Thursday, December 22, 2005
Mathematical, Statistical, And Descriptive Models
I promised yesterday to look a little more at the "spectrum of science" from hard to soft.
What does science do? It observes, it organizes the observations it makes, then it attempts to explain it in such a way that the explanation can predict some related but unobserved behavior. This predictive explanation is known as a theory, or better "a model." Just like a model car helps you understand a real car by being smaller and more manageable, so a scientific model helps you understand whatever it is you are studying.
As I said, traditional physics stands at the very top of the heap of science because the models used are completely and thoroughly explanitory. Using the physical models of Newton, if I want to throw a rock to the moon I can calculate exactly how hard to throw it, when to release it, aimed where and I can tell you with whatever precision you desire exactly where that rock will be at any moment of its journey -- I can even tell you how big a dent it will make on the surface of the moon. That is a fully mathematical, fully deterministic scientific model or theory. This is the best science can do.
One the next level we have statistical models. Let's say I want to determine the time path and destination of a migrating goose. All I can do in this case is study a whole lot of geese. I gather a whole lot of data about where they start, how old they are, what the weather is like, whatever it is I think makes a difference in how the goose I am interested in migrates, and then I plug all that data into my magical statistical analysis. Once that is done I can predict, usually pretty well, how my goose of interest will act, but I have no genuine understanding of what makes the goose behave as he does. All I have really done is a highly sophisticated determination of probabilities.
The difference between a mathematical model and a statistical model is that while a statistical model is predictive it is not explanitory. A mathematical model not only tells me what will happen, but it tells me why and how it happens. I wish I could show this to you in more detail, but I would have to actually do the math and I am afraid I am losing too many of you as it is.
Before we move on to descriptive models, a side note about quantum mechanics. Many contend that the distinctions I lay out here have disappeared because quantum mechanics is statisitical in nature and not deterministic in the sense that traditional physics is. That is not entirely true. In terms of energy, quantum mechanics is competely determinitive, it is only probablisitic with regards to position of a quantum particle. This by the way happens because we cannot even say if a quantum particle really is a particle at all -- it lives in a neither world between matter and energy, so the very concept of location doesn't apply in the same sense that it does for say, a billiard ball.
While it is true Einstein said of quantum mechanics, "I don't think God would play dice with the universe" he was not imputing that quantum mechanics was a purely statistical model in the sense that the goose example above is. Again, I would have to do the math to demonstrate to you any better what I am saying here, but people that understand quantum mechanics as statitical in the same sense as the goose study have got to be laymen that have never actually done quantum mechanical calculations.
Finally, there are descriptive models. You do these every day. Say you have a computer problem. You note the problem appears when you have three specific programs running at the same time. When you are describing the problem to your IT guy, you will tell him, "Whenever I do this, this happens." You will have created a descriptive model in your mind of what is going on inside your computer, you will assume that running those three programs casues the problem. That's all a descriptive model is -- it is an attempt to describe in words what conditions lead to what occurences and take a stab at why that is the case.
Now, I picked this IT example because most of the time, the model you lay on your IT guy will be completely wrong -- that by the way, is why they usually look so disinterested when you are telling them your theory. Your computer does so many things all the time, most of which you have no idea about, that those background tasks are a far more likely source of your problem than those three programs.
Descriptive models are very useful tools, but they are also very limited and also often very wrong. In our example, it may be that those three programs overload a specific memory buffer because they compete for it when you are on the Internet, and the real problem is that your background program that always pings the atomic clock to set your computer clock (something you never see) is not properly getting off the internet. So, the problem is really in a program you never see run, you may not even know is on your computer. To form a good descriptive model, you have to make sure you are seeing everything that is going on, that's very hard to do in some circumstances.
Which brings me to evolution and Intelligent Design. Both are purely descriptive models. Consider this article
What's the article really say? Life is made up of carbon, hydrogen, a little oxygen, and a few other things, arranged in a very complex manner -- not unlike all the programs seen and unseen on your computer. So, what they are saying is if I put all the ingredients into a big bottle and shake it up, I should get life, which is kind of like saying if I get a Windows disk and a Microsoft Office disk and and I put them in a box with a bunch of electronic components I'll get a computer. Yeah, it's possible, it even makes something akin to sense, particularly based on the small amount of information available, and while I can call it a descriptive theory or model, because strictly it is -- it is not predictive or really explanitory and therefore barely useful.
Under such circumstances it is terribly difficult to say what is science and what is not. You can see, I hope, that in forming the descriptive model you have to make a lot of assumptions. Now then, if you want to call what you are doing "science" one of the assumptions you have to make is a lack of the supernatural. Why? Well, the supernatural is not observable, measurable, or ever predictable -- thus if something has a supernatural cause or component, you can never really explain it, so you have no hope of doing science on it.
But note carefully that the lack of a supernatural component is an assumption -- it is not a result of the investigation and observations. Evolution does not prove there is no God, it simply eliminates the possibility in order to call itself science.
Yesterday's post got a great comment from Joe Carter
However, I would take Joe's great suggestion a step further. Evolution isn't science either. It is labeled as such primarily because of it's exclusion of the supernatural, but remember that is presumed as opposed to arising out of the data.
You want to fix education in a way that it allows mention of God? Let's create some new categories -- it's not just science and humanities, there is a bunch of stuff in between. Let's teach the limitations of what we know as well as its extent. Let's distinguish what we learn from our studies from what we impose on our studies.
In my opinion the problem that Intelligent Design attempts to solve would be better solved by properly teaching evolution than tilting up another decriptive model of minimal usefulness, even if it has similar plausibility.
What does science do? It observes, it organizes the observations it makes, then it attempts to explain it in such a way that the explanation can predict some related but unobserved behavior. This predictive explanation is known as a theory, or better "a model." Just like a model car helps you understand a real car by being smaller and more manageable, so a scientific model helps you understand whatever it is you are studying.
As I said, traditional physics stands at the very top of the heap of science because the models used are completely and thoroughly explanitory. Using the physical models of Newton, if I want to throw a rock to the moon I can calculate exactly how hard to throw it, when to release it, aimed where and I can tell you with whatever precision you desire exactly where that rock will be at any moment of its journey -- I can even tell you how big a dent it will make on the surface of the moon. That is a fully mathematical, fully deterministic scientific model or theory. This is the best science can do.
One the next level we have statistical models. Let's say I want to determine the time path and destination of a migrating goose. All I can do in this case is study a whole lot of geese. I gather a whole lot of data about where they start, how old they are, what the weather is like, whatever it is I think makes a difference in how the goose I am interested in migrates, and then I plug all that data into my magical statistical analysis. Once that is done I can predict, usually pretty well, how my goose of interest will act, but I have no genuine understanding of what makes the goose behave as he does. All I have really done is a highly sophisticated determination of probabilities.
The difference between a mathematical model and a statistical model is that while a statistical model is predictive it is not explanitory. A mathematical model not only tells me what will happen, but it tells me why and how it happens. I wish I could show this to you in more detail, but I would have to actually do the math and I am afraid I am losing too many of you as it is.
Before we move on to descriptive models, a side note about quantum mechanics. Many contend that the distinctions I lay out here have disappeared because quantum mechanics is statisitical in nature and not deterministic in the sense that traditional physics is. That is not entirely true. In terms of energy, quantum mechanics is competely determinitive, it is only probablisitic with regards to position of a quantum particle. This by the way happens because we cannot even say if a quantum particle really is a particle at all -- it lives in a neither world between matter and energy, so the very concept of location doesn't apply in the same sense that it does for say, a billiard ball.
While it is true Einstein said of quantum mechanics, "I don't think God would play dice with the universe" he was not imputing that quantum mechanics was a purely statistical model in the sense that the goose example above is. Again, I would have to do the math to demonstrate to you any better what I am saying here, but people that understand quantum mechanics as statitical in the same sense as the goose study have got to be laymen that have never actually done quantum mechanical calculations.
Finally, there are descriptive models. You do these every day. Say you have a computer problem. You note the problem appears when you have three specific programs running at the same time. When you are describing the problem to your IT guy, you will tell him, "Whenever I do this, this happens." You will have created a descriptive model in your mind of what is going on inside your computer, you will assume that running those three programs casues the problem. That's all a descriptive model is -- it is an attempt to describe in words what conditions lead to what occurences and take a stab at why that is the case.
Now, I picked this IT example because most of the time, the model you lay on your IT guy will be completely wrong -- that by the way, is why they usually look so disinterested when you are telling them your theory. Your computer does so many things all the time, most of which you have no idea about, that those background tasks are a far more likely source of your problem than those three programs.
Descriptive models are very useful tools, but they are also very limited and also often very wrong. In our example, it may be that those three programs overload a specific memory buffer because they compete for it when you are on the Internet, and the real problem is that your background program that always pings the atomic clock to set your computer clock (something you never see) is not properly getting off the internet. So, the problem is really in a program you never see run, you may not even know is on your computer. To form a good descriptive model, you have to make sure you are seeing everything that is going on, that's very hard to do in some circumstances.
Which brings me to evolution and Intelligent Design. Both are purely descriptive models. Consider this article
What's the article really say? Life is made up of carbon, hydrogen, a little oxygen, and a few other things, arranged in a very complex manner -- not unlike all the programs seen and unseen on your computer. So, what they are saying is if I put all the ingredients into a big bottle and shake it up, I should get life, which is kind of like saying if I get a Windows disk and a Microsoft Office disk and and I put them in a box with a bunch of electronic components I'll get a computer. Yeah, it's possible, it even makes something akin to sense, particularly based on the small amount of information available, and while I can call it a descriptive theory or model, because strictly it is -- it is not predictive or really explanitory and therefore barely useful.
Under such circumstances it is terribly difficult to say what is science and what is not. You can see, I hope, that in forming the descriptive model you have to make a lot of assumptions. Now then, if you want to call what you are doing "science" one of the assumptions you have to make is a lack of the supernatural. Why? Well, the supernatural is not observable, measurable, or ever predictable -- thus if something has a supernatural cause or component, you can never really explain it, so you have no hope of doing science on it.
But note carefully that the lack of a supernatural component is an assumption -- it is not a result of the investigation and observations. Evolution does not prove there is no God, it simply eliminates the possibility in order to call itself science.
Yesterday's post got a great comment from Joe Carter
I suspect that the problem started in the 1800s when the term "science" began to be applied to almost anything, including such unscientific concepts as Marxism. Perhaps we should stop referring to ID as science, and call it a form of philosophically guided inquiry into natural processes.Joe's right -- as science accomplished much that prior to the 1800's would have been deemed "magic" more things wanted to be called "science" simply to garner that cachet. Thus many areas of study began to exclude the supernatural, not because the area of study demanded it, but because they wanted to to call themselves scientific.
However, I would take Joe's great suggestion a step further. Evolution isn't science either. It is labeled as such primarily because of it's exclusion of the supernatural, but remember that is presumed as opposed to arising out of the data.
You want to fix education in a way that it allows mention of God? Let's create some new categories -- it's not just science and humanities, there is a bunch of stuff in between. Let's teach the limitations of what we know as well as its extent. Let's distinguish what we learn from our studies from what we impose on our studies.
In my opinion the problem that Intelligent Design attempts to solve would be better solved by properly teaching evolution than tilting up another decriptive model of minimal usefulness, even if it has similar plausibility.
