Category: Mathematics

Irrational Thoughts

5/9/2026

Due to a parallel between Dickinson and Frost (discussed HERE), I decided to take a look at Dickinson’s use of “sweep,” “sweeps,” “swept” and “sweeping.” I shared poems with “sweeping” a couple of days ago (HERE), and today I have a quick look at “swept.”

A search of “swept” on the Dickinson Archive generates twenty entries, representing eight poems:

All things swept sole away
Grief is a Mouse –
Like brooms of steel
Like Rain it sounded till it curved
Me prove it now – Whoever doubt
Of all the sounds despatched abroad
The Winters are so short –
To her derided Home

At two lines, “All things swept sole away” is one of if not the shortest poem by Dickinson, (there is a one line fragment included in some editions of her poetry):

All things swept sole away
This – is immensity –

As far as I can tell, this poem was first published in the 1931 volume Letters of Emily Dickinson edited by Mabel Loomis Todd. The two lines are part of an 1881 letter to Thomas Wentworth Higginson. Later, the work was published as a stand alone poem in Thomas Johnson’s 1955 edition of The Complete Poems of Emily Dickinson. It also appears in R. W. Franklin’s 1998 The Poems of Emily Dickinson and in Cristanne Miller’s 2016 Emily Dickinson’s Poems as She Preserved Them. In Miller’s edition, the poem appears in the section entitled “Poems Not Retained” with the footnote, “Sent to TWH c. 1881.” Miller also includes the endnote, “Follows ED’s comment, “It is solemn to remember that Vastness – is but the Shadow of the Brain which casts it –”

Here's the page of the letter with the lines to Higginson in Dickinson’s handwriting:

You can see the complete transcript of the letter in Dickinson's handwriting HERE.

However, in every volume of Dickinson’s letters, the lines are shown as being indented – as if Dickinson included the lines as a poem.

In the handwritten transcript of the letter, though, the two lines are not set off at all – they just appear as the additional lines of the letter.

What do you make of this? Do you think the lines constitute a separate poem? And what do you make of the lines themselves?

Let me ramble here for a minute:

Dickinson’s profound but paradoxical statements reminded me of a debate I had years ago with my eighth grade math teacher. It was a heated discussion which centered on the fact that an infinite space can have boundaries. At the time, I was a non-believer, and it blew my mind in later years when I realized my teacher had been right all along.

Dickinson’s lines and this middle school memory also called to mind a bit of dialogue from “Bart the Genius,” the second episode of the first season of “The Simpsons.” In this episode, Bart is thought to be “gifted,” so – at Principal Skinner’s delight – he is transferred from Springfield Elementary School to the Enriched Learning Center for Gifted Children, where his Learning Coordinator picks up on a previous lesson:

Ms. Mellon: And now we can continue our debate from yesterday. When we left off, Calvin and Tanya were arguing that free will is an illusion.

Ian: If you ask me humankind has freedom, a freedom fraught with paradoxes. Freud shows how childhood shapes our subconscious mind, but this helps us to think for ourselves.

Ms. Mellon: Very good, Ian. Does anyone else have an example of a paradox?

Boy: Without law and order, man has no freedom.

Girl: If you want peace you must prepare for war.

Ms. Mellon: Mm-hmm. Mm-hmm. Well, it seems the smartest child in the class is also the quietest. Bart, what other paradoxes affect our lives?

Bart: Well, you're damned if you do and you're damned if you don't.

Ms. Mellon: Well, I guess that would be a paradox too. (chuckles) Thank you, Bart.

So let’s get back to Dickinson's lines:

It is solemn to remember that Vastness – is but the Shadow of the Brain which casts it – All things swept sole away / This – is immensity –

* If Vastness is an expanse created by “the Shadow of the Brain which casts it,” doesn’t the existence of a shadow imply that there is more; therefore “vastness” is even more vast than the vastness imagined by the brain which created the vastness? (See: “The universe is wider than our views of it.” ~ Henry David Thoreau)

* If all things are swept away -- thus creating immensity in the sense of vastness – then, on the other hand, if all things are gathered, is the immensity created greater or lesser than the immensity of the immensity of all things being swept away?

Allow me to go off on another tangent:

If one individual has a bucket with every possible integer in it, another individual has a bucket with every positive integer (we’ve “swept away” the negative ones), and a third individual has a bucket with every even positive integer (we’ve swept away the negatives and the odd positives), which person has the greatest number of integers in their bucket? If we sweep even more integers, does the immensity in the bucket remain as immense?

And get this: Did you know that it is believed that the digits of pi contain every possible finite sequence of numbers? Therefore, somewhere in that vast, immense string of numbers is my social security number {and yours too} and my Citibank Mastercard number {and yours too) -- along with every other possible number.

Yikes – has my morning’s post become a bit too irrational? Let me refocus. The question at hand involves Dickinson's 1881 letter to Higginson: Should the lines "All things swept sole away /This – is immensity" be thought of as a stand-alone poem?

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Caught Between a Rock and a Odd Place

9/21/2025

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Okay, I have this very strange poem by Dickinson to share – one with which I was not familiar at all – and I got to it in a very odd way (literally “odd”, LOL – you’ll find out what I mean in a minute). And to be honest, this is really a post about two poems.

Here’s the story:

I saw a note on Substack: “Is there anything real that can be described with words?”

Hmm. I have to admit, at first I wondered if the person meant, “Is there anything real that CAN’T be described with words?” Or perhaps, “Is there anything real that can be described WITHOUT words?”

I dunno. I was just confused, but the note said, “Is there anything real that can be described with words?” – so I took a look at the comments to see how people responded.

There was this, “Other than here I communicate exclusively through interpretive dance,” and then this, “Fingers pointing at the moon are possible.” The next person simply said, “No.”

The next comment was this: “All complete descriptions are in the form of propositions constructed of concepts represented by words. Real is anything that exists, as it is. Rocks exist and are really ontological. Dreams exist and are really psychological. We can describe both propositionally, which presupposes the use of language.”

Okay, I re-read that a couple of times, and I have to say, yes, I agree with that – and it seems to be a thoughtful response to the original question. However, the main thing that stuck in my head when I read it, was “Rocks” – and I thought of Emily Dickinson’s poem, “How happy is the little stone” – so I posted that in response:

That same person then responded to my comment with this:

“About as happy as the number 7 :)”

Alrighty then.

But I have to admit, I wasn’t quite sure what that meant, so I explored the number seven, and I found this: “Seven is a happy number: In terms of mathematics, seven is considered to be a Happy Number. A ‘happy number’ is such that when you square each of its digits, add those squares, then repeat the process, eventually you will get an answer of 1.

See below for more info:

To recap: I began by stating that I have a very strange poem to share, and that I got to it in a very odd way (literally ‘odd’), and also I stated that this was really a post about two poems. So far, I have shared one of the two poems, “How happy is the little stone,” and the “odd” path I was on – about the number 7. I’ll continue tomorrow and get to that “very strange poem.”

Stay tuned.

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On the Square

9/17/2025

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In yesterday’s post, I shared info about the date, 9/16/25, a “triple perfect square” date – and then I looked into how many times Dickinson used the word “square” in her poetry. Two times, to be exact; once in “Grief is a mouse,” and once in “I could die to know.” In neither poem did she use “square” in a mathematical sense of a squared number; instead, she used it more in terms of a “public square” – at least that is the case with “Grief is a mouse.” That poem includes the line, “Burn Him in the Public square.”

In “I could die to know,” the word seems to suggest a “public square,” but I think that it is open to other interpretations as well, and the online Dickinson Lexicon appears to support this notion.

I checked the Lexicon to see how Dickinson used the word “square” in her writings, and it offered two definitions:

A tool used for measurement.
Open space or area in a town or city.

Of course, that second definition was used in “Grief is a mouse.” Dickinson literally wrote “public square” in that poem. Does that mean the other definition was used in “I could die to know”? Is the term suggesting “a tool used for measurement”?

Interestingly, the lexicon also provides a definition for Dickinson’s use of “squarely.” The entry states, “See ‘square’; Directly; honestly; in a straightforward manner.”

Oddly enough, though, Dickinson never used the word “squarely” in any of her poems. Only “square” – in the two poems I’ve already mentioned.

In the second poem, “I could die to know,” in the line “To the very Square – His foot is passing,” does Dickinson mean that, as she dreams from her bed, this unseen lover is walking past the public square as cart loads of coal are rattling and rolling past? Does the line also imply that as she dozes in bed when the town comes to life as “Morning's bold face stares in the window,” her lover passes on foot – and everything in life is as it should be, “To the very Square,” calculated and measured precisely?

I gotta say, that capital “H” with him adds to the mystery. Is she talking about “him,” or is she talking about “HIM”? LOL – this made me think of lyrics from Lady Gaga’s song “Born This Way”: “It doesn’t matter if you love him / Or capital ‘H-I-M” – and “God makes no mistakes.”

Okay, so let me wax profoundly a bit – or certainly a bit left of kilter: If the “he” in the poem is “HE” – and not merely “he” – then check out that first line again: “I could die – to know.” Hmm…the speaker will not know if this passer-by even returns her feelings – until she dies? And…does this passer-by even exist? Or is HE merely a part of her dream?

How is that for a measured response? Is it even on the square?

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Square Deal

9/16/2025

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Today, 9/16/25, is a perfect square day.

Well, depending upon how you define a perfect square day.

In this case, 9/16/25, is recognized as a "Triple Perfect Square Day" because each numerical component of the date, when interpreted as month, day, and year (in a two-digit format), is a perfect square.

However, I discovered this chart, HERE, and at first I was a bit confused because 9/16/25 is not on the list. What? How could a professor of Electrical Engineering at the University of Portland in Oregon have been so wrong?

I then found this article, from back in 2016, and it features the very same professor – and the same confusing information.

When I reviewed the article more carefully, though, I realized that his definition of a perfect square day is a little more precise: It’s when the numbers for the month, day, and year are combined to form a single number that is a perfect square. For example, the digits of 9/27/2025 combine to make the number 9, 272,025, and that number is a perfect square. Its square root is 3,045. Today’s date combines to become 9,162,025 – which is not a perfect square.

By the way, don’t confuse all of this with what is known as a square root day; info on that is HERE.

Once I cleared all of this up in my mind, I wondered how often Emily Dickinson used the word “square” in her poetry.

She used the word twice – once each in two different poems, “Grief is a mouse” and “I could die to know.” However, she did not use “square” in a mathematical sense; instead, she used it more in terms of a “public square.”

Well, in one instance, she definitely used the word in that manner. In the first poem, “Grief is a mouse,” she has the line, “Burn Him in the Public square.”

In the other poem, the word seems to suggest a “public square,” but I think that it could be open to other interpretations as well – and the online Dickinson Lexicon doesn’t seem to be on the square.

I’ll get to that tomorrow.

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Can You Dig It?

5/27/2024

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I’ve been posting some of my favorite Dickinson poems about death and grief, and now – after a bit of a bumpy few days about Dickinson’s nonstandard use of “don’t” in a couple of her poems (HERE) – I’m ready to move on to the seventh poem on my list, “A Coffin – is a small domain,” a short poem that explores the paradoxical nature of death.

Here’s a bit of the analysis of the poem at AllPoetry.com: "’A Coffin’ presents a stark image of confinement, while "A Grave" suggests boundless expansion. The coffin, a symbol of mortality, can nevertheless hold a ‘Citizen of Paradise,’ hinting at the transformative power of death.”

And this: “The grave, despite its physical limitations, becomes an expansive realm for the deceased. The intimacy of the coffin contrasts with the vastness of the grave, suggesting a shift from the material to the spiritual.”

I remember as a kid struggling with the idea that an infinite space could have boundaries, so I really dig Dickinson’s opposing images in the poem (LOL – “dig,” a dated word of awareness and admiration, but one that fits so neatly in a discussion about a poem about a grave, dontcha think?)

I love the opposing constructs in the poem – and the math references! For example, that this “diminished plane,” the grave, is a “restricted Breadth / Yet ampler than the Sun.” And this “small Repose” (sounds comfy, no?) has “Circumference without Relief / Or Estimate or End.”

How irrational. Like pi. ; - )

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It All Adds Up

12/31/2016

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We just finished our countdown of the Words of the Year for 2016, and the top Word of the Year was “divided."

How did we land on "divided" as the Word of the Year? Well, of course there was Brexit and the break-ups of One Direction and Brad and Angelina; however, the major force in our decision to crown "divided" as the Word of the Year was the great unifier himself, Donald Trump. He worked diligently to divide our country more than any other force this year -- and not because of his bigly, er, big league and unconventional unifying powers. No, the expansion of our grand canyon was more attributalbe to Trump's skills as a mathematician, especially when it comes to the operations of ambition, distraction, uglification, and division.*

AMBITION: On June 16, 2015, Trump descended into the lobby of Trump Tower as if he were submerging into a swamp to feed his own ego with an announcement that he was running for President. Even a top Trump strategist saw through the charade. Relatively early in the campaign, Stephanie Cegielski wrote, “I don't think even Trump thought he would get this far. And I don’t even know that he wanted to, which is perhaps the scariest prospect of all. He certainly was never prepared or equipped to go all the way to the White House, but his ego has now taken over the driver's seat, and nothing else matters.”

DISTRACTION: Throughout the campaign, Trump was a master of distraction. He duped his followers and the media with diversion, deception and distraction. If someone were to criticize his poor performance in the presidential debates, Trump would tweet about Megyn Kelly, Heidi Cruz, or Alicia Machado (a former Miss. Venezuela). If someone were to report about Trump hiring white supremacists on his staff, he’d tweet about a discourteous audience at “Hamilton.” His tweets came to be known as “weapons of mass distraction.”

UGLIFICATION: Trump disrespected women, belittled Mexicans, disparaged Muslims, mocked the disabled, and more – and then he’d bark invective about anyone who’d call him on it. Trump is the reigning monarch of uglification, and his clan loves it!

DIVISION: By drawing on his skills of ambition, distraction, and uglification, Trump was successful in creating a greater division in our nation so that despite an incredible loss in the popular vote, he squeaked by with enough electoral votes to seize the White House. Поздравляю, товарищ. This fruitful division made "divided" the obvious choice as the 2016 Word of the Year.

Trump’s yuge aptitude as a mathematician, though, reminded us of Emmett Lee Dickinson’s lack of skill in the same area. Therefore, we thought we’d celebrate the start of 2017 with Dickinson’s now classic poem “i suck at logic, stats and trig" (below on the left). His poem inspired E. E. Cummings to pen his poem “i sing of Olaf glad and big" (below on the right).

By Emmett Lee Dickinson:

i suck at logic, stats and trig
with hardest drills recalled a chore:
entrenched as a stunned resist-or

my wellintentioned tutor(grad
MIT-er most distinctly trained)
took erring logic in her sight;
but— teacher of an overwhelmed
nincom (and knocking on my brain
me)aimed at frozen brainwaves of
that helplessness which others ignored
by rushing completely assumed
i grasped their muddy labored love
while my faulty intellect stored
absolute zero per blunt means--
Logic(being in all percents--
a cryptic and most puzzling math
upon the reason God gave me)
responds by acting all annoyed
“Do not dismiss this function graph”

straightway the baffling grid looked blurred
(a well-known expletive was heard)

but— through all kinds of countless drills
(the serving tutor’s tried and true)
my passive mind did curse and kick
until one day a bell did ding
and sum of what was said did stick
i aced my first examining
a long fought battle over time
by means of skillfully reviews
and late maneuvers over night
Logic(a foe that was once sting)
does almost ceaselessly perplex
pi anxiety with side effects

our last exam is late next week
the odds i’m hopeful to defy
i’ll study problems each unique
so that my grade won’t up and die

Christ(so i pray before each test)
i ask a “C”; and logically

it’s possible i’ll pass because
unless statistics lie i will
be average quite successfully

By E. E. Cummings:

i sing of Olaf glad and big
whose warmest heart recoiled at war:
a conscientious object-or

his wellbelovéd colonel(trig
westpointer most succinctly bred)
took erring Olaf soon in hand;
but--though an host of overjoyed
noncoms(first knocking on the head
him)do through icy waters roll
that helplessness which others stroke
with brushes recently employed
anent this muddy toiletbowl,
while kindred intellects evoke
allegiance per blunt instruments--
Olaf(being to all intents
a corpse and wanting any rag
upon what God unto him gave)
responds,without getting annoyed
"I will not kiss your f—ing flag"

straightway the silver bird looked grave
(departing hurriedly to shave)

but— though all kinds of officers
(a yearning nation's blueeyed pride)
their passive prey did kick and curse
until for wear their clarion
voices and boots were much the worse,
and egged the firstclassprivates on
his rectum wickedly to tease
by means of skilfully applied
bayonets roasted hot with heat--
Olaf(upon what were once knees)
does almost ceaselessly repeat
"there is some shit I will not eat"

our president,being of which
assertions duly notified
threw the yellowsonofabitch
into a dungeon,where he died

Christ(of His mercy infinite)
i pray to see;and Olaf,too

preponderatingly because
unless statistics lie he was
more brave than me:more blond than you.

*Charles Lutwidge Dodgson, aka Lewis Carroll, was the first mathematician to identify the operations of Ambition, Distraction, Uglification, and Derision. However, Donald Trump combined Derision with Uglification, and added Division to the mix. To this date, these methods are the heart of the mathematics curriculum at Trump University.

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Irrational Thoughts

Caught Between a Rock and a Odd Place

On the Square

Square Deal

Can You Dig It?

It All Adds Up

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