I am trying to build a particular theory, and I am wondering if there is a quantitative formulation for how much an object has changed.
For example, if an oak seed grows into an oak, how much has it changed? Any insight is appreciated.
I am trying to build a particular theory, and I am wondering if there is a quantitative formulation for how much an object has changed.
For example, if an oak seed grows into an oak, how much has it changed? Any insight is appreciated.
This is the precise answer to that question, I had exactly the same problem. Here are some ideas, from my next book:
First, let's consider change from a thermodynamic perspective.
A gas that is in a thermodynamic system, with a positive temperature, after the process of spontaneous evolution (molecules have exchanged energy, entropy is at its maximum, energy has dispersed between all molecules) will theoretically keep its temperature forever (supposing it is positive), since thermodynamic systems are ideal, closed, they don't interact with the environment. Therefore, it can be said that:
But the fact that the temperature is positive and constant implies that molecular activity exists: inside the container, molecules bounce, as if they would be small balls (not right so, but OK for this analysis). So, at every instant, some molecules have more kinetic energy than the rest, and some have more. Molecular "bouncing" occurs constantly. But the temperature don't change.
In other words, while the molecules in the container are constantly exchanging energy, that is, that change is permanent from a microstatic perspective, the temperature, which is a macrostatic quantity is constant. In other words, while molecular energy changes at each instant for each molecule, the total energy of the container is constant (first law of thermodynamics). So, we can say that:
Simply explained, get a bowl of hot soup. Touch it: it's hot. Remove your hand, and touch it again quickly; the temperature is the same. While all molecules are bouncing, therefore, their kinetic energy is changing, in a period of some seconds, the temperature does not change. In this case, the bowl will get cold after some minutes, but that's because it's not a perfect thermodynamic system. A thermodynamic system is closed, so it can be at the same time temperature forever. Or you can think you live in a hot weather place, so, the temperature of the bowl never changes, it's forever hot.
What happens here? Is there change or not?
Thermodynamic solves this issue stating that temperature is a macrostatic quantity, and that molecular kinetic energy is a microstatic quantity. While microstatic values change constantly, macrostatic values can be constant: no change.
The relationship between kinetic molecular energy and temperature is direct. But temperature represents an average of the kinetic energy of all molecules. Once the three laws were stated, someone noticed there was no relationship between temperature and energy. So, the Zeroth law was stated, suggesting that is a priori from the others (hence the name "Zeroth law").
What it is not commonly considered (and is key to your question) is this: what is the limit between the macrostatic and the microstatic? When do things start to change in this system? This leads to a blatantly obviously corollary:
Therefore,
Let's explain this corollary with a simple example. Imagine that you can change your size the way you like, breaking all physical rules. If you, following the example of the bowl of soup, get to the size of a soup molecule, you will notice that change is permanent. If you quickly change your size to the human normal, you will not notice change. Somewhere in between, you will get to a size where you will not notice change at first sight, but with a closer look, change will be perceived. Again, change is subjective.
Now, out of thermodynamics.
Argument 4 has a huge load. Change, as such, exists permanently in the universe, but the perception of change is subjective. Worst even, it is the opposite: static things are not part of nature:
An equivalent thing of the problem of temperature occurs when you look yourself twice in the mirror: although every single atom has changed radically, you seem to be the same person. You are not the same person. The second time, you are looking for a completely different one. But you perceive yourself as if no change would have occurred.
This is the classic problem of the river: while the river constantly changes, it is the same, which is a paradox.
I have my own further conclusions, I leave you to obtain yours. In any case,
Try getting a measure of change of a glass of water at room temperature at any two instants in time. While the temperature and the volume seem static, volume is constantly reducing, and molecules are increasing and decreasing temperature. If you take only the temperature of half of the water (without physically separating it from the other half), using a very precise thermometer, temperature will change, because at any instant, only the total average is constant, but not the value of the parts. This is the exact case of you reducing your size, as explained before.
Almost every dynamic theory in Physics quantifies change. In a physical theory, commonly, the state of a changing system is encoded with a series of numbers. For each instant of time t, we have slightly different numbers (n_1(t), ...,n_k(t)). A dynamic theory explains how these numbers change as a function of the changing factors. So one way to quantify change is to try to formulate a dynamic model (usually by means of differential equations or finite difference equations) of how an object changes, automatically for each instant you will have a set of numerical indices that would indicate how much the entity has changed.
Here is a gesture toward the construction of such a theory:
(a): first, a puzzle: (i): if a changing thing really changes, then it can't literally be the same before and after the change. But (ii): if it isn't literally the same thing before and after the change, then nothing has changed.
(b): of course, the puzzle was well known to the ancients and is still discussed today. Hence the scholastic distinction between essential and accidental properties, or nagarjunas denial of svabhava all the way up to Lewis' discussions of identity over time. Of course, not everyone has found such arguments for (or against) change coherent. So one's theory will need background resources rich enough to define a notion of change. As noted in (a) above, one of the resources needed will be a conception of identity and hence a conception of objections and properties.
(c): Suppose that (b) has been accomplished, say via regarding objects as bare particulars augmented with essential properties. Then consider any accidental property, say height. Define a metric over it. Doing so with all possible accidental properties will allow you to define a metric over these metrics, and thus quantify change.
(d): (a) is due to Copi. for (b) see the thinkers mentioned. (c): be aware that there are a fair amount of competing notions of object out there. This one is probably the easiest with which to quantify change.
Suppose you start from the perspective of physics. An object is a collection of particles related to each other in a particular way. You can in principle count all the particles of different types- so many atoms of carbon, so many of oxygen etc- and you might find a way to categorise and quantify the arrangement of those particles, eg by considering how they are connected at a molecular level and so on. You might also consider the macroscopic properties of the object- for example, the branches of your oak tree might be moving in the wind.
The problems you will face are as follows:
Tracking the change of an object as large and complex as an oak tree, in terms of its fundamental components, is utterly impractical.
Considering change in terms of physics alone leaves you with no way to deal with other types of change- eg change of mood in humans.
Defining an object is not always possible. Consider a cloudy sky. How can you precisely determine the boundary of a particular cloud? Suppose two clouds merge- how can you say which of them has changed? Take your acorn- it grows into an oak tree by combining with tons of material from the soil. Does it make sense to talk about the acorn having changed into the oak tree, when really the acorn was just a catalyst that allowed tons of material in the soil to reassemble into a tree?
Differentiating between microscopic and macroscopic change. An object such as a glass of water on a table has a set of fixed macroscopic properties, such as position, mass etc, but at a molecular level there is continuing random change. How would you design a classification system to determine the boundary between microscopic and macroscopic properties? Suppose your 'glass of water' consisted of five molecules of glass and two of water- its 'position' could hardly be defined in a meaningful sense. Now imagine growing that microscopic glass of water into a full size one by adding a molecule at a time- where on that transition does it become meaningful to consider macroscopic change?