『日本語は哲学する言語である』小浜逸郎著　新たな哲学の地平を切り開く画期的な試み

The Key to Everything

by Geoffrey West

Penguin, 479 pp., $30.00

Geoffrey West spent most of his life as a research scientist and administrator at the Los Alamos National Laboratory, running programs concerned not with nuclear weapons but with peaceful physics. After retiring from Los Alamos, he became director of the nearby Santa Fe Institute, where he switched from physics to a broader interdisciplinary program known as complexity science. The Santa Fe Institute is leading the world in complexity science, with a mixed group of physicists, biologists, economists, political scientists, computer experts, and mathematicians working together. Their aim is to reach a deep understanding of the complexities of the natural environment and of human society, using the methods of science.

Scale is a progress report, summarizing the insights that West and his colleagues at Santa Fe have achieved. West does remarkably well as a writer, making a complicated world seem simple. He uses pictures and diagrams to explain the facts, with a leisurely text to put the facts into their proper setting, and no equations. There are many digressions, expressing personal opinions and telling stories that give a commonsense meaning to scientific conclusions. The text and the pictures could probably be understood and enjoyed by a bright ten-year-old or by a not-so-bright grandparent.

The title, Scale, needs some clarification. To explain what his book is about, West added the subtitle “The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies.” The title tells us that the universal laws the book lays down are scaling laws. The word “scale” is a verb meaning “vary together.” Each scaling law says that two measurable quantities vary together in a particular way.

We suppose that the variation of each quantity is expressed as a percentage rate of increase or decrease. The scaling law then says that the percentage rate for quantity A is a fixed number k times the percentage rate for quantity B. The number k is called the power of the scaling law. Since the percentage changes of A and B accumulate with compound interest, the scaling law says that A varies with the kth power of B, where now the word “power” has its usual mathematical meaning. For example, if a body is falling without air resistance, the scaling law between distance fallen and time has k=2. The distance varies with the square of time. You fall 16 feet in one second, 64 feet in two seconds, 144 feet in three seconds, and so on.

Another classic example of a scaling law is the third law of planetary motion, discovered by the astronomer Johannes Kepler in 1618. Kepler found by careful observation that the time it takes for a planet to orbit the sun scales with the three-halves power of the diameter of its orbit. That means that the square of the time is proportional to the cube of the distance. Kepler measured the periods and diameters of the orbits of the six planets known in his time, and found that they followed the scaling law precisely. Fifty-nine years later, Isaac Newton explained Kepler’s laws of planetary motion as consequences of a mathematical theory of universal gravitation. Kepler’s laws gave Newton the essential clues that led to the theoretical understanding of the physical universe.

There is a scaling law in biology as important as Kepler’s third law in astronomy. It ought to have the name of Motoo Kimura attached to it, since he was the first to understand its importance, but instead it is known as the law of genetic drift. Genetic drift is one of the two great driving forces of evolution, the other being natural selection. Darwin is rightly honored for his understanding of natural selection as a main cause of evolution, but he failed to include genetic drift in his picture because he knew nothing about genes.

Genetic drift is the change in the average composition of a population due to random mutations of individual genes. Genetic drift causes species to evolve even in the absence of selection. Genetic drift and natural selection work together to drive evolution, selection being dominant when populations are large, genetic drift being dominant when populations are small.

Genetic drift is particularly important for the formation of new species, when populations may remain small for a long time. The predominance of genetic drift for small populations is due to a simple scaling law. Genetic drift scales with the inverse square root of population. This means that genetic drift is ten times faster for a population of ten thousand than for a population of a million. The scaling is the same for any kind of random mutations. If we observe any measurable quantity such as height, running speed, age at puberty, or intelligence test score, the average drift will vary with the inverse square root of population. The square root results from the statistical averaging of random events.

West is now making a huge claim: that scaling laws similar to Kepler’s law and the genetic drift law will lead us to a theoretical understanding of biology, sociology, economics, and commerce. To justify this claim he has to state the scaling laws, display the evidence that they are true, and show how they lead to understanding. He does well with the first and second tasks, not so well with the third. The greater part of the book is occupied with stating the laws and showing the evidence. Little space is left over for explaining. The Santa Fe observers know how to play the part of a modern-day Kepler, but they do not come close to being a modern-day Newton.

The history of each branch of science can be divided into three phases. The first phase is exploration, to see what nature is doing. The second phase is precise observation and measurement, to describe nature accurately. The third phase is explanation, to build theories that enable us to understand nature. Physics reached the second phase with Kepler, the third phase with Newton. Complexity science as West defines it, including economics and sociology, remained in the first phase until about the year 2000, when the era of big data began. The era started abruptly when information became cheaper to store in electronic form than to discard. Storing information can be an automatic process, while discarding it usually requires human judgment. The cost of information storage has decreased rapidly while the cost of information discard has decreased slowly. Since 2000, the world has been inundated with big data. In every science as well as in business and government, databases have been storing immense quantities of information. Information now accumulates much faster than our ability to understand it.

Complexity science at the Santa Fe Institute is driven by big data, providing abundant information about ecological and human affairs. Humans can visualize big data most easily when it is presented in the form of scaling laws—hence the main theme of West’s book. But a collection of scaling laws is not a theory. A theory of complexity would give us answers to deeper questions. Why are there ten thousand species of birds on this planet but only five thousand species of mammals? Why are there warm-blooded animals but no warm-blooded plants? Why are human societies so often engaged in deadly quarrels? What is the destiny of our species? These are questions that big data may illuminate but cannot answer. If complexity science ever moves into the third phase, some of these old questions will be answered, and new questions will arise
.

West’s first chapter, “The Big Picture,” sets the stage for the detailed discussions that follow, with a section called “Energy, Metabolism, and Entropy,” explaining how one of the basic laws of physics, the second law of thermodynamics, makes life precarious and survival difficult. Entropy is disorder. The second law states that entropy inexorably increases in any closed system. West comments, “Like death, taxes, and the Sword of Damocles, the Second Law of Thermodynamics hangs over all of us and everything around us…. Entropy kills.” His big picture is seriously one-sided. He does not mention the other side of the picture, the paradox of order and disorder—the fact that, in the real worlds of astronomy and biology, ordered structures emerge spontaneously from disorder. The solar system, in which planets move in an orderly fashion around the sun, emerged from a disordered cloud of gas and dust. The fearful symmetry of the tiger and the beauty of the peacock emerge from a dead and disordered planet.

The astronomer Fang Lizhi published with his wife, Li Shuxian, a popular book,Creation of the Universe (1989), which includes the best explanation that I have seen of the paradox of order and disorder. The explanation lies in the peculiar behavior of gravity in the physical world. On the balance sheet of energy accounting, gravitational energy is a deficit. When you are close to a massive object, your gravitational energy is minus the amount of energy it would take to get away from the mass all the way to infinity. When you walk up a hill on the earth, your gravitational energy is becoming less negative, but never gets up to zero. Any object whose motions are dominated by gravity will have energy decreasing as temperature increases and energy increasing as temperature decreases.

As a consequence of the second law of thermodynamics, when energy flows from one such object to another, the hot object will grow hotter and the cold object will grow colder. That is why the sun grew hotter and the planets grew cooler as the solar system evolved. In every situation where gravity is dominant, the second law causes local contrasts to increase together with entropy. This is true for astronomical objects like the sun, and also for large terrestrial objects such as thunderstorms and hurricanes. The diversity of astronomical and terrestrial objects, including living creatures, tends to increase with time, in spite of the second law. The evolution of natural ecologies and of human societies is a part of this pattern. West is evidently unaware of Fang and Li’s insight.

The factual substance of West’s book is contained in eighty-one numerical diagrams, displaying a large number of scaling laws obeyed by various observed quantities. The first diagram, concerning the metabolic rate of animals, shows twenty-eight dots, each labeled with the name of a warm-blooded animal species, beginning with mouse and ending with elephant. The dots are displayed on a square graph, the horizontal position of the dot showing the average body mass of the species and the vertical position showing its average rate of consumption of energy. The diagram shows the twenty-eight points lying with amazing accuracy on a single straight line. The slope of the line on the page demonstrates the scaling law relating energy consumption to mass. Energy consumption scales with the three-quarters power of mass. The fourth power of energy consumption scales with the cube of mass. This scaling law holds accurately for mammals and birds. Cold-blooded animals such as fish and reptiles are excluded because they have no fixed body temperature. Their consumption of energy varies with their temperature, and their temperature varies with the weather.

Similar diagrams display similar scaling laws obeyed by other quantities. These laws are generally most accurate for anatomy and physiology of animals, less accurate for social institutions such as cities and companies. Figure 10 shows heart rates of mammals scaling inversely with the one-quarter power of mass. Figure 35 shows the number of patents awarded in the United States scaling with the 1.15 power of the size of the population. Figure 36 shows the number of crimes reported in cities in Japan scaling with the 1.2 power of population. Figure 75 shows that commercial companies in the United States have a constant death rate independent of age—the life expectancy of a company at any age is about ten years. The short lifetime of companies is an essential feature of capitalist economics, with good and bad consequences. The good effect is to get rid of failed enterprises, which in socialist economies are difficult to kill and continue to eat up resources. The bad effect is to remove incentives for foresight and long-range planning.

The closest that West comes to a theory of complexity is his discussion of fractals. A fractal is a structure with big and small branches that look similar at all sizes, like a tree or the blood-vessels of a mammal. When you magnify a picture of a small piece of it, the result looks like the whole thing. The mathematician Benoit Mandelbrot began the study of fractals in the 1960s and called attention to the ubiquity of fractals in nature. Since fractal structure is independent of scale, it leads naturally to scaling laws. West discusses in detail the example of the mammalian blood-vessel system, whose fractal branching evolved to optimize the distribution of nutrients through one-dimensional vessels in three-dimensional tissues. Optimal branching results in the observed scaling law, the total blood flow scaling with the three-quarters power of the mass. Most of the scaling laws in biology can be understood in a similar way as resulting from the fractal structure of tissues.

But this theoretical discussion of fractals is not a theory of complexity. Fractals have the simplest kind of complex structures, with rigid rules of construction. Accurate scaling laws result from simplicity, not from complexity. When West moves from biology to economics and sociology, the fractal structure is less clear and the scaling laws become less accurate. Cities and companies have structures that are only roughly hierarchical and not dictated by theory.

West loves big cities and uses his scaling laws to demonstrate their superiority as habitats for human societies. In a chapter entitled “Prelude to a Science of Cities,” he writes:

The great metropolises of the world facilitate human interaction, creating that indefinable buzz and soul that is the wellspring of its innovation and excitement and a major contributor to its resilience and success.

This lyrical view of modern cities is widely shared, and explains part of the enormous growth of cities. During the present century, billions of people will move from villages to cities, and the population of the planet will become increasingly urban.

West presents in his Figure 45 the scaling law relating the number of telephone conversations in cities to the number of inhabitants. The number of conversations scales with the 1.15 power of the population. The law is exactly the same in the two countries, Britain and Portugal, that maintain the most complete record of telephone calls. West considers telephone conversations to be a good indication of quality of life. More conversations mean more social interaction, more business deals, more exchange of ideas—more opportunities for individuals to push the society forward. His word “buzz” expresses his vision of the great city as the place where human progress happens. He sees the nonlinear scaling law confirming his view that the great city empowers each individual inhabitant to be a more effective innovator.

West does not mention another scaling law that works in the opposite direction. That is the law of genetic drift, ment
ioned earlier as a crucial factor in the evolution of small populations. If a small population is inbreeding, the rate of drift of the average measure of any human capability scales with the inverse square root of the population. Big fluctuations of the average happen in isolated villages far more often than in cities. On the average, people in villages are not more capable than people in cities. But if ten million people are divided into a thousand genetically isolated villages, there is a good chance that one lucky village will have a population with outstandingly high average capability, and there is a good chance that an inbreeding population with high average capability produces an occasional bunch of geniuses in a short time. The effect of genetic isolation is even stronger if the population of the village is divided by barriers of rank or caste or religion. Social snobbery can be as effective as geography in keeping people from spreading their genes widely.

A substantial fraction of the population of Europe and the Middle East in the time between 1000 BC and 1800 AD lived in genetically isolated villages, so that genetic drift may have been the most important factor making intellectual revolutions possible. Places where intellectual revolutions happened include, among many others, Jerusalem around 800 BC (the invention of monotheistic religion), Athens around 500 BC (the invention of drama and philosophy and the beginnings of science), Venice around 1300 AD (the invention of modern commerce), Florence around 1600 (the invention of modern science), and Manchester around 1750 (the invention of modern industry).

These places were all villages, with populations of a few tens of thousands, divided into tribes and social classes with even smaller populations. In each case, a small starburst of geniuses emerged from a small inbred population within a few centuries, and changed our ways of thinking irreversibly. These eruptions have many historical causes. Cultural and political accidents may provide unusual opportunities for young geniuses to exploit. But the appearance of a starburst must be to some extent a consequence of genetic drift. The examples that I mentioned all belong to Western cultures. No doubt similar starbursts of genius occurred in other cultures, but I am ignorant of the details of their history.

West’s neglect of villages as agents of change raises an important question. How likely is it that significant numbers of humans will choose to remain in genetically isolated communities in centuries to come? We cannot confidently answer this question. The answer depends on unpredictable patterns of economic development, on international politics, and on even more unpredictable human desires. But we can foresee two possible technological developments that would result in permanent genetic isolation of human communities.

One possibility is that groups of parents will be able to give birth to genetically modified children, hoping to give them advantages in the game of life. The children might be healthier or longer-lived or more intellectually gifted than other children, and they might no longer interbreed with natural-born children. The other possibility is that groups of people will emigrate from planet Earth and build societies far away in the depths of space. West considers neither of these possibilities. His view of the future sees humans remaining forever a single species confined to a single planet. If the future resembles the past, humans will be diversifying into many species and spreading out over the universe, as our hominin ancestors diversified and spread over this planet.

So long as we remain on planet Earth, there are strong social, political, and ethical reasons to forbid genetic modification of children by parents. If we are scattered in isolated communities far away, those reasons would no longer be relevant to our experience. A group of humans colonizing a cold and airless world would probably not hesitate to use genetic engineering to adapt their children to the environment. Konstantin Tsiolkovsky, the nineteenth-century prophet of space colonization, already imagined the colonists endowed with green leaves to replace lungs and with moving-picture skin patterns to replace voices. How long will it take for the technologies of space transportation and genetic engineering to bring Tsiolkovsky’s dreams to reality?

Advances in technology are unpredictable, but two hundred years is a reasonable guess for cheap and widely available space travel and genetically modified babies—perhaps one hundred years to develop the science and another hundred years to develop the applications. It is likely that in two hundred years public highways will be carrying passengers and freight around the solar system, with a large enough volume of traffic to make them affordable to ordinary people. At the same time, farmers will be breeding microbes, as well as plants and animals designed to live together in robust artificial ecologies. The option to include humans in the ecology will always be available.

Cheap space travel requires two kinds of public highways, one for escape from high-gravity planets such as Earth, the other for long-distance travel between low-gravity destinations. The high-gravity highway could be a powerful laser beam pointing upward from the ground into space, with spacecraft taking energy from the beam to fly up and down. If the volume of traffic is large enough to keep the beam active, the energy cost per vehicle would be comparable with the energy cost of intercontinental travel by jet planes today. The low-gravity highway could be a system of refueling stations for spacecraft driven by ion-jet engines using sunlight as an energy source. Both the high-gravity and the low-gravity systems are likely to grow within two hundred years if we do not invent something better in the meantime.

Cheap deep-space survival requires genetic engineering of warm-blooded plants. These could grow on the surface of any cold object in the solar system, using energy from the distant sun, water, and other essential nutrients from the frozen soil. A plant would be a living greenhouse, with cold mirrors outside concentrating sunlight onto transparent windows, and roots and shoots inside the greenhouse kept warm by the sunlight. Inside the greenhouse would be a cavity filled with breathable air at a comfortable temperature, serving as a habitat for a diverse ecology of microbes, plants, animals, and humans. The warm-blooded plants could grow the mirrors and the greenhouses and provide nourishment for the whole community. Small objects in the solar system, such as asteroids and comets and satellites, have enough surface area to provide homes for a much larger population than Earth. If ever the solar system becomes overcrowded, life can spread out further, over the galaxy and the universe.

A chapter in Scale with the title “The Vision of a Grand Unified Theory of Sustainability” gives us West’s view of the future. He sees the rapid growth of big cities and big data causing human activities to scale with time at super-exponential speeds. The acceleration cannot be sustained, since it would lead to a mathematical singularity, with observed quantities becoming infinite within a finite time. The idea of the singularity, an imminent world crisis driven by the explosive growth of artificial intelligence, was promoted by Ray Kurzweil in his book The Singularity Is Near(2005). It is generally regarded as belonging to science fiction rather than to science, but West takes it seriously as a consequence of known scaling laws.

The approaching singularity would force a radical change in the organization of human society, to make our existence sustainable. But the scaling laws would again result in another singularity, forcing another radical change. West foresees a future of repeated approaches to one
singularity after another, until the Grand Unified Theory of Sustainability teaches us how to build a truly sustainable society. He leaves the description of the permanent sustainable society to our imagination. The only feature he insists on is the Grand Unified Theory, which will set the rules of human behavior for an endless future. The theory will govern our lives, so that we will be compelled to live within our means.

The last time humans invented a grand unified theory to make our existence sustainable was when Karl Marx came up with dialectical materialism. The theory had great success in changing human behavior over large areas of our planet. But the changes did not prove to be sustainable, and the theory did not remain unified. It seems likely that West’s theory will run into similar difficulties.

The choice of an imagined future is always a matter of taste. West chooses sustainability as the goal and the Grand Unified Theory as the means to achieve it. My taste is the opposite. I see human freedom as the goal and the creativity of small human societies as the means to achieve it. Freedom is the divine spark that causes human children to rebel against grand unified theories imposed by their parents.

1. 1

   See , The Most Wanted Man in China: My Journey from Scientist to Enemy of the State, translated by Perry Link (Holt, 2016), The New York Review, May 26, 2016. 

2. 2

   See my “,” The New York Review, October 13, 2016. 

 

とても興味深く読みました：

ゼロ除算の発見と重要性を指摘した：日本、再生核研究所

 

 

 

ゼロ除算は定義が問題です：

再生核研究所声明　１４８（2014.2.12）　100/0=0,  0/0=0　－　割り算の考えを自然に拡張すると　―　神の意志

 

再生核研究所声明１７１（2014.7.30）掛け算の意味と割り算の意味　―　ゼロ除算100/0=0は自明である？

 

 

Title page of Leonhard Euler, Vollständige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity.

私は数学を信じない。　アルバート・アインシュタイン / I don’t believe in mathematics. Albert Einstein→ゼロ除算ができなかったからではないでしょうか。

1423793753.460.341866474681。

 

Einstein’s Only Mistake: Division by Zero

 

#divide by zero

TOP DEFINITION

  

A super-smart math teacher that teaches at HTHS and can divide by zero.

Hey look, that genius’s IQ is over 9000!

    

by  October 21, 2009

 

 

Dividing by zero is the biggest  known to mankind. It is a proven fact that a succesful division by zero will constitute in the implosion of the universe.

You are dividing by zero there, Johnny. Captain Kirk is not impressed.

Divide by zero?!?!! OMG!!! Epic failzorz

    

 

3

  

 by  is undefined.

Divide by zero is undefined.

    

by  October 28, 2006

 

1) The number one ingredient for a catastrophic event in which the universe enfolds and collapses on itself and life as we know it ceases to exist.

2) A mathematical equation such as a/0 whereas a is some number and 0 is the divisor. Look it up on  or something. Pretty confusing shit.

3) A reason for an error in programming

Hey, I divided by zero! …Oh shi-

a/0

Run-time error: ’11’: Division by zero

    

by  September 08, 2006

 

When even math shows you that not everything can be figured out with math. When you divide by zero, math kicks you in the shins and says “yeah, there’s kind of an answer, but it ain’t just some number.”

It’s when mathematicians become philosophers.

:
Let’s say you have ZERO apples, and THREE people. How many apples does each person get? ZERO, cause there were no apples to begin with

 because of dividing by zero:
Let’s say there are THREE apples, and ZERO people. How many apples does each person get? Friggin… How the  should I know! How can you figure out how many apples each person gets if there’s no people to get them?!? You’d think it’d be infinity, but not really. It could almost be any number, cause you could be like “each person gets 400 apples” which would be true, because all the people did get 400 apples, because there were no people. So all the people also got 42 apples, and a million and 7 apples. But it’s still wrong.

        

by  February 15, 2010

 

 

Leonardo Da Vinci, el gran artista del Renacimiento

Uno de los más grandes pintores de toda la historia es recordado a 566 años de su fallecimiento 

A 566 años de su nacimiento, Leonardo da Vinci, autor de “La Gioconda” (1503-1519), uno de los retratos más emblemáticos de la historia de la pintura, es considerado uno de los más grandes genios de la humanidad.

Leonardo di ser Piero da Vinci, hijo de un rico notario florentino y una campesina, nació el 15 de abril de 1452 en la villa toscana de Vinci, Italia.

Desde sus primeros años, el pequeño Leonardo mostró un fuerte interés por la pintura y pasaba gran parte de su tiempo dibujando animales mitológicos de su propia invención, inspirados en una profunda observación del entorno natural en el que creció.

El portal “biografiasyvidas.com”, señala que al cumplir 14 años y gracias al apoyo de su padre, ingresó como aprendiz en el taller del artista Andrea del Verrocchio, quien le enseñó pintura, escultura, técnicas y mecánicas de la creación artística.

En este periodo, el joven Leonardo frecuentó al también artista Antonio Pollaiuollo, quien le permitió hacer sus primeros estudios de anatomía.

Se sabe que su primer trabajo fue la construcción del orbe de cobre, diseñado entre 1466 y 1471 y proyectado por Brunelleschi para coronar la iglesia de Santa Maria dei Fiori; al que le siguió el cuadro “Bautismo de Cristo” (1472-1475), obra con la que superó a su maestro y que permeó de dinamismo.

A este periodo creativo pertenecen sus obras “San Jerónimo” (1480) y el gran panel “La adoración de los Magos” (1481), que fueron calificados como innovadores y dinámicos, características que otorgó la maestría en los contrastes de rasgos, en la composición geométrica de la escena y en el extraordinario manejo de la técnica del claroscuro del artista.

A los 30 años, en 1482, el artista decidió dejar Florencia para viajar a Milán, donde se presentó ante el poderoso duque Ludovico Sforza, en cuya corte permaneció 17 años, no sólo como pintor sino como inventor hidráulico, mecánico y arquitecto.

Siguiendo las bases matemáticas fijadas por León Bautista Alberti y Piero della Francesca, Leonardo comenzó sus apuntes para la formulación de una ciencia de la pintura, al tiempo que se ejercitó en la ejecución y fabricación de laúdes.

Estimulado por la dramática peste que asoló Milán, el artista proyectó espaciosas villas, hizo planos para canalizaciones de ríos e ingeniosos sistemas de defensa ante la artillería enemiga.

Dentro del ámbito del arte, fue elegido para la realización de una monumental estatua ecuestre en honor de Francesco, el fundador de la dinastía Sforza, en la que trabajó durante 16 años, pero que no logró concretar.

Para el año 1490, el artista crea “Hombre de Vitrulio”, una de las imágenes más conocidas del arte renacentista, que se trata de la solución simbólica de Leonardo a un antiguo problema matemático que tuvo cierta importancia también en la alquimia, conocido como “la cuadratura del círculo”.

Según el sitio especializado en ciencia y tecnología “pijamasurf.com”, en el dibujo, el círculo es el espíritu y el cuadrado la materia, la base en una estructura arquitectónica y aquel que conecta a la materia y al espíritu es el hombre, quien tiene la sustancia que combina ambos: el alma.

En 1494, su amistad con el matemático y fraile franciscano Luca Pacioli le permitió ilustrar su libro “De divina proportione” (1497-1509), trabajo que le valió ser reconocido como el creador de la moderna ilustración científica y emprender diversos proyectos de pintura, arquitectura, anatomía, geografía, botánica, hidráulica y aerodinámica.

Entre 1495 y 1497, el polímita florentino experimenta con la témpera y el óleo sobre una preparación de yeso, para crear “La última cena”, una de las pinturas más famosas del mundo, que representa la última cena entre Jesús y sus discípulos.

A finales de 1499, la llegada de los franceses a Milán obligaron a da Vinci a abandonar la ciudad para llegar a Venecia, donde fue contratado como ingeniero militar, puesto desde el cual proyectó una cantidad de artefactos cuya realización concreta se hizo hasta los siglos XIX y XX.

Luego de 20 años de ausencia, en 1500 Leonardo da Vinci regresó a Florencia, ya siendo considerado uno de los artistas más prominentes de Italia.

De acuerdo con la página “lecturalia.com”, en 1503 realizó la “Gioconda”, su obra conocida en todo el mundo, y a partir de 1506 su vida transcurrió entre Florencia y Milán, realizando varios trabajos como arquitecto para nobles locales.

A partir de 1513 radicó en Roma, donde preparó algunos de sus trabajos más interesantes como inventor, pero tras encontrar siempre obstáculos por parte de la Iglesia Católica, decidió abandonar esta labor y trasladarse a Francia, donde proyectó palacios y ciudades.

Da Vinci dejó un gran número de bocetos y dibujos de todas sus creaciones, siempre consideradas un compendio propio de notas, sin intención de divulgación o enseñanza.

El sitio “theartwolf.com” afirma que “no hay artista más legendario que Leonardo da Vinci. En toda la historia del Arte, ningún otro nombre ha generado más debates, más discusiones y más horas de estudio”.

El 2 de mayo de 1519, el pintor, artista, arquitecto, escultor, filósofo, científico, escritor, paleontólogo, botánico y genio del Renacimiento, Leonardo da Vinci, dueño de una genialidad sin igual, murió en Clos Lucé, Francia, a los 67 años de edad. 

OA

 

ゼロ除算の発見と重要性を指摘した：日本、再生核研究所

 

再生核研究所声明 424(2018.3.29): 　レオナルド・ダ・ヴィンチとゼロ除算

次のダ・ヴィンチの言葉を発見して、驚かされた：

ダ・ヴィンチの名言 格言｜無こそ最も素晴らしい存在

我々の周りにある偉大なことの中でも、無の存在が最も素晴らしい。その基本は時間的には過去と未来の間にあり、現在の何ものをも所有しないというところにある。この無は、全体に等しい部分、部分に等しい全体を持つ。分割できないものと割り切ることができるし、割っても掛けても、足しても引いても、同じ量になるのだ。

レオナルド・ダ・ヴィンチ。ルネッサンス期を代表する芸術家、画家、彫刻家、建築技師、設計士、兵器開発者、科学者、哲学者、解剖学者、動物学者、ファッションデザイナーその他広い分野で活躍し「万能の人（uomo universale：ウォモ・ウニヴェルサーレ）」と称えられる人物

そもそも西欧諸国が、アリストテレス以来、無や真空、ゼロを嫌い、ゼロの西欧諸国への導入は相当に遅れ、西欧へのアラビヤ数字の導入は　レオナルド・フィボナッチ（1179年頃～1250年頃）によるとされているから、その遅れの大きさに驚かされる：

フィボナッチはイタリアのピサの数学者です。正確には「レオナルド・フィリオ・ボナッチ」といいますが、これがなまって「フィボナッチ」と呼ばれるようになったとされています。
彼は少年時代に父親について現在のアルジェリアに渡り、そこでアラビア数字を学びました。当時の神聖ローマ皇帝・フリードリヒ2世は科学と数学を重んじていて、フィボナッチは宮殿に呼ばれ皇帝にも謁見しました。後にはピサ共和国から表彰もされました。

ローマ数字では「I, II, III, X, XV」のように文字を並べて記すため大き�
��数を扱うのには不便でした。対してアラビア数字はローマ数字に比べてとても分かりやすく、効率的で便利だったのです。そこでフィボナッチはアラビア数字を「算術の書」という書物にまとめ、母国に紹介しました。アラビア数字では0から9までの数字と位取り記数法が使われていますが、計算に使うにはとても便利だったために、ヨーロッパで広く受け入れられることになりました。（

historicalmathematicians.blogspot.com/2012/03/blog-post.html　　02/03/2012 -）

ゼロや無に対する恐怖心、嫌疑観は現在でも欧米諸国の自然な心情と考えられる。ところが上記ダ・ヴィンチの言葉は　如何であろう。無について好ましいものとして真正面から捉えていることが分かる。ゼロ除算の研究をここ４年間して来て、驚嘆すべきこととして驚かされた。ゼロの意味、ゼロ除算の心を知っていたかのような言明である。

まず、上記で、無を、時間的に未来と過去の間に存在すると言っているので、無とはゼロのことであると解釈できる。ゼロとの捉え方は四則演算を考えているので、その解釈の適切性を述べている。足しても引いても変わらない。これはゼロの本質ではないか。さらに、凄いこと、掛けても割っても、ゼロと言っていると解釈でき、それはゼロ除算の最近の発見を意味している:  0/1 =1/0=0。－　ゼロ除算を感覚的に捉えていたと解釈できる。ところが更に、凄いことを述べている。

この無は、全体に等しい部分、部分に等しい全体を持つ。これはゼロ除算の著書DIVISION BY ZERO CALCULUS（原案）に真正面から書いている我々の得た、達したゼロに対する認識そのものである：

{\bf Fruitful world}\index{fruitful world}

\medskip

 

For example, in very and very general partial differential equations, if the coefficients or terms are zero, we have some simple differential equations and the extreme case is all the terms are zero; that is, we have trivial equations $0=0$; then its solution is zero. When we see the converse, we see that the zero world is a fruitful one and it means some vanishing world. Recall \index{Yamane phenomena}Yamane phenomena, the vanishing result is very simple zero, however, it is the result from some fruitful world. Sometimes, zero means void or nothing world, however, it will show some changes as in the Yamane phenomena.

\medskip

 

{\bf From $0$ to $0$; $0$ means all and all are $0$}

\medskip

 

As we see from our life figure, a story starts from the zero and ends to the zero. This will mean that $0$ means all and all are $0$, in a sense. The zero is a mother of all.

\medskip

 

その意味は深い。我々はゼロの意味をいろいろと捉え考え、ゼロとはさらに　基準を表すとか、不可能性を示すとか、無限遠点の反映であるとか、ゼロの2重性とかを述べている。ゼロと無限の関係をも述べている。ダ・ヴィンチの鋭い世界観に対する境地に驚嘆している。

以　上

*057 Pinelas,S./Caraballo,T./Kloeden,P./Graef,J.(eds.): Differential and Difference Equations with Applications: ICDDEA, Amadora, 2017. (Springer Proceedings in Mathematics and Statistics, Vol. 230) May 2018 587 pp. 

2017年11月15日(水)
テーマ：

The null set is conceptually similar to the role of the number “zero” as it is used in quantum field theory. In quantum field theory, one can take the empty set, the vacuum, and generate all possible physical configurations of the Universe being modelled by acting on it with creation operators, and one can similarly change from one thing to another by applying mixtures of creation and anihillation operators to suitably filled or empty states. The anihillation operator applied to the vacuum, however, yields zero.

Zero in this case is the null set – it stands, quite literally, for no physical state in the Universe. The important point is that it is not possible to act on zero with a creation operator to create something; creation operators only act on the vacuum which is empty but not zero. Physicists are consequently fairly comfortable with the existence of operations that result in “nothing” and don’t even require that those operations be contradictions, only operationally non-invertible.

It is also far from unknown in mathematics. When considering the set of all real numbers as quantities and the operations of ordinary arithmetic, the “empty set” is algebraically the number zero (absence of any quantity, positive or negative). However, when one performs a division operation algebraically, one has to be careful to exclude division by zero from the set of permitted operations! The result of division by zero isn’t zero, it is “not a number” or “undefined” and is not in the Universe of real numbers.

Just as one can easily “prove” that 1 = 2 if one does algebra on this set of numbers as if one can divide by zero legitimately3.34, so in logic one gets into trouble if one assumes that the set of all things that are in no set including the empty set is a set within the algebra, if one tries to form the set of all sets that do not include themselves, if one asserts a Universal Set of Men exists containing a set of men wherein a male barber shaves all men that do not shave themselves3.35.

It is not – it is the null set, not the empty set, as there can be no male barbers in a non-empty set of men (containing at least one barber) that shave all men in that set that do not shave themselves at a deeper level than a mere empty list. It is not an empty set that could be filled by some algebraic operation performed on Real Male Barbers Presumed to Need Shaving in trial Universes of Unshaven Males as you can very easily see by considering any particular barber, perhaps one named “Socrates”, in any particular Universe of Men to see if any of the sets of that Universe fit this predicate criterion with Socrates as the barber. Take the empty set (no men at all). Well then there are no barbers, including Socrates, so this cannot be the set we are trying to specify as it clearly must contain at least one barber and we’ve agreed to call its relevant barber Socrates. (and if it contains more than one, the rest of them are out of work at the moment).

Suppose a trial set contains Socrates alone. In the classical rendition we ask, does he shave himself? If we answer “no”, then he is a member of this class of men who do not shave themselves and therefore must shave himself. Oops. Well, fine, he must shave himself. However, if he does shave himself, according to the rules he can only shave men who don’t shave themselves and so he doesn’t shave himself. Oops again. Paradox. When we try to apply the rule to a potential Socrates to generate the set, we get into trouble, as we cannot decide whether or not Socrates should shave himself.

Note that there is no problem at all in the existential set theory being proposed. In that set theory either Socrates must shave himself as All Men Must Be Shaven and he’s the only man around. Or perhaps he has a beard, and all men do not in fact need shaving. Either way the set with just Socrates does not contain a barber that shaves all men because Socrates either shaves himself or he doesn’t, so we shrug and continue searching for a set that satisfies our description pulled from an actual Universe of males including barbers. We immediately discover that adding more men doesn’t matter. As long as those men, barbers or not, either shave themselves or Socrates shaves them they are consistent with our set description (although in ma
ny possible sets we find that hey, other barbers exist and shave other men who do not shave themselves), but in no case can Socrates (as our proposed single barber that shaves all men that do not shave themselves) be such a barber because he either shaves himself (violating the rule) or he doesn’t (violating the rule). Instead of concluding that there is a paradox, we observe that the criterion simply doesn’t describe any subset of any possible Universal Set of Men with no barbers, including the empty set with no men at all, or any subset that contains at least Socrates for any possible permutation of shaving patterns including ones that leave at least some men unshaven altogether.

 

 I understand your note as if you are saying the limit is infinity but nothing is equal to infinity, but you concluded corretly infinity is undefined. Your example of getting the denominator smaller and smalser the result of the division is a very large number that approches infinity. This is the intuitive mathematical argument that plunged philosophy into mathematics. at that level abstraction mathematics, as well as phyisics become the realm of philosophi. The notion of infinity is more a philosopy question than it is mathamatical. The reason we cannot devide by zero is simply axiomatic as Plato pointed out. The underlying reason for the axiom is because sero is nothing and deviding something by nothing is undefined. That axiom agrees with the notion of limit infinity, i.e. undefined. There are more phiplosphy books and thoughts about infinity in philosophy books than than there are discussions on infinity in math books.

 

 

ゼロ除算の歴史：ゼロ除算はゼロで割ることを考えるであるが、アリストテレス以来問題とされ、ゼロの記録がインドで初めて６２８年になされているが、既にそのとき、正解1/0が期待されていたと言う。しかし、理論づけられず、その後１３００年を超えて、不可能である、あるいは無限、無限大、無限遠点とされてきたものである。

An Early Reference to Division by Zero C. B. Boyer

 

OUR HUMANITY AND DIVISION BY ZERO

Lea esta bitácora en español
There is a mathematical concept that says that division by zero has no meaning, or is an undefined expression, because it is impossible to have a real number that could be multiplied by zero in order to obtain another number different from zero.
While this mathematical concept has been held as true for centuries, when it comes to the human level the present situation in global societies has, for a very long time, been contradicting it. It is true that we don’t all live in a mathematical world or with mathematical concepts in our heads all the time. However, we cannot deny that societies around the globe are trying to disprove this simple mathematical concept: that division by zero is an impossible equation to solve.
Yes! We are all being divided by zero tolerance, zero acceptance, zero love, zero compassion, zero willingness to learn more about the other and to find intelligent and fulfilling ways to adapt to new ideas, concepts, ways of doing things, people and cultures. We are allowing these ‘zero denominators’ to run our equations, our lives, our souls.
Each and every single day we get more divided and distanced from other people who are different from us. We let misinformation and biased concepts divide us, and we buy into these aberrant concepts in such a way, that we get swept into this division by zero without checking our consciences first.
I believe, however, that if we change the zeros in any of the “divisions by zero” that are running our lives, we will actually be able to solve the non-mathematical concept of this equation: the human concept.
>I believe deep down that we all have a heart, a conscience, a brain to think with, and, above all, an immense desire to learn and evolve. And thanks to all these positive things that we do have within, I also believe that we can use them to learn how to solve our “division by zero” mathematical impossibility at the human level. I am convinced that the key is open communication and an open heart. Nothing more, nothing less.
Are we scared of, or do we feel baffled by the way another person from another culture or country looks in comparison to us? Are we bothered by how people from other cultures dress, eat, talk, walk, worship, think, etc.? Is this fear or bafflement so big that we much rather reject people and all the richness they bring within?
How about if instead of rejecting or retreating from that person—division of our humanity by zero tolerance or zero acceptance—we decided to give them and us a chance?
How about changing that zero tolerance into zero intolerance? Why not dare ask questions about the other person’s culture and way of life? Let us have the courage to let our guard down for a moment and open up enough for this person to ask us questions about our culture and way of life. How about if we learned to accept that while a person from another culture is living and breathing in our own culture, it is totally impossible for him/her to completely abandon his/her cultural values in order to become what we want her to become?
Let’s be totally honest with ourselves at least: Would any of us really renounce who we are and where we come from just to become what somebody else asks us to become?
If we are not willing to lose our identity, why should we ask somebody else to lose theirs?
I believe with all my heart that if we practiced positive feelings—zero intolerance, zero non-acceptance, zero indifference, zero cruelty—every day, the premise that states that division by zero is impossible would continue being true, not only in mathematics, but also at the human level. We would not be divided anymore; we would simply be building a better world for all of us.
Hoping to have touched your soul in a meaningful way,
Adriana Adarve, Asheville, NC
…/our-humanity-and-division…/

 

5000年？？？？？

2017年09月01日(金)NEW ! 
テーマ：数学
Former algebraic approach was formally perfect, but it merely postulated existence of sets and morphisms [18] without showing methods to construct them. The primary concern of modern algebras is not how an operation can be performed, but whether it maps into or onto and the like abstract issues [19–23]. As important as this may be for proofs, the nature does not really care about all that. The PM’s concerns were not constructive, even though theoretically significant. We need thus an approach that is more relevant to operations performed in nature, which never complained about morphisms or the allegedly impossible division by zero, as far as I can tell. Abstract sets and morphisms should be de-emphasized as hardly operational. My decision to come up with a definite way to implement the feared division by zero was not really arbitrary, however. It has removed a hidden paradox from number theory and an obvious absurd from algebraic group theory. It was necessary step for full deployment of constructive, synthetic mathematics (SM) [2,3]. Problems hidden in PM implicitly affect all who use mathematics, even though we may not always be aware of their adverse impact on our thinking. Just take a look at the paradox that emerges from the usual prescription for multiplication of zeros that remained uncontested for some 5000 years 0
0 ¼ 0 ) 0
1=1 ¼ 0 ) 0
1 ¼ 0
1) 1ð? ¼ ?Þ1 ð0aÞ This ‘‘fact’’ was covered up by the infamous prohibition on division by zero [2]. How ingenious. If one is prohibited from dividing by zero one could not obtain this paradox. Yet the prohibition did not really make anything right. It silenced objections to irresponsible reasonings and prevented corrections to the PM’s flamboyant axiomatizations. The prohibition on treating infinity as invertible counterpart to zero did not do any good either. We use infinity in calculus
for symbolic calculations of limits [24], for zero is the infinity’s twin [25], and also in projective geometry as well as in geometric mapping of complex numbers. Therein a sphere is cast onto the plane that is tangent to it and its free (opposite) pole in a point at infinity [26–28]. Yet infinity as an inverse to the natural zero removes the whole absurd (0a), for we obtain [2] 0 ¼ 1=1 ) 0
0 ¼ 1=12 > 0 0 ð0bÞ Stereographic projection of complex numbers tacitly contradicted the PM’s prescribed way to multiply zeros, yet it was never openly challenged. The old formula for multiplication of zeros (0a) is valid only as a practical approximation, but it is group-theoretically inadmissible in no-nonsense reasonings. The tiny distinction in formula (0b) makes profound theoretical difference for geometries and consequently also for physical applications. T

とても興味深く読みました：

 

 

10,000 Year Clock
by Renny Pritikin
Conversation with Paolo Salvagione, lead engineer on the 10,000-year clock project, via e-mail in February 2010.

For an introduction to what we’re talking about here’s a short excerpt from a piece by Michael Chabon, published in 2006 in Details: ….Have you heard of this thing? It is going to be a kind of gigantic mechanical computer, slow, simple and ingenious, marking the hour, the day, the year, the century, the millennium, and the precession of the equinoxes, with a huge orrery to keep track of the immense ticking of the six naked-eye planets on their great orbital mainspring. The Clock of the Long Now will stand sixty feet tall, cost tens of millions of dollars, and when completed its designers and supporters plan to hide it in a cave in the Great Basin National Park in Nevada, a day’s hard walking from anywhere. Oh, and it’s going to run for ten thousand years. But even if the Clock of the Long Now fails to last ten thousand years, even if it breaks down after half or a quarter or a tenth that span, this mad contraption will already have long since fulfilled its purpose. Indeed the Clock may have accomplished its greatest task before it is ever finished, perhaps without ever being built at all. The point of the Clock of the Long Now is not to measure out the passage, into their unknown future, of the race of creatures that built it. The point of the Clock is to revive and restore the whole idea of the Future, to get us thinking about the Future again, to the degree if not in quite the way same way that we used to do, and to reintroduce the notion that we don’t just bequeath the future—though we do, whether we think about it or not. We also, in the very broadest sense of the first person plural pronoun, inherit it.

Renny Pritikin: When we were talking the other day I said that this sounds like a cross between Borges and the vast underground special effects from Forbidden Planet. I imagine you hear lots of comparisons like that…

Paolo Salvagione: (laughs) I can’t say I’ve heard that comparison. A childhood friend once referred to the project as a cross between Tinguely and Fabergé. When talking about the clock, with people, there’s that divide-by-zero moment (in the early days of computers to divide by zero was a sure way to crash the computer) and I can understand why. Where does one place, in one’s memory, such a thing, such a concept? After the pause, one could liken it to a reboot, the questions just start streaming out.

RP: OK so I think the word for that is nonplussed. Which the thesaurus matches with flummoxed, bewildered, at a loss. So the question is why even (I assume) fairly sophisticated people like your friends react like that. Is it the physical scale of the plan, or the notion of thinking 10,000 years into the future—more than the length of human history?

PS: I’d say it’s all three and more. I continue to be amazed by the specificity of the questions asked. Anthropologists ask a completely different set of questions than say, a mechanical engineer or a hedge fund manager. Our disciplines tie us to our perspectives. More than once, a seemingly innocent question has made an impact on the design of the clock. It’s not that we didn’t know the answer, sometimes we did, it’s that we hadn’t thought about it from the perspective of the person asking the question. Back to your question. I think when sophisticated people, like you, thread this concept through their own personal narrative it tickles them. Keeping in mind some people hate to be tickled.

RP: Can you give an example of a question that redirected the plan? That’s really so interesting, that all you brainiacs slaving away on this project and some amateur blithely pinpoints a problem or inconsistency or insight that spins it off in a different direction. It’s like the butterfly effect.

PS: Recently a climatologist pointed out that our equation of time cam, (photo by Rolfe Horn) (a cam is a type of gear: link) a device that tracks the difference between solar noon and mundane noon as well as the precession of the equinoxes, did not account for the redistribution of water away from the earth’s poles. The equation-of-time cam is arguably one of the most aesthetically pleasing parts of the clock. It also happens to be one that is fairly easy to explain. It visually demonstrates two extremes. If you slice it, like a loaf of bread, into 10,000 slices each slice would represent a year. The outside edge of the slice, let’s call it the crust, represents any point in that year, 365 points, 365 days. You could, given the right amount of magnification, divide it into hours, minutes, even seconds. Stepping back and looking at the unsliced cam the bottom is the year 2000 and the top is the year 12000. The twist that you see is the precession of the equinoxes. Now here’s the fun part, there’s a slight taper to the twist, that’s the slowing of the earth on its axis. As the ice at the poles melts we have a redistribution of water, we’re all becoming part of the “slow earth” movement.

RP: Are you familiar with Charles Ray’s early work in which you saw a plate on a table, or an object on the wall, and they looked stable, but were actually spinning incredibly slowly, or incredibly fast, and you couldn’t tell in either case? Or, more to the point, Tim Hawkinson’s early works in which he had rows of clockwork gears that turned very very fast, and then down the line, slower and slower, until at the end it approached the slowness that you’re dealing with?

PS: The spinning pieces by Ray touches on something we’re trying to avoid. We want you to know just how fast or just how slow the various parts are moving. The beauty of the Ray piece is that you can’t tell, fast, slow, stationary, they all look the same. I’m not familiar with the Hawkinson clockwork piece. I’ve see the clock pieces where he hides the mechanism and uses unlikely objects as the hands, such as the brass clasp on the back of a manila envelope or the tab of a coke can.

RP: Spin Sink (1 Rev./100 Years) (1995), in contrast, is a 24-foot-long row of interlocking gears, the smallest of which is driven by a whirring toy motor that in turn drives each consecutively larger and more slowly turning gear up to the largest of all, which rotates approximately once every one hundred years.

PS: I don’t know how I missed it, it’s gorgeous. Linking the speed that we can barely see with one that we rarely have the patience to wait for.

RP: : So you say you’ve opted for the clock’s time scale to be transparent. How will the clock communicate how fast it’s going?

PS: By placing the clock in a mountain we have a reference to long time. The stratigraphy provides us with the slowest metric. The clock is a middle point between millennia and seconds. Looking back 10,000 years we find the beginnings of civilization. Looking at an earthenware vessel from that era we imagine its use, the contents, the craftsman. The images painted or inscribed on the outside provide some insight into the lives and
the languages of the distant past. Often these interpretations are flawed, biased or over-reaching. What I’m most enchanted by is that we continue to construct possible pasts around these objects, that our curiosity is overwhelming. We line up to see the treasures of Tut, or the remains of frozen ancestors. With the clock we are asking you to create possible futures, long futures, and with them the narratives that made them happen.

 

2018.3.18．午前中　最後の講演：　日本数学会　東大駒場、函数方程式論分科会　講演書画カメラ用　原稿 
The Japanese Mathematical Society, Annual Meeting at the University of Tokyo. 2018.3.18. 
 より

*057 Pinelas,S./Caraballo,T./Kloeden,P./Graef,J.(eds.): Differential and Difference Equations with Applications: ICDDEA, Amadora, 2017. (Springer Proceedings in Mathematics and Statistics, Vol. 230) May 2018 587 pp. 

 

 

 

Castle s03e04 Episode ScriptPunkedThere are two kinds of folks who sit around thinking about how to kill people: psychopaths and mystery writers.I'm the kind that pays better.Who am I? I'm Rick Castle.Castle.Castle.I really am ruggedly handsome, aren't I? Every writer needs inspiration and I found mine.I'm Detective Kate Beckett.Beckett.Beckett? Could you get some backup, please? And thanks to my friendship with the mayor, I get to be on her case.Do I look like a killer to you? Yes, you kill my patience.And together we catch killers.I hate this case.I know.Isn't it great? I have delicately placed one graham cracker, exactly six marshmallows atop a perfectly melted chocolate bar.In an omelet, darling? Really? Not an omelet.- A s'more-let.- Uh-huh.- Care for one? - No, thank you! What about you, sweetheart? Are you ready for your taste buds to be launched into breakfast nirvana? Sure, thanks.Is it okay if my friend Ashley comes over tonight? Yes, of course.Now eat.- Are there marshmallows in this? - Yes.- And chocolate? - Yes.That's the point.It's a s'more-let.Uh.I gotta go.Love you! Love you! Bye, honey.Mmm! This is almost as good as my chocolate mousse chimichanga.Ah-ha! I knew you'd reconsider! It's kind of like David Hasselhoff.At first you're repulsed, but then strangely, you're drawn in.No, still repulsed.Bye! What's up with Alexis? She seems a little out of it.Isn't it obvious? - What? - Oh, she's in love.Alexis? Oh, come on, darling.In case you haven't noticed, she's not a little girl anymore.Thank you, Mother.I think if Alexis were in love, she would've told me.Uh-uh.The fact that she hasn't told you, is how we know it's real.- Mother? - Okay.And the fact that she mentioned it to me last night.Who is he? Where did she meet him? I don't know! She wouldn't say.No! Diva's honor, she didn't tell me anything.She didn't even tell me his name.I can't believe she told you and not me.I'm supposed to be her go-to guy.Oh, darling! Of course, you are! It's just, you know, it's first love.It's magical, ethereal.It defies logic.- Richard, your phone? - Mmm.Uh! Beckett.Maybe it's a nice murder, darling.Brighten your day.Good boy.Castle.When Alexis took her first steps, I was there to catch her when she fell.The first time she rode her bike without training wheels, I was the maniac chasing her down the street, screaming for her to watch out for the old lady with the walker.Even her first word Let me guess? "Daddy"? - No, it was "denouement." - Oh.I stressed story structure from an early age.Anyway I'm afraid that this is the beginning of the end of our special thing.You know, I wouldn't worry, Castle.I mean, I've seen the way that she looks at you.Your real problem is that girls who adore their daddies, usually end up marrying guys just like them.- They do? - Dr.Parish! Good morning.Got an ID? Not yet.How come you guys never bring me coffee? I'm here before you, doing all the work.You can have the rest of mine.Actually, I don't drink coffee, but would it kill you to bring me a bear claw? Speaking of killing Single GSW to the chest.Large caliber.Probably a.45.Lividity suggests time of death around midnight.Hey.I have those boxers.Thomas Nash.Very pricey British brand.Amazingly soft.They're silk.Just saying, he was probably very comfortable when he was shot and killed.So what was this guy doing out here practically naked at midnight? Don't bother with any of your perverted theories, Castle.I found fibers in the bullet hole.Which means he was wearing clothes when he was shot.That doesn't make any sense.The killer shot him, and then hung around to take his bloody clothes off him? Well, maybe the killer was worried that there was forensic evidence on the clothes that would connect them.Yo, Uni found this wallet out in a garbage can near Fifth.Photo on the license matches Captain Underpants here.Sorry, my nephew loves those books.Daniel Goldstein, 25.Lives in SoHo.Yeah, he's also got a work ID for Berman Rose down on Wall Street.So he lived downtown and he worked downtown.What was he doing way up here? - Let's take this down to the lab.- Right.So, I wear boxers.What do you wear? Thongs? Cheekies? I told you mine.Bloomers? Granny panties? Commando? His clothes were taken? Why would anyone take his clothes? We don't know, Miss Goldstein.Can you tell us what your brother might have been doing in the park? That late? I have no idea.Well, the place where Daniel was found is known for drug activity.Was he using? No, he barely even drank.Did he have any enemies or conflicts that you know of? No, no.Look, none of this makes any sense.It's just, it's not like him.Our parents both died in a car accident when he was 12, and since then, he's always been so cautious.What about dating? Was there anyone special in his life? He wished, but no.He barely had a social life, or social skills.I mean, he was such a sweetheart, but a dork, you know? And he was always at work anyway.At Berman Rose.What did he do for them? He created financial products.He was this incredible math genius.Got his PhD from MIT.I thought for sure he'd be a professor or something, but these hedge funds, they hire guys like him.They pay them obscene amounts of money.Twenty-five years old, he bought my apartment for me.Excuse me.What's up? Lab got a fingerprint off our vic's wallet.Anyone good? Uh.Awaiting court dates on three aggravated assault cases in the past month, Mr.D'André.You inflicted dozens of broken bones, gouged out one of your victim's eyes, bit off part of an ear of another one.Sounds like committing murder was inevitable.I'm just curious, why did you take his clothes? Wasn't me.Well, then why were your fingerprints on a dead man's wallet? Did he just happen to drop it and you politely picked it up for him? And why did my detectives find this unregistered.45 in your apartment, which just happens to match the size of the bullet hole in my victim? Hey.If you're so innocent, Mr.D'André, why did you resist arrest and try to put one of my detectives through a wall? You know, the right turtleneck, and no one's even gonna notice, bro.Maybe a scarf.Ow! Why don't you just confess to the truth? It's gonna come out sooner or later.He was already dead.With a wallet lying conveniently next to him? Look, if you're not going to admit to it, you might at least want to try coming up with a story that's a little more convincing.It's what happened! Like you weren't scared.I want this guy to fry, Beckett.- Ow.- Oh, he will.As soon as Lanie confirms that that bullet is a.45.It's not a.45.Are you sure? I'm positive.- Thirty-eight? - Nope.It's not a.44, or.357, or.22, or.9 mm, or any other kind of bullet I've ever seen.So, it's a new kind of bullet? Oh, no, not new at all.Check it out.It's round.See that white coating? Yeah.What is it? Oxidation? Lead oxide, to be exact.Rust? Yep.Based on the amount of it, I'd say that bullet is 200 years old.Two-hundred-year-old bullet can only mean one thing.Time-traveling killer! Ergo, the killer could have entered present time through a time ripple, killed Goldstein, and then gone back through the time ripple.Which means we just have to find the time ripple.Could you please stop saying "time ripple"? Yeah.Sounds kind of dirty, doesn't it? But if the ripple closed, time machine! We need a time machine.Well, in this century, we still haven't ruled out our big buddy, Mr.D'André.Yeah, he just doesn't seem like the time travel type to me.Can't be a time-traveling killer.Bullet had 200 years of rust on it.If the killer had been a time traveler, bullet would have been brand new.Unless time travel causes rust.On your brain.Have you followed up with the victim's sister regarding the antique bullet? Yep.She has no clue about antique bullets or guns, but there's somebody who does.Abe Sandrich.Antique weapons expert you requested.Reminds me I'm starving.
I like.45's.Catch the right angle, this sucker could take your head clean off, but it's not the gun you're looking for.Why's that? Barrel would've had to be modified.This one's factory-fresh.Do you think D'André the Giant was telling the truth when he said he found the wallet in the grass? Well, the killer did take Goldstein's clothes, so it's possible that the wallet might've fallen out when he left the crime scene.What kind of a pistol would've fired that bullet? We usually just call 'em lead balls.For obvious reasons.I'd say a whole lot of 18th century flintlocks.Too many brands to even speculate.You'll need to find the actual pistol to match it to this lead ball.And how many people would own that kind of antique pistol? Hard to say.They're considered collectibles, so they don't have to be registered.Making it pretty smart to kill someone with one.Oh, yeah.Guns may be old, but they got plenty of killing left in 'em.So, is D'André our guy? I'm afraid not.What? Why did he go all Hulk Hogan on me? Well, why did the scorpion sting the frog? It's his nature.Yeah, well, D'André'll be seeing nature from behind bars from now on for assaulting an officer I'll see he gets the max, Detective.Thank you, Captain.You know, you can take a couple days if you like? Catch some movies.- Read Naked Heat.- No.No need, sir.Still no luck with the clothes.Unis looked in every garbage can within a five block radius of the park.What is so special about these clothes that our killer would take them? Maybe the killer came through the time ripple naked and needed the clothes.Like in The Terminator.Sadly, I don't have a better theory at this point.So, the question is, what did a Wall Street number-cruncher like Goldstein get himself into? Castle and I'll go to his firm.You guys see if you can track down any antique gun enthusiasts on social media sites or local clubs.Maybe someone from Goldstein's life'll pop.You got it.You know, I just don't get how someone could shoot Goldstein, steal his clothes, and then not hang onto his wallet.Just doesn't make any sense.No.Maybe giant moths killed him and ate his clothes.Could be.Hey! Castle, if this case is boring for you, you don't have to stay.No, I'm just checking my e-mail and my texts to see if Alexis called.I can't believe she told my mother she's in love and is holding out on me.- Oh.- I'm gonna call her.No, no.You have to let her tell you in her own time when she's ready.I'm the cool dad.Why can't she be ready? Wait.Listen to me.My dad tried to do the same thing when I was her age and I ended up dating a grunge rocker who smelled like wet flannel and clove cigarettes, for seven months.You do not mess with a teenage girl and her hormones.You're right.I won't call her.Did you say something about a giant moth? No.In his underwear? Danny's been working for me for two years, but, I just don't know what he'd have been up to in the park.He wasn't exactly the outdoors type.What about antique guns, Mr.Murphy? Do you know anything about them? Antiques? No.No, he wasn't into guns at all.Well, I understand that he worked long hours.Do you know when he left last night? Yeah, right around 9:30.- Hey! Let me help you with that.- Thanks.This is Julia Foster, Danny's assistant.This is Detective Beckett and Richard Castle.- Hi.- Hi.Were you here last night when Goldstein left? Of course.Any idea where he was heading? No.He just said good night.And what about during the day? Was there anything out of the ordinary? Any strange phone calls? No, just the usual unhappy investor.Although Although what? The Lower Tide Fund.What's that? It was one of the financial products Daniel created for us.A synthetic CDO-cubed.English? A really big bet that prices would return to historical norms.So what happened? It tanked.Hundreds of millions of dollars were lost overnight.When was this? Three months ago.There must've been a lot of angry investors.We fielded scores of less than complimentary messages from clients.More like apoplectic.And a lot of them blamed Danny.All right, well, I'll need a copy of all of these messages and a list of anyone who lost their money in the fund.Any luck connecting antique gun owners to investors in Goldstein's failed fund, Detectives? Nah.So far I've seen a lot of cool, old guns on these social media sites for antique gun lovers, but none of the owners pop in Goldstein's life.Irwin "Quick Draw" Finkelstein.Proud owner of a Remington Outlaw, made in 1875.Now that's a great-looking gun.Check it out, Esposito.Yeah, that's nice.See, back then, they were into the artistry of it all.Yeah, they're like little sculptures that can kill.Well, this list of Lower Tide Fund investors? They all lost more than a million bucks a piece.A million dollars? If I had that kind of scratch, I'd put it in something safe.Like my mattress.Check it out.Ivan "Yosemite Sam" Podofski.Wait a minute.Ivan Podofski? Yeah.What you got? Boom.Looks like we have a winner.You're right.He does kind of look like Yosemite Sam.On a bad hair day.Yeah, well, in addition to having an antique gun collection, Mr.Podofski here lost more than four million bucks in our vic's Lower Tide Fund.He also left this message for Goldstein the day the fund flat-lined.They had a way of handling folks like you in the old country, Goldstein.It's called a firing squad! You think he offered him a blindfold and a cigarette? They had a way of handling folks like you in the old country, Goldstein.It's called a firing squad! I think some context is in order.I had only just lost four million dollars.Yes, and in that context, you threatened to kill Mr.Goldstein and then he was killed.Where were you last night between 11:00 and 1:00? Asleep in my bed.- And can anyone vouch for that? - Me.Myself and I got your back, too? Okay.Look, I know how this appears, but I think there is an explanation.Fire away.Several months ago, I had a consultation at Berman Rose.When I mentioned my guns, Goldstein asked if I knew how he could get a hold of a Sherlock Holmes gun.So you're pointing the finger at Sir Arthur Conan Doyle? I'm saying that Goldstein clearly had an interest in antique guns.Maybe that interest got him killed.If you're so confident that Goldstein got mixed up with someone else, I'm sure you won't mind submitting your collection for testing with Ballistics.These are antiques, Detective.Would you prefer being arrested for murder? Ballistics is taking possession of Podofski's guns.They should have preliminary results by tomorrow.They never prefer to be arrested for murder.All right, keep at it.Yeah.Yo, just got a hit from Goldstein's car from Traffic Enforcement.Parking ticket from last night.- No way.- What? - This has got to be a joke.- What are you talking about, Castle? Goldstein drives a DeLorean.The car used as a time machine in Back to the Future.There's no way that's a coincidence.The ticket was written at two in the morning.That's post-mortem.Car should still be there.Yeah.East 82nd between Lex and 3rd.That's a few blocks from the park.Yeah, but if you're gonna park illegally, why not park closer? Because he was going somewhere on that block.Three more parking tickets in the last several months, all on 82nd between Lex and 3rd.So he was going somewhere regularly on that block.Maybe a girlfriend? Unless you think that's where that time ripple is.Could be.Look into it.Pick that car up.Gotcha.Gotta be kidding me.Ha! Well, it's definitely Goldstein's car.Or time machine.Yep.If I'm not mistaken, that's a flux capacitor in there.And that is the reactor core.Maybe Castle was right.Goldstein came back to the future and he got whacked, huh? - Why'd he keep coming here? - I don't know.Maybe there's something in the car that'll help.Hope so.A lot of doors to knock on.Patty, I got a vic's car that needs towing.It's at 238 East 82nd.It's an '81 to '82 DeLorean.New York plates, J-L-D Hey, Javi! Let me call you back.Excuse us, sir.I'm Detective Ryan, this is Detective Esposito.Do you mind if we ask you a few questions? Ah! Top of the morning to you, constables! Lord Henry, at your service.Uh, thanks.Do you mind telling us where you got those clothes? Not at all, dear boy.I picked them up at the haberdashery across the park.Well, gentlemen, if that is all, I shall bid you good day.Just a second, pal.You know, we think those clothes might've been involved I said, good day! - Sir, we need you to come down - Good day! Whoa, whoa! No! Hey! Ah! You all right, bro? I'm fine.Unhand me, you rogue! All right, thank you, Ryan.How's Esposito? At home, resting.So, our Lord Henry's story checks out.Ryan found a matching ascot in a garbage can where Henry said that he found the clothes.Our guy might be unstable, but he's not our killer.So why was Goldstein wearing this costume? Well, it's Victorian, antique.Kind of fits with the whole time-traveler theory, don't you think? I don't know what to think, but the plot thickens.Forensics back on the clothes? Between the garbage can and our homeless guy, there was quite a list of gross-out substances, of which I will spare you the details, but I did find something interesting on the right-hand glove and the right sleeve of the shirt.Potassium nitrate and sulfur.Gunshot residue? So Goldstein did not go quietly into the night.He had a gun.And he fired back.I got something here.Beckett! Another antique.Looks exactly like the one that killed Goldstein.Yes, it does.Let's say that our killer Let's say that our killer was standing over here.Goldstein was killed all the way over there.Nice flat area between them.What are you getting at, Castle? Some kind of game? Not a game.Goldstein was wearing formal, turn-of-the-century clothes.He shot an antique bullet identical to the one he was killed with.Probably fired from an identical gun.Four, five, six, seven.Lanie said he was killed at about midnight? St.James Church is right over there.Thanks.On Madison.I bet they could hear the bells chiming all the way from over here.Ha! They stood at about 40 paces from one another.Wasn't a game.This was an old-fashion duel.- Who dares besmirch - God! Don't shoot! my honor It's okay, Ashley.He's not going to shoot you.What the heck, Dad? I might be asking you the same Ashley? This is Ashley? Ash, this is my dad, Rick.And I have no idea why he's waving a gun.So nice to meet you, Mr.Castle.You too, Ashley.And I have a perfectly good reason why I'm waving a gun.Excuse us.Explain yourself.I got this gun for research for a case.Which you might know if you had checked in with me today.What's that supposed to mean? Let's just say one of us has nothing to hide.Perhaps you'd like to explain yourself? What? That I was kissing a boy? Is that a problem? You tell me.Dad, the only reason I invited Ashley over tonight was so you could meet him.Yes, well me meeting Ashley has smeared the lip gloss all over your face.I really should be going.You can stay, Ashley.Oh, the gun.My bad.Please, Ashley, stay.- You can check out the gun.- No, thanks.Call me later? Yeah.If it's okay with your gun? Dad.Yeah, it's okay with me.Thank you.And I just want you to know how much I respect Alexis.I mean, you don't have to worry about issues of respect.She's probably the most respectable person I know.And I respect you, too.It's good to know that.Thank you.I like him.He's respectful.Got it.Thanks.- Hey.- Hey.So, lvan Podofski's antique gun collection all cleared ballistics.Well, at least some guy in Ballistics had fun firing them off.I also checked with Goldstein's sister and coworkers.None of them know anything about duels or Victorian clothes or what Goldstein was doing on East 82nd.Sounds like he had a secret life.That somehow led to a duel.Maybe he figured someone besmirched his honor.Maybe it was about a girl.As a matter of fact, Alexis, her new boyfriend, who has a girl's name, by the way, he thought I was going to shoot him last night.Hey.- Hey.How's Esposito? He's sleeping in.Mostly because he can't move.Did you figure out what Goldstein was doing on East 82nd? No, but get this.I'm going through Goldstein's car, and I find a pile of receipts he must've been planning to submit for reimbursement.One of them is from three weeks ago at a café.On it, he wrote, "Coffee with Troy Kenworth." And that name kind of rings a bell.One of the angry Lower Tide Fund investors? No.But his father, Charles Kenworth, was.Guy loses two million bucks.And then he loses his house, his marriage.And then two months ago, he killed himself.- Did Troy have any priors? - Yeah.More like afters.After his father committed suicide, he was charged with assault in four separate bar fights.Revenge! Oldest motive for murder in the book.Maybe Troy thought someone besmirched his father's honor.And then he forced Goldstein to settle the score.Yeah, I was the one who found his body.The report says that he used a shotgun.Hey.Why aren't you in there? Beckett's doing a mothering thing.Wanted to limit the testosterone in the room.I can't imagine walking in on that.Yeah.Pretty messy.I try not to think about it.I understand.But since then, Mr.Kenworth, you have charges pending in four assault cases.I started drinking too much, lashed out.But those were just random people at bars.I mean, they weren't even responsible for your father's suicide.But Goldstein He put your father in the fund that lost him all of his money.I could understand blaming him.I did.But then I talked to him, and he said that he warned Pop to diversify.And the fact is, Dad and Mom had been having problems for years.When we lost the house and I had to drop out of school, it was the last straw.And Mom left him.That's what pushed him over the edge.And ever since his death, Mom had been struggling to make payments on our apartment.Is that why you went to go and see Goldstein three weeks ago? Look, I wanted to find out if any money was left in the account.And what did Goldstein tell you? The truth.All the money's gone.That must have made you pretty angry.Okay, I know what you're getting at.But that meeting is what turned me around.I haven't had a drink since.Mom and I have been able to stay in our place.I might even go back to school next semester.All because Danny is a stand-up guy and he gave me a job.That's where I was the night he got killed.At Berman Rose? No.What kind of a job did Danny give you? I can't say.Look, I had to sign a confidentiality agreement, okay? I can be fired.Or you could be arrested.Is this job on 82nd between Lex and 3rd? What was the exact number of pounds that Mr.Fogg bet that he could travel around the world in 80 days? - Twenty thousand.- Correct, sir.Name the volcano that led to the center of the earth.Oh! I want to say NYPD.Open the damn door.Hello! - Where are we? Victorian London.When are we? What is this place? Gaslamp.A privat
e steampunk society.Straight ahead, is our club president, Owen Peterson.He's on the penny-farthing.All right then.It's that time machine from Time And Away.I love that movie.Owen.Give us a poem.Steampunk? It's a subculture that embraces the simplicity and romance of the past, and at the same time couples it with the hope and promise and sheer super-coolness of futuristic design.You're cloned, you say? There are more of you? Well, the more the merrier, to ewes all I'll be true! - Excuse me, Mr.Peterson.I'm - Can I try that? I don't know what to tell you, Detective.We all heard about Danny yesterday.It's hard to believe.We saw him here the night before.Well, the way you and your friends were yucking it up makes me feel like you weren't so upset.We're just romantics, Detective.Look at the world, don't like what we see.So we recreate it here.An oasis where human potential and ingenuity is limitless.Where there's poetry and wonder and meaning, even in death.What time did he leave that night? Around 11:30.- Did he tell you what he was doing? - No.He went to the park for a duel.What do you mean, a duel? The kind where people shoot at each other.They were using antique guns.Do you know anything about that? Dueling pistols.With lead balls with white coating.This has been fired recently.They're just for show.Adam, stop! Stop! Out of the way.Get out of the way! I think he's going for the time machine! It's just a bunch of interviews, I don't know why you didn't take the whole day off.Because I'm fine! Pardon me.Stop him! Hey, Esposito! How's your neck? Yeah, I shot him.He just kind of crumpled over backwards.But I thought he was kidding.I jogged over, expecting him to jump up any second.But he was just lying there, so still.And then I saw the blood.And I hear Julia.She's on her knees screaming, "No, please, God, no!" I freaked out and we took his clothes and I just ran.Julia? You mean Goldstein's assistant? He was in love with her.Had they been seeing each other a long time? No.No, Dan just kissed her once a couple weeks ago out at a bar.But she wasn't interested in him.So you were involved with her? Not really involved.But, Dan caught us fooling around in my office late one night last week.And you couldn't think of a better way of settling this other than a duel? We just thought it'd be funny.And Danny swore that we couldn't get hurt.Shooting at each other? He ran all these complex equations.He said, said that at 40 paces, there was no chance that we could actually hit each other.Something about 18th Century guns having no rifling in the barrel.So if you couldn't kill each other, what was the point of the duel? To impress Julia.She would never get serious with geeks like us.But we figured that maybe if she saw us duel over her, then Maybe that one of us could Julia confirmed that she was the only other person present at the duel.No one else knew.All right, let her go.How do you point the gun at someone and shoot and not expect to kill them? Well, they were blinded by the romance of it all.And Goldstein did the math.Well, between this and the Lower Tide Fund, maybe he's not such a genius.Maybe he's just unlucky.Well, then I've got a problem because I have to make a recommendation to the DA between murder and manslaughter.The difference being life in prison or just a couple of years.I mean, are antique guns really so inaccurate? Only one way to find out.That's your target! That's my target! Shoot your target! Manslaughter, it is.Yeah.Hey, Dad.Hey! There's my girl.Come here.Come here.Sorry, hang on.There.There you go.Hey, about last night - It was unexpected.- Yeah.I'm sorry.I'm sorry, too.I should have told you Ashley was a boy.Oh, why spoil the surprise? So, I have a question for you.But it's a little embarrassing.Ooh! - I love when you embarrass yourself.- Dad.Well, hey, listen.You can ask me whatever you want.And I promise I'll do my best to make it as un-embarrassing as possible.How do you know when you're in love? I know it's an emotion, a feeling, and you can't exactly define.Like, technically, how you know when you're feeling it, but since I've never felt it before, how do I know what I'm feeling is even it at all? Except, of course, for the fact that I'm feeling all these things I've never felt before.Like in my stomach and my throat and even kind of in my ears.I mean, which just has to mean that it's love, right? Considering I only feel them when I'm with Ashley or thinking about him? I mean, that's gotta be love, right? 'Cause I'm feeling all these things I've read about in poems and heard about in songs but never completely understood.But now I do! I understand, and I'm listening to all this music and reading all this poetry in a completely new and glorious light, which I just think has to mean that it's love.What do you think? I can't stop thinking about him, Daddy.I don't even want to because he's just the greatest, sweetest, most adorable guy and his nose crinkles when he laughs and I'm just so happy.Thanks, Dad.I love you.I feel so much better now.I'm glad we had that talk.Beckett.How do you know when you're in love? All the songs make sense.Adam Murphy didn't kill Goldstein.But he confessed.And I believe that he believes he did it.But he didn't.Do tell.It bothered me that we couldn't hit the target at the shooting range.And so I ran ballistics on the dueling pistols.The bullet that hit Daniel Goldstein didn't match either one of them.Adam couldn't have killed him.You're talking full-on, grassy knoll, conspiracy theory? Not theory.Fact.There was a third shooter and that's our killer.Hey, Beckett! Did you find Adam Murphy's bullet? Lead ball.Yup! He didn't kill Goldstein, but he did kill Squirrelstein.What are the odds, huh? Oh, no! They took his clothes, too! Could you? Aw! - Yeah, I know.I'm sorry.Okay, so we know that Goldstein was standing right over here.Facing Adam, who's right over there.Right.And if our killer wanted to shoot him without either of them seeing him, he would be standing right over There, by that clump of trees.Detective, I've got clothing fibers.This thread look familiar? Oh, I'd recognize that burgundy velvet anywhere.Kind of says "steampunk," doesn't it? Matter of fact, I think I know the murder weapon.Volcano in Journey to the Center of the Earth.Sneffels! Castle.Couldn't stay away, huh? Can I get you guys something? Sure, Troy.We're looking for a shooter.Actually, I think we already found one.Nice uniform, by the way.We found your father's shotgun.We know that you modified it in order to shoot antique lead ball bullets.What are you talking about? Adam Murphy already confessed, right? Turns out Adam Murphy couldn't have done it.It's a sciencey, ballistics thing.It was pretty clever firing your father's shotgun at the exact moment that Adam and Goldstein fired their guns.Making Adam believe that he was the one that killed Goldstein, right as the church bells chimed midnight.Isn't that right? Seeing him in here every night in that ridiculous outfit, just throwing around all that money.Why should he get to live like that when my dad's dead? Knowing that our shooter was a staff member at the club led us straight back to Troy.He overheard Goldstein and Murphy planning the duel and took his opportunity.And then Troy's alibi fell apart as soon as we started interviewing other staff members who couldn't remember seeing him there half an hour before or after the duel.Dueling over a girl.Avenging the death of a loved one.Cuts to the heart of romance.And the tragedy.Speaking of tragedy, did you hear about Detective Esposito? No, what about him? Oh! He Oh! God, no! Dude.What happened? - Esposito! - No.I don't want to hear it.No.I'm okay.Hey! No, I really am fine, bro.- We got this stuff from storage.- You should have seen your faces! Captain, you really sold that."Speaking of tragedy, did you hear about Detective Esposito?" - Hey.- Sir.- That was good.- I'm not really that fine.- Oh, yeah, let me just Sorry.- Neck brace, please.Neck brace.- Just lock it down, lock it.- Yeah, yeah.Kate! Josh.What are you doing here? Oh, I got your text.You mean the text where I said I was gonna pick you up? Yeah, I was nearby.Well, Josh, this Captain Montgomery, Richard Castle, Detectives Esposito and Ryan.- Hey, boys.Boys? - Catch any bad guys today? - Every day.- You all set? - Yeah.Let me just get my stuff.Okay.So, you and Beckett? Mmm.What about us? You tell me.You're the writer! Yeah! Yeah.And you are? Kate hasn't told you about me, has she? What's to tell? Hey, you ready to go? Yeah.I'll see you around.Bye, guys.Later.Just you? Yes.Thanks for that talk last night.I feel so much better.Hey, you can always talk to me.Or at me.Yeah.Being in love is exhausting.Yeah, you got that right.You okay, Dad? You seem distracted.What are you talking about? You have my undivided attention.Good.Because I want to go on a date tonight.How's that sound? Of course.Great! Have a good time! I meant with you, Dad.You'll always be my go-to guy.Did Gram put you up to this? I have no idea what you're talking about.Pity date.I'll take it.You're a terrible liar.Read more: https://www.springfieldspringfield.co.uk/view_episode_scripts.php?tv-show=castle&episode=s03e04