and the mathematician Lancelot Hogben dismissed all such notions as the ‘dark superstitions and fanciful puerilities which entranced people who were living through the childhood of civilisation’. 4
But that is to miss the point. The Pythagoreans were entranced by such things as the shape of crystals and the patterns made by frost. They suspected, rightly, that there is a mathematical reason for this. Again, consider the fact that women have two breasts, and that in female animals, the number of teats is always a multiple of two, never an odd number. Again, the Pythagoreans suspected that the processes of living nature are governed by mathematical laws, and they were right.
Let us return to an earlier question: what is music ‘saying’? Why do certain musical phrases fill us with a curious delight? Around 1910, a Viennese composer named Arnold Schoenberg decided that, since he could see no obvious answer to the problem of why music touches our feelings, the answer must lie in the word 'habit’—or conditioning. Schoenberg decided that he would create a different tone scale, and write music that was based on a number of notes arranged in arbitrarily chosen order—rather than one that ‘appeals’ to the ear. But he proved mistaken in his assumption that music is ‘arbitrary’. Almost a century later, his works and those of his disciples still sound strange and dissonant—although their dissonance is undeniably successful in expressing neurosis and tension—and their inclusion in a modern concert programme is enough to guarantee a decline in ticket sales. Any Pythagorean could have told him that his theory was based on a fallacy—a failure to grasp that there is a hidden mathematical reason why a certain order of notes strikes us as harmonious, and why arbitrary notes fail to convey a sense of musical meaning.
It is when the same insights are applied to the realm of living things that we begin to grasp the essence of Egyptian thought. Arthur C. Clarke’s 2001 popularised the idea that a computer might develop human feelings; and, in fact, many computer scientists argue that a sufficiently complex computer would be alive—that if it was complex enough to behave like a living thing, then by any sensible definition it would be a living thing. In The Emperor's New Mind , Oxford scientist Roger Penrose expended a great deal of ingenuity in demonstrating that this is a fallacy—that even if a computer was more complex than a human being, it would still not be ‘alive’.
Most biologists now accept the view that life evolved accidentally with the action of sunlight on carbon compounds: that these compounds ‘accidentally’ built up into cells that could reproduce themselves, and that these cells were the first sign of ‘life’ on earth. Penrose’s arguments about computers apply equally to this theory. No matter how complex an arrangement of carbon molecules, it would still not be alive.
The Egyptians would have found these ideas about ‘living’ computers and carbon molecules unutterably perverse. For them there were two distinct realities: matter and spirit. In living beings the two interact, and the laws that govern the interaction are mathematical. It is not meaningless to ask why carrots are long and pointed, and melons are round, and marrows are long and round. Life obeys unknown mathematical laws.
Gurdjieff also attached great importance to the concept of alchemy. In his major work, Beelzebub’s Tales to his Grandson , he explains that what is generally called alchemy is a pseudo-science, but that there was—and is—a genuine alchemy, a ‘great science’, that was known to the ancients before man began to degenerate.
It may also be noted that, in Beelzebub’s Tales , Gurdjieff makes Beelzebub—a higher being from a solar system in the Milky Way—explain that Egypt was originally populated by survivors from Atlantis, which was destroyed in two cataclysms, and that the Sphinx and the Giza
But that is to miss the point. The Pythagoreans were entranced by such things as the shape of crystals and the patterns made by frost. They suspected, rightly, that there is a mathematical reason for this. Again, consider the fact that women have two breasts, and that in female animals, the number of teats is always a multiple of two, never an odd number. Again, the Pythagoreans suspected that the processes of living nature are governed by mathematical laws, and they were right.
Let us return to an earlier question: what is music ‘saying’? Why do certain musical phrases fill us with a curious delight? Around 1910, a Viennese composer named Arnold Schoenberg decided that, since he could see no obvious answer to the problem of why music touches our feelings, the answer must lie in the word 'habit’—or conditioning. Schoenberg decided that he would create a different tone scale, and write music that was based on a number of notes arranged in arbitrarily chosen order—rather than one that ‘appeals’ to the ear. But he proved mistaken in his assumption that music is ‘arbitrary’. Almost a century later, his works and those of his disciples still sound strange and dissonant—although their dissonance is undeniably successful in expressing neurosis and tension—and their inclusion in a modern concert programme is enough to guarantee a decline in ticket sales. Any Pythagorean could have told him that his theory was based on a fallacy—a failure to grasp that there is a hidden mathematical reason why a certain order of notes strikes us as harmonious, and why arbitrary notes fail to convey a sense of musical meaning.
It is when the same insights are applied to the realm of living things that we begin to grasp the essence of Egyptian thought. Arthur C. Clarke’s 2001 popularised the idea that a computer might develop human feelings; and, in fact, many computer scientists argue that a sufficiently complex computer would be alive—that if it was complex enough to behave like a living thing, then by any sensible definition it would be a living thing. In The Emperor's New Mind , Oxford scientist Roger Penrose expended a great deal of ingenuity in demonstrating that this is a fallacy—that even if a computer was more complex than a human being, it would still not be ‘alive’.
Most biologists now accept the view that life evolved accidentally with the action of sunlight on carbon compounds: that these compounds ‘accidentally’ built up into cells that could reproduce themselves, and that these cells were the first sign of ‘life’ on earth. Penrose’s arguments about computers apply equally to this theory. No matter how complex an arrangement of carbon molecules, it would still not be alive.
The Egyptians would have found these ideas about ‘living’ computers and carbon molecules unutterably perverse. For them there were two distinct realities: matter and spirit. In living beings the two interact, and the laws that govern the interaction are mathematical. It is not meaningless to ask why carrots are long and pointed, and melons are round, and marrows are long and round. Life obeys unknown mathematical laws.
Gurdjieff also attached great importance to the concept of alchemy. In his major work, Beelzebub’s Tales to his Grandson , he explains that what is generally called alchemy is a pseudo-science, but that there was—and is—a genuine alchemy, a ‘great science’, that was known to the ancients before man began to degenerate.
It may also be noted that, in Beelzebub’s Tales , Gurdjieff makes Beelzebub—a higher being from a solar system in the Milky Way—explain that Egypt was originally populated by survivors from Atlantis, which was destroyed in two cataclysms, and that the Sphinx and the Giza
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