What is Pi?

So I've been considering numbers like .618 and other numbers which I think are needed to form a mathematical picture of digital evolution. The problem is how a form grows without "blurring" like a too much enlarged digital picture. You need to line up the angles, lengthen without disturbing the aligned angles and do this by increasing the number of cells. Nature does this, I believe by using the "Golden" angle and section, the logarithmic spiral and Fibonacci numbers. These are united in the formula I used to write X plus the square root of x = 1: X = .382 Its square root is .618
Today I'm changing the way I write that because I think I can relate Pi to the formula:
X squared plus X = 1 X = .618 X squared = .382
4 times the square root of X = Pi : the square root of X is .786
The advantage of this formula is that first it explains what Pi is, namely the result of the ratio between a square and a circle of the same diameter, but more important it gives a way of calculating lengths of curves plus relating curves to the Golden angle and section.

On .618

On .618

Past History of .618
There is a number .618, which from the time of the Egyptians, has been considered a constant in nature like Pi (3.14). The Egyptians used it in setting proportions when they built the Pyramids and the Greeks used it in building the Parthenon. The Renaissance rediscovered it and Leonardo used it in his pictures. Kepler tried to use it to build a cosmography. It was swept into the rubbish bin when Kepler showed that the form of the planetary orbits was an ellipse not a circle because .618 builds forms that are circles, spheres or spirals with inscribed triangles or squares, not ellipses.
Fall from Grace of .618
Ejected from the heavens, it was not allowed to remain on earth because it was assumed that astronomical forms and organic forms were basically the same. This has been assumed since earliest times. The basis of nature worship is the idea that life and the stars emerge from a common matrix (aka Mother Nature) and develop their forms in a common way.
Renaissance of .618 Explained
But I don't think that this is so. There is an observable difference between organic and non-organic forms which relates organic forms but not inorganic forms to .618. The difference is that in a symmetrical non-organic form such as a snowflake or a crystal or even a virus the opposite sides of the symmetry, The points of the snowflake, are joined by a lines passing straight through the center whereas in an organic form which appears to have a similar symmetry similar lines do not pass through the center or even intersect somewhere else. They form sets of triangles. But the lines from the points of a organic form, for instance from the petals of a flower, do pass through a center if they are considered as built up in time one after another - each petal separated from the previous petal by the Golden Angle. The Golden Angle is 222.5 degrees or .618.
So since this difference exists it seems to me that .618 is part of organic nature but not inorganic.
Need to Unify .618
In trying to understand how forms could be built up, I encountered the difficulty that the fame of .618 had caused it to be considered in very different ways. For instance, as the Golden Angle, it is seen as .618x360. But as the Golden Section it is seen as 1 + .618. There is a construction called The Flying Squares in which subdivisions are created by a formula involving the square root of 5, yet if you simply look at the form of the Flying Squares you are looking at Fibonacci numbers so that subdivisions could be created without the square root of 5. After 34 all adjacent Fibonacci numbers are in the ratio .618. But how does it all fit together to build natural form? .618 - E Pluribus Unum
To see how it fits together to build organic form we could start with how it fits mathematically and then look for a physical law. I fit it together in this way.
There is a number and only one number and that number is .382 which meets these two conditions: X divided by the square root of X equals the square root of X and X plus the square root of X equals 1.
.618 is the square root of .382.
.618 + .382 = 1 and .382/.618 = .618

Everything else flows from this unique relationship and can be defined in terms of it.
The Golden Angle and .618 Newly Understood
The Golden Angle is a version of X plus the square root of X = 1 in which X times a number plus the square root of X times the same number equals the number. The two decimals, .382 and .618, equal one so any number multiplied by them is divided into two fractions of itself which, added together, equal itself.
X times 360 degrees plus the square root of X times 360 degrees = 360 degrees
.382 times 360 = 137.5; .618 times 360 = 222.5; 137.5 + 222.5 = 360
The other relationship X divided by the square root of X = the square root of X also holds so that the two angles 137.5 and 222.5 have the relationship that 137.5/222.5 = .618 is in the same ratio as 222.5 / 360 = .618. The smaller angle is to the larger as the larger is to the whole - the definition of the Golden Angle.
The Golden Section and .618 Newly Understood
The Golden Section is a version of X divided by the square root of X = the square root of X.
X times Length divided by the square root of X times Length equals the square root of X because the Length is in the numerator and denominator and cancels out.
For instance a line is ten feet long:
.382 X 10/ .618 X 10 = 3.82/6.18 = .618
6.18/ 10 = .618
The other relationship X + the square root of X = 1 holds so that the length is divided into two fractions equal to the whole length. The larger fraction is the length multipied by .618 so naturally this fraction divided by the whole length equals .618. The two fractions of the length as a ratio equal .618 and the larger fraction divided by the whole has the same ratio .618. This is the definition of the Golden Section (and the mean and extreme ratio.)
Coming Next - Fibonacci and .618
Star Attraction - Fibonacci and the Flying Squares
Next I will show how Fibonacci numbers fit into this but first I have to figure out how to get pictures into this blog because Fibonacci numbers require the Flying Squares to understand them.

Natural Fibonacci Numbers and Others

Natural Fibonacci Numbers
The Fibonacci number series starts with 1, 1, 2, 3, 5, 8, 13, 21, 34. The ratio between adjacent numbers in this series after 21/34 is .618 plus many other numbers. The Fibonacci number series that starts with 1, 1 could becalled the natural series since in nature it would start with 1.
Other Fibonacci Numbers
Any number could be the start of a Fibonacci number series since the series is started by adding zero to a number (FN) twice and continued by adding together the two previous totals. The natural Fibonacci series tells us how many times the original number (FN) each new total will be when the series does not start with one.
1xFN, 1xFN, 2xFN, 3xFN, 5x FN, 8xFN, 13xFN, 21xFN, 34xFN
Since the series has this form, the ratio between adjacent numbers in the series will be .618 (plus many other numbers not the same ones as the natural Fibonacci series) from the ninth number, 34x FN, in the series on.
Before that the ratios would be the same as in the natural Fibonacci series 1/2, 2/3, 3/5, 5/8. 8/13, 13/21. These ratios are said to be tending toward .618 but really they are themselves - the description of the ratio between the number of times the FN is occurring. After the ninth number the ratio never changes.
So if , in nature, a form began with a large number of cells present - a branch from a stem perhaps - it still would take on the Fibonacci ratios if in cell division the two previous numbers were ADDING together.

On Growth and Form

The problem of the growth of a natural form once the form is established is defined as: at the same angle a relative increase in length caused by a relative increase in number of cells. It's just like a problem in perspective or trying to increase a digital picture in size without losing sharpness. By length I mean extension at one point ( length, width, height)
Concentric circles as Escher shows solve the problem of length and angle. The logarithmic spiral as Darcy Thompson shows also solves the problem of increasing lengths at the same angle. The log spiral is the path between concentric circles.
Cells increase - but in what ratio? It could just as well be Fibonacci as geometric and Fibonacci would be better for keeping everything aligned on a spiral.
To unite everything in alignment, .618 could have been used in spiraling growth which solves all the problems because .618 is a number, a length, an angle and a ratio. But so far God only knows what really happened.

The Incoherence of the Philiosphers (2)

AL-GHAZLI CITED ON JIHADIST VIDEO
I see that an American jihadist has issued a video in which he mentions "the incoherence" of the doctrines in the West. If you wanted to be as shallow as he is, you could say "what could be more incoherent than Sunni Moslems blowing up Shia Moslem shrines as is happening in Iraq? or Arab Moslems commiting a genocide against African Moslems as is happening in Darfur?"
But it's more interesting to me that he mentions "The Incoherence". It makes this philosophical discussion seem ... relevant? timely? The Incoherence of the Philosophers in banned in Turkey because the book is connected in Islamic history with the decision to turn away from free discussion inside Islam. Many sites which discuss Al-Ghazli bring this up. In my opinion he would never have called for a turning from free discussion and the sections being quoted today make that particularly plain.
Al-Ghazli may have shown "the incoherence of the philosophers" as of his day. He never would have said that there was no point in reading or discussing philosophers now that he had shown their errors. In today's sections he specifically limits his discussion to the narrow set of issues where there is substantial and significant disagreement between Avicenna (and Aristotle) and religion. This leaves a wide area for discussion and Al-Ghazli was quite definite that religion should not be intruded into this area by excitable, ignorant defenders of Islam. He would not have decided it was time for an end to free discussion.
If the Islamists come to power in Turkey - or elsewhere - they may try to suppress free discussion citing Al-Ghazli. Then readers of this site will be able to instantly reply: Do not try to advance the cause of religion by increasing ignorance for did not Al-Ghazli say “a rational foe is better than an ignorant friend." '

TODAY'S SECTIONS
In today's sections Al-Ghazli is discussing how he will refute the philosophers. These sections are called Introductions but they are quite important because in them Al-Ghazli marks out boundaries between philosophy (and science since the two were bound together in Avicenna's work)and religion. He points out several ways in which unnecessary conflicts arise: namely, poor translations, purely verbal disputes, disputes over points irrelevant to religion, disputes caused by someone insisting that philosophy has challenged Muhammed's words. He is very hard on this last practice, saying: "The harm inflicted on religion by those who defend it not by its proper way is greater than the harm caused by those who attack it in the way proper to it. As it has been said: “a rational foe is better than an ignorant friend.”
He points out that Muhammad's words words must be distinguished from comments on those words and from poor translations. Then too, the words might be metaphorical. When Muhammd is cited as an authority all these points must be kept in mind.
Current jihadists who think Al-Ghazli would support their melding of Islam with an easy ignorance buttressed by a solid dose of hatred, cruelty and lies, are very wrong.

I remind readers that I have removed parentheses inserted by translators and spelled out references - i.e. "they" has been changed to "the followers of Avicenna" or "the Greek philosophers"

INTRODUCTION (CONTINUED PREVIOUS POST)
Al-Ghazli makes a definite statement about Avicenna's physics and metaphysics, a challenge to his followers. He says Aristotle, Avicenna and other philosophers are using "supposition and surmise without verification and certainty." The weak-minded assume after reading these philosophers on mathematics that their physics and metaphysics must be equally demonstrable. Not so says Al-Ghazli. If their metaphysics was as well founded as their mathematics they would all agree as they do about mathematics whereas in fact they disagree. A point to keep in mind is that Aristotle and Avicenna asserted the eternity of the world whereas the Old Testament and Koran asserted "In the beginning God created heaven and earth."

I, Al-Ghazli, teacher in Islam, have transmitted this story to let it be known that there is neither firm foundation nor perfection in the doctrine Aristotle and Avicenna's followers hold which opposes Islam; that they judge in terms of supposition and surmise, without verification or certainty; that they use the appearance of their mathematical and logical sciences as evidential proof for the truth of their physical and metaphysical sciences, using this as a gradual enticement for the weak in mind. Had the physical and metaphysical sciences of Aristotle, Avicenna and their followers been as perfect in demonstration, free from conjecture, as their mathematical, they would not have disagreed among themselves regarding physics and metaphysics, just as they have not disagreed in their mathematical sciences.
WE ONLY KNOW ARISTOTLE IN TRANSLATION AND THIS TOO HAS LED TO DISPUTES AMONG THE FOLLOWERS OF THE PHILOSOPHERS WHICH THERE IS NO NEED TO DELVE INTO. WE WILL DISCUSS WHAT AVICENNA AND AL-FARABI, THE MOST IMPORTANT ISLAMIC FOLLOWERS OF ARISOTLE'S ERRORS, HAVE SAID.
We only know Aristotle in translation and this too has led to disputes among the followers of the philosophers which there is no need to delve into. We will discuss what Avicenna and Al-Farabi, the most important Islamic followers of Arisotle's errors, have said.
Moreover, the words of the translators of the words of Aristotle are not free from corruption and change, requiring exegesis and interpretation, so that this also has aroused conflict among them. The most reliable transmitters and verifiers among the philosophers in islam are Al-Farabi Abu Nasr and Avicenna. Let us then confine ourselves to refuting what these two have selected and deemed true of the doctrines of their leaders in error. For what they have abandoned and scorned to pursue no one contests is error and needs no lengthy examination to refute. Let it then be known that we are confining ourselves to the Greek philosophers’ doctrines according to the transmission of these two men so that the discussion would not spread far and wide - as far and wide as the spread of Greek philosophy.

A Second Introduction
There are three parts to the dispute among philosophers. These parts have led to sects among them.
Let it be known, then, that the dispute between the philosophers and others of their sects has three parts.
There is a part which is concerned with disputes which are purely verbal even though the issue is important. For instance, Avicenna and Al-Farabi say the world's creator is a substance by which they mean self subsisting and non-material through others use this word to mean material and not self-subsisting, i.e., occupies space.
There is a part in which the dispute reduces to the purely verbal, as, for example, their naming the world’s Creator -exalted be He above what they say- a substance, with their explanation of [this] substance as that which does not exist in a subject, that is as the self-subsisting that does not need something else which substantiates it. They did not intend by this substance, as their opponents intend, that which occupies space.

We as philosophers will not get into this kind of verbal dispute. It may be that a usage by a philosopher is unprecedented and not sanctioned by the lawyers. This is a problem in theocratic state. "You must not, however, allow the true nature of things to become confused for you because of customs and formalities." It is a question about saying in controversial way something that is true. Questions about the use of words can be investigated freely (by others) because it is just like asking whether a certain act is acceptable under religious law. But bogging down on the use of words is not relevant to our philosophical quest. This how we should look at disputes of the first "part" or type.
We will not plunge into a refutation of this because once the meaning of self-subsistence becomes agreed upon, then the discussion regarding the use of the term “substance” to express this meaning becomes a lexical investigation. If language sanctions its use, then the permissibility of its use in religion reverts to investigations within the religious law. For the prohibiting and permitting of terms derives from what the outer meaning of the religious texts indicates. Now, you may say that this type of naming has been mentioned by the theologians in relation to the divine attributes but was not introduced by the lawyers in the discipline of the religious law. You must not, however, allow the true nature of things to become confused for you because of customs and formalities. For you now know that it is an investigation about the permissibility of uttering an expression whose meaning is true of the thing named. It is thus similar to investigating the permissibility of a certain act-hence within the province of the religious law.
The second part of the dispute among philosphers is concerned with issues that are more than verbal but are not relevant to the principles of religion. An example of this is the statement that the earth is round and that this is the cause of eclipses.
The second part of the dispute of the philosophers is the part in which their doctrine does not clash with any religious principle and where it is not a necessity of the belief in the prophets and God’s messengers, God’s prayers be upon them, to dispute with the philosophers about it. An example of this is their statement: “the lunar eclipse consists in the obliteration of the moon’s light due to the interposition of the earth between it and the sun, the earth being a sphere surrounded by the sky on all sides. Thus when the moon falls in the earth’s shadow, the sun’s light is severed from it.” Another example is their statement: “the solar eclipse means the presence of the lunar orb between the observer and the sun. This occurs when the sun and the moon are both at the two nodes at one degree.”

We should not try to refute these theories. It is not a religious duty and as a matter of fact it harms religion. When someone who knows something by geometrical or mathematical proofs is told that his knowledge is contrary to religion, he does not think his proofs are wrong, he thinks religion is wrong. Defending religion illogically is more harmful than attacking it logically. “a rational foe is better than an ignorant friend.”
This topic is also one into the refutation of which we shall not plunge, since this serves no purpose. Whoever thinks that to engage in a disputation for refuting such a theory is a religious duty harms religion and weakens it. For these matters rest on demonstrations, geometrical and arithmetical, that leave no room for doubt. Thus when one who studies these demonstrations and ascertains their proofs, deriving thereby information about the time of the two eclipses and their extent and duration, when this someone is told that this is contrary to religion, that individual will not suspect his proofs, he will only suspect religion. The harm inflicted on religion by those who defend it not by its proper way is greater than the harm caused by those who attack it in the way proper to it. As it has been said: “a rational foe is better than an ignorant friend.”
Suppose someone challenges you on an issue like that of the eclipses by saying that you are contradicting Muhammed. What follows shows how to handle this kind of challenge.
If it is said by a religious believer who thinks the philosophers must be refuted about the nature of eclipses that God’s messenger Muhammed (God’s prayers and peace be upon him) said, “The sun and moon are two of God’s signs that are eclipsed neither for the death nor the life of anyone; should you witness such events, then hasten to the remembrance of God and prayer.” how, then, does this agree with what the philosophers state?"
The answer in this particular case is that Muhammed said that an eclipse was not a sign of the life or death of anyone but to pray when it occurs. This does not contradict the argument that eclipses are caused by the earth being a sphere. Some say that revelation says that an eclipse is a miracle as indicated by “but if God reveals himself to a thing it submits itself to him,”
We say: There is nothing in what Muhammad said that contradicts what the philosophers have stated about eclipses since there is nothing in what Muhammad said except the denial of the occurrence of the eclipse for the death or life of anyone and the command to pray when it occurs. Why should it be so farfetched for the religious law that commands prayer at noon and sunset to command, as recommendable, prayer at the occurrence of an eclipse? If the religious believer responds that at the end of this saying, Muhammad said, “But if God reveals Himself to a thing it submits itself to Him,” and the religious believer says this proves that the eclipse is submission by reason of revelation, we answer:
The answer is to point out that this second saying has a questionable place in the canon of Muhammad's sayings, the true saying being the one Al-Ghazli cited first. And if on some other occasion the saying were truly part of the Koran, it should be seen as metaphorical like many other sayings. This is how to handle disputes of the second type or part. There is nothing atheists like better than to have a rejection of a clear demonstration like the proof that eclipses are caused by the spherical nature of the earth made into a religious requirement. It makes refuting religion easy for them.
This addition is not soundly transmitted and hence the one who transmits it must be ruled as conveying what is false. The correctly related tradition is the one we have mentioned. How is this not so? And if the transmission of the addition were sound, then it would be easier to interpret it metaphorically rather than reject matters that are conclusively true. For how many an apparent scriptural meaning has been interpreted metaphorically on the basis of rational proofs rejecting their literal sense that do not attain the degree of clarity of the astronomical demonstrations regarding the eclipse! The greatest thing the atheists rejoice in is for the defender of religion to declare that these astronomical demonstrations and their like are contrary to religion. Thus the atheist’s path for refuting religion becomes easy if the likes of the above argument are rendered a condition for its truth.

All that matters is the question of whether the world is god's act and whether it originated in time or is eternal - how eclipses happen, whether the universe is an octagon, a hexagon or a sphere, whether in thirteen layers or more or less is about as important to the religious question as how many layers an onion has or how many seeds there are in a pomegranate. So sort all questions into one of the three kinds and do not hold religious disputes about the first two, only the third.
This is because the inquiry at issue for religion about the world is whether the world originated in time or is eternal. Moreover, once its temporal origination is established, it makes no difference whether it is a sphere, a simple body, an octagon, a hexagon; no difference whether the highest heaven and what is beneath them are thirteen layers, as they say, or lesser or greater. For the relation of the inquiry into these matters to the inquiry into divine matters is similar to the relation of looking at the number of layers of an onion or the number of seeds in a pomegranate. What is matters is only the world’s being God’s act, whatever mode it has.
The third type of question or third part of the dispute the philosophers have is the type of question that does touch the principles of religion. These include the doctrine of Creation from nothingness and of the resurrection of the body and other equally important principles which Avicenna and his followers have denied. Here the philosophers must be shown to be false using principles they acknowledge.
The third part is one where the dispute pertains to one of the principles of religion, such as upholding the doctrine of the world’s origination and of the positive attributes of the Creator, or demonstrating the resurrection of bodies, all of which the philosophers have denied. It is in this topic and its likes, not any other, that one must show the falsity of their doctrine.

A Third Introduction
How is it best to carry on this third kind of dispute? WhatAl-Ghazli will do is show those who think the philosophers are free of contradictions that Avicenna and his followers, are full of contradictions and are incoherent. Sometimes they are Sunnis, sometimes Shiites. He does not propose a physics or a metaphysics of his own but challenges them on their own ground using their own principles.
Let it be known that our objective is to alert those who think well of the philosophers and believe that their ways are free from contradiction.
For this reason, I do not enter into argument objecting to the philosophers, except as one who demands and denies, not as one who claims and affirms. I will render murky what Avicenna's followers believe in by showing conclusively that they must hold to contradictory and varying consequences of their theories. Thus I will force on them at one time necessary adherence to Mu‘tazilite doctrine, at another to that of the Karramiyya, at yet another to that of the Waqifiyya. I, however, will not rise to the defense of any one doctrine, but will make all the islamic sects as one group against the followers of the philosophers. For islamic sects differ in matters of detail, whereas these philosophers and their followers challenge the very principles of religion. Let all believers in Islam then strive against them. For in the face of hardships rancors depart.

I've been working all summer on Fibonacci numbers as related to growth of form in nature, to log spirals, to the Golden Angle and to the Golden Section. These are my conclusions: the root of the matter is the relationship of .618 to these other forms. What is .618 in itself? .618 is the square root of .382 and .618 + .382 add up to 1 - these two together make it a number which can form the relationship in angles, lengths, and numbers : little is to big as big is to the whole. This verbal formula doesn't sound mathematical but it defines the relationship which is common to Fibonacci numbers, the Golden section , the Golden angle, log spirals and natural growth of form. Using this common relationship natural form can be analysed mathematically

The Incoherence of the Philosphers (1)

DANCING IN THE DARK
These days it can be hard to keep a balance and keep the truth when thinking about Islam. All kinds of Islamic governments are basing their foreign policy on the ignorant premise that "The Protocols of the Elders of Zion" is a guide to Israeli thinking. The Protocols are well-known to be a nineteenth century Russian forgery aimed at inciting anti-semiticism. You wonder what to say to anyone who hasn't bothered to verify the major document behind their foreign policy. Then you see the continual fauxtography frauds exposed in the Lebanon war. It's evident that this has been going on all along. The amount of falsehood is sickening and the ignorance, hatred, cruelty, and indifference to truth that fosters it all is a portrait of a sick society.

DESTROYING PALESTINE TO SAVE IT
Then you listen to the Iranian who wants to get his finger on the trigger of a nuclear weapon SO THAT HE CAN PULL THE TRIGGER. I mean - anything that hit Israel would blow radioactive dust all over the east end of the Mediterranean, Gaza, the West Bank, Jordan, Lebanon and part of Syria - right away. Look at a map sometime - Israel is tiny. It's like they say - Israel is tiny - and surrounded by large states with large populations. In the Name of God, the Compassionate, the Merciful, where does the Iranian think the radioactive dust will mainly go? And what does he mean by saying he'll get Palestine for the Palestinians by sprinkling the area - and very likely them - with radioactive dust? And then ...the wind blows west, he wrecks the Mediterranean, the wind blows east and back the stuff comes on Iraq passing over and poisoning the Al-Aqsa mosque on the way. The wind - another Zionist plot. Or what if the bomb misses Haifa or Tel Aviv and detonates in the Mediterranean - won't this cause a tsunami-like wave that will drown low-lying Egypt and wreck the Mediterranean? Libya, Tunisia, Morocco - will they be grateful for that?

AL-GHAZLI - VOICE OF ANOTHER AND BETTER ISLAM
Anyhow, as a Christian, I want to keep a place in my heart for Islamic believers despite the current prominence of a band of hate-filled, ignorant liars. They aren't the only people in Islam and this isn't the only time Islam has been on the world stage. So I turned to other years and other teachers in Islam and I found the great Al-Ghazli, author of The Incoherence of the Philosophers. I liked him a lot and I thought I'd post his work in sections with a few comments from time to time. He really shows that the present band of ignorant liars are a decadent form of Islam. What's probably the most surprising part so far is reading his discussions of the "outside" of the universe and what came "before" time. His views and those of Avicenna are those advanced as new by Einstein and others.
Then, too, though he lived in the eleventh century, Al-Ghazli was sure that that the earth went round the sun and that eclipses were caused by the lineup of the sun and moon.
He distinguished the problems important to religion from all other philosophical problems, saying that a teacher in Islam should only be concerned with the problems relevant to religion.

BANNED IN TURKEY
It's strange that his name and his work should be associated with the movement in Islam which put an end to free inquiry but this is the historical fact. As a result his work was banned in Turkey by Kemal Ataturk as part of Ataturk's modernizing program. It's still banned there. Maybe I haven't gotten to the bad parts yet. But I think Al-Ghazli was probably misused by a lot of people who never bothered to read him - the type we have with us today who love reading the Protocols and bathing in hatred.

AL-GHAZLI AND THE PROBLEM OF PHILOSOPHICAL DOUBT
Al-Ghazli lived in the twelfth century. The philosopher we call Avicenna was roiling the waters in the Islamic world. Those who followed him were losing their faith in Islam. "Their doubt is the outcome of their being deceived by embellished imaginings akin to the glitter of the mirage" says Al-Ghazli. He wanted to return men to an understanding of that God who one day would reward his faithful with a Paradise "from whose heights the greatest ascents of the understanding stand low and from whose distant stretches the utmost reaches of the arrows of the imagination waste away", with a bliss which '"neither eye has seen nor ear, heard, nor has occurred to the heart of men,”'. He wanted to return men to the true teaching of Muhammad and his companions "pure keys of guidance and lanterns in the dark." We don't have to agree with him to see he was a man to respect.

THE PLAN OF ACTION
I'll give an overview of the sections and then precede each section with a few bolded sentences explaining what I think Al-Ghazli is saying. Let me make it clear too that I have taken out all the parentheses which the translators used when they added phrases to make it clear to what or whom Al-Ghazli was referring. And I have sometimes added in "Avicenna", "Avicenna's followers", "the Greek Philosophers" and other similar expressions where Al-Ghazli is translated as saying "they", "their", "these" and other pronouns. In English it's easier to understand Al-Ghazli if his frequent references to the other side of the dispute are made concrete.

TODAY'S SECTIONS
Al-Ghazli begins with a prayer for enlightenment. "We ask God ... to make us among those who saw the truth as truth, preferring to pursue and follow its paths, and who saw false as false, choosing to avoid and shun it." Then he explains the problem as he saw it. The philosophers were attracting people away from Islam. Yet it could be shown that it was not the great Greek philosophers but their interpreters (Avicenna) who were irreligious. Furthermore, the followers of Avicenna who accuse believers of being mere "imitators" were themselves merely "imitating" Avicenna. To prove this Al-Ghazli intends to show that Avicenna is involved in logical contradictions which his followers ignore because they are not thinking philosophically as they claim but following or "imitating" like the believers. There is this difference between them and the believers however - they are imitating error.



ASKING GOD'S BLESSING ON THE SEARCH FOR TRUTH

In The Name of God, the Compassionate, the Merciful
We ask God in His majesty that transcends all bounds and His munificence that goes beyond all ends to shed upon us the light of His guidance and to snatch away from us the darkness of waywardness and error; to make us among those who saw the truth as truth, preferring to pursue and follow its paths, and who saw false as false, choosing to avoid and shun it; to bring us to the felicity He promised His prophets and saints; to make us attain that rapture and gladness, favored bliss and joy (once we depart from this abode of delusion) from whose heights the greatest ascents of the understanding stand low and from whose distant stretches the utmost reaches of the arrows of the imagination waste away; to grant us, after arriving at the bliss of paradise and emerging from the terror of the judgment day, that which "neither eye has seen nor ear, heard, nor has occurred to the heart of men,” and that He may bestow His prayers and His assured peace upon the prophet, the chosen, Muhammad, the best of men, and upon his virtuous family and his companions pure keys of guidance and lanterns in the dark.

THERE IS A PROBLEM OF UNBELIEF AMONG SOME OF THE ISLAMIC INTELLIGENTSIA
I have seen it: there are those who, believing themselves better than their companions and peers by virtue of a superior quick wit and intelligence, have rejected the Islamic duties regarding acts of worship, disdained religious rites pertaining to the offices of prayer and the avoidance of prohibited things, and belittled the devotions and ordinances prescribed by the divine Law, not halting in the face of its prohibitions and restrictions. On the contrary, they have entirely cast off the reins of religion through various other beliefs, following therein a troop “who [leave and shun] God’s way, intending to make it crooked, who are indeed disbelievers in the hereafter” [Qur’an 11:19].

THE JEWS AND THE CHRISTIANS IMITATE. THE INTELLIGENTSIA IMITATE. THE JEWS AND CHRISTIANS IMITATE THEIR FOREFATHERS; THE ISLAMIC DOUBTERS IMITATE THE PHILOSOPHERS IN SPECULATING AND EVEN MERELY IMAGINING ABOUT HOW THINGS ARE.
There is no basis for the Islamic doubters unbelief other than traditional, conventional imitation just exactly like the imitation of Jews and Christians. In the case of Jews and Christians their upbringing and that of their offspring has followed a course other than the religion of Islam, their fathers and forefathers having followed these religions without thought. This group of philosophical doubters imitates what they know of speculative investigation, which is unbelief. The unbelief is the consequence of their stumbling over the tails of sophistical doubts in their investigation of beliefs and opinions, doubts that divert from the direction of truth. Their doubt is also the outcome of their being deceived by embellished imaginings akin to the glitter of the mirage, This has happened to groups of speculative thinkers, followers of heretical innovation and whim.

THE GREEK PHILOSOPHERS HAVE A GREAT NAME AND THE LEADERS IN UNBELIEF (AVICENNA) EXAGERRATE THESE PHILOSOPHERS' INTELLIGENCE AND LEARNING, ADDING THAT THESE MIGHTY MINDS REJECTED REVEALED RELIGION AND ITS TEACHING AS MAN-MADE LAWS AND TRICKS.
The source of their unbelief is their hearing high-sounding names such as “Socrates,” “Hippocrates,” “Plato,” “Aristotle,” and their like, and the exaggeration and misguidedness of certain of the followers of these philosophers in describing their minds, the excellence of their principles, the exactitude of their geometrical, logical, natural, and metaphysical sciences, and in describing the philosophers as being alone -by reason of excessive intelligence and acumen- capable of extracting these hidden things; the source of philiosophical unbelief is also hearing what [Avicenna and his followers have to say about Aristotle, Plato and Socrates which is] that the certainty of their intellect and the abundance of their merit runs along with denial of revealed laws and religious confessions and rejection of the details of religious and sectarian teaching, the greatest philosophers believing these laws and teachings to be man-made laws and embellished tricks.

WHEN SOME OF THE ISLAMIC INTELLIGENTSIA HEARD AVICENNA'S ATTACK ON RELIGION THIS AGREED WITH SOMETHING IN THEMSELVES. THEY PUT ON AND WORE PHILOSOPHICAL UNBELIEF LIKE THE LATEST FASHION IN THE MOST EXPENSIVE CLOTHES. THEY FEEL PHILOSOPHICAL UNBELIEF IS A VIRTUE WHICH EXALTS THEM ABOVE THE COMMON MASS OF BELIEVERS WHO THEY SEE AS MERE IMITATORS OF THE RELIGION OF THEIR FATHERS. IN FACT AVICENNA'S FOLLOWERS ARE IMITATING ALSO AND WHAT THEY ARE IMITATING IS ERROR.
When this struck the hearing of some of the Islamic intelligentsia, that which was reported by Avicenna of the Greek philosophers’ unbelief finding agreement with their nature, they adorned themselves with the embracing of unbelief, siding with the throng of the virtuous who are Avicenna's followers, as they claim, affiliating with them, exalting themselves above aiding the masses and the commonality, and disdaining to be content with the religious beliefs of their forebears. They have done this, thinking that the show of cleverness in abandoning the imitation of what is true by embarking on the imitation of the false is a beauteous thing, being unaware that moving from the one to the other is folly and confusedness.

IMBECILES ARE SMARTER THAN AVICENNA'S FOLLOWERS BECAUSE IMBECILES DO NOT HASTILY EMBRACE ERROR WITH PRIDE AND WITHOUT VERIFICATION
What rank in God’s world is there that is lower than the rank of one who adorns himself with the abandonment of the truth that is traditionally believed by the hasty embracing of the false as true, accepting it without reliable report and verification? The imbeciles among the masses stand detached from the infamy of this abyss; for there is no craving in their nature to become clever by emulating those who follow the ways of error. Imbecility is thus nearer salvation than acumen severed from religious belief; blindness closer to wholeness than cross­eyed sight.

WHEN I SAW WHAT WAS HAPPENING I DECIDED TO WRITE THIS BOOK WITH TWO POINTS IN MIND. I WANTED TO SHOW THAT THE GREATEST OF PHILOSOPHERS DISAGREE AMONG THEMSELVES AND WITHIN THEMSELVES ON METAPHYSICAL ISSUES TO THE POINT OF INCOHERENCE BUT THAT THEY AGREE THAT THERE IS A GOD AND A JUDGEMENT DAY. ONLY A FEW PERVERSE AND NEGLIGIBLE PHILOSOPHERS WERE ACTUALLY AS IRRELIGIOUS AS AVICENNA'S FOLLOWERS CLAIM. YOU SHOULD KNOW THOUGH THAT THE THE GREAT PHILOSOPHERS, RELIGIOUS THOUGH THEY WERE, FELL INTO ERROR ON CERTAIN CRUCIAL POINTS SO ALL THEIR WORK WAS A WASTE OF TIME.

When I perceived this vein of folly throbbing within these dim­wits, I took it upon myself to write this book in refutation of the ancient philosophers, to show the incoherence of their belief and the contradiction of their word in matters relating to metaphysics; to uncover the dangers of their doctrine and its shortcomings. These shortcomings in truth which is ascertainable by reason are objects of laughter for the rational and a lesson for the intelligent -I mean the kinds of diverse beliefs and opinions the philosophical unbelievers particularly hold that set them aside from the populace and the common run of men. I will do this, relating at the same time the Greek philosophical doctrine as it actually is, so as to make it clear to those who embrace unbelief through imitation of Avicenna that all significant thinkers, past and present, agree in believing in God and the last day; that their differences reduce to matters of detail extraneous to those two pivotal points (the prophets, supported by miracles, have been sent to be sure that those of us who do not study metaphysics know the truth about these points); that no one has denied these two beliefs other than a remnant of perverse minds who hold lopsided opinions, who are neither noticed or taken into account in the deliberations of the speculative thinkers like Aristotle. Among philosophers unbelievers are counted only among the company of evil devils and in the throng of the dim-witted and inexperienced. I will do this so that whoever believes that adorning oneself with imitated unbelief shows good judgment and will impress everyone with one’s quick wit and intelligence would desist from his extravagance, as he learns the truth - that Aristotle and Plato, those prominent and leading philosophers he emulates are innocent of the imputation that they deny the religious laws; that on the contrary they believe in God and His messengers, but that they have fallen into confusion in certain details beyond these principles, erring in this, straying from the correct path, and leading others astray. We will reveal the kinds of imaginings and vanities in which they have been deceived, showing all this to be unproductive extravagance. God, may He be exalted, is the patron of success in the endeavor to show what we intend to verify.

LET ME START BY EXPLAINING HOW I INTEND TO PROCEED - WHAT I WILL DO AND WHAT I WILL NOT DO AND WHY.
Let us now begin the book with introductions that express the pattern of discourse followed therein.

I AM NOT GOING TO DISCUSS THE LONG AND SAD TALE OF EVERY GREEK PHILOSOPHER'S DIFFERENCES WITH EVERY OTHER GREEK PHILOSOPHER BUT I WILL CONCENTRATE ON THE CONTRADICTIONS IN THE GREATEST OF THEM, ARISTOTLE.
First Introduction
Let it be known that to plunge into narrating the differences among the philosophers would involve too long a tale. For their floundering about is lengthy, their disputes many, their views spread far apart, their ways divergent and convergent. Let us then restrict ourselves to showing the contradictions in the views of their leader, who is the philosopher par excellence and “the first teacher.” For he has, as they claim, organized and refined their sciences, removed the redundant in their views and selected what is closest to the principles of their capricious beliefs -I mean, Aristotle. He has answered all his predecessors, even his teacher, known among them as “the divine Plato,” apologizing for disagreeing with his teacher by saying: “Plato is a friend and truth is a friend, but truth is a truer friend.” (to be continued)