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Geography 530 Urban and Economic Geography Dr. Philip Coppack JOR 609 How many? Please take a piece of paper and write down your guess. Don’t be shy. You’re advancing science TIME SPACE SCALES The Space Economy Questions we will explore: • • • • • • • How are economic activities organized in space? What patterns exist in space and time? What processes giving rise to those patterns? Why are things where they are? Who decides about supplying and demanding? How do the various spatial scales interact? How are ‘sectoral’ divisions structured? STRUCTURE OF THE SPACE ECONOMY The Space Economy Methods stuff we will look at: • Economic classification systems • National and international data sources • Common economic analysis methods: • Index numbers • Ratios and quotients • Current and constant dollar conversions • Gompertz curves • Game theory and decision trees STRUCTURE OF THE SPACE ECONOMY Course Material WEBSITE ADDRESS www.geography.ryerson.ca/coppack/geo530 ***THIS IS NOT A BLACKBOARD SITE*** COURSE MECHANICS www.geography.ryerson.ca/coppack/geo530 COURSE EVALUATION: Paper proposal Paper final draft In-class MC (5x10%) 20% (due dates see schedule) 30% (due dates see schedule below) 50% (due dates see schedule below) There is no final exam for this course. NOTE: Quizzes will be run in the first 50 minutes of the class hour and will be comprised of 40 multiple choice/short answer questions. If you miss a quiz, you will lose the grade for it – no exceptions, otherwise you will be swamped. COURSE MECHANICS www.geography.ryerson.ca/coppack/geo530 Course Project RESEARCH PROPOSAL (20%) You will write a 3 page proposal exploring a research topic in Economic Geography. RESEARCH PAPER (30%) You will use that proposal to write a 5 page research paper, using the corrected proposal as the first 3 pages. Both parts follow a very explicit rubric that is detailed in the document on the website. Examples of good and poor efforts from the past will be provided. COURSE MECHANICS www.geography.ryerson.ca/coppack/geo530 COURSE OUTLINE AND COURSE PROJECT (Please Read It All) COURSE MECHANICS www.geography.ryerson.ca/coppack/geo530 Introduction Stuff Date Lectures 1 Introduction. Jan 14th Course mechanics. The Space Economy – definition and structure Modeling: what it is and how it is used. Landscapes: homogeneity, isotropy and reality(ies). COURSE MECHANICS Assignments Distribute proposal-paper assignment with course outline. Economic Process Topics 2 Engines of Growth and Change: Demographics and Urbanisation. Jan 21st Population growth, fertility, survival, dependency. Population structure: transition and pyramids. Renaissance, mercantilism, and revolution. Cities as points of socio-economic transformation. Urban growth versus urbanization. Demographic transition, urbanization, and economic transformation. 3 Economic Change and Economic Base Theory Jan 28th Macroeconomic Eras – two flavours: revolutions and capital. Globalisation since 1945. Colonialisation and decolonialisation. The fundamental structure of geographic economies. Basic and non-basic economic activities. The B/NB ratio and the multiplier concept. 4 Cycles, Agglomeration and Scale. Feb 11th Booms, busts and the financial/banking system. Economic cycles: Kondratieff, Keynes, inventory and product. Internal scale economies. External scale economies. Spatial demand and supply. Spatial demand curves and surfaces. Urban agglomeration. COURSE MECHANICS Structure of the firm. Quiz #1 Lectures 1,2 www.geography.ryerson.ca/coppack/geo530 Data and Methods of Analysis 5 Economic Classifications, Data, Methods, Decision Making, Feb 11th Game Theory. Economic indicators, indices, data, and sources. Current and constant dollars. Location quotients. Shift-share analysis. Gini coefficients, Lorenz and other curves. Productivity, capacity utilisation, and input-output. Relative and absolute change, rates and levels of change. Decision Making and Perception. Decision Theory and Probability. Decision Trees, and Game Theory. Feb 16TH STUDY WEEK COURSE MECHANICS Quiz #2 Lectures 3,4 Sectors of the Economy 6 Feb 25th Agricultural, Resource Location, Urban Economics and Land Use. Von Thunen and the concept of bid rent. Models of urban structure - an overview. Alonso and urban economic rent theory. Peak value intersections. The economics of urban slums. The economics of urban sprawl. Zimmerman's Axiom: resources aren't, they become – economics of resource commodities. 7 Manufacturing: from weight watching to getting satisfaction. Mar 4th Weber and the weight loss hypothesis: maximization approaches. Losch and the pursuit of profit as a locational determinant: optimization approaches. Smith and the margins of profitability: behavioral approaches. Simon and satisficing: decision making approaches. Model of change. Industrialisation, Deindustrialisation, Industrial restructuring. Concepts and definitions. Measuring degree and type of change. 8 Retail and Services Location. Mar 11th Christaller and central place theory: range, threshold, K patterns. Distance decay and the economics of urban demand and supply. Breakpoint and gravity models. Office location. COURSE MECHANICS The locational determinants of public sector services. Proposal due Quiz #3 Lectures 5,6 Return proposal www.geography.ryerson.ca/coppack/geo530 Movement Topics 9 Interaction and Time Space Quiz #4 Mar 18th Arrow of time. Lectures 7,8 Time-space cubes, prisms and paths. Discretionary and obligatory events. Time-space convergence. Proxemics and social distance. Interaction Interaction models: gravity & distance decay. 10 Transportation and Diffusion. Final Paper Mar 25th Networks. Due Network analysis tools. Transportation Economics. Modes of transportation. The cost of traffic jams. Diffusion: what it is. Modelling diffusion – Hagerstrand. NOTE: FRIDAY MARCH 27th IS THE LAST DATE TO DROP COURSES WITHOUT ACADEMIC PENALTY. IT IS BETTER TO DROP A COURSE THAN TO FAIL A COURSE. REMEMBER: ‘F’ IS COURSE MECHANICS FOREVER. www.geography.ryerson.ca/coppack/geo530 Growth and Development Topics 11 Economic Growth & Regional Development: April 1st Defining growth & development. Heartland hinterland. Development models. Circular and cumulative causation. The Canadian experience. 12 Course wrap-up April 8th Quiz #5 Lectures 9,10 The on-line Faculty Course Survey will be available between March 20th and March 30th 2015. COURSE MECHANICS The Space Economy A Definition "... a system by which people seek to satisfy their wants from the means of production at their disposal, in the face of spatial disparity between these wants and the resources necessary for their satisfaction.“ Lloyd & Dicken, Location In Space, 1977, p65. STRUCTURE OF THE SPACE ECONOMY The Space Economy A Definition Implicit in this definition are concepts such as: • Demand • Supply • The Production System Macro & Micro Economic Constructs: • marginality • elasticity • opportunity costs • scale economies • comparative cost advantage • The Spatial System • The Geographic System • Decision Making • Distance DecaySTRUCTURE OF THE SPACE ECONOMY The Space Economy The Production Network INPUTS of materials and nonmaterials (raw materials, labour, land, capital, enterprise) After Peter Dicken, Global Shift. TRANSFORMATION of inputs into semi finished or finished products or services DISTRIBUTION of those goods and services to where they are demanded (i.e. movement channels) STRUCTURE OF THE SPACE ECONOMY CONSUMPTION of goods and services by interim and end consumers (i.e. markets) The Space Economy The Technology & Spatial Contexts Technology/research and development (product design, process technology) INPUTS TRANSFORMATION DISTRIBUTION CONSUMPTION Logistic services (movement of materials, products, people, information across space; technology dependent) After Peter Dicken, Global Shift. STRUCTURE OF THE SPACE ECONOMY The Space Economy The Control & Authority Contexts FINANCIAL SYSTEM Technology/research and development (product design, process technology) INPUTS TRANSFORMATION DISTRIBUTION CONSUMPTION Logistic services (movement of materials, products, people, information across space; technology dependence) REGULATION, COORDINATION, CONTROL SYSTEM After Peter Dicken, Global Shift. STRUCTURE OF THE SPACE ECONOMY The Space Economy The Geographic Context SOCIO-CULTURAL SYSTEM FINANCIAL SYSTEM Technology/research and development (product design, process technology) INPUTS TRANSFORMATION DISTRIBUTION CONSUMPTION Logistic services (movement of materials, products, people, information and technology) REGULATION, COORDINATION, CONTROL SYSTEM ENVIRONMENTAL SYSTEM STRUCTURE OF THE SPACE ECONOMY After Peter Dicken, Global Shift. The Space Economy The Nature of Service Inputs to the Production Process UPSTREAM INPUTS Service inputs prior to the production process; e.g. feasibility studies, finance/venture capital, product conception & design, R&D, market research. After Peter Dicken, Global Shift. ONSTREAM PRODUCTION INPUTS Services specific to the goods production process itself; e.g. quality control, equipment, leasing, logistics of supply, maintenance, repair. I T D C ONSTREAM PARALLEL INPUTS Service inputs necessary for the operation of any type of firm; e.g. accounting, legal, HR functions, transportation, communications, IT, insurance, finance, real estate, security, custodial, STRUCTURE OF THE SPACEcatering. ECONOMY DOWNSTREAM INPUTS Service inputs post production necessary to final sales; e.g. advertising, distribution, transportation, repairs, maintenance, client training. Linkages in the Space Economy Types: Vertical: The input and output ends of a production chain. Horizontal: Between different products – e.g. pharma companies start making cleaning products. Lateral: Between similar products – e.g. motorcycle companies start making cars. Control: Owned Affiliated Independent Foreign Direct Investment 2013 = US$1.3 trillion … or at least that’s one version of the story. STRUCTURE OF THE SPACE ECONOMY Linear System + Finite World = Problems Resource Depletion Environmental Degradation Income Inequality Solutions? Exploit Others Others “Develop” Apply Technology Fixes But the linear system in a finite world still exists. STRUCTURE OF THE SPACE ECONOMY Supposedly represents you Mediates STRUCTURE OF THE SPACE ECONOMY Represents stockholders Check it out: http://storyofstuff.org/movies/story-of-stuff/ STRUCTURE OF THE SPACE ECONOMY Globalisation and the Territorial Economic System A. Economic System Economic Sectors: Primary (Resources) Secondary (Manufacturing) Tertiary (Services) P S T Firms: Large firms (TNCs) Medium Firms (regional) Small firms (local) THEMES - GLOBAL SYSTEM Globalisation and the Territorial Economic System B. Territorial System Regions Nations Sector based trading blocs Regional based trading blocs Regionally isolated nations Regionally integrated nations Globally isolated nations THEMES - GLOBAL SYSTEM Globalisation and the Territorial Economic System C. The complexity of the global economic and territorial system. Some national economies are only partly integrated, or depend solely on one economic sector P S T Flows of goods and especially capital are less restricted in the economic system than they are across the territorial system Flashpoints exist at the intersections of economy with territory. THEMES - GLOBAL SYSTEM The Production Process and the Physical Environment INPUTS FROM ENVIRONMENT Local and global environment as supplier of resources and energy. EXTRACTION PROCESSING FABRICATION CONSUMPTION Recycled products Non-productive output Local and global environment Local and global environment EXTERNALITIES as pollution dump. as energy dump. OUTPUTS TO ENVIRONMENT Source: After Dicken 2003, p26 STRUCTURE OF THE SPACE ECONOMY Globalisation: Changes in the Social, Economic and Cultural Systems Changes to transportation and communications technology as goods and people need to be moved and information and money exchanged. PROCESSING EXTRACTION Changes to space as subsistence activities become cash based traded activities. FABRICATION Changes to space as industrial development and demographic change drives urbanization. Changes to economic system as capitalism begins, a wage economy develops, and employment changes. CONSUMPTION Changes to cultural attitudes as consumption drives behaviour through demonstration effect and product homogenization. $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ TIME SPACE SCALES $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Some numbers to set the stage Global GDP in current dollars, 2012 = $72.9 trillion. Global market capitalisation 2012 = $53.2 trillion. U.S. GDP in current dollars, 2012 = $16.2 trillion (22%). U.S. market capitalisation 2012 = $18.7 trillion (35%). Canada GDP in current dollars, 2012 = $1.8 trillion (2.4%). Canada market capitalisation 2012 = $2.0 trillion (3.7%). Ontario GDP in current dollars, 2013 = $695 billion (0.95%). Cost of 2008 financial crisis by 2012 = $22 trillion (US alone). 33% of global capitalization value lost = $17.6 trillion. Bill Gates current net worth = $82 billion Sources: http://www.gao.gov/assets/660/651322.pdf. http://data.worldbank.org/data-catalog/world-development-indicators. We’ll have lots of fun looking at the ins and outs of the 2008 crisis in two weeks, including… … wait for it … the fact that we are doing the very same thing again, right now. Sad but true. Modelling No, not this (not quite anyway) though it is about idealized distortions of reality! MODELLING Modelling Spatial approach to geography is based on modelling. Modelling attempts to understand the world by abstracting it using assumptions. That is, it attempts to understand real world complexity by simplifying it. Once simplified, modelling attempts to find the general rules of behaviour underlying the spatial patterns. By way of illustration, let’s go to the beach… MODELLING Modelling A day at the beach st level of abstraction 1 short blonde Photo = copious detail, but much thrown out single ill old smart not-so-good looking nasty poor healthy rich blue suits good looking tall extrovert nice introvert naughty big female lying-on-stomach small obese young male not-so-smart red suits MODELLING skinny sitting couples thin Modelling A day at the beach ● ● ● ●● ●●● ● ●● ● ● ●● ● ●● ● ● ● ● ● ● ●● ● ● MODELLING ● ● ● ●● ● ●● ● ● ● ● Modelling ● A day at the beach ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ●● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●●●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● MODELLING ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● 2nd level of abstraction ● ● ● ● Dot density ●map ● ●●● ● ● ●● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● Modelling ● ● ● ● ● ● ●● ● ●● ● ● ● ● ●● ● ●● 3rd ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● level of abstraction ● ● ● map ● Isoline ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ●●●● ● ● ●● MODELLING ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ●● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● A day at the beach ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● Modelling ● A day at the beach? 4th level of abstraction mathematical function – a density surface d = q/v Density = quantity/volume How many points per unit area are encompassed by an isoline? MODELLING Landscapes Homogeneity & Isotropy Heterogeneity & Reality Sameness and Equality By simplifying a landscape through modelling we: Make it homogenous (the same) when it is really heterogeneous (different across space). We create artificially isotropic conditions (we create a reality that isn’t really there). MODELLING Homogeneity & Isotropy Important concepts: Isotropic plane: a theoretical abstraction that says the economic landscape is flat and equal in all physical attributes. Economic Person: a theoretical actor on the isotropic plane who is equal in all attributes and behaviour. Assumptions: a theoretical set of initial conditions that govern the behaviour of the actors on the isotropic plane. Because modelling uses such ‘unrealistic’ concepts to understand complex reality, we must always test the processes we discover through modelling, against the real world. MODELLING Ode to Assumptions In the land of Ceteris Paribus. On the isotropic plain. Lived a people with the same income, same sex, same tastes, same name. MODELLING TIME, SPACE, AND TIME-SPACE To be dealt with later in their own lecture: Arrow of time Time-space totality Time-space prism Time-space paths Discretionary events Obligatory events Time-space convergence Proxemics and social distance But for now the big picture – time scales… TIME AND SPACE SCALE The Sheer Scale of Geologic Time The Pliocene 0.1% (uh oh) The Cenozoic 1.5% (dinos leave the party) The Phanerozoic 12%* (party time!) The Precambrian 88% (not much happening) Homo supersizerous The Age of the Earth 4.6 billion years - 100% *includes Cenozoic and Pliocene. TIME AND SPACE SCALE Human Time Scales Bulk of Human History = 99.9% 4mya 2mya ≈≈ ‘Civilized’ Human History = 0.02% 10,000ya ≈≈ 250ya Now SCALE AND CHAOS The big picture about being big and small: • • • • • • • Map scale Orders of Magnitude Koch Snowflake Fractals Coastline Paradox Butterfly Effect Chaos Theory TIME AND SPACE SCALE MAP SCALES Maps cannot be to real size so scales are used to indicate the relationship between the map and the area they represent. Representative fraction (e.g. 1:50,000): Means 1 unit on the map is equal to 50,000 units on the ground. It doesn’t matter what units: e.g. 1 cm = 50,000 cm. Lexical scale: Means “in words”, so 1:50,000 could read as 1 inch equals 50,000 inches. Bar scale: A graphical device that can be used as a measuring rod to ascertain what the scale on the map would be. TIME AND SPACE SCALE 1.616X10-35m Planck length http://www.powersof10.com/ 1X10-24m Diameter neutrino 1X10-18m Diameter of Up or Down quark 3X10-15m Diameter of helium nucleus 3X10-9m Width of DNA 2X104m Width of Toronto 1.5X1011m Earth distance to Sun 4.1X1016m Distance to nearest star 9.5X1020m Diameter of Milky Way http:// htwins.net/scale2 / Diameter of observable universe (co-moving) TIME AND SPACE SCALE 8.8X1026m The Koch Snowflake THE KOCH SNOWFLAKE: “To construct a Koch curve, begin with a triangle of sides of length 1.0. At the middle of each side, add a new triangle one-third the size, and so on. The length of the boundary is 3 * 4/3 * 4/3 . . . ∞ Yet the area remains less than the area of a circle drawn around the original triangle. Thus, an infinitely long line surrounds a finite area!” (Gleick 1987: 99) TIME AND SPACE SCALE Mandelbrot and Fractals TIME AND SPACE SCALE Fractals and Nature Real Conch Mathematical Conch TIME AND SPACE SCALE Eat your Fractals! Romanesque Cauliflower TIME AND SPACE SCALE Fractals and ?? TIME AND SPACE SCALE Nautilus Shell Each follow a Fibonacci spiral Romanesque cauliflower TIME AND SPACE SCALE Florida Panhandle Stream order can be described using the Fibonacci sequence and use the Golden Ratio. TIME AND SPACE SCALE The Coastline Paradox What is the length of the coastline of Britain? 12 200 km ‘fractal rulers’ 2,400 km 28 100 km ‘fractal rulers’ 2,800 km 68 50 km ‘fractal rulers’ 3,400 km The Ordnance Survey of Britain gives the “official” length of the main island coastline as 17,819km. TIME AND SPACE SCALE Edward Lorenz and the butterfly effect Predictability: Does the flap of a butterfly's wings in Brazil set off a tornado in Texas? Presented before the American Association for the Advancement of Science, December 29, 1972 TIME AND SPACE SCALE Edward Lorenz and the butterfly effect While running a climate model he found that a 1/10,000th of a percent change in the input altered the model’s output dramatically. He realized two things: That small changes in inputs have large effects. That since data are always slightly wrong, then models can never be exact in their predictions. From this came Chaos Theory. TIME AND SPACE SCALE Edward Lorenz and the butterfly effect. Patterns in nature can look chaotic but still have structure Frontal weather systems The cirrus in this photo is extremely high up in the stratosphere but the cumulus is low down. But both mark the approach of a weather front. TIME AND SPACE SCALE Edward Lorenz and the butterfly effect. Patterns in nature can look organized but be highly unpredictable in the details Tropical Cyclones Hurricane Isaac unexpectedly stalled just south of New Orleans with rainfall equal or greater than Katrina. Hurricane Sandy hit New York, a rare and unpredictable occurrence. TIME AND SPACE SCALE Edward Lorenz and the butterfly effect. Patterns in nature can look organized and be highly predictable in the details Schooling fish. The school’s volume is divided equally among the number of fish it contains such that a given unit of volume will always contain at least one fish – but not a given individual fish. That’s why predators round up fish into schools and fish like to school. TIME AND SPACE SCALE Edward Lorenz and the butterfly effect. Human patterns can also look chaotic but be highly predictable in the details The phantom traffic jam. Someone touches their brake and two miles back traffic comes to a halt. That is the effect of a tiny change in forward velocity being amplified by slow human reaction time. TIME AND SPACE SCALE Edward Lorenz and the butterfly effect. Human patterns can look chaotic, be highly unpredictable in the details but highly predictable as a whole. The Wisdom Of The Crowd. TIME AND SPACE SCALE The Wisdom of the Crowd The behaviour or opinions or decisions of individuals can be chaotic, but the average behaviour of a crowd can be highly predictable and surprisingly accurate. Mathematician Marcus Du Sautoy’s j e l l y b e a n experiment: 5,410 jelly beans 160 guesses Guesses ranged from 450 to 50,000 Average of all guesses was 5,414 – just 4 over the real number. You can see this excerpt from his show The Code at http://www.youtube.com/watch?v=982E49KAMyw I also recommend http://www.youtube.com/watch?v=eimuAboXSdo. SPACE the SCALE patterns. See if youTIME canANDsee Number of Popcorn Kernels The Wisdom of the Crowd Regression to the Mean Popcorn Experiment 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 There are 39 guesses. The mean of guesses is 5,933. Note that the running mean approximates the actual number closer and closer. 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 Guess Number Guesses Number Actual Mean TIME AND SPACE SCALE Running Mean