THE FINAL MYSTERY

DISCOVERING THE UNIMAGINABLE
“A mystery lurks beneath the magic carpet of science, something that scientists have not been telling, something too shocking to mention.” 1
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Science is the only tool humanity possesses to discover how the world is made. From Galileo and moon landings, to the internet and iPads, science has been spectacularly successful. Yet strangely, at the root of this success Barrow says:

“there lies a deeply ‘religious’ belief - a belief in an unseen and perfect transcendental world that controls us in an unexplained way, yet upon which we seem to exert no influence whatsoever.” 2
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A perfect transcendental world? This is not about some fringe cult or the paranormal or extra sensory perception or UFO's, it is the opinion of one of the world's leading scientists and mathematicians. He believes that:

“The reason why mathematics is so successful in describing the way the world works is because the world is at root mathematical.” 3
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Not only does mathematics seem to be the blueprint of our physical world, Erwin Schrödinger, (Nobel Prize in Physics, 1933, and a leading figure in the Quantum Revolution) believed that:

“mathematical truth is timeless, it does not come into being when we discover it.” 4
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Timeless? Something outside of time, something that exists before we discover it? Gives you a shiver up your spine!

Eugene Wigner (Nobel Prize in Physics, 1963), a hero of theoretical physics, wrote in a now iconic essay:

“the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it... It is difficult to avoid the impression that a miracle confronts us here.” 5
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Something beyond reason? A miracle?
Roger Penrose, who is one of the world's leading mathematicians, and the Emeritus Rouse Ball Professor of Mathematics at the University of Oxford says:

“the truths that mathematicians seek are, in a clear sense, already 'there', and mathematical research can be compared with archaeology; the mathematicians job is to seek out these truths as a task of discovery rather than one of invention.” 6
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Stephen Hawking, a former Lucasian Professor of Mathematics at the University of Cambridge, defined the mystery of mathematics precisely like this:

“Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe?” 7
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About the mystery that lies beneath science, David Layzer, a Professor of Astrophysics at Harvard University says:

“why it is that the regularities which lie deep beneath the outward appearance of our physical world are actually mathematical, and even more mysterious; why they should be in the least bit accessible to the human mind ... these are the great mysteries at the heart of humankind's most sustained and successful rational enterprise.” 8
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Describing mathematics as a code, Marcus du Sautoy (Professor of Mathematics, University of Oxford) says:

“The fact that the code provides such a successful description of nature is for many one of the greatest mysteries of science.” 9
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About the actual nature of what mathematics might be, Peter Atkins, Professor of Chemistry at the University of Oxford thinks:

“It is possibly not too extravagant to claim that the answer to the question of why mathematics works will be the final answer to all questions of being” 10
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The final answer to all questions of being? Another hair-raiser? Elsewhere he wonders whether:

“the deep structure of the world is mathematics: the universe, all it contains, is mathematics, nothing but mathematics, and physical reality is an awesome manifestation of mathematics.” 11
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So what is mathematics? One might well ask, where is maths located? One of the most chilling aspects is the realisation that it is the only thing we know of that exists outside of time and space. It's not as though you can see it, or touch it or hear it. You can't even taste it or smell it, let alone actually measure it. Yet it exists. It has proved itself through the success of science to be the blueprint for all that does exist. Professor David Deutsch at the University of Oxford, who is the founder and a pioneer of Quantum Information Science, describes it like this:

“Mathematical entities are part of the fabric of reality because they are complex and autonomous...although they are by definition intangible, they exist objectively and have properties that are independent of the laws of physics.” 12
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Independent of the laws of physics? This suggests it is more comprehensive than the physical world. It appears to mean that it is in some way bigger than anything 'physical', like a multiverse. Bigger even than an infinite number of physical universes! Max Tegmark, Professor of Physics at the famous Massachusetts Institute of Technology, describes maths in a similar way to Roger Penrose:

“There is nothing fuzzy about mathematical structures. They are 'out there' in the sense that mathematicians discover them rather than create them, and that contemplative alien civilisations would find the same structures, (a theorem is true regardless of whether it is proven by a human, a computer or an alien)... a mathematical structure cannot change - it is an abstract, immutable entity existing outside of space and time.” 13
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So it seems that mathematics is 'out there', something beyond time and space, something independent of the human mind, and something that existed long before evolution contrived the human brain. This is not about religious experience or ethereal angels, it is much more concrete and fundamental, it is about what creates our reality. Marcus du Sautoy points out that:

“when we start to look closely at all this complexity, surprising patterns begin to emerge. It is these patterns that I believe point to an underlying code at the very heart of existence, and that controls not only our world and everything in it, but even us.” 14
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Since our universe and a multiverse beyond can only be constructed from different forms of 'matter', it would seem that mathematics is a mystery beyond even a multiverse. John Barrow concludes that:

“The meaning of mathematics will emerge as a key question that must eventually be answered in any quest for a fundamental understanding of the physical world.” 15
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That is why discovering the nature of mathematics will surely be the greatest revolution ever to confront human consciousness. So what evidence is there? Actually, most of the greatest discoveries in the history of science have been made using mathematics alone. Many of them beyond anything ever imagined by humans. I want to explore this next.

The Book Chapter 23
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