**ACME Klein Bottle's Frequently Asked Questions
last updated **

**Are you serious, or is this some kind of joke?**

I do make & sell glass Klein Bottles. I fill orders quickly and guarantee
satisfaction. Over six hundred presumably happy mathematicians now own my Klein
Bottles.** **

All the same, since Klein Bottles don't have many practical uses, this Klein Bottle business had better be fun. So fun is what I'm having. This is both my business and hobby.

**Who's behind Acme Klein Bottle?**

Just me, Cliff Stoll. Nobody else. No management. No employees. No investors. No profits, either.

**Are you the same guy that ...**

Yep, same guy.

**OK, so what is a Klein Bottle?**

It's a mathematical surface which has only one side. See So what is a Klein Bottle?

**Do you make these Klein Bottles yourself?**

Not any longer. I tend to overwork the welds and have burned myself too often. Worse, I take a long time to make a Klein Bottle. To keep prices reasonable, I design the Klein Bottles and make the first few, then I turn the manufacturing over to professional glassblowers.

**How do you make glass Klein Bottles?**

Using Pyrex tubing and a glass lathe.

Unlike most art-glass, scientific (laboratory) glassware is made by rotating hollow glass tubing in a flame. The turning machine, called a glass lathe, looks much like a machinist's lathe, except there's a torch instead of a cutting tool. As the tubing turns on its axis, we heat the areas we want to inflate, then blow through a flexible straw, creating pressure inside the tube. This pressure (from my lungs) pushes out the walls of the glass tubing, much like inflating a balloon.

After we get a nice pear-shape, we torch off the bottom. Next, we prepare the
inside neck -- we flare a stub of glass (that'll be the bottom flare) and bend
it so it'll meet the side. Then prepare the outside loop from another length
of tubing. The trick is to assemble the Klein Bottle from three pieces of glass
yet make it look like it's from one piece of glass. This means clean, continuous
welds, and smooth spline curves throughout. (Scientific glassblowing is also
called Lampwork, which is not the same as art glassblowing**)**

**Why Pyrex?**

Borosilicate glass (Pyrex is a Corning trademark) has a low coefficient of expansion, which makes welding pieces easier. All our Klein Bottles are handmade, so we can't get uniform temperatures throughout the bottle. With a small coefficient of expansion, the glass isn't as likely to break while working, annealing, and cooling. Borosilicates have the disadvantage of being a more difficult to work, as they require higher temperatures and tend to vitrify more easily than more common soda-lime glass.

Pyrex is Corning's trademark for borosilicate glass. Other trademarked flavors of borosilicate include Duran, Kimax, Bomex, and Simax.

**What about your wool Klein Bottle hats?**

I spent a year working with three knitters to develop a design for Klein Bottle hats. Now, a group of home knitters make these according to my design.

**Do you make money off this?**

Not much. Hand worked glass and hand-knit wool is expensive, and I sell a few every week. Seems that not many people need zero volume, boundary free, nonorientable manifolds. Even so, I occasionally speak on "Low Dimensional Topology for Fun and Profit".

**How long have you been making Klein Bottles?**".

**Do you really guarantee these?**

Yes. If you're not happy with the Klein Bottle, return it within a year. I'll refund your money. And if it breaks in the first three months (for any reason - even if you drop it), I'll replace it for $10. Every few months, someone calls for a replacement. So far, exactly two people have asked for refunds.

**Can I safely send my credit card to you?**

Yep. I handle credit card orders over the secure server, Foxycart. No problems and no complaints. I use the "PayPal Payflow" credit card processor. I never see your credit card number - it goes securely and directly to the bank.

I also accept payments via email and PayPal. My "seller reputation" is over 500, but I'd rather be known for my reputation in the field of mathematics. (My Erdös number is 3)

**What's your privacy policy?**

**How do you package these?**

Your glass Klein Bottle will be double-wrapped in foamwrap & bubblewrap, then snuggled in packing pillows or packing peanuts (usually cornstarch-biodegradable peanuts), inside an oversized box, with at least 3cm (typically 6cm) between the glass and the box-wall. I guarantee safe arrival - if it arrives cracked, I will immediately replace it. (seldom - happened once during 2010, not at all during 2011, once in 2012, none in 2013, none in 2014.)

I usually take photos of the packing process and email links to the pictures to customers. This way, you will see the exact Klein Bottle and the exact packaging which the postman will deliver.

**How long does it take to get a Klein Bottle?**

I try to ship your Klein Bottle the same day that I receive the order. If an item is listed on my website, then it is in stock. I run out of any items, I'll update the web page immediately.

In the USA, I usualy use the US Post, Priority Mail or First-Class Mail. This is 2 or 3 day service. I can also send things by UPS Overnight delivery, although this costs much more (around $50).

Klein Bottles to Canada take about a week via Airmail.

Overseas shipping is via postal "First Class International Mail" which is airmail service, and takes about a week to London, England; 10 days to Berlin, 12 days to Sydney and Tokyo. Faster overseas service is via Express Mail/EMS, which takes 4 or 5 days to Europe, Australia, and Japan.

Packages to Italy often take 20 to 40 days to be delivered. During 2011, I sent about 20 airmail packages to Italy, and five of them took over a month to arrive. Express Mail to Italy takes about 10 days to arrive.

Incidentally, UPS now charges dimensional weight for all shipments, so it's become expensive to send lightweight packages via UPS overnight, UPS 2-day, or UPS 3-day service. Dimensional weight hits lightweight boxes in this way: Any box with a density under 0.146 gm/cm^3 will be charged as if it has a density of 0.146 gm/cm^3. This is bad news for Acme's customers ... a typical Klein Bottle in an 11x7x7 inch box weighs 1 pound. This shipment has a density of 1 pound/539 cubic inches or 0.05 gm/cm^3 ... so UPS jacks up their price to a "billable weight" of 3 pounds. That's one reason why I recommend using Priority Mail rather than UPS 3-day service.

**What comes with my Klein Bottle?**

I pack your glass Klein Bottle in bubblewrap and packing peanuts. I include a calibration decal, a calibration certificate/guarantee, a sheet describing what a Klein Bottle is, a warning not to move it into 2-dimensional space, an invoice, and instructions on how to apply the decal. Much of the literature is from my web pages.

**Do you barter or trade stuff for Klein Bottles?**

Yes -- to my delight, I've traded Klein Bottles for a silicon wafer (thanks Marty!), a pair of chainmail Mobius Loops (from Benjamin Kleber -- WOW!), a Neodymium glass boule, and a boxful of fascinating sliderules (thanks Jackson -- and my smiles to Jerome!). I'm always interested in the mechanical, the old and the offbeat, such as mechanical calculators (especially a Friden Calculator or a Curta calculator), a Teletype machine, an IBM Key Punch, one of those wonderful Teachspin Muon Detectors, or other such physics/math/mechanics puzzles or gizmos.

**What do you do with defective Klein Bottles?**

Somtimes I have Klein Bottles with minor flaws or cosmetic blemishes, like oven marks, chips, or weld spatter. You can get 'em for half-price -- check the seconds webpage to see what's available. I occasionally give these to high school math circles.

**I want a model but you're out of stock...**

Sad to say, I don't backorder; I have a hard time just keeping track of orders that I'm shipping today. Best bet is to check into the website every few weeks ... I'll change the webpage when the manifold is back in stock

**I need a lot of Klein Bottles...**

Wholesale prices on Klein Bottles? Zooks! I usually stock several dozen to several hundred Klein Bottles of each type, and can send them out on short notice. I an offer a small discount for orders over 10 items. Please ask.

**Do you make Klein Bottles in Color?**

No. Due to environmental laws, Pyrex/borosilicate glass tubing is rarely available in color. Because of this, I can't make bright colored glass Klein Bottles. I once made some colored Klein Bottles using colored plastisols -- I just dipped my regualar glass Klein Bottles into colored plastic coatings. The effect was nice, but after a dozen, I stopped making them - I couldn't easily get uniform coloration.

**Do you Engrave Klein bottles?**

No. Pyrex glass is pretty much heat-proof -- so laser-engraving machines tend to melt the glass, rather than scoring or etching it. Worse, the glass has compound curves, so the laser beam gets out of focus. I used to engrave these, but the failure rate was so high that I've stopped. I suggest that you write your greeting or sentiment on the Klein bottle using an indelible Sharpie pen..

**Can I visit?**

Yes, but since I have a family, please call ahead. I try not to interrupt meals and evening storyhour so we try to limit visits to midmorning or midafternon. There's a map and directions here.

**Where are you?**

This entire Klein Bottle sales & distribution is run out of my backyard garage at 6270 Colby Street in Oakland, California ... close to Berkeley and across the bay from San Francisco. Figure an hour from Silicon Valley, what with the traffic jams.

**When are you there?**

I'm a house-daddy, so my kids take precedence over topology. I'll usually answer the phone (510 654 3958) in mid morning, Pacific time. When I'm away for more than a day or two, I'll post a note to the web page. If you wish to visit, please call first, because I often go on hikes with my family.

**Yes**

Did this question and its answer get interchanged?

**Would you make one of these for smoking?**

Nope. I make Klein Bottles, not bongs, not hookahs. A Klein Bottle is homeomorphic to a sphere with 2 crosscaps. A waterpipe (or bong) needs an input and an output, so it's likely to be homeomorphic to a cylinder, and therefore not a Klein Bottle. It's possible to make something resembling a Klein Bottle into a waterpipe, but I'm not interested in doing so. There's too many other nifty topological shapes to create!

**Wait a second -- Klein Bottles only exist in 4-dimensions. You
can't make one!**

YES YOU CAN!

Mathematicians call my glass objects "3-dimensionally immersed Klein Bottles". That is, they are Klein Bottles which have been tranferred into 3-dimensions, without cusps or folds. Also, every small patch of the immersed Klein Bottle is locally Euclidean. A mathematical immersion allows self-intersection, which, indeed, my Klein Bottles do have. My Klein Bottles are non-orientable, just like 4-D Klein bottles, because orientabilty is invarient with immersion.

A 3-dimensional *embedding* of the Klein Bottle is
impossible. This would transfer the Klein Bottle into 3-D without
self-intersection.

There is another 3-D immersion of a Klein Bottle (called the figure-eight immersion), but isn't as interesting or as useful. I may make one of these just for the heck of it.

**What's the big deal - doesn't an ordinary wine bottle have one
side?**

Well, if there's a cork in the wine bottle, then topologically it's a hollow sphere. It has two sides: an inside and an outside. An ant walking on the surface can't get from one side to the other without making a topological change (popping the cork)

If the wine bottle is uncorked, then it's topologically equivalent to a disc (if you assume the glass has zero thickness) or a solid sphere (if you assume the glass has thickness and mass. A topologist will point to the circle at the top of the bottle -- its lip -- as an edge which separates the inside of the wine bottle from the outside. This edge will not disappear if you deform the bottle. So once you make the bottle-walls arbitrarily thin, the wine-bottle becomes a disc. Again, an ant walking on it can get from one side to the other only by crossing an edge.

My Klein Bottles do not have a "lip" or an edge. The surface smoothly runs from inside to outside without actually crossing an edge. So if you make the glass arbitrarily thin (it's actually 2 or 3 mm thick), it will not change its topological properties. An ant can fully explore the entire surface without ever crossing any edge.

The nexus -- that pesky circle of self-intersection ought to be located in the 4th dimension. If this were a true Klein Bottle, the two surfaces would cross each other without intersecting. The side loop should jump into the 4th dimension for a few millimeters while it crosses the wall of the Klein Bottle. Too bad I can't demonstrate this...

**What do you mean "Zero Volume"?**

It's been mathematically proven that any bounded surface in 3-space must divide our universe into two parts: the "inside", which is bounded, and the "outside", which is unbounded. A true Klein Bottle is a bounded surface without a boundary. Because it lacks a boundary, it doesn't divide the universe into an inside & outside, and so, the true Klein bottle cannot exist in 3-space. (this is related to the Jordan Curve problem)

A true Klein Bottle has zero volume. It is a 2-dimensional manifold (which pretty much means a 2-dimensional surface). Every small piece of the Klein Bottle is 2-dimensional -- that is, if you shatter a 4-dimensional Klein Bottle, you will get 2-dimensional pieces. However, to assemble these pieces, you need a 4-dimensional space. Since the true Klein Bottle has no edge and only one side (see above), it does not enclose a volume. Math folk say that it is a 2-dimensional manifold which exists in R4.

To a topologist, an uncorked wine bottle also has no volume, since it can be stretched into a 2-dimensional disk (two sides, one edge). A sphere is a closed surface which *does* enclose a volume. A Klein Bottle, although it is a closed surface with no edge, does not enclose any volume.

Ignoring the thickness of the walls, my Klein Bottles have zero volume because they have no boundary. And yes, you can pour water into (and out of) my Klein Bottles, but they are still topologically zero volume.

**Nonorientable?**

If you draw the letter "R" on a clear label, then slide that label around the outside of a sphere, when you return it to the same place, the letter looks exactly the same. So a sphere is orientable. On a Klein Bottle, you can slide that label around so that the letter reads backwards. To do this, you'll have to slide the label all the way inside the Klein Bottle (you'll need a long pipecleaner). When it's on the other side of the glass from where it started, the label will read as the mirror image. That's nonorientable.

The Oxford English Dictionary says nonorientable means: "a figure in the surface can be continuously transformed into its mirror image by taking it round a closed path in the surface"

**Have you tried other Klein Bottle Immersions? What about the Projective
Plane or Boy's Surface?**

I'd like to make a glass figure eight immersion, but have not yet had time. Same with other topological manifolds. If you want one of these, please send me e-mail and I'll put the design onto the front burner.

**Do you sell perfume bottles or bottles for soy sauce?**

Every few weeks, someone asks me to make five hundred perfume bottles or ten thousand aromatherapy bottles. In short, I don't make ordinary bottles ... only extraordinary ones. Your best bet for wholesale glass bottles and plastic bottles is www.ebottles.com. They're a good source for generic glass & plastic bottles and have no minimum order.

**Hey - you're selling 10 DeutschMark bills and calling 'em ****
Portraits of Gauss****.**

Yep. While in Berlin, I was delighted to find the great mathematician on a banknote, so I brought home a dozen and I have a few of these uncirculated and unfolded banknotes for sale.You can't get 'em in Germany anymore. Sadly, many nice looking banknotes were pushed aside by the Euro.

**What does ACME mean?**

ACME is an English word meaning the peak, or highest point. It's derived from the Greek word <alpha-kappa-mu-eta> meaning mountain peak.

Long ago in America, the telephone book was the supreme reference guide to local businesses. Around 1925, business owners realized that the phone book listed businesses alphabetically. Since the first one listed often received the most phone calls, many businesses were renamed to the beginning of the alphabet. Soon, many small shops were named Acme - plumbers, florists, mechanics, contractors, etc. Many small businesses were named Acme - and by 1938, it had become a joke, seen in the Looney Tunes Cartoons showing Wile E. Coyote using Acme Dynamite. There's a catalog of Looney Tunes Acme products.

As an acrynym, ACME is said humorously to mean, "American Company Makes Everything". It's sometimes is used as a fictional corporation name (in the same way as "John Doe"). It's the fictional detective agency in Carmen Sandiego series. An Acme Thread is a lead-screw with square cross section, often found on piano stools and vises. And, of course, Acme Klein Bottles.

**What else are you working on?**

I've recently made a Klein Bottle Wine Bottle, as well as a glass Klein Bottle Vase.

I'm also working on **Boy's Surface**, an R-3 immersion of the Projective
Plane. With the help of Charles Pugh of UC/Berkeley, I'm working on one of these.
It ain't easy -- requires bending non-cylindrical tubing around a tight radius.
I'm trying both acrylic plastic tubing and Pyrex glass.

I'm also making a Cup of Tantalus. And a Glass Cadogen Tea Pot. And thanks to a collaboration with Stan Wagon, my Erdös Number is 3.

Can you help me rebuild a 50 year old Friden STW or SBT or SRQ mechanical calculator, or a Friden 132 electronic calculator?

Funny you should ask. Maybe - I'm becoming increasingly experienced in repairing these. Drop a note for more information.

Do you still use callsign K7TA?

Only on 40 meter CW. But that's a different story