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Evo-seti : life evolution statistics on earth and exoplanets. / / Claudio Maccone
| Evo-seti : life evolution statistics on earth and exoplanets. / / Claudio Maccone |
| Autore | Maccone Claudio |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2020] |
| Descrizione fisica | 1 online resource (lvii, 837 pages) : illustrations |
| Disciplina | 576.839 |
| Soggetto topico | Exobiology |
| ISBN | 3-030-51931-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- OVERCOME Theorem, that is PEAK-LOCUS Theorem, Proven by Maxima -- 1 OVERCOME Theorem, that is PEAK-LOCUS Theorem -- 2 Evo-Entropy(p): Measuring "How Much Evolution" Occurred -- 3 Perfectly LINEAR Evo-Entropy When the Mean Value Is Perfectly Exponential (A GBM): This Is just the Molecular Clock -- 4 Introducing EE, the Evo-SETI Unit: An Amount of Information Equal to the Evo-Entropy Reached by Life Evolution on Earth Nowadays -- 5 Conclusions About Evo-Entropy -- Appendix -- References -- Evo-SETI Mathematics: Part 1: Entropy of Information. Part 2: Energy of Living Forms. Part 3: The Singularity -- 1 Introduction -- 2 Part 1: Entropy of Information as the Measure of Evolution, Peak-Locus Theorem, and Scale of Biological Evolution (Evo-SETI Scale) -- 2.1 Purpose of This Chapter -- 2.2 A Simple Proof of the b-Lognormal Probability Density Function (PDF) -- 2.3 Biological Evolution as the Exponential Increase of the Number of Living Species -- 2.4 Biological Evolution on Earth Was just a Particular Realization of Geometric Brownian Motion in the Number of Living Species -- 2.5 During the Last 3.5 Billion Years Life Forms Increased like a Lognormal Stochastic Process -- 2.6 Mean Value of the Lognormal Process L(t) -- 2.7 L( t ) Initial Conditions at ts -- 2.8 L( t ) Final Conditions at te > -- ts -- 2.9 Important Special Cases of mL ( t ) -- 2.10 Boundary Conditions When mL ( t ) Is a First, Second or Third Degree Polynomial in the Time (t - ts) -- 2.11 Peak-Locus Theorem -- 2.12 Evo-Entropy(p): Measuring "How Much Evolution" Occurred -- 2.13 Perfectly Linear Evo-Entropy When the Mean Value Is Perfectly Exponential (a GBM): This Is just the Molecular Clock -- 2.14 Introducing EE, the Evo-SETI Unit: An Amount of Information Equal to the Evo-Entropy Reached by Life Evolution on Earth Nowadays.
2.15 Markov-Korotayev Alternative to Exponential: A Cubic Growth -- 2.16 Evo-Entropy of the Markov-Korotayev Cubic Growth -- 2.17 Comparing the Evo-Entropy of the Markov-Korotayev Cubic Growth to a Hypothetical (1) Linear and (2) Parabolic Growth -- 2.18 Conclusions About Evo-Entropy -- 2.19 Life as a Finite b-Lognormal as Assumed by This Author Prior to 2017 -- 2.20 b-Lognormal History Formulae and Their Applications to Past History -- 3 Part 2: Energy of Living Forms by "Logpar" Power Curves -- 3.1 Introduction to Logpar Power Curves -- 3.2 Finding the Parabola Equation of the Right Part of the Logpar -- 3.3 Finding the b-Lognormal Equation of the Left Part of the Logpar -- 3.4 Area Under the Parabola on the Right Part of the Logpar Between Peak and Death -- 3.5 Area Under the Full Logpar Curve Between Birth and Death -- 3.6 The Area Under the Logpar Curve Depends on Sigma Only, and Here Is the Area Derivative W.R.T. σ -- 3.7 Exact "History Equations" for Each Logpar Curve -- 3.8 Considerations on the Logpar History Equations -- 3.9 Logpar Peak Coordinates Expressed in Terms of ( b,p,d ) Only -- 3.10 History of Ancient Rome as an Example of How to Use the Logpar History Formulae -- 3.11 Area Under Rome's Logpar and Its Meaning as "Overall Energy" of the Roman Civilization -- 3.12 The Energy Function of d Regarded as a Function of the Death Instant d, Hereafter Renamed D -- 3.13 Discovering an Oblique Asymptote of the Energy Function, Energy(D), While the Death Instant D Is Increasing Indefinitely -- 3.14 The Oblique Asymptote for the "History of Rome" Case -- 3.15 What if Hadn't Rome Fallen? Discovering the Straight Line Parallel to the Asymptote but Starting at the Rome Power Peak -- 3.16 Energy Output of the Sun as a G2 Star Over the About 10 Billion Years of Its Lifetime -- 3.17 Energy Output of an M Star Over 45 Billion Years of Lifetime. 3.18 Mean Power in a Lifetime -- 3.19 Lifetime Mean Value -- 3.20 Logpar Power Curves Versus b-Lognormal Probability Densities -- 3.21 Conclusions About Logpars -- 4 Part 3: Before and After the Singularity According to Evo-SETI Theory -- 4.1 Every Exponential in Time Has just a Single Knee: The Instant at Which Its Curvature Is Highest -- 4.2 GBM Exponential as Mean Value of the Increasing Number of Species Since the Origin of Life on Earth -- 4.3 Deriving the Knee Time for GBMs -- 4.4 Knee-Centered Form of the GBM Exponential -- 4.5 Finding WHEN the GBM Knee Will Occur According to the Author's Conventional Values for ts and B -- 4.6 Ray Kurzweil's 2006 Book "the Singularity Is Near" -- 4.7 Kurzweil's Singularity Is the Same as Our GBM's Knee in Our Evo-SETI Theory -- 4.8 Measuring the Pace of Evolution B by the Average Number m0 of Species Living on Earth NOW -- 4.9 An Unexpected Discovery: The "Origin-to-Now" ("OTN") Equation Relating the Time of the Origin of Life on Earth (ts) to m0 (the Average Number of Species Living on Earth Right Now) -- 4.10 Solving the "Origin-to-Now" Equation NUMERICALLY for the Two Cases of -3.5 and -3.8 Billion Years of Life on Earth -- 4.11 But... Biologists Are UNABLE to Measure m0 Experimentally! -- 4.12 Lognormal pdf of the GBM -- 4.13 Finding the GBM Parameter σ -- 4.14 Numerical Standard Deviation Nowadays for the Two Cases of Life Starting 3.5 and 3.8 Billion Years Ago -- 4.15 Numerical σ for the Two Cases of Life Starting 3.5 and 3.8 Billion Years Ago -- 4.16 Conclusions -- References -- SETI, Evolution and Human History Merged into a Mathematical Model -- 1 SETI and Darwinian Evolution Merged Mathematically -- 1.1 Introduction: The Drake Equation (1961) as the Foundation of SETI -- 1.2 Statistical Drake Equation (2008) -- 1.3 The Statistical Distribution of N Is Lognormal. 1.4 Darwinian Evolution as Exponential Increase of the Number of Living Species -- 1.5 Introducing the 'Darwin' (D) Unit, Measuring the Amount of Evolution that a Given Species Reached -- 1.6 Darwinian Evolution Is just a Particular Realization of Geometric Brownian Motion in the Number of Living Species -- 2 GBM as the Key to Stochastic Evolution of All Kinds -- 2.1 The N(t) GBM as Stochastic Evolution -- 2.2 Our Statistical Drake Equation Is the Static Special Case of N(t) -- 2.3 GBM as the Key to Mathematics of Finance -- 3 Darwinian Evolution Re-defined as a GBM in the Number of Living Species -- 3.1 A Concise Introduction to Cladistics and Cladograms -- 3.2 Cladistics: Namely the GBM Mean Exponential as the Locus of the Peaks of b-Lognormals Representing Each a Different Species Started by Evolution at Time t = b -- 3.3 Cladogram Branches Are Increasing, Decreasing or Stable (Horizontal) Exponential Arches as Functions of Time -- 3.4 KLT-Filtering in Hilbert Space and Darwinian Selection Are "the Same Thing" in Our Theory... -- 3.5 Conclusions About Our Statistical Model for Evolution and Cladistics -- 4 Lifespans of Living Beings as b-Lognormals -- 4.1 Further Extending b-Lognormals as Our Model for All Lifespans -- 4.2 Infinite b-Lognormals -- 4.3 From Infinite to Finite b-Lognormals: Defining the Death Time, d, as the Time Axis Intercept of the b-Lognormal Tangent Line at Senility s -- 4.4 Terminology About Various Time Instants Related to a Lifetime -- 4.5 Terminology About Various Time Spans Related to a Lifetime -- 4.6 Normalizing to One All the Finite b-Lognormals -- 4.7 Finding the b-Lognormals Given b and Two Out of the Four a, p, s, d -- 5 Golden Ratios and Golden b-Lognormals -- 5.1 Is σ Always Smaller Than 1? -- 5.2 Golden Ratios and Golden b-Lognormals -- 6 Mathematical History of Civilizations. 6.1 Civilizations Unfolding in Time as b-Lognormals -- 6.2 Eight Examples of Western Historic Civilizations as Finite b-Lognormals -- 6.3 Plotting All b-Lognormals Together and Finding the Trends -- 6.4 b-Lognormals of Alien Civilizations -- 7 Extrapolating History into the Past: Aztecs -- 7.1 Aztecs-Spaniards as an Example of Two Suddenly Clashing Civilizations with Large Technology Gap -- 7.2 'Virtual Aztecs' Method to Find the 'True Aztecs' b-Lognormal -- 8 b-Lognormal Entropy as 'Civilization Amount' -- 8.1 Introduction: Invoking Entropy and Information Theory -- 8.2 Exponential Curve in Time Determined by Two Points Only -- 8.3 Assuming that the Exponential Curve in Time Is the GBM Mean Value Curve -- 8.4 The 'No-Evolution' Stationary Stochastic Process -- 8.5 Entropy of the 'Running b-Lognormal' Peaked at the GBM Exponential Mean -- 8.6 Decreasing Entropy for an Exponentially Increasing Evolution: Progress! -- 8.7 Six Examples: Entropy Changes in Darwinian Evolution, Human History Between Ancient Greece and Now, and Aztecs and Incas Versus Spaniards -- 8.8 b-Lognormals of Alien Civilizations -- 9 Conclusion: Summary of Technical Concepts Described -- References -- Evolution and Mass Extinctions as Lognormal Stochastic Processes -- 1 Introduction: Mathematics and Science -- 2 A Summary of the 'Evo-SETI' Model of Evolution and SETI -- 3 Important Special Cases of mL(t) -- 4 Introducing b-lognormals -- 5 Peak-Locus Theorem -- 6 Entropy as the Evolution Measure -- 7 Evo-SETI -- 8 Mass Extinctions of Darwinian Evolution Described by a Decreasing GBM -- 8.1 GBMs to Understand Mass Extinctions of the Past -- 8.2 Example: The K-Pg Mass Extinction Extending Ten Centuries After Impact -- 9 Mass Extinctions Described by an Adjusted Parabola Branch -- 9.1 Adjusting the Parabola to the Mass Extinctions of the Past. 9.2 Example: The Parabola of the K-Pg Mass Extinction Extending Ten Centuries After Impact. |
| Record Nr. | UNINA-9910444452703321 |
Maccone Claudio
|
||
| Cham, Switzerland : , : Springer, , [2020] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Evo-seti : life evolution statistics on earth and exoplanets. / / Claudio Maccone
| Evo-seti : life evolution statistics on earth and exoplanets. / / Claudio Maccone |
| Autore | Maccone Claudio |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2020] |
| Descrizione fisica | 1 online resource (lvii, 837 pages) : illustrations |
| Disciplina | 576.839 |
| Soggetto topico | Exobiology |
| ISBN | 3-030-51931-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- OVERCOME Theorem, that is PEAK-LOCUS Theorem, Proven by Maxima -- 1 OVERCOME Theorem, that is PEAK-LOCUS Theorem -- 2 Evo-Entropy(p): Measuring "How Much Evolution" Occurred -- 3 Perfectly LINEAR Evo-Entropy When the Mean Value Is Perfectly Exponential (A GBM): This Is just the Molecular Clock -- 4 Introducing EE, the Evo-SETI Unit: An Amount of Information Equal to the Evo-Entropy Reached by Life Evolution on Earth Nowadays -- 5 Conclusions About Evo-Entropy -- Appendix -- References -- Evo-SETI Mathematics: Part 1: Entropy of Information. Part 2: Energy of Living Forms. Part 3: The Singularity -- 1 Introduction -- 2 Part 1: Entropy of Information as the Measure of Evolution, Peak-Locus Theorem, and Scale of Biological Evolution (Evo-SETI Scale) -- 2.1 Purpose of This Chapter -- 2.2 A Simple Proof of the b-Lognormal Probability Density Function (PDF) -- 2.3 Biological Evolution as the Exponential Increase of the Number of Living Species -- 2.4 Biological Evolution on Earth Was just a Particular Realization of Geometric Brownian Motion in the Number of Living Species -- 2.5 During the Last 3.5 Billion Years Life Forms Increased like a Lognormal Stochastic Process -- 2.6 Mean Value of the Lognormal Process L(t) -- 2.7 L( t ) Initial Conditions at ts -- 2.8 L( t ) Final Conditions at te > -- ts -- 2.9 Important Special Cases of mL ( t ) -- 2.10 Boundary Conditions When mL ( t ) Is a First, Second or Third Degree Polynomial in the Time (t - ts) -- 2.11 Peak-Locus Theorem -- 2.12 Evo-Entropy(p): Measuring "How Much Evolution" Occurred -- 2.13 Perfectly Linear Evo-Entropy When the Mean Value Is Perfectly Exponential (a GBM): This Is just the Molecular Clock -- 2.14 Introducing EE, the Evo-SETI Unit: An Amount of Information Equal to the Evo-Entropy Reached by Life Evolution on Earth Nowadays.
2.15 Markov-Korotayev Alternative to Exponential: A Cubic Growth -- 2.16 Evo-Entropy of the Markov-Korotayev Cubic Growth -- 2.17 Comparing the Evo-Entropy of the Markov-Korotayev Cubic Growth to a Hypothetical (1) Linear and (2) Parabolic Growth -- 2.18 Conclusions About Evo-Entropy -- 2.19 Life as a Finite b-Lognormal as Assumed by This Author Prior to 2017 -- 2.20 b-Lognormal History Formulae and Their Applications to Past History -- 3 Part 2: Energy of Living Forms by "Logpar" Power Curves -- 3.1 Introduction to Logpar Power Curves -- 3.2 Finding the Parabola Equation of the Right Part of the Logpar -- 3.3 Finding the b-Lognormal Equation of the Left Part of the Logpar -- 3.4 Area Under the Parabola on the Right Part of the Logpar Between Peak and Death -- 3.5 Area Under the Full Logpar Curve Between Birth and Death -- 3.6 The Area Under the Logpar Curve Depends on Sigma Only, and Here Is the Area Derivative W.R.T. σ -- 3.7 Exact "History Equations" for Each Logpar Curve -- 3.8 Considerations on the Logpar History Equations -- 3.9 Logpar Peak Coordinates Expressed in Terms of ( b,p,d ) Only -- 3.10 History of Ancient Rome as an Example of How to Use the Logpar History Formulae -- 3.11 Area Under Rome's Logpar and Its Meaning as "Overall Energy" of the Roman Civilization -- 3.12 The Energy Function of d Regarded as a Function of the Death Instant d, Hereafter Renamed D -- 3.13 Discovering an Oblique Asymptote of the Energy Function, Energy(D), While the Death Instant D Is Increasing Indefinitely -- 3.14 The Oblique Asymptote for the "History of Rome" Case -- 3.15 What if Hadn't Rome Fallen? Discovering the Straight Line Parallel to the Asymptote but Starting at the Rome Power Peak -- 3.16 Energy Output of the Sun as a G2 Star Over the About 10 Billion Years of Its Lifetime -- 3.17 Energy Output of an M Star Over 45 Billion Years of Lifetime. 3.18 Mean Power in a Lifetime -- 3.19 Lifetime Mean Value -- 3.20 Logpar Power Curves Versus b-Lognormal Probability Densities -- 3.21 Conclusions About Logpars -- 4 Part 3: Before and After the Singularity According to Evo-SETI Theory -- 4.1 Every Exponential in Time Has just a Single Knee: The Instant at Which Its Curvature Is Highest -- 4.2 GBM Exponential as Mean Value of the Increasing Number of Species Since the Origin of Life on Earth -- 4.3 Deriving the Knee Time for GBMs -- 4.4 Knee-Centered Form of the GBM Exponential -- 4.5 Finding WHEN the GBM Knee Will Occur According to the Author's Conventional Values for ts and B -- 4.6 Ray Kurzweil's 2006 Book "the Singularity Is Near" -- 4.7 Kurzweil's Singularity Is the Same as Our GBM's Knee in Our Evo-SETI Theory -- 4.8 Measuring the Pace of Evolution B by the Average Number m0 of Species Living on Earth NOW -- 4.9 An Unexpected Discovery: The "Origin-to-Now" ("OTN") Equation Relating the Time of the Origin of Life on Earth (ts) to m0 (the Average Number of Species Living on Earth Right Now) -- 4.10 Solving the "Origin-to-Now" Equation NUMERICALLY for the Two Cases of -3.5 and -3.8 Billion Years of Life on Earth -- 4.11 But... Biologists Are UNABLE to Measure m0 Experimentally! -- 4.12 Lognormal pdf of the GBM -- 4.13 Finding the GBM Parameter σ -- 4.14 Numerical Standard Deviation Nowadays for the Two Cases of Life Starting 3.5 and 3.8 Billion Years Ago -- 4.15 Numerical σ for the Two Cases of Life Starting 3.5 and 3.8 Billion Years Ago -- 4.16 Conclusions -- References -- SETI, Evolution and Human History Merged into a Mathematical Model -- 1 SETI and Darwinian Evolution Merged Mathematically -- 1.1 Introduction: The Drake Equation (1961) as the Foundation of SETI -- 1.2 Statistical Drake Equation (2008) -- 1.3 The Statistical Distribution of N Is Lognormal. 1.4 Darwinian Evolution as Exponential Increase of the Number of Living Species -- 1.5 Introducing the 'Darwin' (D) Unit, Measuring the Amount of Evolution that a Given Species Reached -- 1.6 Darwinian Evolution Is just a Particular Realization of Geometric Brownian Motion in the Number of Living Species -- 2 GBM as the Key to Stochastic Evolution of All Kinds -- 2.1 The N(t) GBM as Stochastic Evolution -- 2.2 Our Statistical Drake Equation Is the Static Special Case of N(t) -- 2.3 GBM as the Key to Mathematics of Finance -- 3 Darwinian Evolution Re-defined as a GBM in the Number of Living Species -- 3.1 A Concise Introduction to Cladistics and Cladograms -- 3.2 Cladistics: Namely the GBM Mean Exponential as the Locus of the Peaks of b-Lognormals Representing Each a Different Species Started by Evolution at Time t = b -- 3.3 Cladogram Branches Are Increasing, Decreasing or Stable (Horizontal) Exponential Arches as Functions of Time -- 3.4 KLT-Filtering in Hilbert Space and Darwinian Selection Are "the Same Thing" in Our Theory... -- 3.5 Conclusions About Our Statistical Model for Evolution and Cladistics -- 4 Lifespans of Living Beings as b-Lognormals -- 4.1 Further Extending b-Lognormals as Our Model for All Lifespans -- 4.2 Infinite b-Lognormals -- 4.3 From Infinite to Finite b-Lognormals: Defining the Death Time, d, as the Time Axis Intercept of the b-Lognormal Tangent Line at Senility s -- 4.4 Terminology About Various Time Instants Related to a Lifetime -- 4.5 Terminology About Various Time Spans Related to a Lifetime -- 4.6 Normalizing to One All the Finite b-Lognormals -- 4.7 Finding the b-Lognormals Given b and Two Out of the Four a, p, s, d -- 5 Golden Ratios and Golden b-Lognormals -- 5.1 Is σ Always Smaller Than 1? -- 5.2 Golden Ratios and Golden b-Lognormals -- 6 Mathematical History of Civilizations. 6.1 Civilizations Unfolding in Time as b-Lognormals -- 6.2 Eight Examples of Western Historic Civilizations as Finite b-Lognormals -- 6.3 Plotting All b-Lognormals Together and Finding the Trends -- 6.4 b-Lognormals of Alien Civilizations -- 7 Extrapolating History into the Past: Aztecs -- 7.1 Aztecs-Spaniards as an Example of Two Suddenly Clashing Civilizations with Large Technology Gap -- 7.2 'Virtual Aztecs' Method to Find the 'True Aztecs' b-Lognormal -- 8 b-Lognormal Entropy as 'Civilization Amount' -- 8.1 Introduction: Invoking Entropy and Information Theory -- 8.2 Exponential Curve in Time Determined by Two Points Only -- 8.3 Assuming that the Exponential Curve in Time Is the GBM Mean Value Curve -- 8.4 The 'No-Evolution' Stationary Stochastic Process -- 8.5 Entropy of the 'Running b-Lognormal' Peaked at the GBM Exponential Mean -- 8.6 Decreasing Entropy for an Exponentially Increasing Evolution: Progress! -- 8.7 Six Examples: Entropy Changes in Darwinian Evolution, Human History Between Ancient Greece and Now, and Aztecs and Incas Versus Spaniards -- 8.8 b-Lognormals of Alien Civilizations -- 9 Conclusion: Summary of Technical Concepts Described -- References -- Evolution and Mass Extinctions as Lognormal Stochastic Processes -- 1 Introduction: Mathematics and Science -- 2 A Summary of the 'Evo-SETI' Model of Evolution and SETI -- 3 Important Special Cases of mL(t) -- 4 Introducing b-lognormals -- 5 Peak-Locus Theorem -- 6 Entropy as the Evolution Measure -- 7 Evo-SETI -- 8 Mass Extinctions of Darwinian Evolution Described by a Decreasing GBM -- 8.1 GBMs to Understand Mass Extinctions of the Past -- 8.2 Example: The K-Pg Mass Extinction Extending Ten Centuries After Impact -- 9 Mass Extinctions Described by an Adjusted Parabola Branch -- 9.1 Adjusting the Parabola to the Mass Extinctions of the Past. 9.2 Example: The Parabola of the K-Pg Mass Extinction Extending Ten Centuries After Impact. |
| Record Nr. | UNISA-996418448803316 |
|
Maccone Claudio
|
||
| Cham, Switzerland : , : Springer, , [2020] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||