What were Saturday s BIG ideas?

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Linda Blair
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1 What were Saturday s BIG ideas? 1. NEED REPLACING There is no single scientific method (multiple ways including empirical & theoretical)

2 Scientific Ways of Knowing Induction -> Approach is observing (Empiricists) 1. Natural Observation observation of natural system without manipulation 2. Experimentation observation of natural system with manipulation Deduction -> Approach is modeling (Theoreticians) 1. Numerical modeling quantitative models designed to make predictions of geometry or behavior of natural systems Let s explore a theoretical approach in the context of some recent articles, etc.

3 Boron comedy? 9/02/09/oops-make-that-four-forms-ofpure-boron/

4 Boron? And yes, the Late Night writers got the science right. I am really impressed, Dr. Oganov wrote in an . I just saw it and am surprised they even got (absolutely correct) information and even a picture of our new structure! It s amazing

5 Scientific Ways of Knowing Induction -> Approach is observing (Empiricists) 1. Natural Observation observation of natural system without manipulation 2. Experimentation observation of natural system with manipulation Deduction -> Approach is modeling (Theoreticians) 1. Numerical modeling quantitative models designed to make predictions of geometry or behavior of natural systems

6 Now on to a big deal in the development of modern science I dig the wig. Isaac Newton ( )

7 Time s People of the Century 20th: Albert Einstein 19th: Thomas Edison 18th: Thomas Jefferson 17th: Issac Newton Every day is a bad hair day.

8 Newton is the man of the century for this reason: by imagining--and proving--a rational universe, he in effect redesigned the human mind. Newton gave it not only intellectual tools undreamed of before, but with them, unprecedented self-confidence and ambition. In a sense, all the change that shaped the world until the onset of modernity had its origins in Newton's mind. For what he showed was this: the universe is knowable and governed by universal laws- -therefore predictable, therefore perfectible by human reason and will. - from Time magazine

9 In short, Newton almost single-handedly invented a new way of knowing NUMERICAL MODELING Modeling uses a theoretical approach, which in turn uses deductive logic Deductive logic - using rules to understand examples Given Model/Concept Expected Data Therefore, theoretical approaches set up a set of rules and predict the consequences of those laws given a particular situation.

Analysis requires pretty good math skills, because it is only in quantitative analysis that one can rigorously follow through the consequences of a set of general laws.

10 Analysis requires pretty good math skills, because it is only in quantitative analysis that one can rigorously follow through the consequences of a set of general laws. Luckily, Newton was reasonably good at math (ok, he was really good - he invented calculus) "Taking mathematics from the beginning of the world to the time when Newton lived, what he has done is much the better part." Gottfried Leibniz..and I hate his guts (and I didn t steal calculus from him) Leibniz

11 So, what s the deal with the apple Newton saw an apple fall and the moon, and realized that the same force that made the apple fall also kept the moon in orbit. A definite aha moment

Newton did a lot, but the most significant was the book: Philosophiae Naturalis Principia Mathematica (1687), but referred to by those in the know as Principia

12 Newton did a lot, but the most significant was the book: Philosophiae Naturalis Principia Mathematica (1687), but referred to by those in the know as Principia "The Principia is pre-eminent above any other production of human genius." Pierre-Simon Laplace And here is the amazing thing - it is written in plain English.

13 The Three Laws of Principia Law #1: Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces imposed on it. Law #2: The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which the force is impressed. Law #3: To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. So simple A talking fruit

Newton s Law #1: It took centuries for scholars to collectively shake off the notions that the natural state of an object was at rest and that the constant motion could only happen with continual

14 Newton s Law #1: It took centuries for scholars to collectively shake off the notions that the natural state of an object was at rest and that the constant motion could only happen with continual pushing. It was not so obvious to realize that in fact, constant motion only happens with no pushing at all. The abstract concept of an object moving at uniform velocity (constant speed and direction) in the absence of any outside force crystallized with the work of Galileo, but Newton said it the best. Luckily, the first law is now simple to understand because of the advent of air hockey.

15 Let s give Newton s 1 st law a spin

Newton s Law #2: This law defines what a force is, and suggests that it is proportional to the acceleration of the object. It also suggests that Force has both a magnitude and a direction.

16 Newton s Law #2: This law defines what a force is, and suggests that it is proportional to the acceleration of the object. It also suggests that Force has both a magnitude and a direction. Oh, and the constant of proportionality is the mass of the object. Hence, Force = Mass x acceleration In truth, this was probably already figured out by Galileo. A good portion of engineering Is based on this idea (for better or worse)

17 Let s weigh in on Newton s 2 nd Law

18 Newton s Law #3: The third law is the most subtle and surprising of the three laws. As Newton adds, Whatever draws or presses another is as much drawn or pressed by that other. It says that forces always come in pairs, action and reaction. There is no such thing as a single, isolated force vector, alone without another partner somewhere. The implication is that nothing no outside agent is capable of acting on things while being immune from being re-acted on in turn. That is, no action can be taken in isolation. Like, man, I feel so connected to the world because, like, everything is interwoven and the sun and the moon and even Neptune is a little attracted to me and so, like, that means. A new-age fruitcake fruit

19 No one should get frozen out of understanding Newton s 3rd law

20 Theoretical approaches They are as useful, insofar as they make useful predictions. All models are wrong; some models are useful G.E. Box

So, for example, let s say that we want to figure out what Galileo could not measure accurately enough: How long does it take a object to fall vertically (55 m)?

21 So, for example, let s say that we want to figure out what Galileo could not measure accurately enough: How long does it take a object to fall vertically (55 m)? Law #1: There must be a force on the ball, because it starts to move downward Law #2: It must move downward at a constant acceleration, because F=ma (IMPORTANT!) Law #3: The Earth is moved very slightly toward the ball, because forces come in pairs.

22 If acceleration is constant, we can make some calculations Distance = initial position + initial velocity * time + ½ (acceleration * time 2 ) OR, if position = 0 and initial velocity= 0, then: Distance = ½ (acceleration * time 2 ) acceleration = 9.8 m / sec 2

23 Notice how the dropped ball moves further during the same time steps, as it moves downward.

24 Are Newton s three laws really laws?

25 A brief review: A scientific law attempts to describe an observation in nature Whereas a scientific theory attempts to explain it A scientific hypothesis is an educated guess

26 Are Newton s three laws really laws? Yes! Newton s three laws describe observations. In this example, they also provide the framework for how to usefully think about them.

But, Newton s laws are not correct (in detail). Newton s three laws aren t technically correct. Albert Einstein hypothesized that if material travels really fast, really weird things can happen.

27 But, Newton s laws are not correct (in detail). Newton s three laws aren t technically correct. Albert Einstein hypothesized that if material travels really fast, really weird things can happen. Laws, as well as theories, are subject to change!! But, Newton s laws are still extremely predictive tools for relatively slow speeds. 186,000 miles per second isn t just a good idea, it is the law*. *Note this is funny if it is funny because it equates a scientific law with a law law.

28 What were today s BIG ideas? And then, were they disciplinary knowledge, science inquiry, or nature of science?

Classical mechanics: Newton s laws of motion

Classical mechanics: Newton s laws of motion Homework next week will be due on Thursday next week You will soon be receiving student evaluations Occam s razor Given two competing and equally successful