The Reality of Time, and Einstein’s Spider Web E-Book

Rocco Vittorio Macrì

• Herausgeber: Youcanprint
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch
• Veröffentlichungsjahr: 2020

Beschreibung

The greatest mystery of all, the enigma of Time, shone like a blinding quasar upon the eyes of the creator of the Theory of Relativity, Albert Einstein. Indeed there has been no significant thinker, from antiquity down to the present day, who has not confronted the mystery of Time and made it an essential part of his own philosophy. Even in Plotinus’ days the problem of Time was considered to be “ancient” and “continually revived”. Thinking about Time is much like ploughing the ocean. Despite this, the Twentieth Century saw an unprecedented and new operational definition set forth by Einstein, who stripped the notion of Time of all metaphysical content, and made it ontologically eliminable. The verdict in our days is, "Time does not exist." Yet there have not been wanting thinkers who have attempted to swim against the current, to throw down the gauntlet to “the Murderer of Time”, to the Demolisher of the Absolute, showing that the Time is not an illusion, Time is real. These stirring moments in the history of intellectual endeavour are collected here, revivifying the philosophical face of every dissident. The subject is interesting not only to experts in the field, but also to every inquiring mind thirsting for historical truth. The reader who is fascinated by the fundamental ideas of physics and philosophy will find great satisfaction here. In addition he will find here the ultimate roots of our contemporary Weltanschaaung.

Leseprobe

TABLE OF CONTENTS

Acknowledgements

Foreword

Conceptual Abstract of the Work

Introduction

I – The Great Cataclysm Caused by Relativity

II – The Genesis of Relativity

III – Epistemically Determined and Undetermined Motion (EDM and EUM)

IV – Newtonian Synthesis and Frame Swap

V – Einstein’s Approach to Relativity

VI – The Concept of “FLOP” and the Weak Points of Relativity

VII – Time: the Heart of Relativity

VIII – Major Premise

IX – Minor Premise

X – The Point Regarding the Concept of Time

XI – Bergson and the Arrow of Time

XII – Maritain in Defence of Simultaneity

XIII – Dingle’s Syllogism and the Twin Paradox

Appendix

Bibliography

Rocco Vittorio Macrì

THE REALITY OF TIME,

AND EINSTEIN’S SPIDER WEB

The Missteps of a Genius Against theReality of Time

THE SCIENTIFIC-PHILOSOPHICAL FOUNDATIONS OF THE THIRD MILLENNIUM

© YCP – 2020

Title | The Reality of Time, and Einstein’s Spider Web

Subtitle | The Missteps of a Genius Against the Reality of Time

Author | Rocco Vittorio Macrì

ISBN | 9788831674164

Italian Original Edition: La realtà del tempo e la ragnatela di Einstein, 2 ed.

© 2015, 2020

© All rights reserved to the Author

No reproduction of any part may take place

without the written permission of the Author.

© Cover: Author

Youcanprint Self-Publishing

Via Roma, 73 – 73039 Tricase (LE) – Italy

www.youcanprint.it

[email protected]

Facebook: facebook.com/youcanprint.it

Twitter: twitter.com/youcanprintit

to Umberto Bartocci

Franco Selleri

Lee Smolin

masters of research and effort against the tide

Two roads diverged in a wood, and I –

I took the one less traveled by,

And that has made all the difference

Robert Frost

All rights reserved. No part of this book may be used or reproduced in any manner whatsoever without written permission, except in the case of brief quotations embodied in critical articles or reviews.

ACKNOWLEDGEMENTS

This new edition is being printed in several languages. This is the author’s reaction to the unexpected success of the first Italian version of this book. The volume was, in fact, initially, rather “niche”, addressed to the class of experts in science who also had a background in the field of philosophical refinement. However, the effort to eradicate at its roots the concealing mathematical symbolism enveloping the Theory of Relativity has borne fruit beyond all expectations: it has been rewarded with the outwardly gratifying and not-at-all-superficial understanding of these concepts even by those who are far from experts in this difficult subject.

We finally have an idea of the feedback that Einstein himself was curious to obtain when he asked, referring to the new physics emerging in his day, “how non-physicists would ridicule it if they could follow its curious development”. The verdict that we find delivered as a result of this leads us to believe strongly that the scientist, however intelligent, rational and expert he may be, needs the common sense of the layman: as you will of course remember, it was basically a child – to quote the famous Hans Christian Andersen fairy tale “The Emperor’s New Clothes” – who first arrived at the truth, exclaiming “But the king is naked!” … while all the “wise” adults stood there, instead, infected by and submissive to the dominant thought of the day; subject to what the Scholastics called the argumentum ad verecundiam. A hole in the ground is far more easily recognized when it is not covered with shrubs and scattered foliage, and even a child could report its presence; similarly, it would be easy to recognize potential holes scattered throughout contemporary physics if they were not concealed by the cryptic ocean of enveloping mathematical symbols.

The words of the mathematician Umberto Bartocci, one of the most penetrating minds on the international scene, are extremely enlightening in this respect, quoted here as they are found in one of his works on Special Relativity, I fondamenti della Relatività (“The Foundations of Relativity”), Lecce 2016, edited by the present author: “That certain theories are expressed in the language of mathematics means absolutely nothing regarding their possible significance, or their greater value compared to other theories that do not have the same formal credentials, since mathematics is like a magician’s hat, from which anything that was put in it earlier can emerge. Those who are skilled in its treatment can use it to support theses of any kind, though of course often through hidden contaminations between different levels of speech. There is nothing that is too absurd for a good mathematician to describe … A mathematics which turns – with great sorrow descending upon the present author, who is a trained mathematician – into a sort of latinorum for several modern Don Abbondios, who use it as a rhetorical expedient to justify cultural fashions, or even worse, confusing people’s minds and distancing the most sensitive intellects from ‘science’”.

Rendering the present book more flowing and understandable even for the non-expert has been seen therefore as an imperative in publishing this new revised and expanded version. It has been enriched by the addition of an Appendix, a work which appeared earlier in the volume Asimmetrie Antirelativistiche (“Anti-Relativist Asymmetries”), edited by the writer (Lecce 2015), entitled “Forced and Broken Symmetries in Special Relativity”, which now finds its most appropriate place at the end of this work. The examples evoked are deliberately written in an elementary fashion, in a manner that is almost childish; reduced to the bone, irreducible further, even bordering on the “crude”. This is just what the famous epistemologist Paul Feyerabend urges us to do, when he writes that in order to escape the instrumental, concealing and tyrannical sophistication of complex scientific-mathematical language, it is necessary to become crude and “child-like”: “Methodology today is so crowded with refined and empty reasoning that it is extremely difficult to perceive the simple errors at its base. It is a bit like fighting the hydra: when one finally manages to cut off one of those threatening heads, it is replaced by eight formalizations. In this situation, the only answer is superficiality: when complexity loses content, the only way to maintain contact with reality is to be crude and superficial, and that is what I intend to be”.

This new edition has been enriched by a Foreword written by Dr. Ing. Antonio La Gioia, Professor of Technical Physics at the Faculty of Engineering and the Faculty of Architecture of the University La Sapienza in Rome, and holder of international patents related to the Environment and Energy (Turbine ad effetto Todeschini-Magnus-La Gioia), whom I thank for the esteem shown by him, and for our long and enchanting discussions regarding the philosophical and humanistic realities of Physis. Moreover, a heartfelt thanks to the fantastic President of the International Centre of Psychobiophysics Fiorenzo Zampieri, an eclectic and profound mind, for having greatly supported me and for having given me this pearl entitled “Conceptual Abstract of the Work”.

But in this long list of thanks my first thought goes to the already mentioned Prof. Umberto Bartocci, my mentor and inner interlocutor. A deep and brilliant mind, not subjugated by the conventions of the majority, following the path of knowledge as a sort of “countercurrent archaeologist” within the history of scientific thought and the foundations of physics and mathematics – digging down to their very roots – he has managed to bring to the light of day more than one hidden truth; there are indeed many precious pearls and fragments in the deeps, some considered impossible to find until his efforts to find them, which he has managed to bring to the surface. This is the result of an incessant search that spans an entire lifetime.

Docent in Geometry and History of Mathematics at the Department of Mathematics at the University of Perugia from 1976 to 2005, after teaching at the Universities of Rome and Lecce, the professor’s academic career began with studies and research in the field of algebraic geometry and number theory at Trinity College at the University of Cambridge as a fellow of the Italian National Research Council (CNR). In 1969 he became assistant, at the University of Rome, to Beniamino Segre, President of the most prestigious Accademia Nazionale dei Lincei – an institution whose original centre was Galileo himself – and holder of the chair of the Institutions of Higher Geometry. He then became a consultant (referee) for several mathematical and physical journals, such as Physics Essays, Foundations of Physics, Apeiron, etc., and in the five-year period between 2000 to 2004 he was responsible for the publication of the Italian language journal Episteme. A genius of great mathematical and scientific acumen, and at the same time possessing powerful philosophical skills, capable of interacting on par with the great mathematicians of the past such as Gauss, Lobachevsky, Bolyai and Riemann, even to the point of questioning the value of non-Euclidean geometries (see, for example, “The Fifth Postulate of Euclid” in Anti-relativistic Asymmetries, op. cit.), Bartocci has no rivals in the field of the foundations of science. In the purely mathematical field he has defended the need for a return to a “classical foundation”, based on the mental categories of space and time according to Kant’s transcendental approach, as against the more common and “comfortable” formalistic approach; just as his research into the history of scientific thought and the foundations of physics and mathematics have led him to a critical judgement regarding the view of the world provided by current physical theories, he maintains the need for an authentic pluralism in the scientific field also.

Bartocci has been the centre of the epistemic vortex for an entire generation of scientists and scholars who have found, under his open-mindedness and enthusiasm, a way to enter the “Stargate” of the awakening of a new world-view; his research group “Geometry and Physics” – to which the author belonged – has reflected and refracted this new world-view, much like an epistemic prism, ready to colour the world with new nuances. It is via his counter-tendency school of thought – in the Platonic-Aristotelian sense – that, if we could but raise our eyes to the sky, we could see new horizons behind the Milky Way, new cognitive possibilities. The Mathematics Department of the University of Perugia became, thanks to our Professor, a pole of attraction for divergent thinking, a new Athens of the 20th century. It is at this crossroads of independent scientists that the writer was able to enrich himself by meeting and exchanging ideas with the most original and sublime brains on the planet, such as Stefan Marinov, Roberto Monti, Marco Mamone Capria, Franco Selleri, Giancarlo Cavalleri, Fabio Cardone, Giuliano Preparata, Federico Di Trocchio, Ardeshir Mehta, Paul Marmet, J. Barretto Bastos Jr, Silvio Bergia, Emilio Del Giudice, Ludwig Kostro, W.A. Rodrigues, James Paul Wesley, George Galeczki, Al Kelly, André Assis, Francisco Müller, Patrick Cornille … why, not even the great Niels Bohr with his school in Copenhagen could boast such a concentration of divergent and “explosive” brains. My intellectual debt is doubled, then, because I have had the honour and fortune to share ideas and opinions in an extended and continuous way with our mathematician, to the point of elevating him to the level of my inner interlocutor in all my scientific-philosophical works. This very volume would never have come to light without the long reflections over the past decades engaged in an incessant confrontation and exchange of ideas with my friend Umberto Bartocci. The work is dedicated to him.

But the realization of this work is also the result of decades of reflections, insights, fervid passion and confrontations with friends and acquaintances with a powerful independence of thought who have followed me along this life-long journey. These are enlightened minds whom I should like to thank here: starting with my uncle Giuseppe Prestia, who could boast two degrees and circa ten books published; writer, philosopher, man of letters, poet and artist: my “philosopher uncle”, as I call him. To him goes my gratitude for having instilled in my mother’s milk the first “drops of philosophy” since I was still an infant. How could I ever forget the powerful lessons of philosophy that were imparted to me at the age of 10-12? It was like being placed in contact with Plato (whom my uncle embodied in an incomparable way; and my uncle lived, moreover, just a few metres away from that “golden” sea which Plato himself had touched, those waters were also crossed by Pythagoras, Parmenides and Aristotle): the juices from those three massive volumes of Abbagnano’s History of Philosophy were squeezed out, page after page, with a thousand additional comments and endless reflections.

But philosophical reflections were intertwined with the scientific ones right from the start. And here – in alphabetical order – I mention my fraternal childhood friends Antonio Panetta (electrical and nuclear engineer) and his son Fabio (physicist and electronic engineer), Giuseppe Crimeni (architect, creative and profound mind) and his brother Riccardo (the “prince” of thought-experiments), and to them goes my recognition and gratitude for the endless and unforgettable hours spent together experimenting and building all sorts of chemical, physical, electronic devices, and meditating, contemplating, and elaborating myriads of alternative and original physical and philosophical theories. Just to give a small example, a mere grain of sand compared to the whole: how could I ever forget our first radio, constructed – together with Antonio – using a simple variable capacitor, a coil and a germanium diode? We were just 11 years old. And our first transistor, the AC128 (together with the AC127) with which we made our first flip-flop? And what about our beloved BC108 NPN in silicon? How many circuits and assemblages … suggested as they were from time to time by Antonio’s uncle, the venerable Giovanni Panetta – a recognized and unsurpassed master of electronics – whom, when knocking on his door in our most desperate hours, we could always see, despite his venerable age, attentive and bent over circuits of his own design, with the smoking tip of the soldering iron in his hand, or with the ends of the multimeter or the oscilloscope. It was, for us, like asking the advice of a Wizard or an Oracle! Then came the integrated 555 and the first operational integrated circuit boards … it was a golden age for us, because electronics underwent its greatest evolution at that time: the first leap came when we switched from the thermionic valve stage to germanium transistors, with the second arriving when we switched to silicon; with the third came integrated circuits, and with the fourth we were in front of the microprocessor and all the digital electronics: all this passed through our hands! We could have written a whole book about our “friends” – viz., the electronic circuits and devices – similar to the famous book Primo Levi wrote about the Periodic Table of Elements. And, speaking of elements, if we are to touch the field of chemistry, we could give rise to an even longer story; we had in fact begun to handle test tubes and stills at the tender age of 6, repeatedly exchanging or bartering chemical compounds, such as the one which has remained indelibly in our minds: that of some cobalt chloride granules with some potassium permanganate crystals. These passions lasted a long time, and we took them with us in our thoughts during our university studies at the Turin Institute of Chemistry and at the Polytechnic of the same city.

But it is my duty to thank also the powerful, crystalline and uncontaminated minds – giants of independence of thought – who have always fascinated me, like those of my friends Marco Rossi, Natale Loccisano, Stefano Bagnato: to talk to them is, even today, a source of high inspiration. And then my gratitude for having always supported me goes to the late Franco Selleri, Professor of Theoretical Physics at the University of Bari, recognized worldwide as the greatest exponent of physical realism, and for having been De Broglie’s favorite “son”. His opening salvo was dazzling, like that of the just-named French Nobel laureate: as soon as he had graduated, the world of physics was stunned by his solution contained in his doctoral thesis on inelastic proton-proton impacts, which he was soon able to develop as the exchange model of a single pion. A great and immediate international success!

I also have to thank Professor Marco Mamone Capria of the Mathematics Department of the University of Perugia, an internationally recognized expert in Relativity, for the many important moments of reflection, comparison and exchange of ideas during the past decades; as well as Professor Fabio Cardone, one of the most important Italian experimental physicists and winner of the National Galileo Galilei Prize for Physics, for his support, friendship and the great open-mindedness shown during the elaboration of our thought-experiments.

A sincere thanks then goes to my philosopher friend Paolo Capitanucci, lecturer of the History of Scientific Thought, “the highest guardian of the supreme logos”, as I call him, for the decades-long deep meditations bounced off each other on the philosophical foundations of science. For the countless reflections on the ultimate nature of space and time, my thanks go to my friend Renato Burri, researcher and director of the International No Profit Research Laboratories Associates, who has been carrying out research, studies and design activities in the various fields of technical-scientific disciplines for over 40 years: electronics, computer science, physics, biophysics and predictive mathematical models; and likewise, space and time were always the nucleus of the themes I discussed with my friend Claudio Cappelletti, nuclear engineer, and to whom I am greatly thankful for the numerous comparisons on the fundamentals of physics; thanks also go out to Professor Lino Conti, Professor of the History of Scientific Thought at the Faculty of Philosophy of the University of Perugia, former supervisor of my thesis in philosophy, for always listening to me as an equal in our exchanges of views, which continued to the bitter end, even in television broadcasts where the debate often converged on epistemological, relativistic and historiographic issues.

It was precisely by concentrating on a particular “relativistic” during one of these broadcasts of our debates – through repeated and successive replays on my Mac, and by focussing all my attention on Conti’s masterly intervention regarding “Einstein Train”, admirable for its expositive clarity – that I found arise in my mind, finally, a powerful resolutive insight for constructing the rebuttal to Einstein regarding simultaneity which the reader will find in these pages in Chapter XII. How not to express, then, my gratitude to my dear Lino Conti? Likewise I should like to express my gratitude and admiration to his colleague Carlo Vinti, Professor of History of Modern and Contemporary Philosophy at the University of Perugia, Director of the Department from 2000 to 2013 and a profound scholar of contemporary French epistemological thought. Vinti caused me to become enamoured of French epistemology. His limpid eyes, his intellectual purity and his child-like (“fanciullino”) enthusiasm, and his works on the subject written in an incomparable way, led me to pay the utmost attention to the vertiginous minds of Pierre Duhem, Gaston Bachelard, Henri Poincaré, Gaston Milhaud, Émile Meyerson and Édouard Le Roy, in which science and philosophy intertwine in an inextricable way, like the faces of a two-faced Janus. The reader will surely get a whiff of this “French perfume” in the chapters of this book.

Finally, I would like to thank my friends who have managed to touch the blue elevator button of my mind, such as Alan and Joy Blakeslee, Barry Taubman and Antonio D’Addio (“the Cosmic Poet”, as I call him: celestial mind), Angelo Gentile, Francesco Jeraci, Alessandro Palermo, Osvaldo Massetti, Franco Tasselli, Paolo Marini, Alessio Migliorati and the very profound Edmondo Zaroli, well-known artist, musicologist and painter from Perugia, traveling companion in those Pindaric flights of the mind that tries to contemplate the cosmos, aware, however, that the key to understanding “the outside” – the object – “lies inside”, in the subject. I am also grateful to his daughter Maja for having translated into English the Appendix of this book; a translation that was later perfected by Ardeshir Mehta. A special thanks then goes to Mariarita Trampetti for having strongly encouraged and supported me during the phase of the first draft of this project. I owe to her the force and thrust – the activation energy – which was necessary for my “take-off”.

But last though most certainly not least, I must give immense thanks especially to the translator of this work into English (but whose contribution goes above and beyond the confines of the English language), who has done a job not only of translation as it is commonly understood, but of taking great care of the very thrust of the text in order not to betray – indeed, even to enlighten – its philosophical finesse, collecting and transposing in a harmonious way all the nuances and subtleties of my attempts. Such a refined work could only be done by Ardeshir Mehta, friend and companion of endless streams of thought regarding not merely Relativity but wider philosophical questions as well, and one of the most independent minds on the planet: author of several books and a large number of articles dealing with a very wide range of subjects, from Gödel’s Theorem to the Israeli kibbutz, from ancient Zarathushtra and the Vedas of India to nanotechnology and futurology, from Cantor’s diagonal procedure to the fundamental nature of reality … with, of course, the Theory of Relativity being among them. Ardeshir already has, in his very name – even that being engraved upon him by the unforgettable Indian political figure, philosopher and lawyer Mahatma Gandhi, a close friend of his parents – a sense of his mission, namely, the search for truth; Gandhi, and in particular his philosophy of satyāgraha or “strict adherence to truth”, was fundamental in Ardeshir’s upbringing and throughout his development as a philosopher and as a person. Ardeshir left India at the age of twenty-one to visit the most interesting places in Europe, and in particular Italy, where he lived for a few years; thereafter he conducted a long sojourn in Israel, there carrying out nine years of studies and research; and after a few more years back in India, has finally settled in Canada. All this experience has earned him an in-depth knowledge of eight languages which at one time or another he spoke fluently, in addition to a not-altogether-meagre understanding of twelve others! My recognition and gratitude goes out to him.

FOREWORD

by Antonio La Gioia

The more one immerses oneself in reading the Acknowledgements and the Introduction of Rocco Vittorio Macrì’s book The Reality of Time, and Einstein’s Spider Web, the more powerfully does one become aware of the many social and political considerations that emerge from the world of education: of high school, of university and of the highest levels of academia.

And it feels good to realize that in other minds the same needs and the same desires for knowledge which have animated my own professional and university life have also germinated.

In the Acknowledgements and in the Introduction and in the rest of the book, the reader will find a large number of connections and approvals from elevated minds, all of which facilitate the work of the one who is about to write this Foreword.

It is enough to anticipate that in all these chapters we shall find described the works of minds that have demonstrated signs of great scientific vigour.

The most inspired points that gratify the reader are all the more strongly brought to the fore when it is seen that Prof. Bartocci and Prof. Feyerabend are mentioned.

Perhaps one does feel the lack, in such an attentively-written book, of any reference to Socrates, to honour his having been the first to make a clear distinction between knowledge and wisdom.

And to remember, moreover, the respect for man and for life that emerges from his dialogues.

All the same, in reading this book one understands that it is an act of courage on the part of a man who has lived as many lives as there are personages mentioned in it (almost 400).

The author, one immediately notices, has not been contaminated by the world of competition, as one can understand from his eagerness to be clear and profound, and never banal.

This aspiration animates the tempo of his work, in which rationality and enthusiasm merge with each other in brilliant and erudite justifications, without ever penalizing the contrary theses that have been analyzed.

The key to reading the book, which deliberately shuns the medium of mathematics, lies in an acute observation by Bartocci that pays attention to “the apparent mathematical erudition behind the mask of scientific formalism”.

And in addition, we must recall Feyerabend’s firm warning that “the only way of keeping in touch with reality is to be crude and superficial”.

Macrì renders this awareness the more noble by integrating his bottomless philosophical and scientific acumen with real life, along with its social and humanistic aspects, having delved into the world of knowledge, guided by intuition and common sense.

Aspiring to simplicity.

A.L.G. – University “La Sapienza” of Rome

CONCEPTUAL ABSTRACT OF THE WORK

by Fiorenzo Zampieri

No one could write a prologue to this book, so great is the wealth contained within it in terms of deep reflections, profound intuitions, brilliant ideas, elenchic demonstrations and unsettling twists: who would be able to follow such a breadth of studies and scientific-philosophical finesse? And yet the exposition of all these is done in a style that does not bore the reader. Quotes, references, information and comparisons are endless. This knowledge has unimaginable dimensions. And all this amazes me.

It is on tiptoe, therefore, that I dare to peek behind the curtain of the structure of this work, focusing my attention on the outermost gems that barely emerge, rather than on the many that are hidden and deliberately occluded. Yes, because our author seems to follow Descartes, that giant of naked thought and of maximum simplicity, in his masked progress: Larvatus prodeo. In his Cogitationes privatae, the Philosopher writes: “Actors, taught not to let any embarrassment show on their faces, put on a mask. I will do the same. So far, I have been a spectator in this theatre which is the world, but I am now about to mount the stage and I come forward masked.” And, in this work, there are many hidden or partly-hidden pearls. And since it aims first of all to be an investigation into the nature of time, here are the reasons why the author places at the top of the pyramid his resolute insight regarding the crucial problem of the relativistic treatment of time: simultaneity.

It is a question of reanalyzing the most important thought-experiment in the history of scientific thought: the so-called thought-experiment of “Einstein’s Train”. As Macrì explains, this is the foundation of the Theory of Relativity, as it provides the starting hypothesis, the dogma of the relativization of simultaneity. Thanks to this kind of postulate, Einstein became in fact the one who “touched the untouchable”: time! Here the “epistemic net” of the author (one of his neologisms), which embraces an almost boundless knowledge of Physics and Philosophy, deciphers and brings to light the drama of our time. Here are his thoughts, as they appear in a letter addressed to me not long ago, which I think it is appropriate to insert here to give the reader a conceptual abstract of the entire volume:

Time. Stolen from the hands of philosophers and put under the scientist’s microscope to be analyzed, Einstein has rendered metaphysical realities simply … physical! The resulting verdict – says physics following the Einsteinian revolution – is that what is simultaneous for me may not be simultaneous for you! Aristotle’s “before and after” is rent asunder and becomes invertible. The unitary idea of time, sacred and venerated before Einstein, is now shattered. Time is ontologically nullified. This means that millennia of certainties born of common sense have passed by without anyone noticing the deception unmasked by Einstein. Heraclitus was mistaken, and with him the entire host of giant thinkers who believed in the evidence of time. Time must be a mere illusion.

Philosophy, as a result, is shaken and turned back on itself. Since that fateful day – June 30, 1905 – it has found itself continuously reduced in substance, like an inflated balloon which day after day is destined to deflate more and more: a pastime for those who have no mathematical skills. To Science, and only to it – writes Stephen Hawking – may be addressed those questions which for centuries have been pertinent to philosophy, because “philosophy is dead”, not having kept pace with the most recent developments in physics. And this has happened because Einstein showed the path to it by reducing time to a number, until it could be frozen to a zero, or indeed, even reversed, by sliding it backwards along the negative axis of the abscissae. “So,” Hawking adds, “scientists have become the bearers of the torch of discovery in our quest for knowledge”.

A new Renaissance, then, wherein the artist and the philosopher give way to the “homo mathematicus” – to use the words of Gaston Bachelard. Are we not in an age in which the scientist dons the garb of supreme authority stripped away from Aristotle? Is it not Science that is revered today, disrespecting philosophy? And this entire reversal came into being because the new “Master of those who know” – Albert Einstein – managed to put time under the slide of his microscope! Even to pretend that the most firm point in our intuitive power, namely the absoluteness of simultaneity, is a bluff created by our mental coordinates, by common sense (common to all humanity) which now also finds itself rolling towards Popper’s “World 3”: that of ideas initially revered and subsequently rendered defunct. Thus every certainty of antiquity crumbles.

Already the first mathematicians had tried to undermine granitic certainties. It is not for nothing that Morris Kline – a well-known historian of mathematics – entitled his masterpiece Mathematics: the Loss of Certainty. For example, Euclidean geometry – a product of the exquisite theoretical spirit of the Greeks, the pillar of that Platonic absolute that had to withstand the changes in the world of sense, the Protagorean doxa and the Heraclitean panta rhei – was undermined in the nineteenth century: Euclidean dethronement was implemented by Riemann through his concept of curvature to multi-extended varieties, a concept which followed Gauss’s theory of curved surfaces and which “decentralized” Euclidean geometry, the way Copernicus decentralized the Earth, and reduced it to just one of many possible metric geometries. After two millennia of “glorious connection to the absolute”, Euclidean geometry suffered the same fate that had seen the Earth exiled to the periphery and man crushed towards the amoeba: the loss of certainty, the process of relativization of the foundation, the decay from substantia to accidens. Thus did that hyperuranic barrier which Plato had admirably erected crumble under the attacks of the Relativists. In particular, at the beginning of the 20th century the very intuitive foundation of geometry suffered a first attack by the German mathematician David Hilbert, who, by introducing a rigorous axiomatic perspective which ignores any reference to intuition, arrived at the demolition of intuitively evident truths in favour of an extreme formalism. Other attacks came later – in addition to the development of non-Euclidean geometries – from the development of abstract algebra-manipulating mathematical entities using purely formal procedures, avoiding any interpretation of their nature. However, the decisive blow came with the advent of the second scientific revolution, starting with Einstein’s Theory of Relativity, which irreversibly sealed the loss of intuition and common sense, giving way to pure operationism: “Therefore, not only is the general doctrine of intuition understood as an infallible source of knowledge a myth, but [so is] our intuition of time, […] just as our intuition of space is”, Karl Popper explained in his Objective Knowledge: An Evolutionary Approach.

Now, however, it must be made clear that this point of relative and no-longer-absolute simultaneity, which is the foundation of Einstein’s entire theory, is in its turn seen totally naked, and when not plastered over with mathematical structures, is not supported by the formula. It is the purest thought of the meta-scientist Einstein: a philosophical thought! Consequently, it takes on the appearance, in the philosopher’s eye, of an Achilles’ heel: here, right at the very foundation of the Theory, the philosopher can unmask the potential logical hole and bring down the entire castle in a domino-effect-like cascade.

And this seems to be the intention of the author of this work: examining the second part of Chapter XII with some attention, the reader will find the “bomb” placed right under the relativistic scaffolding. Further clarifications and specifications have been added in the second, long, note of the Appendix. The reader, expert or neophyte, will not be able to turn his back and ignore the power of the unrolled argument: it takes on apodeictic overtones, and appears absolutely invincible! Here in action is the terrifying effectiveness of the FLOP – the Potential Logical Falsifier – an incisive and revolutionary concept born of the author’s passionate and decades-long reflections.

But, as we were saying, the pearls hidden within this volume are many. It is impossible to speak of them all: to do so would necessitate as many volumes as there are pages in this book. We must stop here, trusting to the attentive eye of the reader. Step by step we shall be able to trace those flights of the mind capable of exploring original paths.

Let us end this excursus with a note of historical and stylistic character: I am moved by Macri’s style, able to tell what he knows. Nobody, I say nobody, can lay claim to have delved so deeply into so many topics and with so much insight. No one can find adequate words to indicate the pathos, the human tension of the drama he is recounting.

This book is the story of the human tension of so many acute and penetrating minds which have left us with doubts, certainties, research, seeds of truth, disappointments, fears, errors. This is what I feel. In reading I stopped several times, moved and amazed by so much humanity and so much knowledge.

F.Z. – President of the International Centre of Psychobiophysics