Wednesday, January 17, 2018

Penrose Connections


Two years ago I was granted a sabbatical to study the history of mathematics in northern Europe from the Renaissance to the present, and I kept a blog at this link about that trip.  Two months ago opportunity came up to revisit one of the locations I had spent time in on sabbatical, the amazing city of Edinburgh.

Even though I was there "just for fun" this time, I couldn't help but look into some of the things related to math that I had missed initially.  One mathematician I'm quite interested in is Roger Penrose whose "impossible shapes" made it into the movie Inception.

Penrose's mathematical work takes inspiration from many places, including the world of art.  He collaborated with artist M. C. Escher, and he had an uncle who was an artist and a collector of surrealist art.  This uncle was Roland Penrose, and his collection is housed at "Modern Two" in Edinburgh.  The rest of this blog consists of photographs I took in the Roland Penrose Gallery of "Modern Two."  They may give a sense of one influence in the life of mathematician Roger Penrose.




Maternity by Miro
Never Again by Tanguy
Magritte
The Black Flag by Magritte
Untitled by Roland Penrose
The Joy of Living by Ernst
Hat in Hand, Hat on Head by Ernst
By Roland Penrose




Monday, December 18, 2017

Edinburgh for Inklings

Dear Inklings,

I thought this would be a good venue through which to share about my and David's recent celebratory trip to Scotland.  I'll just choose two highlights - reason for celebration - and bell ringing (since that ties in with our recent reading of Sayers' Nine Tailors).

REASON FOR CELEBRATION:

On November 2, 2017 we celebrated 10 years of stroke recovery for David.  Among other reasons for our trips, climbing Arthur's Seat in Edinburgh seemed a particularly good way to celebrate that recovery:
St. Margaret's Loch, ruins of St. Anthony's Chapel, and Arthur's Seat
Arthur's Seat
Ten years ago David suffered a massive stroke and spent a month in rehab relearning how to walk (as well as relearning a lot of other things).  Last month he climbed to the top of Arthur's Seat, which towers over the city of Edinburgh.  I consider this a picture of triumph!

BELL RINGING AT ST. CUTHBERT'S:

I had worshiped in St. Cuthbert's last spring during my sabbatical.  It is Presbyterian, which is closely related to my faith tradition - and it is also where John Napier, a mathematician I'd been there to study the previous year, had served as elder in the 1500s.  

While looking into worship times for this fall, I noticed that bell-ringing practice would be taking place on Tuesday night while we were there.  I looked into attending practice and was told by one of the clergy that I might be allowed to sit in - certainly if I were a bell-ringer from elsewhere I would be - but that it wouldn't be a sure thing since I was not myself a bell-ringer.  Because David and I had only three days and so much we wanted to see, I decided not to plan around that possibility but rather to hope to at least show up in the surrounding kirkyard to hear the practice from outside.

After a long day of walking, while David saved me a seat at Shandwick's for dinner a couple of blocks away, I (foolishly?) headed back down into the kirkyard.  I ADORE creepy cemeteries and make a point of seeking them out.  And in the daytime this is one of the creepiest I've ever seen.  At night  .  .  .  in the dark  .  .  .  quite far below the level of the street  .  .  .  alone  .  .  .  umm  .  .  .  let's just say I REALLY wanted to hear those bells!

First a video of practice and then some pictures of the kirk:


My camera picked up a lot of light and made it look brighter down there than it actually was  .  .  .  just sayin'  .  .  .

Tombstone in St. Cuthbert's kirkyard taken earlier in the day

St. Cuthbert's as seen from Edinburgh Castle
Edinburgh Castle as seen from the south side of St. Cuthbert's
St. Cuthbert's viewed from the south
Though our "related" mystery reading was by Sayers, I thought it worth noting that mystery writer Agatha Christie was married in the small WWI Memorial Chapel of this kirk, which is where the evening service David and I attended was held.  I don't have pictures of the inside, but I snapped one of the entrance to this chapel.

For bell-ringing comparison, here is a video I took during my sabbatical on my way to worship Sunday morning.  Sadly, you can barely hear this wonderful artistry above the street noise!

Thursday, December 07, 2017

Our Trees: In Memorium

Learning By Doing



They're taking down a tree at the front door,
The power saw is snarling at some nerves,
Whining at others. Now and then it grunts,
And sawdust falls like snow or a drift of seeds.
Rotten, they tell us, at the fork, and one
Big wind would bring it down. So what they do
They do, as usual, to do us good.
Whatever cannot carry its own weight
Has got to go, and so on; you expect
To hear them talking next about survival
And the values of a free society.
For in the explanations people give
On these occasions there is generally some
Mean-spirited moral point, and everyone
Privately wonders if his neighbors plan
To saw him up before he falls on them.

Maybe a hundred years in sun and shower
Dismantled in a morning and let down
Out of itself a finger at a time
And then an arm, and so down to the trunk,
Until there's nothing left to hold on to
Or snub the splintery holding rope around,
And where those big green divagations were
So loftily with shadows interleaved
The absent-minded blue rains in on us.
Now that they've got it sectioned on the ground

It looks as though somebody made a plain
Error in diagnosis, for the wood
Looks sweet and sound throughout. You couldn't know,
Of course, until you took it down. That's what
Experts are for, and these experts stand round
The giant pieces of tree as though expecting
An instruction booklet from the factory
Before they try to put it back together.

Anyhow, there it isn't, on the ground.
Next come the tractor and the crowbar crew
To extirpate what's left and fill the grave.
Maybe tomorrow grass seed will be sown.
There's some mean-spirited moral point in that
As well: you learn to bury your mistakes,
Though for a while at dusk the darkening air
Will be with many shadows interleaved,
And pierced with a bewilderment of birds
.
~by Howard Nemerov



Wednesday, November 01, 2017

Reminder

For God is in heaven, and you upon earth.
—Ecclesiastes 5:2
Don’t take your eyes off the road.
Accept nothing as given.
Watch where you put your hands.
You’re here and God’s in heaven.
Be careful where you step.
The drop-off’s somewhere near.
The fog won’t lift tonight.
God’s in heaven. You’re here.
That word you wish to say,
That score you’d like to even—
Don’t hurry either while
You’re here and God’s in heaven.
The earth says, “Take the wheel.
But no matter how you steer,
I’ll still go round in circles.
God’s in heaven. You’re here.”
by Mark Jarman

Monday, August 07, 2017

The End of Liars

But the king will rejoice in God; Everyone who swears by Him will glory, For the mouths of those who speak lies will be stopped.
~Psalm 63:11 

Friday, June 16, 2017

Haply May Remember, Haply May Forget

When I am dead, my dearest, 
Sing no sad songs for me; 
Plant thou no roses at my head, 
Nor shady cypress tree: 
Be the green grass above me 
With showers and dewdrops wet; 
And if thou wilt, remember, 
And if thou wilt, forget. 

I shall not see the shadows, 
I shall not feel the rain; 
I shall not hear the nightingale 
Sing on, as if in pain: 
And dreaming through the twilight 
That doth not rise nor set, 
Haply I may remember, 
And haply may forget. 

~Christina Rossetti

Rossetti Grave at Highgate Cemetery, London, April 2016

Monday, March 20, 2017

Suggestions

This blog seems to be becoming "Mostly Math" instead of "Mostly Poetry." Once again I'm posting one side of a "private" math conversation.  Feel free to take it or leave it - or try to figure out what is going on!

******************

Here are copies of a few problems involving the graphing of rational expressions from my precalc notes.  My notes are usually pretty sloppy - work presented on the board being prettier, but, hopefully, this gives you some ideas.

Rational Graph Problem 1:


Rational Graph Problem 2:



And now moving on to math that I think is prettier, but I'm not sure why this image decided to go in upside-down (and no matter what I do they won't flip)!!  This is the beginning of my notes on the binomial theorem, which relates to combinatorics and Pascal's Triangle:

Binomial Theorem Introduction:





And, last but not least, we have Mathematical Induction.  Part of why I think this is pretty is because you often get to use sigma notation in the proofs - see the second-to-last and third-to-last pictures, although there's not much sigma notation there.

Mathematical Induction:






I wish we lived closer!  It would be so much fun to go over these with you rather than just sending pictures.  I also wish I had time to Skype right now, but this semester is TOTALLY kicking my butt!  A good resource for further explanation of these topics is the Khan Academy videos.  The best way to get there (to navigate) is to go to YouTube and then search for the topic and type "khan" - rather than trying to go to the Khan Academy site, which for some reason wants you to sign in, even though it's free, and that makes it a little hard to navigate.

I hope this helps!!!!

Sunday, February 26, 2017

The Poem as Mask

When I wrote of the women in their dances and wildness, it was a mask,
on their mountain, gold-hunting, singing, in orgy,
it was a mask; when I wrote of the god,
fragmented, exiled from himself, his life, the love gone down with song,
it was myself, split open, unable to speak, in exile from myself.

There is no mountain, there is no god, there is memory
of my torn life, myself split open in sleep, the rescued child
beside me among the doctors, and a word
of rescue from the great eyes.

No more masks!  Mo more mythologies!

Now, for the first time, the god lifts his hand,
the fragments join in me with their own music.

~ Muriel Rukeyser (1968)

Monday, October 24, 2016

For My Students Only :-)

Upper Bound Theorem as presented in earlier version of text!





Friday, August 12, 2016

L'Chaim



i thank You God for most this amazing
day:for the leaping greenly spirits of trees
and a blue true dream of sky; and for everything
which is natural which is infinite which is yes
(i who have died am alive again today,
and this is the sun’s birthday; this is the birth
day of life and of love and wings: and of the gay
great happening illimitably earth)
how should tasting touching hearing seeing
breathing any–lifted from the no
of all nothing–human merely being
doubt unimaginable You?
(now the ears of my ears awake and
now the eyes of my eyes are opened)
e.e. cummings
1894-1962


Sunday, August 07, 2016

Why?

Why do the wicked prosper, growing old and powerful?
Job 21:7 

Monday, March 21, 2016

World Poetry Day

To celebrate world poetry day, I offer Emily Dickinson's 466:

I dwell in Possibility –
A fairer House than Prose –
More numerous of Windows –
Superior – for Doors –

Of Chambers as the Cedars –
Impregnable of eye –
And for an everlasting Roof
The Gambrels of the Sky –

Of Visitors – the fairest –
For Occupation – This –
The spreading wide my narrow Hands
To gather Paradise –

Thursday, January 21, 2016

Seattle Monorail Ride


Well, this is an experimental post.  I don't even know if this video will show up on most computers or phones.  It's with my new camera, which I didn't realize recorded in AVCHD instead of mp4.  I'm checking it out on different computers to see which ones will play it.

It's a very short clip of the start of the monorail ride back to downtown Seattle from the Space Needle, a trip that goes through that very interesting structure on the way.  If you can't see this and really want to experience the monorail in Seattle I would recommend a trip to the city.  It's truly an amazing place that I have fun exploring!


Sunday, November 15, 2015

Lemmens Fanfare in D Major

I was supposed to have played this in my church for postlude tonight but didn't get time enough in the midst of a busy semester to practice with the organ at my home church (and each organ is a unique instrument).  I wanted to capture the level I had gotten this to before I lose some facility with it - with end of semester and finals now approaching.  Hopefully I can pick this up again in the future and get more time on the other instrument  .  .  .

Wednesday, November 11, 2015

Vast Expense

“The evening passes fast away.
’Tis almost time to rest;
What thoughts has left the vanished day,
What feelings in thy breast?

 “The vanished day? It leaves a sense
Of labour hardly done;
Of little gained with vast expense—
A sense of grief alone?

“Time stands before the door of Death,
Upbraiding bitterly
And Conscience, with exhaustless breath,
Pours black reproach on me:

“And though I’ve said that Conscience lies
And Time should Fate condemn;
Still, sad Repentance clouds my eyes,
And makes me yield to them!

“Then art thou glad to seek repose?
Art glad to leave the sea,
And anchor all thy weary woes
In calm Eternity?

“Nothing regrets to see thee go—
Not one voice sobs’ farewell;’
And where thy heart has suffered so,
Canst thou desire to dwell?”

“Alas! the countless links are strong
That bind us to our clay;
The loving spirit lingers long,
And would not pass away!

“And rest is sweet, when laurelled fame
Will crown the soldier’s crest;
But a brave heart, with a tarnished name,
Would rather fight than rest.

“Well, thou hast fought for many a year,
Hast fought thy whole life through,
Hast humbled Falsehood, trampled Fear;
What is there left to do?

“’Tis true, this arm has hotly striven,
Has dared what few would dare;
Much have I done, and freely given,
But little learnt to bear!

“Look on the grave where thou must sleep
Thy last, and strongest foe;
It is endurance not to weep,
If that repose seem woe.

“The long war closing in defeat—
Defeat serenely borne,—
Thy midnight rest may still be sweet,
And break in glorious morn!

~Emily Bronte (1818-1848)

Saturday, November 07, 2015

The Waking

I wake to sleep, and take my waking slow.   
I feel my fate in what I cannot fear.   
I learn by going where I have to go.

We think by feeling. What is there to know?   
I hear my being dance from ear to ear.   
I wake to sleep, and take my waking slow.

Of those so close beside me, which are you?   
God bless the Ground!   I shall walk softly there,   
And learn by going where I have to go.

Light takes the Tree; but who can tell us how?   
The lowly worm climbs up a winding stair;   
I wake to sleep, and take my waking slow.

Great Nature has another thing to do   
To you and me; so take the lively air,   
And, lovely, learn by going where to go.

This shaking keeps me steady. I should know.   
What falls away is always. And is near.   
I wake to sleep, and take my waking slow.   
I learn by going where I have to go.

~ Theodore Roethke

Wednesday, November 04, 2015

East and West

Edna St. Vincent Millay

“The world stands out on either side
No wider than the heart is wide;
Above the world is stretched the sky,
No higher than the soul is high.
The heart can push the sea and land
Farther away on either hand;
The soul can split the sky in two,
And let the face of God shine through.
But East and West will pinch the heart
That can not keep them pushed apart;
And he whose soul is flat—the sky
Will cave in on him by and by.”

-Edna St. Vincent Millay

Wednesday, August 12, 2015

L'Chaim!

Thoreau somewhat paraphrased:

“  .  .  . I wished to live deliberately  .  .  .  and not, when I came to die, discover that I had not lived. I did not wish to live what was not life, living is so dear; nor did I wish to practice resignation, unless it was quite necessary. I wanted to live deep and suck out all the marrow of life  .  .  .  as to put to rout all that was not life  .  .  . ”

Monday, August 10, 2015

Wedding Photos - Anthony and Brianna

Well, I've gotten really lazy with my blog. I'm finding it easier and easier and faster and faster to use facebook instead, but I have quite a number of  friends who are not on facebook and want to see wedding pictures, so here goes (a few of hundreds!)  I think you can enlarge the pictures by clicking on them.

Here is a professional photo of the bridal party before the wedding:


Here is the bridal party (including flower girls) in the church for photos before the wedding:


Here are my beautiful nieces Ava and Sierra who served as flower girls:


Here is the beautiful bride just before the wedding:


Grandpa Lambooy gives Anthony advice as Grandpa Fernandes and Grandma Meyer look on.  (Grandma Meyer was clearly concerned about Brianna's train, as she is holding it up in all the pictures we have during this time!)


Parents of the groom:


Parents of the bride:


I'm including the next two photos because people asked me about how my hair was done.  I'm a tomboy and can't do anything with hair or make-up, so HUGE thanks to Gaby for doing my hair and to Rohaizad for doing my make-up!!!!



Mom's lighting their candles:


Parental promises:


Vows and other wedding photos:




The get-away car - Brianna's Uncle Mark and Aunt Lisa's Woodie!


Professional shots of the "get away"



Reception time - best man toast:


So appreciative of our family and friends, all of whom on our side had to come from a distance - Northern California, Oregon, Michigan, Baltimore, Virginia and Illinois!





Everybody Dance Now!



(Wait - is that my son up in the air?  Why, yes, yes it is.)




Chinese lanterns:


A beautiful end to a beautiful day!




We love you, Anthony and Brianna!  All the best to you!!