How do you define "a model"?

[Robittybob1]

I was asked to model my hypothesis. How does one even start doing that?

[StringJunky]

https://en.wikipedia.org/wiki/Scientific_modelling

[Klaynos]

A testable (in principle), mathematical description of some aspect of the universe.

[Robittybob1]

https://en.wikipedia.org/wiki/Scientific_modelling

There is a list of types of models so which one should I have tried? https://en.wikipedia.org/wiki/Scientific_modelling#Types_of_scientific_modelling

 

A lot of models seem to rely on computer graphics, but I think they were wanting something else.

A testable (in principle), mathematical description of some aspect of the universe.

Can you give me an example? (Please)

Edited March 11, 2015 by Robittybob1

[Strange]

As an example, Newton's law of gravitation is a mathematical model. It can be used to predict the path of cricket balls and planets and can therefore be tested.

 

Any scientific hypothesis or theory must be based on one ore more mathematical models.

Edited March 11, 2015 by Strange

[swansont]

Another example: you can model certain systems as harmonic oscillators. You have a restoring force of the form F = -kx. You can add damping to the oscillator, and forcing. The terms could be position-dependent, or speed-dependent, or whatever is proposed as the behavior of the system. From that you can derive the energy of the system, position as a function of time, and other parameters. That's an example of a model.

[studiot]

Processes can be classified into two broad categories (amongst other methods of classification)

 

Analysis and synthesis.

 

Which, roughly translated means breaking down and building up.

 

The term model is applied to both, but synthesis is often forgotten, especially in Science Forums.

 

The essence of a model is that it embodies (we hope) the same properties of some characteristic we are interested in.

It will (almost) certainly also have many characteristics and properties that are different from our interest and mostly these will only match of some defined range so it is important not to overstep these when using a model.

 

The process of syntheses is used by designers and constructors; here another word for model is 'pattern'.

So a dressmaker, a foundry worker, a woodworker, and others will make a pattern to follow to make a dress, a casting or a cutout.

In these cases the property common is shape. A dressmaking pattern is made of paper, but the dress is made of cloth.

Economist, sociologists and other disciplines create 'models' that they can impose (synthesis) on an ecomony, a business sonciety etc.

 

 

For the purpose of analysis we have a similar situation

 

Take a bunch of childs blocks.

To the child the important property might be colour.

He will sort into red and blue.

So his model is 'blocks are red or blue'

 

A geometer would sort them into balls and cubes and prisms, regardless of colour.

So his model is about shape.

 

A topologist would say that a cube and a ball and a prisma re all the same, but a doughnut is different.

 

In general the model is a simpler system so that we can handle it more easily, finally translating the wanted property in the model to the target object.

In synthesis the model controls that property, in analysis the model reflects that property.

Edited March 11, 2015 by studiot

[StringJunky]

A model is a schematic compact presentation that contains just enough information to describe the mechanism of an idea. The mechanism is the system of how all the described interdependent elements interact and what the possible outputs are given some change in one those elements.

[swansont]

Here's an example, of sorts, that includes the context of why it's important.

 

Someone on twitter has recently claimed that his model of gravitational waves would effect he electron-proton mass ratios, and that this should be measurable in atomic clocks. At this point, that's not a model. That's a conjecture. To do some actual science, one would need to know how big the effect is, so we know what to look for in an experiment.

 

A model would tell us this information. It would tell us how big the effect on m_e/m_p is, and how the hyperfine states of the clock are affected, so that we can translate this assertion into a quantifiable prediction of what is to be measured. Models allow us to make specific predictions. The better the model, the more specific the prediction.

 

That allows us to tell us if the model is wrong — it has to have the power of being falsifiable. If you predict something will increase, that's a fairly "low resolution" model - it would only exclude observation that clearly decreased. If the result is supposed to jump, we want to know how high. A good model will tell us this.

 

Also note that "ad hoc" solutions are much less valuable. If you are just fitting an equation to known result but don't have a science-based mechanism for that equation, that's not really model. The various spectroscopic formulas for Hydrogen (Paschen, Lyman, Balmer) were ad-hoc. Just pattern-recognition. There wasn't an actual working model until you had the Bohr model (and that was replaced by QM)

[Robittybob1]

As an example, Newton's law of gravitation is a mathematical model. It can be used to predict the path of cricket balls and planets and can therefore be tested.

 

Any scientific hypothesis or theory must be based on one ore more mathematical models.

How much of that model did Newton work out himself? Thanks to all who have replied to my question. I still haven't fully understood how I go about converting an idea into a model.

I had thought deeply on how I could model it in a physical mechanical way but it became impossible for me to construct, so that was out, so what do you do next? Get financial backing to overcome the difficulty! That would be one solution.

[Strange]

How much of that model did Newton work out himself?

 

http://www-istp.gsfc.nasa.gov/stargaze/Sgravity.htm

 

He then used his formula to derive Kepler's laws and thereby confirmed the model.

 

 

Get financial backing to overcome the difficulty!

 

A basic education in maths might be a better start. There are some good on-line resources. Take a look at Coursera, for example.

[Greg H.]

Converting your idea into a model is relatively straightforward, but it does require relatively thorough knowledge of the existing subject matter.

 

What does your idea say? For example, if your idea is "The speed of sound transmission varies by the density of the medium", then you would need to come up with an equation that expresses that idea. That equation could then be used to test the idea.

 

So fir instance, your equation might be that the speed of sound in the atmosphere multiplied by the density of the object will give you the speed of sound through that object.

 

Other scientists can then take your equation, and the known values (speed of sound and density of an object) and test your idea under controlled conditions (to eliminate other variables). if it pans out, hooray. If not, you go back to the drawing board. In the case of our example, we may find that our predictions are close, but consistently not quite right. In that case, we may go looking for some other reason why the calculations seem to be so close. (In the case of our example, the speed of sound also depends on the stiffness of the medium in question).

 

All a "model" is in this case is a mathematical representation of what your idea is trying to express. Of course, the more complex the idea, the more complex the equation.

Edited March 11, 2015 by Greg H.

[Robittybob1]

Converting your idea into a model is relatively straightforward, but it does require relatively thorough knowledge of the existing subject matter.

 

What does your idea say? For example, if your idea is "The speed of sound transmission varies by the density of the medium", then you would need to come up with an equation that expresses that idea. That equation could then be used to test the idea.

 

So fir instance, your equation might be that the speed of sound in the atmosphere multiplied by the density of the object will give you the speed of sound through that object.

 

Other scientists can then take your equation, and the known values (speed of sound and density of an object) and test your idea under controlled conditions (to eliminate other variables). if it pans out, hooray. If not, you go back to the drawing board. In the case of our example, we may find that our predictions are close, but consistently not quite right. In that case, we may go looking for some other reason why the calculations seem to be so close. (In the case of our example, the speed of sound also depends on the stiffness of the medium in question).

 

All a "model" is in this case is a mathematical representation of what your idea is trying to express. Of course, the more complex the idea, the more complex the equation.

Interesting answer. Would the "idea" have to be based initially on some observations? There would be some data that suggests the speed of sound varies with density. I could imagine you would then graph density verses speed and see what sort of curve one gets.

Slope and shape will reveal what type of relationship you would be dealing with.

When I first read what you wrote I thought yo were saying someone would just make up a formula!

So will all models rely on some initial data?

Why did Newton make gravity proportional to mass not volume? Different objects weighed the same when their mass was the same rather than their size or volume. Observational data seem so essential.

How did he work out it was proportional to mass times mass? Deduction?

From that link about Newton that Strange gave us:

 

 

It wasn't obvious to Newton, That falling apple... sure, there was mass pulling it down, but there was also mass pulling it sideways in all directions, pulls which largely canceled. Even if the sum-total of all pulls pointed towards the center of the Earth, who was to say it obeyed the same inverse-square law as a mass concentrated at a point? Newton did not trust the above calculation until he proved to his satisfaction that the Earth's attraction could always be replaced by the one of a mass concentrated at its center.

Making a discovery often involves groping and guessing, before a clear pattern emerges. We, who know that pattern and take it for granted, may feel the discovery was obvious. But it need not have appeared at first.

Amazing! It takes time trials and errors to get there!

Edited March 11, 2015 by Robittybob1

[Greg H.]

Some models are built to explain an observed phenomenon (such as my example) some are built based on a current model to try and better explain some area that we don't understand well. I'm not a scientist by trade, but I think the basic idea is that if you want other scientists to think seriously about your idea, a model is the best way to accomplish that because it lets them objectively evaluate the idea based on its predictions.

 

In some respects, science is a lot like the criminal justice system.

It's not about what you know, or what you believe.

It's what you can prove that matters.

Edited March 11, 2015 by Greg H.

[imatfaal]

Some models are built to explain an observed phenomenon (such as my example) some are built based on a current model to try and better explain some area that we don't understand well. I'm not a scientist by trade, but I think the basic idea is that if you want other scientists to think seriously about your idea, a model is the best way to accomplish that because it lets them objectively evaluate the idea based on its predictions.

 

In some respects, science is a lot like the criminal justice system.

It's not about what you know, or what you believe.

It's what you can prove that matters.

 

I think it is more like the criminal justice system than you tell.

 

It is not what you know, or what you believe; it is what you can persuade others to believe.

 

In criminal justice it is the jury of your peers, and in science it is again the judgment of your academic peers. The basis of their decision will be different - but in the end you are looking to persuade people that your explanation of the facts/world is the correct one.

[Robittybob1]

 

I think it is more like the criminal justice system than you tell.

 

It is not what you know, or what you believe; it is what you can persuade others to believe.

 

In criminal justice it is the jury of your peers, and in science it is again the judgment of your academic peers. The basis of their decision will be different - but in the end you are looking to persuade people that your explanation of the facts/world is the correct one.

Would a model have made a difference then? I can think of a demo model. "Still not good enough", could have been the reply.

So you are saying it is a matter of changing the jury's view that counts the most, but you also have to convince the judge for he gets to sum up the case too.

[imatfaal]

Would a model have made a difference then? I can think of a demo model. "Still not good enough", could have been the reply.

So you are saying it is a matter of changing the jury's view that counts the most, but you also have to convince the judge for he gets to sum up the case too.

 

In both cases the judge does not weigh the evidence or determine fact/fiction - but determines whether the evidence is deemed admissible; in a court of law that might be the prohibition against hearsay testimony and in the scientific journals the need for repeatable observations rather than anecdote.

 

In this case and most cases in speculations where a model is lacking what is required is a set of statements (hopefully mathematical - but definitely quantitative in some way) that would allow another member to judge the merits of the speculation.

 

If I say that I reckon the characteristics of a bicycle determines its top speed then really I am saying nothing at all - the response is "yeah and...", "so what", "meh" - I need to be more specific. I could do this and make it clear that I have no real model at all - ie by saying that I have noticed my orange bike is faster than my white bike; personal, anecdotage, untested etc. Or I could do this and show that I do have a model - that lighter, more aerodynamic, better fitting, good pressure tyres, and well maintained bicycles will change a rider's performance by around 10 percent on an average over a decent number of trips. The science behind this hypothesis could be explained (and argued with) - less mass to carry up hill and accelerate, less drag, good conversion of effort to acceleration, lowered rolling friction, less mechanical friction. Preferably I could then present data to back this up. I could then try to explain what contribution each factor makes - and explore whether any of these factors are interdependent etc. The crucial difference between the first useless idea and the better second form is that the second form can be carried forward, explored and critiqued - whereas the first is too nebulous, personal, and unsubstantiable. Unfo - your speculation remained too long in the first "I reckon..." category

[swansont]

Would the "idea" have to be based initially on some observations?

No, not directly. Special relativity was based on applying the concept of an invariant speed of light, which comes from the equations of electromagnetism. Not from anything that was observed (except in a very indirect, abstract way, in the sense that Maxwell's equations are based on observation).

[Robittybob1]

No, not directly. Special relativity was based on applying the concept of an invariant speed of light, which comes from the equations of electromagnetism. Not from anything that was observed (except in a very indirect, abstract way, in the sense that Maxwell's equations are based on observation).

Right, one day I might get around to the Maxwell's equations, but I was a very practical physics person who would do things such as this person in the short YT clip of levitating a ping pong ball with a dryer https://www.youtube.com/watch?v=-myUNjYjhIA. The airflow keeps the ball centralized in the flow so in fact he is able to tip the system to nearly 45 degrees. OK one can look at that and understand the physics of it but if you said I have to write down the mathematics of that demonstration before you'd accept it, I would struggle.

Would the demonstration be a sufficient model in itself?

 

.....

In this case and most cases in speculations where a model is lacking what is required is a set of statements (hopefully mathematical - but definitely quantitative in some way) that would allow another member to judge the merits of the speculation.

 

..... Unfo - your speculation remained too long in the first "I reckon..." category

Good reply, and thanks for the opinion. I'm feeling quite beaten today, but hopefully I'll recover.

 

Ok we were discussing a lot of relatively simple physics but each step was disputed. How can that be? When faced with that I found it became impossible to make progress no matter how well I thought I explained each step.

 

Each accepted aspect of physics will hold true - if there is an electrical current there will be a resistance and heating. (baring the superconductor situation). So if a motion created that current and it is flowing around a body there with be a viscosity (a friction) factor to overcome.

 

These are just simple physics that can't really be disputed, can they? So they don't have to be modeled as well, surely not.

[ajb]

Another simple example would be to compare 'what goes up must come down' with properly applying the equations of constant acceleration to an object thrown up in the air. For sure if I throw a stone in the air it will come back down again. However, with the application of mathematics I can say so much more, like if I know the starting velocity I know how high I can throw the stone. Or if I drop a stone down a well can use the time it takes to hit the ground to tell me how deep the well is. And so on... Just by using 'what up must come down', which is not a wrong statement, provided the object is not thrown with sufficient velocity to escape the Earth, it tell us far less that some simple mechanics does.

[Robittybob1]

Another simple example would be to compare 'what goes up must come down' with properly applying the equations of constant acceleration to an object thrown up in the air. For sure if I throw a stone in the air it will come back down again. However, with the application of mathematics I can say so much more, like if I know the starting velocity I know how high I can throw the stone. Or if I drop a stone down a well can use the time it takes to hit the ground to tell me how deep the well is. And so on... Just by using 'what up must come down', which is not a wrong statement, provided the object is not thrown with sufficient velocity to escape the Earth, it tell us far less that some simple mechanics does.

The art of throwing the javelin is something I practiced as a kid. You had to throw it up and make it come down point first. Has it ever been analysed mathematically, and could it teach you any more than a bit of practice could?

A good technique could have helped, gym work to build up muscle strength too. Yes it appears it is a bit of a science.

Edited March 12, 2015 by Robittybob1

[ajb]

The art of throwing the javelin is something I practiced as a kid.

That is interesting as the tip of a javelin can be described by an effective theory that is second order in time derivatives.

[swansont]

Right, one day I might get around to the Maxwell's equations, but I was a very practical physics person who would do things such as this person in the short YT clip of levitating a ping pong ball with a dryer https://www.youtube.com/watch?v=-myUNjYjhIA. The airflow keeps the ball centralized in the flow so in fact he is able to tip the system to nearly 45 degrees. OK one can look at that and understand the physics of it but if you said I have to write down the mathematics of that demonstration before you'd accept it, I would struggle.

Would the demonstration be a sufficient model in itself?

 

Possibly. You need to be sure it scales up (or down). Showing a ping-pong ball in a blow-dryer does not mean that the system would work with everything being bigger (or smaller) — not all parameters scale linearly. And that scaling is where the mathematical model comes in.

[Greg H.]

That is interesting as the tip of a javelin can be described by an effective theory that is second order in time derivatives.

 

People are always amazed when they finally realize the amount of complex mechanics calculations they do in their head without ever even realizing it.

[Bignose]

Ok we were discussing a lot of relatively simple physics but each step was disputed. How can that be?

This is pretty much how all of science works.

 

#1 We don't have a universal equation of everything at this moment. That means, we have a lot of different equations for different situations. Each one of those equations have assumptions implicit in their derivation and domains of validity where they are known accurate and considered applicable. So, any time anyone uses an equation in science, the very first question is: is this equation valid for this situation? Or is it appropriate to use this model here?

 

#2 The above question is important because if you start misusing equations or models when they aren't applicable, it is like building a house on sand. Without a solid foundation, the house will collapse. In the same way, if you use an equation incorrectly early in a development, all conclusions based on that are suspect and probably not sound, either. It doesn't matter how logical or aesthetically pleasing a result is, if it is based on a poor assumption, it is rejected.

 

So, in the end, yes. In science every step is indeed disputed. It is the framework that has led to all the successes we enjoy from science today.

Edited March 12, 2015 by Bignose