Object Encapsulation: Is it Possible?

[pairofstrings]

TL;DR

Is it possible to write an equation that encapsulate all?

Is it possible to encapsulate an object which has quantity, structure, space, change into a single equation? I am just asking if it is possible or not, I am not asking anyone to tell me how. Assume that there is a book. Is it possible to write everything about this book in a single equation? Let's not worry about what is written inside the book. Book has cover and a few pages. As book is a 3-D object is it possible to write quantity, structure, space, change of this object in a single equation.
Thank you.

 

[.Scott]

What's so special about an equation? Why not write the information in paragraph form?

 

[Filip Larsen]

Is it possible to encapsulate an object which has quantity, structure, space, change into a single equation?

If you by "object" refer to a real world extended object with all its physical and mechanical characteristic and behaviors and by "single equation" mean to write that up into a single unified meaningful mathematical form, then in general, no. Different physical aspects of real-world objects are in general modeled by different laws, which in in general has different and independent mathematical structure.

 

[pairofstrings]

If you by "object" refer to a real world extended object with all its physical and mechanical characteristic and behaviors and by "single equation" mean to write that up into a single unified meaningful mathematical form, then in general, no.

That means, if I am describing quantity, strucutre, space, change of an object then I would need four different statements - one for quantity, one for structure, one for space, one for change?

The 3-D object book lying somewhere has clear message that the quantity of book is one.
Similarly the object has structure, there could be space, and change..

 

[jbriggs444]

That means, if I am describing quantity, strucutre, space, change of an object then I would need four different statements - one for quantity, one for structure, one for space, one for change?

The 3-D object book lying somewhere has clear message that the quantity of book is one.
Similarly the object has structure, there could be space, and change..

So you have four parameters that you wish to encode values for within a single equation: Quantity, Structure, Space and Change. Call them $Q$, $S_t$, $S_p$ and $C$. Suppose that the values that you wish to encode are $q$, $s_t$, $s_p$ and $c$. Then write down the following equation:$$(Q-q)(S_t-s_t)(S_p-s_p)(C-c)=0$$
QED.

You can also encode the contents of all the libraries in the world into a single integer. The approach is rather straightforward. You start by putting all the libraries in the world into a sequential computer file filled with eight bit bytes. Use MIME encoding if you want the pictures as well as the text. Now consider that computer file as a large integer expressed in base 256. Done.

 

[hutchphd]

I think it was a Feynman argument that the equation that rules everything is $$U=0$$ where U is defined as the "unworldliness"...the rest is detail. I don't know the reference but probably the Lectures.

 

[pairofstrings]

So you have four parameters that you wish to encode values for within a single equation: Quantity, Structure, Space and Change. Call them $Q$, $S_t$, $S_p$ and $C$. Suppose that the values that you wish to encode are $q$, $s_t$, $s_p$ and $c$. Then write down the following equation:$$(Q-q)(S_t-s_t)(S_p-s_p)(C-c)=0$$
QED.

You can also encode the contents of all the libraries in the world into a single integer. The approach is rather straightforward. You start by putting all the libraries in the world into a sequential computer file filled with eight bit bytes. Use MIME encoding if you want the pictures as well as the text. Now consider that computer file as a large integer expressed in base 256. Done.

Thanks for the reply.
In this equation, I don't see any object like circle conceived.
The equation doesn't show me the quantity, structure, space, change for the circle. Its some random variables arranged in some way.

When there is an equation of circle for which I am trying to define quantity, structure, space, change then from this equation it should be evident that the context is circle and all the rest of the stuff along with other stuff in the equation is quantity, space, change..

Example:
Equation of circle says that the distance between the point from center of circle to other points on a plane should be equally spaced.

Should that be the structure of a circle(?) then is it possible to embed quantity, space, change into this equation?

 

[jbriggs444]

In this equation, I don't see any object like circle conceived.

Well, you tell us. What is the quantity, structure, space and change for a circle? Once you know, you can fill those into the equation.

Edit: Possibly you need to be asking a different question. Rather than asking whether there is an equation that encompasses everything about a particular entity, you should be asking whether there is a quantity of information that encompasses everything about it.

And perhaps you should establish a way to talk about how one might go about encoding or transmitting that information. That might lead to a way to quantify information.

Then one might Google things like "Information Theory" or "Claude Shannon".

As I recall, Claude came at the problem space from the point of view of data transfer over a noisy channel and chose to model the channel as delivering discrete messages with a definite probability of being misread. Despite the seeming irrelevance, this leads to exactly the problem space that you need to be working in.

 

[Mark44]

Is it possible to encapsulate an object which has quantity, structure, space, change into a single equation?

IMO, no it is not, unless we're talking about extremely simple objects. Your question seems to be related to one you asked some time ago, in which you asked whether one could encapsulate all of the qualities of, say, a chair. As an example of why I don't believe such encapsulation is possible, consider the sound that a musical instrument makes. Although we can approximate the sound of a piano, guitar, or other instrument digitally (as is done on CDs and DVDs), many audiophiles prefer the analog sounds of vinyl records or reel-to-reel tapes as being closer to the sound of the recorded instrument.
As already noted, sounds and other attributes are not represented by equations, but rather, by sequences of numbers that can be decoded to represent (with more-or-less detail) the sound or image that was recorded.

 

[DaveE]

A single equation? Why. May things are described by multiple equations (linear algebra, for example). Yes you can usually reformulate these as a single equation (perhaps a matrix or tensor equation), but I think that just obscures the reality, things are often systems, not simple equalities. Not everything is correlated with other things.

This reminds me of medieval arguments about how many angels can fit on the head of a pin. Why? Why do you care about this particular representation of the world?

 

[Mark44]

A single equation? Why.

Why do you care about this particular representation of the world?

Very good questions,, indeed.

 

[pairofstrings]

If you by "object" refer to a real world extended object with all its physical and mechanical characteristic and behaviors and by "single equation" mean to write that up into a single unified meaningful mathematical form, then in general, no.

IMO, no it is not, unless we're talking about extremely simple objects.

A single equation? Why.

Why is the science world trying to write an equation no more than one inch long for things like "Unified Theory"? Is it because it's physics? And when it comes to math world, I should never limit my imagination?

 

[jbriggs444]

Why is the science world trying to write an equation no more than one inch long for things like "Unified Theory"?

Laws of physics tend to be compact. They pretty much have to be in order to be useful and discoverable. Initial conditions can be arbitrarily complex.

 

[Mark44]

From post #1:

Is it possible to encapsulate an object which has quantity, structure, space, change into a single equation?

Why is the science world trying to write an equation no more than one inch long for things like "Unified Theory"? Is it because it's physics?

The formulas in physics are very different from the type of equation you asked about in post #1. Here are a few examples from physics:

• $F = ma$
• $\tau = I \alpha$
• $E = mc^2$

Each of these equations describes one aspect of some object, such as the force that can accelerate an object of mass m, the torque that cause rotational acceleration of an object with moment of inertia I, or the energy equivalent of an object of mass m.

These and other equations do not completely describe some object (such as your earlier example in this thread of a book in a library). In short, these equations do not describe the volume of the book, its number of pages, the color and material of the binding, etc.

And when it comes to math world, I should never limit my imagination?

My advice would be to learn some mathematics (or physics) before letting your imagination run wild.

 

[pairofstrings]

The formulas in physics are very different from the type of equation you asked about in post #1. Here are a few examples from physics:

• $F=ma$
• $τ=Iα$
• $E=mc^2$

Each of these equations describes one aspect of some object, such as the force that can accelerate an object of mass m, the torque that cause rotation of an object with moment of inertia I, or the energy equivalent of an object of mass m.

The above equations could be a few statements about some object. What I am trying to know is, if I could write one aspect of an object in an equation then is it possible to "embed" the remaining aspects into the same equation.

 

[jbriggs444]

The above equations could be a few statements about some object. What I am trying to know is, if I could write one aspect of an object in an equation then is it possible to "embed" the remaining aspects into the same equation.

The notion is nonsense.

You could embroider the equation on a tapestry and use some subtle encoding in the thread count to add extra information, I suppose. But why would you?

 

[pairofstrings]

Nice.
Thanks for the replies.

 

[DaveC426913]

The above equations could be a few statements about some object. What I am trying to know is, if I could write one aspect of an object in an equation then is it possible to "embed" the remaining aspects into the same equation.

The notion is nonsense.

I think what he's getting at is, if you described an object using, say, m for mass, could you then add other properties of the object by substituting some other equation, containing other properties (say, volume and density) for m, until you have one long equation with a bunch of properties.

(The answer is still no, since properties like mass are fundamental, not derivable from other properties.)

 

[WWGD]

In order to be of some use you wouod have to define all your terms , starting with ' structure' in much more detail. Specially if you want a more detailed answer.

 

[hutchphd]

For Feynman's argument see equation 25.32 et seq
https://www.feynmanlectures.caltech.edu/II_25.html

 

[Filip Larsen]

For Feynman's argument see equation 25.32 et seq
https://www.feynmanlectures.caltech.edu/II_25.html

But its just a mathematical notation that semantically doesn't really describe anything by itself. Or in other words, just saying $U = \sum{U_i} = 0$ doesn't really mean anything before you give the details of each $U_i$. It is a bit like saying the the universe follows the variational principle because you can use the same mathematical method (calculus of variations) to analyze each individual physical problem even though they model different situations applied under different physical laws.

 

[pairofstrings]

I think what he's getting at is..

I am one in quantity, living in space, I have structure and few activities.

Mathematics may encompass many other different types of quantities, structures, spaces, changes - I believe that is why mathematics exist.
Me in existence also have quantity, structure, space, change - which is mathematics.

So, what I am trying to do is, describe an object in a single equation.
The single equation should be self-sufficient to talk describe about itself.

 

[hutchphd]

You are that equation.

 

[Mark44]

I am one in quantity, living in space, I have structure and few activities.

But if you think a single equation can describe you, I'm afraid you are sadly mistaken.

So, what I am trying to do is, describe an object in a single equation.

Unless the object is extremely simple, this is not a reasonable thing to do

The single equation should be self-sufficient to talk about itself.

Any equation is self-sufficient to talk about itself.

You seem to be obsessed with equations, possibly thinking that they are somehow magic, but with almost no understanding of them.

Back in December, you wrote this (https://www.physicsforums.com/threads/y-for-heart-curve.996738/post-6425031):

The graph of the equation 1 = x + y is easy to draw. It says 'x' is 1 and 'y' is 1.
Therefore, I can plot the point at x = 1 and y = 1.

This clearly shows that you don't understand some very basic concepts of equations and graphs.
I'll repeat what I've said before: Get yourself a basic precalculus textbook, one that presents lots of different functions.

Your scattershot and random approach to learning about graphs is not at all fruitful.

Thread closed.