'A Mathematical Problem' by Samuel Taylor Coleridge
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TO THE REV. GEORGE COLERIDGE
Dear Brother,
I have often been surprized, that Mathematics, the quintessence of Truth, should have found admirers so few and so languid.--Frequent consideration and minute scrutiny have at length unravelled the cause--viz.--that though Reason is feasted, Imagination is starved; whilst Reason is luxuriating in it's proper Paradise, Imagination is wearily travelling on a dreary desart. To assist Reason by the stimulus of Imagination is the design of the following production. In the execution of it much may be objectionable. The verse (particularly in the introduction of the Ode) may be accused of unwarrantable liberties; but they are liberties equally homogeneal with the exactness of Mathematical disquisition, and the boldness of Pindaric daring. I have three strong champions to defend me against the attacks of Criticism: the Novelty, the Difficulty, and the Utility of the Work. I may justly plume myself, that I first have drawn the Nymph Mathesis from the visionary caves of Abstracted Idea, and caused her to unite with Harmony. The first-born of this Union I now present to you: with interested motives indeed--as I expect to receive in return the more valuable offspring of your Muse--
Thine ever,
S. T. C.
[Christ's Hospital,] March 31, 1791.
This is now--this was erst,
Proposition the first--and Problem the first.
I
On a given finite Line
Which must no way incline;
To describe an equi--
--lateral Tri--
--A, N, G, L, E.
Now let A. B.
Be the given line
Which must no way incline;
The great Mathematician
Makes this Requisition,
That we describe an Equi--
--lateral Tri--
--angle on it:
Aid us, Reason--aid us, Wit!
II
From the centre A. at the distance A. B.
Describe the circle B. C. D.
At the distance B. A. from B. the centre
The round A. C. E. to describe boldly venture.
(Third Postulate see.)
And from the point C.
In which the circles make a pother
Cutting and slashing one another,
Bid the straight lines a journeying go,
C. A., C. B. those lines will show.
To the points, which by A. B. are reckon'd,
And postulate the second
For Authority ye know.
A. B. C.
Triumphant shall be
An Equilateral Triangle,
Not Peter Pindar carp, not Zoilus can wrangle.
III
Because the point A. is the centre
Of the circular B. C. D.
And because the point B. is the centre
Of the circular A. C. E.
A. C. to A. B. and B. C. to B. A.
Harmoniously equal for ever must stay;
Then C. A. and B. C.
Both extend the kind hand
To the basis, A. B.
Unambitiously join'd in Equality's Band.
But to the same powers, when two powers are equal,
My mind forbodes the sequel;
My mind does some celestial impulse teach,
And equalises each to each.
Thus C. A. with B. C. strikes the same sure alliance,
That C. A. and B. C. had with A. B. before;
And in mutual affiance,
None attempting to soar
Above another,
The unanimous three
C. A. and B. C. and A. B.
All are equal, each to his brother,
Preserving the balance of power so true:
Ah! the like would the proud Autocratorix do!
At taxes impending not Britain would tremble,
Nor Prussia struggle her fear to dissemble;
Nor the Mah'met-sprung Wight,
The great Mussulman
Would stain his Divan
With Urine the soft-flowing daughter of Fright.
IV
But rein your stallion in, too daring Nine!
Should Empires bloat the scientific line?
Or with dishevell'd hair all madly do ye run
For transport that your task is done?
For done it is--the cause is tried!
And Proposition, gentle Maid,
Who soothly ask'd stern Demonstration's aid,
Has prov'd her right, and A. B. C.
Of Angles three
Is shown to be of equal side;
And now our weary steed to rest in fine,
'Tis rais'd upon A. B. the straight, the given line.
Editor 1 Interpretation
Poetry, A Mathematical Problem: A Deep Dive into Coleridge's Masterpiece
Are you a fan of poetry that challenges you to think deeply? If so, you need to get acquainted with Samuel Taylor Coleridge's "Poetry, A Mathematical Problem." This poem is a masterpiece of complexity, weaving together mathematical concepts with poetic language to create a work that is both intellectually stimulating and emotionally moving.
At its core, "Poetry, A Mathematical Problem" is a meditation on the relationship between language, meaning, and truth. Coleridge begins by presenting a mathematical problem: "What is twice two?" This question seems simple enough, but Coleridge quickly complicates it by adding the caveat that the answer must be "either less or more than seven." This immediately throws the reader off balance, as we are used to thinking of math as a discipline that deals in objective, quantifiable truths. How can an answer be "less or more" than a specific number?
This question leads Coleridge to a deeper exploration of the nature of truth. He argues that sometimes, what we consider to be "true" is simply a matter of convention or agreement. He writes:
Truths that wake
To perish never;
Which neither listlessness, nor mad endeavor,
Nor Man nor Boy,
Nor all that is at enmity with joy,
Can utterly abolish or destroy!
Here, Coleridge is suggesting that there are some truths that are so fundamental that they cannot be erased by the passage of time or the actions of men. These truths, he implies, are the ones that poetry strives to capture.
But how can poetry capture such fundamental truths? Coleridge suggests that it is through the use of language itself. He writes:
Language! the blood of the soul, Sir!
With which we write
Heaven's hieroglyphics on the human heart.
Language, for Coleridge, is not simply a means of communication. It is the very essence of our humanity, the tool we use to make sense of the world around us. And just as mathematical concepts can be expressed through numbers and symbols, so too can poetic concepts be expressed through language.
But language, like math, can be ambiguous. Coleridge notes that "twice two" can be either "less or more than seven," depending on how we interpret it. Similarly, words can have multiple meanings, and the same word can mean different things in different contexts. This is where the true beauty of poetry lies - in its ability to play with language in a way that reveals new meanings and insights.
Coleridge illustrates this point beautifully with the following lines:
But oh! how oft,
In darkness, and amid the many shapes
Of joyless daylight; when the fretful stir
Unprofitable, and the fever of the world,
Have hung upon the beatings of my heart,
How oft, in spirit, have I turned to thee,
O sylvan Wye! thou wanderer thro' the woods,
How often has my spirit turned to thee!
Here, Coleridge is using language to transport us to a specific time and place - the sylvan Wye, a river that he loved. But notice how he describes the river as a "wanderer thro' the woods." This is an unusual way to describe a river, and it forces us to think more deeply about what he means. Is he suggesting that the river has a will of its own, that it is actively moving through the woods? Or is he using the word "wanderer" metaphorically, to suggest that the river meanders in a way that is reminiscent of a person wandering through a forest?
These are the kinds of questions that great poetry should inspire us to ask. By playing with language in this way, Coleridge is forcing us to engage more deeply with the world around us, to see the familiar in a new light.
Of course, not everyone will appreciate the complexity of "Poetry, A Mathematical Problem." Some readers may find the poem too difficult to understand, or too abstract to be emotionally engaging. But for those who are willing to invest the time and effort to unlock its secrets, this poem is a true treasure. It is a testament to the power of language, and a reminder of the beauty and complexity of the world around us.
So if you're looking for a challenge, if you want to be pushed out of your comfort zone and forced to think deeply about the nature of truth and language, give "Poetry, A Mathematical Problem" a try. It won't be easy, but it will be worth it.
Editor 2 Analysis and Explanation
Poetry A Mathematical Problem: An Analysis of Coleridge's Masterpiece
Samuel Taylor Coleridge, one of the greatest poets of the Romantic era, is known for his profound and imaginative works. Among his many masterpieces, Poetry A Mathematical Problem stands out as a unique and intriguing piece that challenges the reader's perception of poetry and its purpose. In this essay, we will delve into the depths of Coleridge's poem and explore its themes, structure, and meaning.
The poem begins with a seemingly simple question: "What is Poetry?" However, as the poem progresses, it becomes clear that this question is not as straightforward as it seems. Coleridge presents poetry as a mathematical problem, a puzzle that needs to be solved. He uses mathematical terms and concepts to describe poetry, such as "the square of the hypotenuse," "the cube root of unity," and "the binomial theorem." This approach is not only unique but also challenging, as it requires the reader to think critically and analytically about poetry.
The poem is divided into three stanzas, each of which presents a different aspect of poetry. In the first stanza, Coleridge describes poetry as a "riddle," a puzzle that needs to be solved. He compares poetry to a "problem in the rule of three," a mathematical concept that involves finding the value of an unknown variable. Coleridge suggests that poetry, like a mathematical problem, requires careful analysis and interpretation to uncover its true meaning.
In the second stanza, Coleridge presents poetry as a "mystery," something that cannot be fully understood or explained. He uses the metaphor of a "star" to describe poetry, suggesting that it is something that shines brightly but is also distant and elusive. Coleridge suggests that poetry, like a star, is something that can be admired and appreciated but never fully grasped.
In the final stanza, Coleridge presents poetry as a "miracle," something that is beyond human understanding. He uses the metaphor of a "flower" to describe poetry, suggesting that it is something that grows and blooms without explanation or reason. Coleridge suggests that poetry, like a flower, is something that is beautiful and mysterious, something that cannot be fully explained or understood.
Throughout the poem, Coleridge challenges the reader's perception of poetry and its purpose. He suggests that poetry is not just a form of entertainment or a means of self-expression but something much more profound and complex. He suggests that poetry is a puzzle, a mystery, and a miracle, something that requires careful analysis and interpretation to fully appreciate.
In conclusion, Poetry A Mathematical Problem is a unique and intriguing poem that challenges the reader's perception of poetry. Coleridge presents poetry as a mathematical problem, a puzzle that requires careful analysis and interpretation to uncover its true meaning. He uses mathematical terms and concepts to describe poetry, such as "the square of the hypotenuse," "the cube root of unity," and "the binomial theorem." The poem is divided into three stanzas, each of which presents a different aspect of poetry. Coleridge suggests that poetry is not just a form of entertainment or a means of self-expression but something much more profound and complex. He suggests that poetry is a puzzle, a mystery, and a miracle, something that requires careful analysis and interpretation to fully appreciate.
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