Old man sweater

This is the last of my Christmas gift knitting ... finished in April!  Robert had been wanting an "old man sweater" since Christmas 2015, when I made an olive green cable cardigan for our nephew, who was then six months old.  I wanted to knit one for him, but I wasn't quite sure what he wanted, and I definitely didn't want to knit him something he wouldn't like.  When the Interweave Knits Winter 2017 issue showed up, with a feature on sweaters for men, I was excited, and with Robert's cooperation, I mashed up two of the patterns in it to make this sweater for him.

He decided he wanted a pullover, not a cardigan, and we agreed that a shawl collar was required.  This would point to the Donegal Sweater, but he thought the collar poofed out too much at the back of the neck, and he wasn't wild about the stitch pattern - he really wanted cables.  He did like the cable panel on the back of the Belfast Cardigan, although he didn't like the overall fit or styling on the model.  So I replaced the decorative panel on the Donegal Sweater with a slightly adapted version of the cables from the Belfast Cardigan (the stitch counts were only off by one, so that was pretty easy).  I measured a ready-to-wear sweater that he wore a lot last fall and winter to choose the size, and then I started knitting.

Unfortunately, I started with the wrong size needles, so I had to re-knit half of the first sleeve when I didn't get gauge, and I was also knitting or sewing several other things for Christmas, so I ended up wrapping one and a half sleeves to put under the tree on Christmas morning.  I finally finished the sweater in April, and Robert loves it!  He got to wear it several times before the weather warmed up too much for wool sweaters, and every time he wore it he eagerly reminded me that I had made his sweater!  The fit is pretty good - the sleeves are a bit long and wide, but that certainly hasn't stopped him from enjoying wearing it.

Pattern: Donegal Sweater, with modifications
Size: 47"
Yarn: Valley Yarns Northampton, Color #50 Medium Grey, 100% wool, seven skeins
Needles:  US6 for ribbing, US9 for body
Started/Completed: December 2016/April 2017
Modifications: Replaced the decorative stitch pattern on front and back with cable panel from the Belfast Cardigan.  Reduced height of the the back neck shawl collar

Knot theory socks finished!

I finished the knot theory socks in time to give them to my advisor on the day of my Ph.D. hooding.

As I said in my first post about these socks, the left sock (on the right in the pictures; it has four crossings) is a braid representation of the figure eight knot.  The right sock (on the left in these photos, and with six crossings) is a braid representation of a link: the Borromean Rings.

The Borromean rings are a 3-component link, meaning that it consists of three pieces of mathematical string, arranged in 3-dimensional space, with the two ends of each string glued together.  If we ignore how they are arranged in space, what we have is a collection of three circles.  The special thing about the Borromean rings is that they are the simplest Brunnian link.  A Brunnian link is a non-trivial link (with any number of components) with the property that if you remove any one component, the rest form an unlink.  (An unlink is a link in which each component is an unknot, and the components don't interact with each other at all.)

I think these socks turned out wonderfully.  I want to make a pair for myself!


Pattern: The cables are my own design. I referenced the book More Sensational Knitted Socks for numbers of stitches in the heel and toe.
Size: 64 stitches
Yarn: Knitpicks Stroll Fingering in Blue Violet Tonal
Needles: US0 (2mm) DPNs
Started/Completed: April 2016/May 2016
Modifications: No pattern to modify!

Knot theory socks!

I'm a knot theorist.  (I've posted about this before.)  I defended my Ph.D. thesis last week, my semester ends next week (with me grading lots of finals ... ), and my graduation will be in mid-May.  I can barely believe I'm actually done, and I'm really excited to start my new job in August!  These knot theory socks are a present for my advisor, to thank her for all of the many, many things she has done for me.  I feel so lucky to have such a great advisor.

So, about the socks: purple is the unofficial team color of our research group, so choosing purple yarn was obvious.  I wanted a design that was knot-theory related, so this sock has a braid on the outside of the leg.

A bit about the math:

A knot is an embedding of a circle into 3-dimensional space.  Intuitively, we can think of a length of string that has been tied up in a knot and then had its ends glued together.  It is in some essential sense still a circle - if you were a tiny ant walking along the string, you would eventually get back to where you started, so all you would be able to tell would be that it is a circle (you wouldn't be able to gather any information about how it was knotted up).  In simplest terms, the basic question of knot theory is how to tell different knots apart.  More generally, knots and links (with more than one circle, but still knotted up somehow) are really important to how mathematicians understand 3- and 4-dimensional spaces.

Every knot and link can be represented as the closure of a braid.  A mathematical braid is a set of strands, all oriented in one direction, that can cross over each other but not loop back on themselves.  To take the braid closure, we glue the top and bottom ends together, with the rightmost top end glued to the rightmost bottom end, and so forth.  If we take the braid closure of the braid on this sock, we get the figure eight knot, which is a really cool knot!

The figure eight knot is the second-simplest non-trivial knot (the simplest is the trefoil), and it has the property of being amphicheiral, which means that it can be stretched and rearranged into its mirror image.  This is a very cool property!

The second sock (which I've already started) will have a braid whose closure is the Borromean Rings.  I'll explain why they're so cool once I've finished knitting the braid.

Being a mathematician improves my knitting

I am a mathematician.  The fact that I am a mathematician shapes the way I think, and slips out when I tell my mom that she doesn't need to worry about my apartment flooding because it's at a local maximum, or how I have a special appreciation for the non-simply-connected geological features at Arches National Park, or in my knitting.  Lately I've been noticing how my mathematical ways of thinking are helping me knit this little cable cardigan (Trellis from Knitty) for my nephew.

Modular Arithmetic: This particular cardigan has an 18-row cable pattern that repeats several times beginning with row 9 of the sweater body, while at the same time you knit a buttonhole every tenth row beginning in row 5.  So I know that I need to put a buttonhole in row 5, 15, 25, 35, and 45.  I want to start counting my rows with row 1 of the CABLE PATTERN, so using the new numbering system for rows, I'll be putting buttonholes in row 7 (this is the second buttonhole), 17, 27, and 37.  Then using modular arithmetic (also known as clock arithmetic) I reduce those modulo 18 and work buttonholes in rows 7, 17, 9, and 1 of the CABLE PATTERN. For me, this is much easier than trying to keep track of one count for the cable pattern and another for the buttonholes - instead, I just track everything in terms of the cable pattern.

Symmetry:  If you look closely at my photos in this post and compare them to the photos in the pattern, you'll notice that I changed some of the cable crossings.  Many mathematicians care a lot about symmetry (non-mathematicians care about this too, of course, but we're trained to notice it wherever we can).  This is a case where I think the pattern-writer was wrong.  If you imagine a vertical line going down the middle of the back of the sweater, in the center seed stitch column, and think of reflecting one side of the sweater across that line, you would get the other side of the sweater.  This is called a reflectional symmetry, and it makes for a much more pleasing image than what is written in the original pattern, with all of the large fancy cables twisting to the "right" and all of the little cables twisting "left."  I fixed this so that the two large fancy cables on each of the front and back twist toward the center, and each of the little cables twists toward the large fancy cable it frames.  

Braids:   This one doesn't really improve my knitting as much as add to my enjoyment.  My research is in knot theory, which is closely related to the study of mathematical braids. Every knitted cable is a braid; in this sweater, each of the fancy cables is a two-strand braid, and each of the little cables is a four-strand braid.  Referring back to symmetry for a moment, the mirror image of a braid is its inverse, so in this sweater we see braids paired with their inverses.  It makes me so happy when my work shows up in other areas of my life!  I'm so glad I'm a mathematician - if I wasn't, I wouldn't be able to properly appreciate this little sweater!