Welcome to the introduction to the Citizen Scientist. The point of the Citizen Scientist, first and foremost, is to share in my own explorations of the world. It's about me learning about the world and exploring it. To some extent Citizen Scientist is a letter from me to my son, for when he's older, and for that reason, this is a column that might sometimes be slanted towards guys, by a guy that refuses to grow up. In this column, we're going to go over the idea of models in science, limits of models, and the idea of math as a vehicle for communicating those models, and new uses of them.
In future columns, I might do some experiments, just explore where my own curiosity takes me.
Science is a method. Its not a religion, a way of life, or a a mystical thing. In cooking you have recipes for making cakes, in building, methods for making different things, and science itself is just a tool for playing and learning from that experience, and being able to share what you learned. When one wishes to explore the world and learn how it works, thus, the scientific method is the method humanity has learned that tends to work best because it is most useful.
The scientific method is very simple. First, you form a model of how you think something works, then you explore that model, and see what you've learned. That's it. It could be as simple as, if I aim magnifying glass on the bug, the bug will burn up. At one point in human history, it actually was that simple. In the dark ages people looking to turn rocks into gold got the idea that if they at least wrote down what they were thinking when they tried something, they could at least make it easier to track what they did. But usually, these days, when we think of models, we think of a story line, a set of rules for how things operate, and then try and affix numbers to those rules using some sort of formal notation, math. We'll see why that's important, later.
But for the moment, forget what you know about "theory" and "fact". There's not a magical point in which "Newton's Theory of Gravity" is suddenly true, or suddenly became wrong. It's "Newton's Model of Gravity", is what it should be called, just like, "Einstein's Model of Gravity", which was discovered later. Newton's Model still works much of the time, and Einstein's happens to be useful when you are dealing with things that are either super heavy, like planets, and stars, and galaxies, or going really fast - like, close to the speed of light, fast. Science is the means by which these models are accumulated and categorized, and the models themselves, are the knowledge.
Isaac Newton - hooray, a geeky guy - when he wasn't trying to invent ways to get gold so he can get women (it's an afflication
that haunts we men through the ages, for sure), came up with this wonderful little equation that related the velocity of an object to time and constant acceleration.
v = at
and
s = s0 + vt + .5at^2
These equations are models and they work pretty well for certain objects falling on the earth, or in a vaccum, for a rocket engine, or even a car. Is it perfect? No, and again, no model is. But saying this or that model is always bad, is like saying a screwdriver is useless when you sometimes need a hammer. Of course Newton's model is the good stuff. We can use it, and we can learn from it. Given Newton's model, for example, we can say that after 5 seconds of falling, an object will be travelling v = 9.8 * 5 = 49 meters per second, or about 110 miles per hour. That makes intuitive sense. After all, if you jumped off something high enough to fall for five seconds, you would be jacked up. Probably would need a closed casket.
Of course, you have to ask the question, well, how high would that be?
That's what the second part of Newton's model does. It will turn out, in the course of things, that the first and second equations are related through something called differentiation and integration. Newton, being the crafty fellow that he was, invented calculus along the way so that he could deal with gravity and acceleration. But we'll skip that for the moment, and instead just look at the equation 2, plug in 5 seconds, use 0 for s0, use 0 for v, (meaning, we're starting from 0 velocity), and plug in .5 * 9.8 * 5 ^ 2 = 122.5 meters. Again, that seems right, because, if you jumped off a building 122.5 meters high, it would take you a few seconds to hit the ground, and you would be jacked up. Probably need a closed casket.
Something to think about, by the way, is that, if you would not live if you drove your car off of a 122.5 meter building, then, you wouldn't live if you hit a wall going 109 miles per hour, either. You'd get jacked up, probably need a closed casket. You've seen the PSA's where they shove cars off a cliff, to make that point, but you can calculate that yourself:
feet = .5 * 9.8 * (mph * 0.45 / 9.8)^2 * 3.28
What I've done with the above is take Newton's basic equation, shuffle it around using some basic algebra to solve for height, and then bake in some conversions for miles per hours to feet. Plug in miles per hour, into the above, and you get roughly how high you would have to fall, to match your current speed, neglecting air resistance. Do that a few times, and we get the below table.
| Going MP/H | Falling Feet |
|---|---|
| 10 | 3 |
| 20 | 14 |
| 30 | 30 |
| 40 | 54 |
| 50 | 85 |
| 60 | 122 |
| 70 | 166 |
| 80 | 217 |
| 90 | 274 |
| 100 | 339 |
Beyond a 100mph, the comparison doesn't work as well, because in the real world you would reach terminal velocity, as your speed of falling would be in equilibrium with atmospheric drag, and you wouldn't get much faster than 110 mph. It's enough to jack you up, closed casket, for sure.
If it is any consolation, though, for curiosity, know that, if there was no atmosphere on the earth, driving a car into a wall going 190 miles an hour is about the same as jumping off of the 102nd floor of the Empire State building. So, at least, if you want to end it all, you can just drive into a wall, rather than bust on everyone's parade in NYC. Of course you might think your car might save you, but, really, at that speed, it won't. And we know Newton's model works more accurately, because an astronaut actually did the experiment on the moon. Check it out: Astronauts on moon The astronaut correctly gives Galileo his props for first making that call about the nature of gravity, but my vote is still for Newton as the man for making Galileo's empirical observations mathematically useful.
The main point though, as you can see, is that science is the process of creating models. Models have a range within which they are useful. They convey relationships between different elements of nature, that you can exploit. You can use mathematical tools to pick them apart like Legos and rearrange them to answer questions that the model authors might not have even anticipated. It is this technique, by the way, that often gets used to determine a good model, versus a bad one. Newton's model is the good stuff, for sure.