Example of models, metaphors and analogies in the sciences

Whatever reason anyone could have for calling a globe the best model or the true model of the earth’s surface, I don’t think that it’s because of how useful it is or how well it fits all the data. I think that most of the time most people including most researchers who need accurate information about the earth’s surface would use flat maps and not a globe. That doesn’t make flat maps true and a globe false. Also, I don’t think that any researcher would try to use only one kind of projection for all purposes, or even try to invent one that could be used that way.

exchemist said:

But not the list, I notice. You need to take last universal common ancestor off it.

But I think you won't because, I suspect, this thread is really not about models or the use of analogy and metaphor in science, but about trying to weaken the concept of common descent by misleading people about it.

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Slick.

Jim said:

NOTE: I edited the thread title from “physical sciences” to “sciences.”

I’m looking for examples of models, metaphors and analogies in the physical sciences. I’ll list a few to begin with.
- Direction of conventional current flow in electric circuits.
- Norton and Thevenin equivalent circuits.
- Flat map projections of the earth’s surface.
- Wave and particle models of the transmission of light.
- Lines of force.
- Planetary model of the atom.
- Schrödinger's cat.
- Colors and spins of elementary particles.
- The Big Bang.
- Tree, web and ring models of the history of life on earth.
- The Last Universal Common Ancestor

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Everything in science is a model...usually a mathematical model that matches best with current data.

The most successful theory in sub-atomic physics is called the Standard Model. Feel free to look it up.

Wave particle dualty is a metaphor.
Big Bang is a model.
Last Universal Common Ancestor is a hypothesis.
Color and Spin are properties of sub atomic particles and is not a model but property names.

Jim said:

I don’t see how any globe that anyone actually uses could be better or more accurate than a flat map, for any purpose other than visualizing the whole earth, or a part of its surface wider than a few hundred miles. Apart from that, flat maps fit the data snd provide more information, more accurately, than any globe that anyone actually uses.

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Well, maps always have distortions of distance. You can get maps that don't distort area. Angles are also tricky. Try plotting an international flight on a map. Your course will be badly off the shortest path. For a globe, it is easier.

Jim said:

I would agree that all the theories in the sciences are models. What I’m thinking is that models are chosen according to how useful they are, or how well they fit some data. In some cases, no single model is the best model for all purposes, and sometimes the model that fits best is not the best model for most purposes. A model is not true or right in any way that makes all other models false or wrong. A model is not true or right in any way that makes it foolish or ignorant for anyone not to believe it. An agreement between researchers to use some model is not an agreement to denounce or ridicule anyone who doesn’t believe it.

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What happens *in practice*, though, is that we have found very, very general models (maps) that we can use to get maps of smaller areas relatively easily. So, if you apply Newtonian mechanics to the construction of a bridge, the same basic equations also apply to the construction of a building, the orbits of a satellite, and he design of a carnival ride. That is *one* map that gives all of these submaps accurately.

Anyone currently using Ptolemy's model of the solar system is foolish and/or ignorant. It is simply false and wrong. It both gets the basic idea of how things work wrong, but it also gives very poor approximations.

Anyone using the phlogiston theory of heat is both foolish and ignorant. Once again, it gets the basic idea wrong and the approximations are poor. It is just easier and a better approximation to use thermodynamics.

Anyone using the model of molecules where water is given by HO (as opposed to H2O) is both foolish and ignorant. The results of using that formula will be disastrous in any chemical plant.

And, if you are modeling energy levels in an atom, you are both foolish and wrong to use Newton's mechanics. The approximation is so bad that any result you get will be unusable.

You *can* use Newton's mechanics, however, to plot a path for a spacecraft to Mars. The approximation is good enough in that situation to give results that are usable and safe.

Jim said:

The point that I’m making is that there isn’t any single model that is the best model for all purposes, and there isn’t any single model that is true or right in any way that makes all other models false or wrong.

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For most of physics there is a *most accurate* model. That is the 'ultimate' model. ALL other models are, in essence, approximations to this one.

Which of the lesser models you use depends on the level of accuracy you need and the amount of work you want to do. But if you want more accuracy, you can always go to the overall model.

Furthermore, the *goal* of science is to find that overall model. It is to find that model that gives the most accurate results in all situations. Then, if you want to use a less accurate model, and you know the conditions for its use, you can feel free.

Polymath257 said:

But if you want more accuracy, you can always go to the overall model.

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Do you mean, a computer model? I don’t think that you could be talking about an actual physical globe, like the one a person might have on a desktop or on top of a cabinet.

Jim said:

Do you mean, a computer model? I don’t think that you could be talking about an actual physical globe, like the one a person might have on a desktop or on top of a cabinet.

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No, in that context, I was suggesting either general relativity or quantum mechanics. Those are the two overarching models in physics. At this point *everything* we know reduces to one or the other (or both).

/E: Usually, computer models are just using computers to do the calculations for some mathematical model. Often a good amount of math has to be done to justify the approximations used for the computations.

Polymath257 said:

For most of physics there is a *most accurate* model. That is the 'ultimate' model. ALL other models are, in essence, approximations to this one.

Which of the lesser models you use depends on the level of accuracy you need and the amount of work you want to do. But if you want more accuracy, you can always go to the overall model.

Furthermore, the *goal* of science is to find that overall model. It is to find that model that gives the most accurate results in all situations. Then, if you want to use a less accurate model, and you know the conditions for its use, you can feel free.

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I’m not sure if you’re disagreeing with something I’ve said, or you’re just clarifying? I’m saying that whatever it means to say that some model is the best or most accurate, it does not always mean that it’s wrong to use any other one. It does not always mean that it’s the best model to use for all purposes, or even for most purposes. An agreement between researchers to use some model is not a license to denounce or ridicule people who don’t believe it.

I’ll add that whatever it means to say that some pictorial representation is the best one, it doesn’t always mean that it’s an actual physical description of whatever it’s representing.

Jim said:

I’m not sure if you’re disagreeing with something I’ve said, or you’re just clarifying? I’m saying that whatever it means to say that some model is the best or most accurate, it does not always mean that it’s wrong to use any other one. It does not always mean that it’s the best model to use for all purposes, or even for most purposes. An agreement between researchers to use some model is not a license to denounce or ridicule people who don’t believe it.

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If you are limiting yourself to reasonably accurate models, I would agree. Also, you need to be aware of the limitations of any model you use.

But, like I said, if you are using the Ptolemaic model for anything other than historical interest or mathematical amusement, you really are either being foolish or ignorant.

And yes, it *can* be wrong to use some models. For example, if you are using Newton's mechanics to model an atom, you will get nonsense. Anyone who does so will be denounced, ridiculed, and ignored. Justifiably. We *know* that model does not give accurate results in that context.

Jim said:

I don’t see how any globe that anyone actually uses could be better or more accurate than a flat map, for any purpose other than visualizing the whole earth, or a part of its surface wider than a few hundred miles. Apart from that, flat maps fit the data snd provide more information, more accurately, than any globe that anyone actually uses.

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Maps are good enough when they cover only a small area. There is little curvature that distorts distances or angles. A world map is entirely useless for navigation. On a Mercator projection Greenland looks as if it is a big as Africa when in reality it is only slightly bigger then Madagascar.

My best hope for this thread is for people who are working to help reduce animosities and hostilities across lines of alienation, to see more clearly how theories from the sciences are being misused in those hostilities. I see deeper reasons for those hostilities, but even so, seeing more clearly how those theories are being misused has been helpful for me, so maybe it could be helpful for some other people too.

One way that I see them being misused is using them as reasons for denouncing and ridiculing other people’s beliefs, and for disparaging their character and capacities. Associated with that is thinking of some theories as being true, or right, in some way that makes it okay to denounce and ridicule people, and disparage their character and capacities, if they persist in not believing those theories.

One way to see more clearly how theories are being misused might be to consider some healthy and beneficial ways of using them. I’m using flat maps of the earth’s surface to explain my ideas about healthy and beneficial ways of using theories. A map is not true or right in any way that makes all other maps false or wrong, without specifying for whom, for what purposes, and in what circumstances.. It can be true in the sense that if a person uses it to measure distances, angles or areas, in whatever way it’s designed to be used, their measurements will be accurate within the tolerances that it’s designed for. It can be the right map for some people to use for some purposes, in some circumstances, in the sense of being the best one available for those people, for those purposes, in those circumstances. I think that all of that applies to all theories, including those in the sciences, as much as it applies to maps.

One way to think of what I want to say is that healthy and beneficial use of theories includes understanding what they’re designed to do, and awareness of their limitations. Some examples of what theories in the sciences are designed to do are to facilitate research, communication about research, and development of technology. I’ll discuss their limitations in another post.

Any more thoughts about this?

The simplest model is not always the best model for all purposes. Here are two functions representing a triangle with its vertices at rectangular coordinates (0,0), (1,1) and (2,0):

f1:
- When x is 0, y is 0
- When x is greater than 0 but not greater than 1, y has two values, 0 and x.
- When x is between 1 and 2, y has two values, 0 and 2 - x.
- When x is 2, y is 0

f2:
When x is at 0 or 2, or between them, y = 0.25
That’s the line that minimizes the sum of the squares of its deviations from the points of the triangle for all values of x from 0 to 2.

f1 exactly matches all the points. f2 is much simpler, but it represents the triangle as a single line.

I’d like to see some discussion here about why and how metaphors are used in the sciences.

Food for thought:
On the Problem and Promise of Metaphor Use in Science and Science Communication

“As Pigliucci and Boundry explain, “the mechanical pictures of living organisms and the cosmos at large converged into an intellectual tradition where theology and science were intimately intertwined” (26, p. 455). Machine metaphors allowed for religious speculation and inferred an inescapable conclusion: that a designer or creator must exist (for all machines have a maker).“

More food for thought:
The Art of the Scientific Metaphor