A Tally Stick

The bark is notched six times, one notch
for every cow left in the pound,
then split, the cowman and the poundman
taking half each, so that when
the cowman comes to claim his stock
six cows are led out from the pound
though neither of the men can count.

Connemara 1610:
A cowman spreads his hands and watches
as a priest names all his fingers.
He starts to count potatoes, hens,
the steps across his single field
whose blades the Lord alone can sum.

And then he pauses at the gate one night
and thinks of seven. Not trees. Not dogs
Just seven. Like The Plough
before God put the stars in.

Mark Haddon

Magma No 31 - Spring 2005

Mark Haddon is the author of 15 children's books, two radio plays and The Curious Incident of the Dog in the Night-Time, winner of the Whitbread Book of the Year 2003.
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Two contrasting takes on "What is Real?":

I am the poet of reality
I say the earth is not an echo
Nor man an apparition;
But that all things seen are real,
The witness and albic dawn of things equally real
I have split the earth and the hard coal and rocks and the solid bed of the sea
And went down to reconnoitre there a long time,
And bring back a report,
And I understand that those are positive and dense every one
And that what they seem to the child they are
[And that the world is not a joke,
Nor any part of it a sham].

– Walt Whitman

View with a Grain of Sand

We call it a grain of sand,
but it calls itself neither grain nor sand.
It does just fine, without a name,
whether general, particular,
permanent, passing,
incorrect, or apt.

Our glance, our touch means nothing to it.
It doesn't feel itself seen and touched.
And that it fell on the windowsill
is only our experience, not its.
For it, it is not different from falling on anything else
with no assurance that it has finished falling
or that it is falling still.

The window has a wonderful view of a lake,
but the view doesn't view itself.
It exists in this world
colorless, shapeless,
soundless, odorless, and painless.

The lake's floor exists floorlessly,
and its shore exists shorelessly.
The water feels itself neither wet nor dry
and its waves to themselves are neither singular nor plural.
They splash deaf to their own noise
on pebbles neither large nor small.

And all this beheath a sky by nature skyless
in which the sun sets without setting at all
and hides without hiding behind an unminding cloud.
The wind ruffles it, its only reason being
that it blows.

A second passes.
A second second.
A third.
But they're three seconds only for us.

Time has passed like courier with urgent news.
But that's just our simile.
The character is inverted, his hasts is make believe,
his news inhuman.

Wislawa Szymborska
Trans. Stanislaw Baranczak and Clara Cavanagh

A further rallying cry for "naïve realism"
(which could be very useful for sixth grade Astronomy?):


William Blake (1757–1827).  The Poetical Works.  1908.
Selections from ‘Milton’
[The Heavens and the Earth]
(Milton, f. 28, ll. 4–16.)

THE SKY is an immortal Tent built by the Sons of Los;
And every Space that a Man views around his dwelling-place,
Standing on his own roof, or in his garden on a mount
Of twenty-five cubits in height, such Space is his Universe:
And on its verge the Sun rises and sets, the Clouds bow        5
To meet the flat Earth and the Sea in such an order’d Space;
The Starry Heavens reach no further, but here bend and set
On all sides, and the two Poles turn on their valves of gold;
And if he move his dwelling-place, his Heavens also move
Where’er he goes, and all his neighbourhood bewail his loss.        10
Such are the Spaces callèd Earth, and such its dimension.
As to that false appearance which appears to the reasoner,
As of a Globe rolling thro’ Voidness, it is a delusion of Ulro.

The following were sent to me by Amie Slate:

If Infinite Worlds, Infinite Centers
by Margaret Cavendish,  1623-1673

If Infinites of Worlds, they must be plac'd
At such a distance, as between lies waste.
If they were joyned close, moving about,
By justling they would push each other out.
And if they swim in Aire, as Fishes do 
In Water, they would meet as they did go.
But if the Aire each World doth inclose
Them all about, then like to Water flowes;
Keeping them equall, and in order right.
That as they move, shall not each other strike. 
Or like to water wheels by water turn'd,
So Aire round about those Worlds do run:
And by that Motion they do turne about,
No further then that Motions strength runs out.
Like to a Bowle, which will no further go, 
But runs according as that strength do throw.
Thus like as Bowles, the Worlds do turne, and run,
But still the Jacke, and Center is the Sun.

Margaret Cavendish was not formally educated, but as a British royalist in exile, she encountered and conversed with great minds of the day, such as Hobbes and Descartes. She wrote and published extensively about Natural Science and was considered eccentric, mad or genius. Cavendish held the view that everything in the universe—including human beings and their minds—is completely material, and that matter thinks. 

"Nature is material, or corporeal, and so are all her Creatures, and whatsoever is not material is no part of Nature, neither doth it belong any ways to Nature…."

"Though Matter might be without Motion, yet Motion cannot be without matter; for it is impossible (in my opinion) that there should be an Immaterial Motion in Nature."

So God does indeed exist but Cavendish held that natural reason cannot perceive or have an idea of an immaterial being. She argued that thinking processes others identified as immaterial are material. Though not esoteric, they are nevertheless wondrous and impressive.

Treatise on Infinite Series
by Jacob Bernoulli, 1655-1705 (anti-newtonian)

Even as the finite encloses an infinite series 
      And in the unlimited limits appear, 
So the soul of immensity dwells in minutia
      And in narrowest limits no limits inhere. 
What joy to discern the minute in infinity! 
      The vast to perceive in the small, what divinity!

Bernoulli seems to have a capacity for certainty yet with room for uncertainty within it. It seems that there is room for something that is still "becoming" within his philosophy. Compared to Cavendish, he seems to feel part of the divine world and not merely a product of it.

by Geoffrey Brock (modern)

I was a math major—fond of all things rational.
It was the first day of my first poetry class.
The prof, with the air of a priest at Latin mass,
told us that we could “make great poetry personal,”
could own it, since poetry we memorize sings
inside us always. By way of illustration
he began reciting Shelley with real passion,
but stopped at “Ozymandias, King of Kings;
Look on my Works, ye Mighty, and despair!”—
because, with that last plosive, his top denture
popped from his mouth and bounced off an empty chair.
He blinked, then offered, as postscript to his lecture,
a promise so splendid it made me give up math:

“More thingth like that will happen in thith cloth.”

by Rita Dove

 I prove a theorem and the house expands:
 the windows jerk free to hover near the ceiling,
 the ceiling floats away with a sigh.
 As the walls clear themselves of everything
 but transparency, the scent of carnations
 leaves with them. I am out in the open
 and above, the windows have hinged into butterflies,
 sunlight glinting where they've intersected.
 They are going to some point true and unproven.

by Aram Saroyan


by Frank Dux

 If the universe is infinite,
 Then I am its centre,
 And so are you.
 And this holds true
 Wherever we go.
 We cannot escape
 Our significance.

Wrong Notes

"Just remember there is no such thing as a wrong note...
What makes a note wrong is when you don't know where to go after that one.
As long as you know how to get to the next note,
there's no such thing as a wrong note." - jazz pianist Art Tatum

"I made the wrong mistakes." 
 - Thelonious Monk, after a disappointing performance

"There were no wrong notes on his pi-
a-no had no wrong notes, oh no...
He played not one wrong note, not one.
His pi-a-no had none, not one."
 - Chris Raschka, on Monk

Something of a Poet

“It is true that a mathematician, who is not somewhat of a poet, will never be a perfect mathematician.” Karl Weierstrass (1815-97)

"Pure mathematics is, in its way, the poetry of logical ideas." Albert Einstein (1879-1955)

“ . . . mathematics is very much like poetry . . . what makes a good poem—a great poem—is that there is a large amount of thought expressed in very few words." Lipman Bers (1914-1993)

“Another key similarity between mathematics and poetry is the appreciative awe experienced by mathematicians and poets when they encounter great work. A great poem like certain mathematical proofs – for example, an elegant rendering of Euclid's proof of the infinitude of the primes – takes my breath away with the depth, power and beauty of the ideas.” JoAnne Growney

Into the Dark
from a letter written by Carl Friedrich Gauss (1777 – 1855) “the Prince of Mathematicians," to Janos Bolyai:

Surely it is not the knowing but the learning, not the possessing but the acquiring, not the being-there but the getting-there, that affords the greatest satisfaction. If I have clarified and exhausted something, I leave it to go again into the dark.

Thank you Amie!


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Here are some of the ideas that I have been exploring.

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 Philip James GuestLos Angeles, CA310.383.2327