Mathematics is the door and key of the sciences and things of this world. . . . It is evident that if we want to come to certitude without doubt and to truth without error, we must place the foundations of knowledge in mathematics.


The triumph of orthodoxy, relentlessly sought between the third and seventh centuries, was as deceptive as it was Pyrrhic. The hidden cost was the suppression of spiritual inspiration and creative imagination. Illusion veiled the fact that those whose insights would have otherwise placed them outside the church found themselves indulging their own trends of thought even within the priestly hierarchy. Exultation in the ending of the classical world and the espousal of blind belief rapidly gave rise to second thoughts, doubts and speculations. The neo-Platonic thought of Proclus found its way into the mystical writings of Dionysius, just as the Platonic conception of the soul entered Christian theology. Hierocles and Boethius composed Platonic philosophical works which were immensely popular for centuries amongst Christians. The rampant diversity of philosophical attitudes and religious feelings so strained all attempts to advocate a unified theology that Anselm of Canterbury was led to adumbrate logical proofs of the existence of God. This occurred as early as the turn of the millennium. The enveloping wings of the Church Triumphant protected the concerns that would flourish briefly in the Renaissance through the resurrected ideals of human dignity, freedom of choice and benevolent reasonableness. These seed-ideas germinated and put forth tender if hardy shoots in the renewed pursuit of a patient understanding of nature by such bold thinkers as Robert Grosseteste and Roger Bacon.

Roger Bacon was born near Ilchester in Somerset around AD. 1214. His family was distinguished and rather wealthy but, while he was still young, the baron's revolt against King Henry III forced several relatives into exile and resulted in the expropriation of the family holdings. Roger Bacon entered Oxford University where he completed his studies and made friends with several remarkable thinkers, including Robert Grosseteste, bishop of Lincoln, chancellor of the university, translator and commentator on Aristotle, first lecturer to the Oxford Franciscans and an advocate of experimental enquiry.

Roger Bacon joined the Franciscan order about 1233, and shortly afterwards journeyed to Paris to study in the most volatile theological centre of the time. There he found Dominicans and Franciscans in hot debate over the issues raised by the translation and dissemination of the works of Plato and Aristotle. Alexander of Hales was the chief spokesman for the Franciscans, and Albertus Magnus stood for the Dominicans. Paris had initially banned the works of Aristotle and Averroes, but Toulouse opened the way to such studies by issuing a catalogue in 1229 proclaiming the ''teaching of the books on natural science that have been banned at Paris". By 1237 Roger Bacon was a regent master at Paris, lecturing on the banned books. Alexander's conservative stance regarding such study drew Roger Bacon's criticism, and he began to set off in fresh directions of thought.

Expressing dismay at the poor translations of classical works available in Europe, the lack of even one reader of Greek at Paris, the dependence upon custom rather than observation in natural science, Roger Bacon drew upon the wealth of Islamic philosophy and science and incorporated Aristotle into his lectures. He felt a deep respect for Petrus de Maharncuria of Picardy, an obscure mathematician who had written a treatise on magnetism. His view of the state of theology was lukewarm. Thinkers could not read the scriptures in any of the ancient tongues, indeed did not read them at all, being content to elaborate upon the enigmatic Sentences of Peter Lombard. For Bacon, the seeming show of knowledge masked a more fundamental ignorance. His various lectures brought him wide recognition, but his profound study of the Islamic Secret of Secrets, which taught that a keen intellect together with a noble character could unravel the mysteries of Nature, was frowned upon by orthodox ecclesiastics. When he won his doctorate and the honorary title Doctor Mirabilis, he was also hailed as the peer of Avicenna and Averroes, as well as Aristotle, the industrious pupil of Plato.

Around 1247 he left Paris and returned to Oxford. There he studied languages carefully, invested in arcane volumes and scientific instruments, and thereafter established a fellowship of like-minded thinkers. Just as Albertus Magnus was so called for his spiritual gifts, Roger Bacon came to be associated with theurgy. Though esteemed highly by many, Bonaventura, the official head of the order, banned his lectures in 1257 and brought him back to Paris where he had to abandon research in favour of solitude. Despite this invaluable period of silence and self-training for almost a decade, his influence spread. Guy de Foulques, papal legate to England, became intrigued with Roger Bacon's work, and when he became Pope Clement IV in 1265 he asked Roger Bacon to write a treatise on the sciences. Bacon had written numerous tracts but now proceeded to outline the results of his painstaking studies. The Franciscan order denied him any practical assistance for his research, yet he wrote major treatises in eighteen months – the Opus Majus, Opus Minor and Opus Tertium. He sent these to Pope Clement together with an expensive concave lens and a map of the world. Clement died soon after, but not before releasing Roger Bacon and allowing him to return to Oxford. He continued to write on a wide range of subjects, but again drew upon him the agonized concern of the Franciscans. In 1278 the Governor-General of the Franciscans, Jerome de Ascoli, who was to become Pope Nicholas IV, threw Roger Bacon into prison wherein he remained for fourteen years. Released around 1292, he immediately resumed his researches. Returning to Oxford, he died about 1294, having inaugurated a new mode of scientific enquiry. Albertus Magnus, dedicated to theurgy, taught Thomas Aquinas who would eventually become the Aristotle of the Catholic church, though his mentor's profound interest in pure science was adapted to the scholastic methods of Aristotle. Roger Bacon, pupil of Bishop Grosseteste and a revolutionary thinker, was immersed in his search for natural laws. Although he was vilified by the orthodox and relegated to the distinguished company of religious heretics, his many manuscripts found refuge in the libraries of England and France, mostly untranslated until now. Roger Bacon's noble vision survived him. Naturally enough, the official church maintained the orthodoxy which would eventually be submerged by a fresh spirit of enquiry and toleration, secular and religious.

Roger Bacon is best known today for his advocacy of sound experimental methods in the study of Nature, the fusion of acute observation with reasoned reflection. He could not accept a natural science based upon the rationalistic elaboration of religious dogmas. Anticipating what would grow into natural theology, he began by rejecting any rigid framework of beliefs. He was much less interested in Aristotle as a logician than as a chronicler of phenomena, and his own commentaries call for renewed testing rather than the mechanical acceptance of Aristotelian methods. Since Aristotle did not grasp at all the fundamental principles of theoretical or practical alchemy, the root of all knowledge in the natural sciences, Roger Bacon concluded that he, "who composed so many and such great books on natural science, was ignorant of these foundations, and therefore his edifice cannot stand". The Secret of Secrets had been translated from the Arabic by Philip of Tripoli while he was in Syria. It purported to be the private teachings Aristotle imparted to Alexander the Great and suggested that the patient study of natural phenomena would reveal many secrets, visible and invisible. This volume included astrology and the search for hidden correspondences between planets, metals and herbs. Around the same time, Leonardo of Pisa composed a magnificent introduction to Islamic algebra, using the numerals devised by the Hindus that later came to be called Arabic. Roger Bacon's broad standpoint was rooted in Pythagorean neo-Platonism, and his experimental method in the study of visible nature was merely one aspect of a fuller programme of training in the intuitive apprehension of the mysteries of Nature and human consciousness.

Roger Bacon's Opus Majus was composed in seven parts. The first drew attention to four offendicula or causes of error: authority, custom, popular opinion based on a lack of skills, and the concealment of ignorance behind the pretence of knowledge. Experiment, which is self-conscious and purposive experience, can validate the claims of genuine authority; external authority cannot supply the fruits of experiment. Custom is often anchored in social expediency, but real knowledge cannot be rooted in ad hoc and peremptory speculations. Experimentation needs the patient development of true skill in meditation and perception, for the senses alone will mislead the uncultivated and disordered mind. Most dangerous of all, however, is the deliberate cloaking of ignorance behind pretended knowledge, the pathetic consolidation of errors arising from fragmentation of consciousness. When these offendicula are purged, one may readily perceive the unity of science and recognize the need for an encyclopaedic approach to Nature. The second part taught that all wisdom may be found in the scriptures but only through intimations. The brilliant insights of ancient philosophers who did not possess orthodox scriptures confirm the reality of divine illumination, which is essential to penetrate to the core of spiritual meaning. Insofar as wisdom can be transmitted, the third part argued, it is in language. But since it is impossible that the peculiar quality of one language should be preserved in another", one cannot understand either scripture or philosophy unless one understands the original tongues. A good translator must thoroughly know the languages of the original and the translation as well as the subject of the text. The Vulgate, the authorized Roman version of the Bible, is unreliable:

For it has been proved that the Latin codices are wholly corrupt in all places on which the import of history rests, so that the text is self-contradictory everywhere.

The honing of the mental faculties tends to eradicate offendicula and make possible spiritual learning, but accuracy and care are no more than prerequisites to understanding. Theology and philosophy require meditation to discover their inner meanings, and this only comes to a mind morally strengthened and intellectually directed towards the divine.

The fourth part of Bacon's Opus Majus concentrated on mathematics, "the alphabet of philosophy". Mathematics is prior to the other sciences, for "the whole excellence of logic depends on mathematics", and "if anyone should descend to the particular by applying the power of mathematics to the separate sciences, he would see that nothing magnificent in them can be known without mathematics". While there will always be observationally variable quantities that cannot be predetermined mathematically, growth in knowledge will be accompanied by the steady shift of the actually observed to the theoretically derived. Science progresses only as observed fact can be subsumed under mathematical principles. The actions of natural bodies can be understood geometrically, for "every multiplication is either with respect to lines, or angles, or figures". Bacon's application of geometry to geography as an illustration of his doctrine was avidly studied by Columbus two centuries later. The fifth part of this majestic work teaches that the physical world is constituted of matter and force, called virtus, species and imago agentis. Matter exists as a primordial plenum in which physical action occurs as transmission or impression along geometrical lines, angles or figures. The dynamic geometrical impress upon a "common corporeity", a universal substance, distinguishes one phenomenon from another. This universal substance is no less than light itself, for light exemplifies the transmission of force so well that optics is the best science to study for an understanding of psychology, physiology and physics. The treatises on optics of Alhazen of Cairo and Al-Kindi fired Bacon's imagination, though he could not agree with the view that light travels between two actual points instantaneously. The "multiplication of species", the transmission of energy, is always through the plenum, for "species is a natural thing, and therefore needs a natural medium, but in a vacuum nature does not exist". Transmission through a medium is less like the flow of water through a channel and more like a pulse propagated from part to part. In this respect, light is like sound.

Sound is produced because parts of the object struck go out of their natural position, where there follows a trembling of the parts in every direction along with some rarefaction, because the motion of rarefaction is from the centre to the circumference, and just as there is generated the first sound with the first tremor, so is there a second sound with the second tremor in a second portion of air, and a third sound with the third tremor in a third portion of the air, and so on. . . . With light the species forms a likeness to itself in the second position of the air, and so on. Therefore it is not a motion as regards place, but is a propagation multiplied through the different parts of the medium.

Light requires time for propagation through space even though, unlike sound, the time needed is imperceptible. Bacon experimented with the construction of lenses, developed the principle of the magnifying glass, and determined that the synthesis of images entering the eye occurs in the joining of the optic nerves.

The sixth part of Opus Majus elaborated the scientia experimentalis which is domina omnium scientiarum. While the notion of a materialistic science did not even dawn on Bacon's noble mind, he clearly saw that the powers of reason had been imprisoned in the presupposition of dogmatic belief and in a host of "theological vices" and could be freed only through a renewed emphasis on experience.

There are two modes of acquiring knowledge, namely, by reasoning and experience. Reasoning draws a conclusion and compels us to grant it, but does not make the conclusion certain, nor does it remove doubt so that the mind may rest on the intuition of truth, unless the mind discovers it by the path of experience.

But experience is of two kinds. One is gained through the senses, which when trained to observe without bias or prejudice, is experiment. The other is interior, the use of disciplined consciousness to explore the realm of mind and soul. The inward experiment is suffused at every stage with some degree of divine illumination. The seven grades of inner experience begin with the intuition required for the certitude found in mathematics and progresses through distinct steps to the consciousness-consuming ecstatic states exemplified in Paul's vision of the "third heaven This is also hinted at in II Corinthians and described in the apocryphal Vision of Paul. Experimental science has the virtues of verifying conclusions directly, discovering truths inaccessible to reason alone – since reason is bound by the premises taken as the starting-point – and penetrating the secrets of Nature to open up both past and future. The general principles used to turn the pages of the book of physical nature also open the book of consciousness.

The seventh and concluding part of Bacon's treatise taught that grammar and logic were of secondary importance, since reason is innate to the human mind and thus is discovered best through meditation, the interior experiment, and points to alchemy as the root science behind chemistry and biology.

There is a science which concerns the generation of things from the elements and all inanimate things; about the elements and the simple and composite humours; about common stones, gems, and marbles; about gold and the other metals; about sulphur and the salts and pigments; about blue and red and other colours. . . . The generation of men and animals and vegetables from the elements and humours has much in common with the generation of inanimate things.

Alchemy, broadly conceived, is the study of the fundamental properties of Nature, the secret correspondences and ratios between seemingly diverse phenomena. For Bacon, speculative alchemy is the understanding experience should provide, and operative alchemy is its application. Lead can be transmuted into gold, ordinary consciousness may be transformed into luminous awareness. Alchemy in its most profound sense provides the keys to understanding material, moral and spiritual evolution. With this understanding, applied through experimental science, man's potential knowledge is unlimited, as is his ability to alter the world. In his Epistola de Secretis Operibus, Bacon offered his vision of what would be accomplished by experiments on the material plane within about seven hundred years.

Machines for navigation can be made without rowers so that the largest ships on rivers or seas will be moved by a single man in charge with greater velocity than if they were full of men. Cars can be made so that without animals they will move with unbelievable rapidity . . . and flying machines can be constructed. . . . Such things can be made almost without limit, and mechanisms, and un-heard of engines.

The moral and spiritual planes of human life cannot be separated from material operation. Progress must be commensurate on all three planes if unconscious or blind black magic is to be avoided. This is possible because the human mind can comprehend the ultimate nature of things external and internal and comprehend them in one unified science.

Light generates heat, heat generates putrefaction, putrefaction generates death. . . . And thus the sun and stars do all sorts of things here below, and the angels move the sky and stars, and the soul moves its body. . . .
Since the work of the rational mind is done especially and most efficaciously by means of words and formed intentions, an astrologer can form words at times which are chosen to have an ineffable power. For when the intention, desire and power of the rational mind, which is more worthy than the stars, come together with the power of the sky ... the mind can follow celestial forces freely without compulsion. . . . Since the rational mind is of greater dignity than the stars, therefore just as the stars and all things exercise their power and species on things outside themselves ... the rational mind, which is the most active substance among all things after Deity and the angels, exercises its species and power on the body, of which it is the actuality, and on things outside itself. This is especially true when, from the strong desire and sure intention and confidence about which I speak, they not only receive power from the sky, but also from the rational mind which is more noble. Because of this they can have a great power of altering the things of this world.

Roger Bacon, anticipating the imaginative mechanisms of Leonardo da Vinci and the philosophy of human dignity of Pico della Mirandola, held high the torch that would ignite the bright creative fire of the Renaissance. Freeing the mind from religious dogma, pointing to the essential unity of man and Nature, showing how the human mind could cooperate with the intelligent hierarchies of the physical and spiritual worlds, he proclaimed the necessity of self-conscious evolution towards divine enlightenment and the possibility of creating a paradise on earth.

Everything is the product of one universal creative effort; the Macrocosm and man are one.