pick up I-70 again. If you like checking out nice homes in forested suburbs, try Evergreen, Conifer, and Genesee Park. Take in a performing event at Red Rocks amphitheater, or just see it. Yes, there is a microbrewery culture there, but someone else will need to help you with that. I'm sure there's even more to the area.
Quondam: Yes, you're correct. The example given, though, was for a two-dimensional being who only understands and moves in two-dimensional space. Then the examples in the video - including a torus - became more complex and included three dimensions.
I tried twisting a paper Mobius strip into a Klein bottle, but I couldn't.
isn't there an art scene of sorts in "lodo" (lower downtown in denver)? it's been a while, but i remember a few galleries i rather liked. there was an espn sports bar nearby as i recall. it's been a few years, so maybe it all fell apart.
oklahoma joes is widely considered the best barbeque in the area for kansas city. arthur bryant's is one of the old-school classics some of the purists like.
maroon indeed....still looks red to me.
Only need strong arms when the car is moving slowly, such as in a parking lot. And I ALWAYS need two hands to turn the wheel.
I took my car on a 2.5 hour road trip to the country today. Listened to Pink Floyd, Fleetwood Mac, and ZZ Top. Reminded myself how much I love the song Rhiannon. It makes me feel confident, empowered, or sexy. I'm not sure which, though. Maybe they're intertwined. Confidence is sexy, right? Or is it sexiness that brings confidence?
I miss Talayna's salad. it had these deep-fried croutons and some kind of cheese substance - combined with lettuce and their special sauce...
cONFIDENCE IS SEXY.
cADDING CAUSES BIZARRE CAPITALIZATIONS.
Or is it sexiness that brings confidence?
Sexiness brings confidence. Some people erroneously think they are sexy and learn the hard way, or never learn, that their confidence is misplaced.
For some, money and power, in lieu of sexiness, brings them confidence . For that variation, one only needs to listen to the news.
I started a thread.
A line on a plane is a two-dimensional entity. Once the plane (with a line on it) is turned into a möbius strip, then the plane becomes a three-dimensional entity and the line on the plane also becomes a three-dimensional entity.
Think of an architectural plan on a sheet of paper. As long as the paper is laying flat the paper and the lines on the paper are two-dimensional. When you roll up the paper, then the paper and the lines on the paper are three-dimensional.
But if you're a theoretical two-dimensional being, there is no such thing as "rolling up" the paper, because there's no conception of the third dimension. I get it, Quondam, but the parameters of the example didn't allow for a third dimension. Yet a being was still able to travel an infinite path that was bounded.
rolling up paper involves Mary Jane...and she makes you think your seeing 3 dimensional, but everything is still flat.
Flatland by Edwin Abbot
A two-dimensional being can only go only in two dimensions, x and y, therefore a two-dimensional being cannot travel along a mobius strip because the differential of every point on a mobius strip relative to every other point on a mobius strip is three-dimensional, x,y,z.
What the example you saw seemed to leave out is that the (so-called) two-dimensional being traveling along a mobius strip was actually traveling through three-dimensions, thus not actually a two-dimensional being. The actual geometry was being misrepresented.
Q, i am eagerly waiting to take delivery of Volume 1, should be here in a couple of weeks.
Quondam: a 2D surface can exist in 3D space. Such a surface could be warped into a sphere, mobius strip or Klein bottle. A 2D being would simply be warped with the surface and remain unabke to perceive the third dimension. Abbot's Flatland deals precisely with this issue.
Nam- I'd recommend the Hunter Museum in Chattanooga. Also, walk along the waterfront and the old city. I haven't been there in a loooonggg time but have always enjoyed Chattanooga. It''s a beautiful little town.
I did read Flatland in grad school, which is probably why I can easily accept an imaginary being that only exists and perceives two dimensions.
Quondam, I do see what you mean by the geometry being misrepresented. In our multi-dimensional world, it is.
The point of the video was that space can be both infinite and bounded, and the example, along with the examples of toroids and Klein bottles and others I'm forgetting, helped me understand that.
This 2d/3d conversation is too hard to grasp without pictures. I need visual aids people!'
Donna, I too read Flatland, summer 1978, Perry, Missouri. Yes, it is easy to imagine an imaginary being that only exists and perceives two dimensions, and such a two-dimensional being can only exist on a flat plane. The point is, however, that the two-dimensional being cannot percieve three dimensional space, even though three-dimensional space does exist. The two-dimensional being just can't see three-dimensional space just like three-dimensional beings cannot see four dimensional space. Thus, a two-dimensional being cannot travel along a Mobius strip because such a being cannot even percieve a Mobius strip because a Mobius strip is not a flat plane.
beta, I hate to admit it, but right now that just sounds bizarre. ;-)
But isn't the point that the 2D being would *perceive* the Mobius strip *as if it were* a flat plane, even though it isn't? And so similarly we humans can only perceive space as having three dimensions when it might actually have 10 or 20?
Here we have two two-dimensinal beings, a white line and a white rectangle, living on the flat plane of my table top. There is also a mobius strip resting upon my table top. Because the two-dimensional beings exist only in the two-dimensional plane of my table top they do not even know that the mobius strip is there. For the line or rectangle to get onto the mobius strip they would have to leave the space they occupy and go into another dimension, which is impossible for them to do, just like it is impossible for us to leave our three-dimensional space and go into another dimension.
The table top is only hypothetically flat and could be the surface of a sphere or part of the surface of a möbius strip.
Also the line has only one measurable dimension - length - making it one-dimensional.
I saw on my homepage that Eileen Brennan passed away, either today or yesterday. She had that trademark gravelly voice. She broke into show biz but if she hadn't, she would have made a darn good cocktail waitress in Las Vegas with her street smart vibe and deep voice. RIP Eileen Brennan, who was native to Los Angeles. It's kind of like getting an architecture job in a location you like - it doesn't hurt to have gone to a-school nearby.
Far from her best, and not as gravelly as she can be, but here's a clip:
I'm with Miles on the dimension thing. Sarah, you might find this helpful, it is a video of a high school student explaining dimensions:
I didn't know about that book, Flatland, I'll have to read that.
i read flatland. i enjoyed it. i also read thermal delight in architecture in school. also a good read.
Q, let's assume X and Y don't have to be straight lines. they're still lines, so you're creating 2 dimensions without a 3rd. in that case, a 2-dimensional entity could exist on your mobius strip, since the mobius strip is created by folding a 2-dimensional plane. their only experience of the third dimension is from your experience of the Z axis; since they're bound to the flat surface they have no 3rd dimension of their own.
didn't einstein's theory of relativity have something to do with that? it's still a 2-d plane that was distorted. or something like that. i don't know.
Once a two-dimensional plane is distorted as a curved surface it is no longer two dimensional, and that is what you all have to realize. You can treat one side of a gable roof as a flat (2D) surface, but you cannot treat a bowed roof or a hyperbolic roof as a flat (2D) surface.
Regarding lines that are not straight. Yes, a curved line is not straight, but it remains two-dimensional as long as the differential of every point along the curve relative to every point along the curve is a factor of x and y. Once that curved line becomes a spring or moves along the curved surface (like a sphere or a mobius strip), the differential of every point along the curve relative to every point along the curve is a factor of x, y and z, hence three dimensions. --curtkram, a two-dimensional curved line can exist on the surface of a mobius strip but only as long as the curved line remains stationary. Once the line moves along the curved surface of the mobius strip it requires three dimensions to do so. The (so-called) infinite loop of the mobius strip requires three dimensions to actually exist.
A mobius strip is not a flat surface; it is a series of curved surfaces, hence three dimensional.
Try drawing an actual mobius strip within a 3D CAD program with only x and y coordinates. It can't be done. A mobius strip cannot exist in two-dimensional space.
Quondam, does your reference above "Flatland, summer 1978, Perry, Missouri" refer to when and where you read it? I find that detail fun within this conversation.
Hey, folks, for those who are not highbrow and could live just about anywhere, here's the list for the Top 10 states for frugal living. I couldn't live in all of these, but some. I noticed that, of the western and eastern states, only Idaho made the list. I think I would be haunted by knowing Sarah Palin came from there, so I'd pass on Idaho, parts of which are very scenic. However, of the other 9, I could do Texas (The Woodlands of Houston), Arkansas (Hot Springs Village or other piney areas, but not Little Rock, which the Clintons called home), Indiana (the capital region) and Mississippi (as long as it was Gulfport or thereabouts, and looked like the FL panhandle).
Check out the slide show:
Donna, yes I read Flatland in Perry, Missouri, right about this time 35 years ago. That part of Missouri wasn't all flat though. The view from Buzzard's Roost in Mark Twain State Park is particularly three-dimensional.
While still an architecture student, I spent the summer of 1978 working for the Historic American Building Survey (HABS) stationed in Perry, Missouri, a very small town (pop. 931) 30 miles west of Hannibal (of Mark Twain fame). It was then that the city of St. Louis (120 miles south) became the 'big city' destination on several weekends. What struck me the most in St. Louis was Eero Saarinen's Gateway Arch--not only is it an incredible site from a distance, but even more amazing when perceived while walking around its base, (and I won't elaborate here about the "otherness" of its elevator ride up to the top observation room inside, which I believe I heard is something you can't do anymore).
On what was my third visit to St. Louis, I was with several of the other student architects I lived and worked with--it was their first trip. We were all around the same age and education level, i.e., early twenties and full of youthful over-confidence. I distinctly remember being asked by Mike, "So, what do you think of the arch?" (Mike and I were room mates, and we often 'discussed' architecture). I said, "I think the arch is very pretty." Well, Mike quickly told me that one just DOES NOT use the word 'pretty' when referring to architecture!--(apparently) pretty has such lowly connotations. I briefly argued that I thought 'pretty' was the best word to describe how I saw the arch, largely because I see its 'prettiness' as pretty much undeniable. I was confident I used the right word to describe how I felt about the arch.
Today, just two weeks into the 21st century, I looked up pretty in Webster's Third International Dictionary:
pretty 1 a : marked by or calling for skillful dexterity or artful care and ingenuity, esp. in coping with some difficult or complicated matter.
I am thus (finally) completely convinced I saw the arch for what it is, and then also described how I saw the arch in a most fitting manner.
Now being somewhat older (and hopefully somewhat wiser), if I were today asked what I thought of the arch, I'd say, "The St. Louis Arch is very likely the prettiest architecture-sculpture hybrid I will have ever perceived."
I'm now going to relate a story that may or may not have something to do with "feelings" and place.
I spent the summer of 1978 in Perry, Missouri (population 831) as a Historic American Building Survey (H.A.B.S.) student team member. Our team was surveying and documenting two small towns and a variety of domestic buildings that were to be demolished after our survey because the land was soon going to be under water once the Salt River Dam was complete. One of the buildings I surveyed along with Barbara Hendricks (a architecture student from Texas) was so remote that Barbara and I were dropped off in the morning and not picked up again until 4 o'clock in the afternoon. The house was named for Samuel Bell, and it was a simple 2 story farm house with a front porch, central hall, and a gable roof running from side to side. I soon discovered that we could easily get on the roof by going out one of the second story windows and onto the lower roof of the one story addition to the back of the house. I suggested we eat our lunch up on the ridge of the roof.
From the ridge of the roof a portion of the Salt River valley lay before us. The view was indeed beautiful, especially its rawness, and it was weird to think that this was all going to be under water in the near future. As a born and raised northeastern urbanite, all of rural Missouri offered me a plethora of new sensory impressions, and at this spot I found myself wondering what the "Indians" may have once thought of this place. Again, I was struck by the natural raw beauty of it all, and I said to Barbara, "I think this place is sacred." Barbara quickly retorted, "there are a lot of other places I'd call sacred before this."
About a month later, toward the end of the summer when most of the team was in the office drafting, our team historian, Travis McDonald (who is today the resident architectural historian of Thomas Jefferson's Poplar Forest), came into the office with exciting news -- demolition of the Samuel Bell house was put to a halt and the archeologists, who were also working in the region that summer, were to set up a dig there because it was discovered that the Samuel Bell house was built upon an Indian burial site. I immediately turned to Barbara and said, "I told you that place was sacred!"
In all honesty, I didn't experience any special "feelings" while I was at the Bell House. It just happened that the notion of sacredness entered my mind as I was giving a little thought to what I saw.
in your picture of the mobius strip, you could say the paper you made it out of is 2-dimensional if you ignore the thickness. when you bent the 2-d paper, you made a 3-d shape.
in autocad, i draft on a 2-d surface. space-time is distorted. that's the sort of thing einstein was talking about with relativity. so, autocad is newtonian physics.
if an entity existed on the 2-dimensional surface of your mobius strip, they would be 2-d. if you bent that 2-dimensional surface, it would not change the state or characteristics of the 2-d entity living on the 2-d surface. they would still be 2-d.
the summer of 1978 was pretty exciting for me. i had my first birthday around then!
That stipple is so pretty.
No, seriously, that stipple is lovely - it gives me feelings of longing. And it exemplifies "skillful dexterity or artful care" beautifully.
I love those stories. Let's keep arguing about dimensions just to keep you here posting on TC, Quondam!
I thought surely that story was going to end in afternoon delight, up on the roof, with Barbara-ann.
I drove by the St. Louis arch when I was a kid. We lived in Ohio, and visited my grandparents in Texas, often. We back through St. Louis, so I'm still not sure why we did that time. I just vaguely remember looking out the window, and climbing to my knees for a better view. Shame we didn't stop, but I'm not sure I would've remembered it much.
I've been reading a book about Graphic Arts procedures, published in 1957. I'm trying to bone up on typefaces and the like. The book is fascinating on some levels, and completely obsolete in others. They hadn't even invented computers when this book came out! I'm taking notes on the parts about typefaces, kerning, and leading (which I always read as LEEDing, and not the as learned LEDing), but I'm skimming over the parts on typeface drawers, and hand-setting type.
curtkram, if a 2D rectangle lived on a strip of paper, and that strip of paper was twisted into a mobius strip, then the 2D rectangle would become a 3D surface.
I don't use AutoCAD; I use ARRIS where every database is three-dimensional by default, meaning every point is assigned a x,y,z coordinate and any three points in space can be assigned as register of the active drawing plane.
Something I drew almost 11 years ago. It looks like these twisted bands are made up of many contiguous 2D rectangles, but the rectangles are actually 3D because all four corner points of each individual rectangle do not fall on the same plane; each rectangle is itself a tiny bent surface.
Of course, any three points will register a plane, so, in reality, the above twisted bands are made up of many, many 2D triangles contiguously arrayed in 3D (x,y,z) space.
Lots of beautiful graphics up above.
For something absurd, a hipster was attacked by a raccoon in NY's Central Park.
One of the comments appropriately asked if the raccoon was given an anti-hypster vaccine, since the hipster was given an anti-rabies vaccine. Spot on.
Man, I miss putting some emo music (usually Elliott Smith) on my headphones and stippling for hours. There was something so wonderfully relaxing and therapeutic about that constant motion of delicateness.
A simple example of two-dimensions: the surface of a sphere. While to our familiar outlook the sphere looks three dimensional, if an object is constrained to lie on the surface, it only has two dimensions that it can move in. The surface of a sphere can be completely described by two dimensions since no matter how rough the surface may appear to be, it is still only a surface. (wiki)
Since space is pretty much accepted as curved - introduced by Einstein with his theory of General Relativity - it seems natural that from a 3D point of view a curved surface is 3D. But to an observer constrained to that surface it would be flat. 3D space is not flat, but to us it looks flat.
It's kind of amusing seeing you argue the 2D point of view from a 3D one. And your drawing is by definition 2D, even according to your more stringent Euclidean definition as I'm viewing it on a flat screen monitor.
I have been working on a series of paintings called Event Horizon 1, 2 and 3. If they were any good, I'd post them here. Maybe I should work on them.