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or should observations define mathematics?

Presently physicists use two different methods to quantify our understanding of the universe.

The first or traditional method is to allow observations to define mathematics.  In other words, they observed how the components of their environment interact and based on those observations derive equations that could explain those interactions.
For example, Isaac Newton made qualitative observations of how objects in his environment interacted with the earth’s gravitational field.  He then applied the understanding gained from them to derive abstract equations that permitted the quantitative predictions of future interactions that could be applied throughout the cosmos.

However, with the advent of higher mathematics and advance computing technology physicists now have the ability to define observations in purely mathematical terms.  In other words, it is possible to derive equations directly from the quantitative results of interactions that can make accurate predictions of future interactions without ever observing them.

For example, String Theory is based purely on analyzing the quantitative results of interactions and then, using only that information define equations that will give accurate quantitative results of future interactions.  The understanding of those interactions is derived solely from the abstract logic of the equations used to define them and not on observing how they take place.

Which method a physicists uses depends on how she or he defines the science of physics.

For example, if one defines physics only in terms of its ability to make accurate predictions of future events then he or she will most likely aspire to the philosophy that mathematics should define observations.

However, if one defines physics in terms of understanding of how and why matter and energy interact with our environment then she or he will more likely embrace the philosophy that observations should define mathematical equations.

Originally, mathematics was a tool used by physicists to either verify or discredit a theoretical model because it gave them the ability to quantitatively check its conceptual validity. 

For example, Einstein first developed a conceptual understanding of space-time, based primarily on the observation that the speed of light was constant in all reference frames and then developed the theoretical structure of Relativity from that understanding.  Later he developed the equations that quantified and verified the accuracy of his conceptual model.  He did not define the equations first and then develop its theoretical structure from them.

However, the proponents of the concept that “mathematics defines observations” have taken the opposite approach to science.  They first observe the quantitative results of interactions between matter and its environment and then, through trial and error define a series of abstract equations, which can predict the quantitative results of those interactions without ever observing how those interactions take place.  They then use those equations to define a theoretical structure.

For example, Quantum Theories define how and why the quantum mechanical aspects of energy/mass interact with our environment based solely on mathematical probability functions or equations.  They then use those abstract equations to define a qualitative theoretical structure.

However, they cannot use the quantitative results of their equations to verify the conceptual accuracy of their theoretical model because it is based purely on them whereas Einstein and Isaac Newton could because theirs were based on a conceptual model derived from direct observations of their environment.

Physics as the name implies is the branch of science concerned with the nature and physical properties of matter and energy.

Therefore, no matter how accurate the quantitative predictions or probability functions of Quantum Theories are there will always be room for doubt as to their validity because they cannot be conceptually verified in terms of the observable properties of the world we live in even though they make extremely accurate predictions of future events. 

In other words any theoretical model involving matter and energy that is based solely on an abstract quantity such as a mathematical equation will always lack a certain degree of scientific creditability because the mind of a mathematician can create fictional worlds just as proficiently as that of science fiction writer.  

Therefore, the answer to the question “Should mathematics define observations or should observations define mathematics” depends on how one defines the science of physics.  If one defines it only in terms of the ability to make quantitative predictions of the interactions of matter and energy with our environment without being concerned with how they are connected to it then mathematics should define observations.  However, if she or he defines it in terms of physically connecting the quantitative predictions of a theoretical model our environment to it he or she should allow observations to define mathematics.

Later Jeff

Copyright 2008 Jeffrey O’Callaghan

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