Okay so about 30 or 40, maybe 50 years
ago my father, who's a bartender, brought
for me a saloon sign, a beer sign, a neon
beer sign for Ballantine ale and beer.
I mean it's a neon sign! Been in my
attic for decades. You know, there's
something cool about the Ballantine logo.
It used to say purity, body and flavor. I
hauled this out of the Attic, got a neon
sign transformer up, and figure - hey I gotta
light this up. Throw a switch and hot
damn! Ballantine ale and beer! The
beautiful thing is this is the neon
representation of a Borromean ring. The
cool thing about a Borromean - or as some
people say a borro-mean - ring is it's a
knot that's not a knot.
One circle, another circle, and another
circle intersect and you can't tear them
apart from one another.
This can't be removed from this, can't be
removed from this - and yet they don't
even have to touch one another. As an
aside you can prove that you can't make
this out of three perfect circles - don't
intersect. These three circles; purity
body and flavor, are interlinked under,
over, under, over, under, over, under, over.
The - of course the neon is a cheat! Look at
this: it goes under, over, over, over, over,
under and on. So it's a projection of the
Borromean rings onto the front window of
a saloon. They had to do this; the neon
sign maker couldn't make a neon sign
that had these correct without pretty
much standing on their head. Partly
because making three circles that
intersect like this, you can show that
they can't be planar circles, they have
to be - at some point or another each
of them has to be slightly out of the plane;
which is gonna be a challenge for a neon artist.
(Brady: But you can do that cos they're slightly out of the plane.)
Yeah! Notice how this guy is out of the plane
and this, this cheat entirely - they should
really go under and back over and then
down. So moreover I'd have to do it
electrically with three different
circuits. Each ring, of course, would need
to be a separate electrical device
because these aren't electrically
connected - they're not physically
touching one another. Here I've got every
electron going through this letter E,
goes through all three of these almost
circles, and then continues on to the B
in beer. The cheat, of course, is they want
it to look like it's right. And that's
good enough to attract people. to hang
out the bait in front of the bar. - (Brady: I think that's cleverer!)
Neon people are clever. Look - look what they've
done with letters, like the letter A.
Euler's topology suggests that the
letter A should not be a makeable letter.
Happily people who make neon don't
listen to topologists. More than that,
they don't keep their entire neon sign
in 2-space. They're perfectly happy to
use 3-space and project their
message onto the 2-space of the window
and ultimately onto the 2-space of our
retinas. Meanwhile I got this wonderful
gift - someone gave me a hot glue gun. And
I'm playing with this hot glue gun, I
realized - hey, you know I can use this to
attach - check this out - to glue magnets
onto strings so that I can make strings
that hook up to one another.
Mathematically this isn't a knot. It only
becomes a knot when the ends are
connected. So a mathematical knot must
have continuity. This is called the
unknot; it's a circle. The unknot can be
wrapped around itself, you know it's not
obvious now that this is an unknot,
but it is. An overhand knot, like this;
this is not yet a knot but becomes a
knot when I connect the ends together. So
here's an overhand, or a trefoil knot;
mathematical trefoil knot. Okay, so I made
three strings that have magnets on 'em; and
I want to make Borromean rings. Let's go
over here, under here, below here, below
here, above here, above here, above there,
below there - connect these. Now let's make
this one the bottom one, this one goes up
there, this one goes up here; and although
it's not as beautiful as the neon knot,
here's a Borromean ring! Over, under, over,
under; this guy's over, under, over, under.
This guy, the purple one: over, under,
over, under.
Now what's wonderfully neat is these are
completely linked with one another, but
disconnecting any one makes everything
fall apart. So I'll disconnect just the
purple, and the other two although still
tied to one another, fall out.
The Borromean rings require each other
in order to form these links. If you can
find a glue gun, a couple magnets and a
couple pieces of string - you've got it
made! There's, there's all the ingredients
that you need to explore knot theory! But
meanwhile I'm saying; well I'm playing
with these knots, I can look over at the
at the knots of neon from a beer company;
well I head over to the glass shop and I
say - oh I'll make a knot out of neon! My
friend Lucas Clark makes a neon knot
which, as far as I know, they're kind of
rare. He makes a neon knot out of, out of
tubing and as you can see it's not a
true knot. Remember how real knots have to
have their ends connected? So this looks
to some people to be a knot, but in fact
it's homeomorphic to a cylinder unless
you're an electron. If you're an electron you
have to travel in an entire circuit
through a transformer and back to the
other way, so to an electron it's a knot.
To my eyeball - ah it's still cool looking.
(Brady: What happened to your dad?)
He died 22 year- 32 years ago. - (Brady: What was his name?)
Cliff. I'm Cliff jr. He was a wonderful man. The
kind of- my dad, oh! He lived to be around
his kids. All he cared about was having
fun with his kids. So, okay Brady, so I'm
six years old my father comes home from
the bar, where he's worked a long time. He
starts drinking some beer and I say, hey
Dad can I have some of your beer? He says
nah, when you're older. So I turned 12, 13
years old - we're listening the radio
together I turned to my father and say,
dad can I have some beer? He said you're
only 12, you can't have beer! The day I
turned 18, went to the draft board
got my draft registration; came home said
dad can I have some beer now? My father
says no not right now, I'll tell you when
it's okay. Well, I never asked him again.
In my whole life I've never had a drop
of alcohol. Never had a beer, wine,
vodka - nothing. But I can't see a beer
sign, I can't see an advertisement for a
wine or a liquor, without thinking
wonderful thoughts about my father.
So it's going back in the Attic now. My
wife and I put it in our front window
for a few days,
entertain our neighborhood. People
started coming up on our porch banging
our door saying, where's the beer?