Poet Mathematician
Mohsen Hashtroudi
Khayyam resembling anyone opened his eyes one day to the world and
other day he concealed countenance in veil of tomb. Annalist has
recorded the date of his birth and death and possibly occurrences and
vicissitudes of time has confiscated him in book of remembrances.
From purposes of what is our discussed, knowing these points are not
so significant. Khayyam's prosperity and failures, his all joys and
griefs, mirth and sorrow proceeded with him to the transient world.
From him, a name, a number of quatrains and some scholarly works in
mathematics and natural sciences have been left. If the criteria of
people's esteems and worth are their renown, in this regard too,
Khayyam is progenitor of scholar dynasty and pioneer of celebrities'
convoy. Since by translation of his quatrains to almost all of
languages in the world, after Fitzgerald1
work, his name is colloquialism of people of all classes.
Khayyam's renown as a poet was so that Khayyam as mathematician and
scientist is eclipsed by Khayyam as poet and in this regard, by
permission of honorable reader, some words would be propounded about
Khayyam's quatrains, philosophical thoughts and artistic paradigms so
that his literary worth is also mentioned. Though utterance of such
duty is so arduous.
Khayyam does not see optimistically this passing transient world at
all. He knows end of anything as no return and unrelenting. He
wishes, from behind of thousand years “like verdure of hoping, you
would grow” and anxious eye would open a way again to the world.
He knows the extensive arena of the world as a field of the living's
vain effort and search. In hallucination world he sees paradox that
have given hand to hand affectionately and friendly and in brick of
crenation of veranda, Caesar's cranium on the bone knee of
Anoushirvan has relied and quieted down.
Wine is the mystery of the universe and since it makes us unaware of
us ourselves, it would give any predicate, regardless of us and so it
is the greatest reality. From transient instants of life, every
instant that passes away with negligence, for him is venerable and
preferential. No doubt, negligence that he purposes, is to take no
negligence of the end, namely, negligence of death. The garden that
Khayyam sees, is sepulcher of deceased darling ones. Narcissus eyes
of friend, violet hair of mistress and cedar stature of beloved have
been missed.
Workroom of potter is warning scenery of deep-minded sage and he sees
father's ash that is a gimcrack in potter's hands.
I saw if any unaware did not see
Ash of my father in hand of any potter
Conundrum of the universe and mystery of living is not conquerable
and anyone in turning of chalice by cupbearer in turn of oneself own,
gets intoxicated and unaware out of the ring.
Friends take seats in nocturnal agora but this night is not followed
by a day and in turn, they evacuate their seats. Whatever it is also
acquired much more erudition and insight, eventually should pass
unaware away.
“Those who went in
pursuit of knowledge
Soared up so high, stretched the edge
Were still encaged by the same dark hedge
Brought us some tales ere life to death pledge.”
Soared up so high, stretched the edge
Were still encaged by the same dark hedge
Brought us some tales ere life to death pledge.”
He sees workroom of
existence without no purpose and anything as a gimcrack of this
workroom.
Potter of workroom
makes any pitcher though subtle and handsome, with the intention of
its return he makes and furbishes it.
Goblet was made by
the Wise Lord
“With love & care to the heights soared
This potter who shaped with such accord
To make and break the same clay, can also afford.”
“With love & care to the heights soared
This potter who shaped with such accord
To make and break the same clay, can also afford.”
He is consternation
passing of time and the caravan of life is wandering about deviated
paths. In such position, he supposes worrying about tomorrow
injudiciously and recommends enjoying transient moment.
“The caravan of
life shall always pass
Beware that is fresh as sweet young grass
Let’s not worry about what tomorrow will amass
Fill my goblet again, this night will pass, alas.”
Beware that is fresh as sweet young grass
Let’s not worry about what tomorrow will amass
Fill my goblet again, this night will pass, alas.”
The triple principles of Khayyam's thoughts is abstracted in
“transience and shortness of life”, “to make the most of
transient life” and “to be free of thought and to conquer mystery
of the universe” and this last point is so significant, since it is
mentioned to the same point in studying his scientific works and
revising his thoughts.
The choice of quatrain form to state thought by Khayyam is a
fundamental point. Since transient and short thought in a short form
is stated more truthfully and sincerely. Furthermore, quatrain
(couplet) in the frame of its own structure is not anomalous to the
form of a logic theorem as indeed the philosopher sage sets forth
circumstance of deduction of a verdict from other verdicts,
Khayyam's literary arts is abstracted in this concise and its comment
and explanation requires more time and more leisure, by permission of
honorable readers, we leave artist Khayyam in this position.
Erudite Khayyam
To introduce erudite Khayyam, we require some preliminary. At the
first we should investigate and study the progress of mathematics and
its coordination with other sciences in Khayyam's era and then we
would view what Khayyam has fulfilled. Here is necessary to be
mentioned that there exists an age in the history of sciences that is
well known as Islamic age but it has not been researched sufficiently
and in particular in Iran if we relinquish a few people who have
proceeded for indigenous verve and interest in rehabilitating and
improving the history of erudite in this country, an important work
has not been fulfilled. (Meanwhile it could be called Mr. Dr.
Mostafavi and his “the world of science” magazine, Mr. Dr.
Mosahab and his research about Khayyam, Mr. Abolghasem
Ghorbani and his papers about a number of erudite and Mr.
Daneshpazhouh and Danaseresht and their study about Abu Rayhan2
and Khawaja Tusi3
and some others insofar as I know.)
In mathematics from the Greek era thereafter brief progress has been
realized in Medieval and Islamic age. Indeed endeavor of scientists
has been more directed to translations of scientific works from Greek
and Syrian to Arabic, furthermore it has been mostly contented with
description and comment of Euclid and same other Greek scientists.
The most significant mathematical work, in the first stage, the
regularization of algebra has been fulfilled by al-Khwarizmi4
so that in European languages, now, the deductive principles of
Algebra have been ascribed to al-Khwarizmi and called algorithm (this
word is anagram of the name al-Khwarizmi).
In the second stage, it includes Khayyam's works in geometry about
parallel postulate and in Algebra about classification and the
solution of cubic equations.
The significance of Khayyam's scientific work is so apparent among
experts that demonstrates him relative to his own era four centuries
closer to contemporary era, namely, Khayyam's works in Algebra belong
to Descartes', Pascal's and Newton's age instead of Khayyam's own
time.
Khayyam's study in Euclid's axiom or parallel postulate
In geometry book known as Euclid's
Elements that the base of geometry is ascribed to him, an
axiom is accepted that is mentioned as Euclid's axiom or parallel
postulate and it is such that from a point out of strict line it can
be drawn just one parallel line with that line so that they are all
in the same plane.
Euclid accepts this axiom definitively and apparently and since
clarity and clearness of this postulate like the other Euclid's
elements is not so manifest from that time, in order to analysing and
leading this axiom to other Euclid's axioms it has been taken efforts
that eventually by Lobachevsky5's
researches it has been led to the foundation and deduction of new
geometry.
Khayyam, in his own contribution to
prove this postulate or to lead it to a simpler one, has also
proceeded a treatise as “Explanations
of the difficulties in the postulates in Euclid's Elements”.
Khayyam's view and analysing method
in this treatise is more or less similar to the mathematicians' works
early the 19th
century and Khayyam's conclusion is so summarized:
“Maybe the system that I apply to explain and reason for this
postulate, be more logic and clear than Euclid's method”. During
Khayyam's research in this work, it is observed that Khayyam seems
uncertain to accept this postulate as a unique indisputable one.
Indeed, as if he sees no impediment logically to deny this
postulate. He accepts inevitably it just empirically.
Consideration of two points here is so important: the first is that
according to Khayyam's view between logic and mathematics, there
exists somehow a close dependency so that introduces parallel
postulate in other form which is in his view more logical than
Euclid's method. The second is that geometry in Khayyam's view is a
science of abstract shapes that are absorbed in abstract space and
this point is so important. Since for Greek the space was not
authentic and the position of objects according to Archimedes'
opinion was considered as the position of objects and shapes and now
we know that the imagination of abstract space has worthy contributed
to progress of mathematics and physics.
The connection between logic and mathematics in Khayyam's view leads
to a postulate that now is considered as a basic foundation of
science in philosophy and it is causality in the concept of
scientific. The leisure is short and the discussion about this
problem is not in scope of these words, it is just sufficient to
mention to it what is discussed in sciences as cause and effect and
the causality relationship between them, is a kind of coordination
and uniformity in measurement and the result of comparisons that has
remained constant and does not change and the point that as “to be
free of thought and to conquer mystery of the universe” is already
mentioned is the same problem that
relationship causality between evident objects whatever is, the
manner of appearing of these objects is constant and Khayyam takes
care of this issue exactly and in his own quatrains he has mentioned
it frequently. Always the sign of beings has been.
Algebra and cubic equations
In the research that Khayyam has carried out, he has required the
expansion of various powers of a “binomial” and has found out the
formation of the coefficients of this expansion as a rule and
regulation that nowadays is known as Pascal's triangle.
The algebraic binomial expansion is nowadays known as Newton's
binomial theorem, since for the first time apparently Newton has
codified these computations. Considering that Khayyam has used this
expansion and the regulation of the formation of its coefficients in
his works, it is clarified that Newton's binomial theorem and
Pascal's triangle have been discovered and innovated almost four
centuries before these scientist by Khayyam. For the first time, this
point was mentioned by Mr. Abolghasem Ghorbani, school teacher
in the Culture Ministry, in one of magazine in Tehran and he
published some papers about it. Sometime after in one of
international congress of the history of sciences that held in Rom,
foreign scientists mentioned it as well and Rozenfeld, professor in
Moscow University, submitted a suggestion concerning to change of the
name Newton's binomial theorem and Pascal's triangle to the name
Khayyam's binomial theorem and Khayyam's triangle to congress.
About the third degree equations, Khayyam is the first that
classified them and mentioned some regulations to solve each of them
by using conic sections. If it is considered that this method is
indeed analytical and geometrical method, then it can be said that
Khayyam is the first that has used analytical geometry to solve
algebraic equations and in this regard, he has innovated analytical
geometry almost four centuries before Descartes.
If is noticed that notations, form of algebraic equations in the
present forms and signs in Khayyam's era has not at all exist, the
significance and worthy of Khayyam's mathematical works would be more
appreciated and better perceptible.
Khayyam has compiled a brief treatise about determination of carat
gold, silver and ingot that has been combined by these two metals,
actually is the explanation of know as Archimedes' method and his
famous experience.
In this case, Khayyam also uses analytical and argumentative method
to explain the famous Archimedes' principle that is not unlike to the
present theoretical method.
The corrections of Zij Malekshahi and Jalali have enjoyed also
Khayyam's endeavors. And here it is
contented with this brief mention.
In the imputation that it has been attributed to Khayyam contrary to
equity and generosity, it should be careful that this erudite
impossibly withholds to teach and this is contrary to ethic and
knowledge to abstain to teach knowledge to apprentices. No doubt,
those who did not know even elementary terminology, asked Khayyam to
explain and the sage was not able to answer of necessity due to
inadequate understanding of questioner and he has silenced and maybe
has avoided to answer. And he has been attributed to withhold and
been oppressed.
Khayyam's scientific position is at least in mathematics so much
honorable and it is believed that he is the greatest mathematician in
his own era and possibly can be said the greatest mathematician in
Islamic age.
In comparison with al-Khwarizmi,
Abu al-Rayhan and Ghiyath al-Din Jamshid al-Kashi6
, all are the top stars in the first place and justly Khayyam is the
most eminent of this group.
The spiritual and scientific worth of Khayyam with regard to this
that this scientist has not proceeded to found philosophical school,
is more appreciated. Since philosophical issue if it has been even
precisely presented and asked, does not have confidential and certain
answer.
The mind of a scientist like Khayyam with clear and reasonable
introductory could not be scientifically and principally like
philosophical issues that are pessimistic and unstable with a view of
sentiment and impressible existence. Furthermore, hypotheses and
sentences of his previous or contemporary philosophers do not
convince Khayyam. Hence he is weary of philosophical issues and
elusive of philosophers. Similarity, though it would be little,
between Khayyam and Buddha can be found that a derisive smile to
deceitful manifestations of life has appeared on both their lips and
has summoned both of them to silence and amnesia. Both of them have
perceived affliction and both have attained maturity through
containment, renunciation, connivance and forgiveness for high
afflictions and their therapy, but none has argued and was
aetiologist and has proceeded to found a new philosophical manner.
Both have seen the life of human as commiseration and compassion and
have salved kindly human's trauma whether individually or socially.
Tolerance and longanimity of heterogeneous thoughts that is well
known as characteristic of Iranian race, is perfectly evident in
Khayyam and can be said that Khayyam is the distillate and extract of
centuries Iranian thoughts, contemplations, search and acquisition
and is the result of a long endeavor, efforts, eminence and
perfection of humanity. His doubt is closer to reality rather than of
unawares' certainty who are claimant of wisdom and his perplexity is
more ordered and regulated than of tranquility of those who reposed.
Here is a position that words are unable and incapable to explain.
1Edward
Fitzgerald
2Abu
al-Rayhan Muhammad ibn Ahmad al-Biruni (973-1048)
3Khawaja
Muhammad ibn Muhammad ibn Hasan Tusi(1201-1274)
4Abu
Abdallah Muhammad ibn Musa al-Khwarizmi (780-850)
5Nicolai
Ivanovich Lobachevsky (1792-1856)
