Mathematics as a Historical Force

The "leaders" of Western democracies, themselves led by public opinion - like a dog walking with its tail raised before its owner, but constantly trying to guess his intentions from the corner of its eye - will never take a step disconnected from public opinion. Therefore, lockdown measures required recognition of mathematical calculation as a motive for action - and the public's poor mathematical thinking ability caused their arrival at a critical delay. Now the dyscalculic public complains about the lack of investment in the healthcare system - instead of raising hell about the failure to invest in virology and epidemiology research - and testifies about itself that it hasn't internalized anything, for there is no system that can withstand an exponential epidemic

By: The Mathematician of Life

Mathematics' revenge: Hey folks, here's a graph of the degeneration of the nation (__source__)

If there is one essential advantage that the coronavirus has contributed to public discourse - which is accustomed to being conducted in slogans and gut feelings - it is the transfer of the discussion (which has not yet had time to be infected with malignant politicization) to the field of quantitative thinking. Mathematics, which is the intellectual engine behind both the scientific revolution and the information revolution (not to mention capitalism and modern economics), has remained alien to both the intellectual world and the public world - which both are hostile to it (and do not know or understand it) alike. Therefore, we will always hear qualitative and narrative explanations and arguments for every phenomenon, while ignoring the only form of thinking that really works, in a proven way, and really extracted humanity from its constant state on the brink of hunger and plague. And no, it's not about "the Enlightenment", but about mathematical thinking.

Therefore, political and public discourse will always be conducted entirely outside any quantitative and measurable sphere, contrary to everything the scientific revolution has taught us about the efficiency of quantifying the world and experiments in it. Even intellectuals - whose mathematical ability usually stopped at the high school level where they turned to the humanities track - will vehemently maintain opposition to quantitative thinking (which nullifies their expertise), and will scatter nonsense about its inability to deal with "complex situations"/"the real world"/"value considerations"/"the human spirit"/fill in your favorite "human superiority" (i.e. what you don't understand). But suddenly - we are all trapped in models, arguing about models, and exposed to a variety of basic mathematical errors - and sometimes even to their actual refutation (the "complex" and "qualitative" reality actually does know mathematics).

Historians, who actually don't know mathematics, will always miss the dramatic historical importance of mathematics, even if they deal with the history of ideas, and will never understand its being a central engine behind the great historical revolutions. It is precisely conceptual achievements in mathematics that explain (for example) why the scientific revolution grew in the Western world and not elsewhere, and why the Greek world did not merit it, and why it was the Europeans who discovered America (to remind us: it was a calculation error, meaning there was a calculation, which allowed such voyages and long-range navigation in the first place).

Without algebra and work on solving equations, and the Cartesian idea of a graph and coordinates (which is the basic idea of the scientific revolution - of the mathematization of physics and measurement, namely the scientific experiment) - Newton would have no language in which he could formulate his equations or quantify his insights (and he would have remained trapped in Aristotelian philosophical qualitative-teleological formulations), not to mention the Copernican revolution. What stuck the scientific and technological world for a millennium and more (see: the Middle Ages) was exactly this: qualitative thinking, or at best practical-engineering, without a mathematical basis. And this is also what sticks every public discussion in our time.

And when there is zero understanding in the most basic field underlying the information revolution - this revolution is also not understood at all - because it is not understood how and why precisely innovations in mathematics grew and were created, and preceded every development in the world of computing, and how one can easily see a direct causal connection between mathematical developments and technological developments (such as computation, the internet, Google, etc.) that usually arrived a decade or two (and sometimes more) after the mathematical background that enabled them (contrary to the claim that necessity is the mother of invention. Mathematical capabilities are too abstract for people of necessity, apparently). Turing, the father of the computer, was not a technologist - he was a mathematician, and his mathematical breakthroughs in the 1930s (which themselves stemmed from the formalist revolution in mathematics, and not "by themselves") preceded the technology, which he personally was a crucial factor in its realization.

So too Shannon and information theory (and his brilliant insight that information is inherently statistical), and other central developments such as algorithms in graph theory (a theory built on Euler's brilliantly simple insight that created network theory: the relationship between two elements in a complex system can be abstracted to the simplest possible question: is there a connection between them or not?) - developments that underlie the internet network, and actually enabled it. The theories of complexity and encryption also developed central tools and algorithms decades before any practical application of them (it should be noted that in the case of encryption there was indeed an engineering component, but it was not what caused real-time developments: today we know that American intelligence preceded the mathematical community by about two decades in discovering modern encryption algorithms of number theory, but it discovered them separately from it, and allowed their widespread application). In fact, in these theories, exceptional intellectual concepts have developed in recent decades in their theoretical power, which the general intellectual world has not yet begun to internalize at all, and its lag behind this philosophical ideational boom - which also stems from a certain irrelevance, and certainly from disconnection, arrogance and ignorance - is only deepening.

Even the celebrated genomic revolution - the second most important revolution in the first two decades of the current century - is mainly a result of new algorithms for sequence processing, thanks to which the genome was deciphered ("sequencing") and its results can be processed (i.e. it is a product of the computing revolution). And the absence of significant mathematical breakthroughs in neuroscience still leaves this field in an embryonic scientific stage, despite the vast capital invested in it. One groundbreaking mathematical insight has a power that surpasses any possible economic investment - even one measured in many billions - and the examples are numerous.

All developments in deep learning, for example, stem entirely from mathematical breakthroughs in 1980-2010 (Hinton et al...) that were achieved even when the engineering community was not interested in the field, and only in 2012 did the engineering-technological revolution arrive, which is expressed in the (current) superiority of these mathematical methods over previous mathematical methods (such as SVM, which was the previous great promise in the field of learning). Theory preceded practice, directed and enabled it. Indeed, without Ben-Gurion, Herzl's vision would not have been realized, but Ben-Gurion is a result of Herzl. This pattern repeats throughout the computing revolution. Mathematicians and theorists almost always precede programmers and hardware people - they are the leaders of the revolution.

So the importance of mathematics is not only as a leading historical factor in the past - but as the most powerful factor in current developments, and the key to understanding them, and certainly the key to developing insights about the future (did someone say "the philosophy of learning"?). But what historian has sufficient background in mathematics to understand its impact on history? And what politician has sufficient background in mathematics to justify or implement public policy using mathematical tools? And what writer has sufficient background in mathematics to describe its impact on modern world and human perceptions? Which prominent intellectual even begins to grasp the depth of the influence of the development of mathematics (an obscure, deep, difficult and closed field) on the world?

Yes, perhaps surprising - but internal mathematical developments are a central driving force in history, and a central blind spot of all humanities (including the history of ideas, which doesn't really know mathematics). It's not just that "without mathematics there would be no modernity", but that central aspects of modernity were directly enabled by conceptual revolutions in mathematics. But who the hell understands mathematics? And also knows the history of mathematics? (Even mathematicians don't understand the history of their field - and are always busy with its present, using blatant anachronisms to understand the past, and trapped in the inability to imagine mathematical conceptual frameworks prior to modern mathematics).

It wasn't "technology" that enabled the information revolution, but a new type of mathematical thinking that enabled the creation of information technology. A primitive first computer could have been produced (and probably even improved) in the ancient world - if the necessary mathematical thinking had existed. The amazing computational mechanism of Antikythera is just one example of the precise production capability of the ancient world, which lacked a conceptual-conceptual revolution - and not engineering capability. But it's hard for us to grasp that it was precisely a conceptual-perceptual innovation, which was ostensibly within reach of any literate culture, that stood between the Greeks (for example) and central "modern" revolutions, such as the scientific revolution, capitalism or perhaps even the information revolution. The existence of a highly sophisticated Greek calculator seems to us a fantastic achievement, as if jumping two millennia forward - but we do not ask why only in modernity did such primitive computing machines develop into a general theory of computation (before the first computers!), not to mention mathematical computational logic, which was formulated in the 19th century before it had any computational application (Boole and Frege). Because for Aristotle - and for more than two thousand years after him - logic was a qualitative and philosophical matter, and only quantitative thinking about the theory of logic created a new kind of logical technology.

Both the philosophy of language and artificial intelligence are direct intellectual descendants of the same brilliant breakthrough by Frege - one of the most influential intellectuals in history, and undoubtedly the greatest logician of all time - that reason is not some spirit that miraculously reaches a conclusion from the premises, but can be formulated and recursively constructed as a function that matches a sentence to its truth value (and no, this is not speculation of the "history of ideas" type. Frege's book was what directly awakened Wittgenstein from his dogmatic slumber, and caused him to switch from engineering to philosophy, which happened after their meeting. Not to mention Frege's influence on Turing, and through him on the entire information revolution, up to artificial intelligence, which is Turing's idea, as we recall). But how many intellectuals who know every peep in the thought of a French/American/English thinker of little historical importance, are capable of explaining even in general terms deep ideas beyond comprehension of giants like Gödel, Cantor, Hilbert and Galois, or even Kolmogorov, Chaitin and Mandelbrot? The fertilizing influence of mathematics on thinking is a matter belonging to the past for them - and indeed is currently occurring in realms far removed from them (Netanya).

The crucial role of mathematics in historical development is not only a modern phenomenon, but also encompasses the important revolutions in ancient history, such as the revolutions of writing, agriculture, urbanization, the invention of money and monumental construction. Thus, for example, the role of mathematics in the invention of writing is crucial, as mathematical counting and calculation preceded writing and created it in practice, both conceptually - as representation, and functionally in the first state organizations (the first written materials are tax calculations, and numbers preceded letters). In fact, it is impossible to imagine any developed human organizational structure without the ability to computationally manage taxation, inventory, and property, and it is possible (although we probably will never know) that a basic accounting conceptual development is what underlaid the agricultural revolution, which was basically a social-organizational revolution, which probably even preceded agricultural domestication per se (the evidence for this is partial).

What we do know is the crucial importance of calculations for the management capability of the first empires, and the application of the computational idea in a wide range of basic developments in the ancient computational revolution (for example: in the invention of money and weight, in irrigation and storage calculations and in astronomical calculations). This is true both in empires that succeeded in developing writing later from numbers, such as cuneiform script, and in empires that did not complete the transition from the numerical state to the writing state (the Inca "quipu script") - there is no empire without calculation, and only calculation enables an empire. Is it not possible that the very existence of calculation - that conceptual development of the ability to numerically-quantitatively manage the world - is what creates empires? Are the idea of abstract calculation from a specific object, and the existence of the number itself - and the idea of the common denominator - not ideas that preceded the idea of money, and only their spread enables the widespread use of money and the development of commerce? Is it not the increasingly sophisticated ideas of interest and fraction calculations, and the idea of percentages out of a hundred (including ownership percentages), which spread in mathematical texts as a standard only in the 15th-16th centuries as a fairly new development (despite its origin in Rome), that enabled the rise of capitalism and the even more abstract quantitative perceptions behind it?

Mathematics also had a crucial influence on the development of philosophy, throughout its length, and on its very invention as a field in ancient Greece. It's not just that whoever doesn't know geometry doesn't enter the Platonic Academy - but that the model of mathematical-geometric proof is what created philosophical thinking in the first place (Pythagoras and Plato acted in the shadow of the development of deductive-mathematical thinking, and as part of the ideational explosion it created - mathematics was the model, and "the world of ideas" cannot be understood without it). "Spiritual" intellectuals will always rejoice to find philosophical depth in every phenomenon, as if philosophy is the depth dimension of humanistic thinking. But behind philosophy, throughout its development since the ancient world and up to the philosophy of language, stands an even more fundamental perceptual depth dimension. The connection - and the completely unreasonable correlation - between the greatest philosophers and mathematical thinking is often perceived as an anecdote - and not as an essential matter, which stands at the root of philosophy. But there is often a close connection between conceptual developments in mathematics and developments in philosophy, because mathematics is not only the queen of sciences, but the queen of thinking in general. That's why so few are able to understand this. It's simply too abstract, too basic, too deep - and so unromantic. This is not how we wanted to imagine the spirit of history and man.

Today, when mathematization is also taking over the social sciences (and even demanding from them - heaven forbid - results that can be reproduced, validated and measured), it seems that even the last of the humanistic disciplines, such as psychology and literature research, are beginning to understand the power and necessity of quantitative thinking (and mathematicians like John Gottman even crack the psychology of love with quantitative tools...). But who still remains at the level of elementary school arithmetic studies (at best) and kindergarten (at worst)? Precisely the public discussion on the most important questions of society. There, "the mathematics of life" and "idle talk" still rule - and there is no demand for validation, for controlled experiments, for models, for predictions, for statistics or even for an explanatory graph. Only once in a hundred years, when there is a need for a policy that really works, and when bodies are counted every day, then all these are remembered.

But all this will not convince the mathematically-challenged - any error in a model will be perceived by these dyscalculic intellectuals as conclusive proof that models don't work (really?) and that there are things that cannot be modeled like "reality" (meaning they don't know - and usually haven't heard - about the ways to do it successfully). Not to mention the zero public energy invested in quantitative discourse, statistical research and measurement policy in relation to moral blather and speaking in slogans, on which opinion leaders, the press and what a wonder - even the elected officials are entrusted. Now, for the first time, various mathematical models, most of them very crude, have entered the public discourse, competing with each other - but heaven forbid that this developing minimal literacy should seep into other areas, less important than epidemics (such as the conflict - where the great secret of the Israeli victory over the intifadas is enormous mathematical-computational superiority over the other side, which was translated into intelligence and thwarting superiority - or the economy - where public understanding is at the kindergarten level (the left) and the calculator (the right), with zero internalization of modern mathematical ideas, even the simplest ones, such as derivative, strategy or correlation).

Only in such a poor intellectual climate, can an intellectual, writer or artist proudly declare his mathematical ignorance (ignorance that is not boasted about in any other field), which actually testifies about him as completely disconnected from any understanding of our world - and our future. After all, who else would boast about their stupidity? No one boasts about their inability to understand Shakespeare, Wittgenstein, or even Einstein. In fact, it is considered an intellectual effort that is a duty and a prerequisite for any real intellectual. Mathematical idiocy is useful idiocy, and the miserable (and common) lack of understanding by intellectuals of the driving force of the computer on which they write their important musings on technology or "artificial intelligence" - is a strong indicator of the depth of their intellectual world. The vast majority of the educated public actually has no idea what mathematics is (calculation? numbers?), and what its marvelous capabilities are for conceptualizing the world, and this public's ability for abstract, scientific and quantitative thinking - stands in absolute correlation to this.

But there is no despair in the world at all. Mathematics, public enemy (and mind) number one in normal times, has become in these days the new hobby of experts in a shekel and statisticians in a penny from all over the public (and woe - even academia). And here, out of all the gross and ridiculous errors and refutations and very Israeli attempts to find a sixth-grade level graph that beats the expert - a new type of public discussion is gradually growing, and some literacy (or at least aspired to) in quantitative thinking, which has been completely absent from the spiritual horizon of intellectuals and public and faith figures to this very day. On the day when public discussion is conducted with graphs - and with all the limitations of these tools, their advantages are enormous compared to any other public discussion tool - we will know that we will never again be ruled by the degenerate junta that manages the Western world in the corona crisis.

Indeed, many tend to mistakenly attribute the crisis of democracies to the weakness of democracy, which allows the rise of hollow populists, but this leadership crisis is actually evidence of the unbalanced excess strength of democracy: the people are the hollow populist, the general public is a public of degenerates, and chooses leaders in its image and likeness. The current weakness is actually of the institutions, and the rise of power is of the public itself - partly thanks to the network discourse that bypasses any institutional discourse, and expresses the authentic stupidity (since time immemorial) of the people, in a popular tsunami of rudeness, wretchedness of soul and shallowness of mind. Therefore, only broader mathematical education of the general public - and not, how ridiculous, moral education - will create a more intelligent public discussion, which will raise more intelligent leaders, who understand in time the meaning of exponential spread. These leaders may even be able to cope with the future, and manage wise policy in the revolutions that mathematics causes and will cause in the world - from artificial intelligence to quantum computing - and maybe even finally succeed in managing reasonable policy in a complex mathematical field, which still struggles with rather crude models (and too much): the economy.

Is it coincidental that the only reasonable leader in the Western world in the last decade, who is also leading a measured and effective response against the virus, has quantitative thinking ability that surpasses all her ignorant colleagues (Dr. Physics and researcher Angela Merkel)? And if we were to set an exam at the level of a first degree course in mathematics and statistics as a threshold condition for leadership, wouldn't we benefit from it? As the world becomes more complex, and the interactions in it become less intuitive, and trends in it accelerate at a much faster rate (and sometimes even at an exponential rate), thinking at the elementary school level is no longer suitable for dealing with it. If we don't understand that we need to set an effective filter to raise the intelligence level of our elected officials, we will end up in a disaster that the corona epidemic will look like a preliminary warning - and wasted - next to it. A yellow card for street thinking. Mathematical thinking is certainly not a sufficient condition for leadership, but when will we understand that in the computer age - which is approaching the age of artificial intelligence - it is a necessary condition?

The polemic on the mathematization of public discourse: The right side

Therefore, political and public discourse will always be conducted entirely outside any quantitative and measurable sphere, contrary to everything the scientific revolution has taught us about the efficiency of quantifying the world and experiments in it. Even intellectuals - whose mathematical ability usually stopped at the high school level where they turned to the humanities track - will vehemently maintain opposition to quantitative thinking (which nullifies their expertise), and will scatter nonsense about its inability to deal with "complex situations"/"the real world"/"value considerations"/"the human spirit"/fill in your favorite "human superiority" (i.e. what you don't understand). But suddenly - we are all trapped in models, arguing about models, and exposed to a variety of basic mathematical errors - and sometimes even to their actual refutation (the "complex" and "qualitative" reality actually does know mathematics).

Historians, who actually don't know mathematics, will always miss the dramatic historical importance of mathematics, even if they deal with the history of ideas, and will never understand its being a central engine behind the great historical revolutions. It is precisely conceptual achievements in mathematics that explain (for example) why the scientific revolution grew in the Western world and not elsewhere, and why the Greek world did not merit it, and why it was the Europeans who discovered America (to remind us: it was a calculation error, meaning there was a calculation, which allowed such voyages and long-range navigation in the first place).

Without algebra and work on solving equations, and the Cartesian idea of a graph and coordinates (which is the basic idea of the scientific revolution - of the mathematization of physics and measurement, namely the scientific experiment) - Newton would have no language in which he could formulate his equations or quantify his insights (and he would have remained trapped in Aristotelian philosophical qualitative-teleological formulations), not to mention the Copernican revolution. What stuck the scientific and technological world for a millennium and more (see: the Middle Ages) was exactly this: qualitative thinking, or at best practical-engineering, without a mathematical basis. And this is also what sticks every public discussion in our time.

And when there is zero understanding in the most basic field underlying the information revolution - this revolution is also not understood at all - because it is not understood how and why precisely innovations in mathematics grew and were created, and preceded every development in the world of computing, and how one can easily see a direct causal connection between mathematical developments and technological developments (such as computation, the internet, Google, etc.) that usually arrived a decade or two (and sometimes more) after the mathematical background that enabled them (contrary to the claim that necessity is the mother of invention. Mathematical capabilities are too abstract for people of necessity, apparently). Turing, the father of the computer, was not a technologist - he was a mathematician, and his mathematical breakthroughs in the 1930s (which themselves stemmed from the formalist revolution in mathematics, and not "by themselves") preceded the technology, which he personally was a crucial factor in its realization.

So too Shannon and information theory (and his brilliant insight that information is inherently statistical), and other central developments such as algorithms in graph theory (a theory built on Euler's brilliantly simple insight that created network theory: the relationship between two elements in a complex system can be abstracted to the simplest possible question: is there a connection between them or not?) - developments that underlie the internet network, and actually enabled it. The theories of complexity and encryption also developed central tools and algorithms decades before any practical application of them (it should be noted that in the case of encryption there was indeed an engineering component, but it was not what caused real-time developments: today we know that American intelligence preceded the mathematical community by about two decades in discovering modern encryption algorithms of number theory, but it discovered them separately from it, and allowed their widespread application). In fact, in these theories, exceptional intellectual concepts have developed in recent decades in their theoretical power, which the general intellectual world has not yet begun to internalize at all, and its lag behind this philosophical ideational boom - which also stems from a certain irrelevance, and certainly from disconnection, arrogance and ignorance - is only deepening.

Even the celebrated genomic revolution - the second most important revolution in the first two decades of the current century - is mainly a result of new algorithms for sequence processing, thanks to which the genome was deciphered ("sequencing") and its results can be processed (i.e. it is a product of the computing revolution). And the absence of significant mathematical breakthroughs in neuroscience still leaves this field in an embryonic scientific stage, despite the vast capital invested in it. One groundbreaking mathematical insight has a power that surpasses any possible economic investment - even one measured in many billions - and the examples are numerous.

All developments in deep learning, for example, stem entirely from mathematical breakthroughs in 1980-2010 (Hinton et al...) that were achieved even when the engineering community was not interested in the field, and only in 2012 did the engineering-technological revolution arrive, which is expressed in the (current) superiority of these mathematical methods over previous mathematical methods (such as SVM, which was the previous great promise in the field of learning). Theory preceded practice, directed and enabled it. Indeed, without Ben-Gurion, Herzl's vision would not have been realized, but Ben-Gurion is a result of Herzl. This pattern repeats throughout the computing revolution. Mathematicians and theorists almost always precede programmers and hardware people - they are the leaders of the revolution.

So the importance of mathematics is not only as a leading historical factor in the past - but as the most powerful factor in current developments, and the key to understanding them, and certainly the key to developing insights about the future (did someone say "the philosophy of learning"?). But what historian has sufficient background in mathematics to understand its impact on history? And what politician has sufficient background in mathematics to justify or implement public policy using mathematical tools? And what writer has sufficient background in mathematics to describe its impact on modern world and human perceptions? Which prominent intellectual even begins to grasp the depth of the influence of the development of mathematics (an obscure, deep, difficult and closed field) on the world?

Yes, perhaps surprising - but internal mathematical developments are a central driving force in history, and a central blind spot of all humanities (including the history of ideas, which doesn't really know mathematics). It's not just that "without mathematics there would be no modernity", but that central aspects of modernity were directly enabled by conceptual revolutions in mathematics. But who the hell understands mathematics? And also knows the history of mathematics? (Even mathematicians don't understand the history of their field - and are always busy with its present, using blatant anachronisms to understand the past, and trapped in the inability to imagine mathematical conceptual frameworks prior to modern mathematics).

It wasn't "technology" that enabled the information revolution, but a new type of mathematical thinking that enabled the creation of information technology. A primitive first computer could have been produced (and probably even improved) in the ancient world - if the necessary mathematical thinking had existed. The amazing computational mechanism of Antikythera is just one example of the precise production capability of the ancient world, which lacked a conceptual-conceptual revolution - and not engineering capability. But it's hard for us to grasp that it was precisely a conceptual-perceptual innovation, which was ostensibly within reach of any literate culture, that stood between the Greeks (for example) and central "modern" revolutions, such as the scientific revolution, capitalism or perhaps even the information revolution. The existence of a highly sophisticated Greek calculator seems to us a fantastic achievement, as if jumping two millennia forward - but we do not ask why only in modernity did such primitive computing machines develop into a general theory of computation (before the first computers!), not to mention mathematical computational logic, which was formulated in the 19th century before it had any computational application (Boole and Frege). Because for Aristotle - and for more than two thousand years after him - logic was a qualitative and philosophical matter, and only quantitative thinking about the theory of logic created a new kind of logical technology.

Both the philosophy of language and artificial intelligence are direct intellectual descendants of the same brilliant breakthrough by Frege - one of the most influential intellectuals in history, and undoubtedly the greatest logician of all time - that reason is not some spirit that miraculously reaches a conclusion from the premises, but can be formulated and recursively constructed as a function that matches a sentence to its truth value (and no, this is not speculation of the "history of ideas" type. Frege's book was what directly awakened Wittgenstein from his dogmatic slumber, and caused him to switch from engineering to philosophy, which happened after their meeting. Not to mention Frege's influence on Turing, and through him on the entire information revolution, up to artificial intelligence, which is Turing's idea, as we recall). But how many intellectuals who know every peep in the thought of a French/American/English thinker of little historical importance, are capable of explaining even in general terms deep ideas beyond comprehension of giants like Gödel, Cantor, Hilbert and Galois, or even Kolmogorov, Chaitin and Mandelbrot? The fertilizing influence of mathematics on thinking is a matter belonging to the past for them - and indeed is currently occurring in realms far removed from them (Netanya).

The crucial role of mathematics in historical development is not only a modern phenomenon, but also encompasses the important revolutions in ancient history, such as the revolutions of writing, agriculture, urbanization, the invention of money and monumental construction. Thus, for example, the role of mathematics in the invention of writing is crucial, as mathematical counting and calculation preceded writing and created it in practice, both conceptually - as representation, and functionally in the first state organizations (the first written materials are tax calculations, and numbers preceded letters). In fact, it is impossible to imagine any developed human organizational structure without the ability to computationally manage taxation, inventory, and property, and it is possible (although we probably will never know) that a basic accounting conceptual development is what underlaid the agricultural revolution, which was basically a social-organizational revolution, which probably even preceded agricultural domestication per se (the evidence for this is partial).

What we do know is the crucial importance of calculations for the management capability of the first empires, and the application of the computational idea in a wide range of basic developments in the ancient computational revolution (for example: in the invention of money and weight, in irrigation and storage calculations and in astronomical calculations). This is true both in empires that succeeded in developing writing later from numbers, such as cuneiform script, and in empires that did not complete the transition from the numerical state to the writing state (the Inca "quipu script") - there is no empire without calculation, and only calculation enables an empire. Is it not possible that the very existence of calculation - that conceptual development of the ability to numerically-quantitatively manage the world - is what creates empires? Are the idea of abstract calculation from a specific object, and the existence of the number itself - and the idea of the common denominator - not ideas that preceded the idea of money, and only their spread enables the widespread use of money and the development of commerce? Is it not the increasingly sophisticated ideas of interest and fraction calculations, and the idea of percentages out of a hundred (including ownership percentages), which spread in mathematical texts as a standard only in the 15th-16th centuries as a fairly new development (despite its origin in Rome), that enabled the rise of capitalism and the even more abstract quantitative perceptions behind it?

Mathematics also had a crucial influence on the development of philosophy, throughout its length, and on its very invention as a field in ancient Greece. It's not just that whoever doesn't know geometry doesn't enter the Platonic Academy - but that the model of mathematical-geometric proof is what created philosophical thinking in the first place (Pythagoras and Plato acted in the shadow of the development of deductive-mathematical thinking, and as part of the ideational explosion it created - mathematics was the model, and "the world of ideas" cannot be understood without it). "Spiritual" intellectuals will always rejoice to find philosophical depth in every phenomenon, as if philosophy is the depth dimension of humanistic thinking. But behind philosophy, throughout its development since the ancient world and up to the philosophy of language, stands an even more fundamental perceptual depth dimension. The connection - and the completely unreasonable correlation - between the greatest philosophers and mathematical thinking is often perceived as an anecdote - and not as an essential matter, which stands at the root of philosophy. But there is often a close connection between conceptual developments in mathematics and developments in philosophy, because mathematics is not only the queen of sciences, but the queen of thinking in general. That's why so few are able to understand this. It's simply too abstract, too basic, too deep - and so unromantic. This is not how we wanted to imagine the spirit of history and man.

Today, when mathematization is also taking over the social sciences (and even demanding from them - heaven forbid - results that can be reproduced, validated and measured), it seems that even the last of the humanistic disciplines, such as psychology and literature research, are beginning to understand the power and necessity of quantitative thinking (and mathematicians like John Gottman even crack the psychology of love with quantitative tools...). But who still remains at the level of elementary school arithmetic studies (at best) and kindergarten (at worst)? Precisely the public discussion on the most important questions of society. There, "the mathematics of life" and "idle talk" still rule - and there is no demand for validation, for controlled experiments, for models, for predictions, for statistics or even for an explanatory graph. Only once in a hundred years, when there is a need for a policy that really works, and when bodies are counted every day, then all these are remembered.

But all this will not convince the mathematically-challenged - any error in a model will be perceived by these dyscalculic intellectuals as conclusive proof that models don't work (really?) and that there are things that cannot be modeled like "reality" (meaning they don't know - and usually haven't heard - about the ways to do it successfully). Not to mention the zero public energy invested in quantitative discourse, statistical research and measurement policy in relation to moral blather and speaking in slogans, on which opinion leaders, the press and what a wonder - even the elected officials are entrusted. Now, for the first time, various mathematical models, most of them very crude, have entered the public discourse, competing with each other - but heaven forbid that this developing minimal literacy should seep into other areas, less important than epidemics (such as the conflict - where the great secret of the Israeli victory over the intifadas is enormous mathematical-computational superiority over the other side, which was translated into intelligence and thwarting superiority - or the economy - where public understanding is at the kindergarten level (the left) and the calculator (the right), with zero internalization of modern mathematical ideas, even the simplest ones, such as derivative, strategy or correlation).

Only in such a poor intellectual climate, can an intellectual, writer or artist proudly declare his mathematical ignorance (ignorance that is not boasted about in any other field), which actually testifies about him as completely disconnected from any understanding of our world - and our future. After all, who else would boast about their stupidity? No one boasts about their inability to understand Shakespeare, Wittgenstein, or even Einstein. In fact, it is considered an intellectual effort that is a duty and a prerequisite for any real intellectual. Mathematical idiocy is useful idiocy, and the miserable (and common) lack of understanding by intellectuals of the driving force of the computer on which they write their important musings on technology or "artificial intelligence" - is a strong indicator of the depth of their intellectual world. The vast majority of the educated public actually has no idea what mathematics is (calculation? numbers?), and what its marvelous capabilities are for conceptualizing the world, and this public's ability for abstract, scientific and quantitative thinking - stands in absolute correlation to this.

But there is no despair in the world at all. Mathematics, public enemy (and mind) number one in normal times, has become in these days the new hobby of experts in a shekel and statisticians in a penny from all over the public (and woe - even academia). And here, out of all the gross and ridiculous errors and refutations and very Israeli attempts to find a sixth-grade level graph that beats the expert - a new type of public discussion is gradually growing, and some literacy (or at least aspired to) in quantitative thinking, which has been completely absent from the spiritual horizon of intellectuals and public and faith figures to this very day. On the day when public discussion is conducted with graphs - and with all the limitations of these tools, their advantages are enormous compared to any other public discussion tool - we will know that we will never again be ruled by the degenerate junta that manages the Western world in the corona crisis.

Indeed, many tend to mistakenly attribute the crisis of democracies to the weakness of democracy, which allows the rise of hollow populists, but this leadership crisis is actually evidence of the unbalanced excess strength of democracy: the people are the hollow populist, the general public is a public of degenerates, and chooses leaders in its image and likeness. The current weakness is actually of the institutions, and the rise of power is of the public itself - partly thanks to the network discourse that bypasses any institutional discourse, and expresses the authentic stupidity (since time immemorial) of the people, in a popular tsunami of rudeness, wretchedness of soul and shallowness of mind. Therefore, only broader mathematical education of the general public - and not, how ridiculous, moral education - will create a more intelligent public discussion, which will raise more intelligent leaders, who understand in time the meaning of exponential spread. These leaders may even be able to cope with the future, and manage wise policy in the revolutions that mathematics causes and will cause in the world - from artificial intelligence to quantum computing - and maybe even finally succeed in managing reasonable policy in a complex mathematical field, which still struggles with rather crude models (and too much): the economy.

Is it coincidental that the only reasonable leader in the Western world in the last decade, who is also leading a measured and effective response against the virus, has quantitative thinking ability that surpasses all her ignorant colleagues (Dr. Physics and researcher Angela Merkel)? And if we were to set an exam at the level of a first degree course in mathematics and statistics as a threshold condition for leadership, wouldn't we benefit from it? As the world becomes more complex, and the interactions in it become less intuitive, and trends in it accelerate at a much faster rate (and sometimes even at an exponential rate), thinking at the elementary school level is no longer suitable for dealing with it. If we don't understand that we need to set an effective filter to raise the intelligence level of our elected officials, we will end up in a disaster that the corona epidemic will look like a preliminary warning - and wasted - next to it. A yellow card for street thinking. Mathematical thinking is certainly not a sufficient condition for leadership, but when will we understand that in the computer age - which is approaching the age of artificial intelligence - it is a necessary condition?

The polemic on the mathematization of public discourse: The right side