Philosophy Discussion Forums

There has been a lot of talk on this subforum about Quantuum mechanics, and it seems there are a fair number of people here that can no longer relate to the findings of quantuum physics because they feel it is all just based on ever-more complex and remote calculations. That none of it is based on any actual observation, or evidence, any more.

That made me thinking whether the Mathematics are not, themselves observations? Math, much like formal logic, only reforms the statements you input, it doesn't alter their content. If you put observations into a calculation, what you get out will, similarily, be observations. If you, for example, observe directly the Speed and the Mass of a baseball, because you throw it with you hand, is the calculated force of that baseball not also an Observation?

Naturally, Math works with it's own set of Axioms, but so does our basic perception.

As I'm sure it's been noted before around here, observartions and the analysis/interpretation of those observations are inseperable. And mathematics is an analytical and interpretative tool.

I'm a great believer, as a general philosophical underpinning to understanding, in continuity - in continuous shades of grey rather than black and white. I think in our attempts to understand the world we often impose artificial divisions on it. I don't think there's anything wrong with that, and I think it is useful and necessary, as long as we are clear that they are artificial and that the boundaries are positioned by us for our own utility. Perhaps one such division is between the concepts of observation and analysis.

I think the complex mathematics involved in quantum mechanics deal with making predictions. But this is similar to traditional physics. The typical person probably couldn't tell you or spot on sight the calculations involved in figuring out the paths of balls on a pool table based on the force of a hit. Understanding the concepts, and being able to philosophically analyze them, is different. Quantum mechanics throws a second wrench in the mix because unlike with the classic physics of pool balls it is hard to understand and agree on even ignoring the mathematics. That's why even macro-analogies of quantum mechanics (e.g. imaging superposition of pool balls on a table as if they were electrons) seem to make little sense, especially to us laymen. I think it is easy to mix up the complication of the math with the non-mathematical oddities of quantum mechanics which essentially disprove classical physics, which raise countless questions that cannot be answered scientifically at least at this time.

Cronos988 wrote:There has been a lot of talk on this subforum about Quantuum mechanics, and it seems there are a fair number of people here that can no longer relate to the findings of quantuum physics because they feel it is all just based on ever-more complex and remote calculations. That none of it is based on any actual observation, or evidence, any more.

That made me thinking whether the Mathematics are not, themselves observations? Math, much like formal logic, only reforms the statements you input, it doesn't alter their content. If you put observations into a calculation, what you get out will, similarily, be observations. If you, for example, observe directly the Speed and the Mass of a baseball, because you throw it with you hand, is the calculated force of that baseball not also an Observation?

Naturally, Math works with it's own set of Axioms, but so does our basic perception.

Mathematics does work from axioms, but basic perceptions do not.

Mathematics has axioms and the calculations made from those axioms (using the symbols and operations that are defined by the system) can be considered to be theorems of the system. They are deductively ' provable' within the system. But the mathematics system is, in its pure form, entirely abstract. It has no explicit correlation with anything in the real world.

In contrast, perception is an inductive process whereby the conclusions are not deductively derivable from any axioms. (There are no axioms.) Instead they are constructed using a pattern creation process from sense-data.

In science, mathematics is applied to observations by an inductive mapping. If it is seen that the data can be described by using sound mathematical formula then that becomes a 'theory'. This theory can subsequently be used to make predictions and be tested against further observations.

When people talk about objects 'obeying' the law of gravity or about particles of 'obeying' the laws of quantum mechanics this is actually a misnomer (or perhaps a popular simplification). The laws of gravity and quantum mechanics are only descriptions of perceptions; it cannot be claimed that the real world actually operates in this way.

Cronos988 wrote:There has been a lot of talk on this subforum about Quantuum mechanics, and it seems there are a fair number of people here that can no longer relate to the findings of quantuum physics because they feel it is all just based on ever-more complex and remote calculations. That none of it is based on any actual observation, or evidence, any more.

I don't know of anyone familiar with the subject of quantum mechanics who doesn't find it frustrating at some level. But despite the seemingly remote and complex calculations, it is not only based on observation and evidence - it is better than any competing theory (at this time) at exhaustively explaining those observations.

I think that is largely why it is so frustrating. It doesn't make common sense, yet no one has yet produced a better theory.

Cronos988 wrote: That made me thinking whether the Mathematics are not, themselves observations? Math, much like formal logic, only reforms the statements you input, it doesn't alter their content. If you put observations into a calculation, what you get out will, similarily, be observations.

As you state, mathematics is really just logic codified into agreed upon symbols with agreed upon axioms. As such each mathematical formula or proof can be seen as a description of reality or a logical argument for some truth. This allows us to make powerful theories which explain a wide rage on phenomena which we observe. However, I do not believe that mathematics can ever substitute for actual physical observation. Since math is just logic we are in danger of going astray should we not verify our theories from time to time in the laboratory. A few years back, I undertook a detailed study of Alchemy and its history for a paper I was writing. What astounded me was how logical and well thought out most of its tenants were. Rather than being the stuff of crackpots, given the empirical evidence and paradigm concerning the world of that day, the work of Alchemists in theory and logic were almost too elegant and too beautiful not to be true. But of course they were hopelessly far off base.

That in my opinion is the true strength of modern science. Where early efforts in Alchemy and Platonic physics rested almost solely on the capacity for logic and intuition about the universe, modern physics lies about equally between empirical observation and logical analysis. Arguing solely from our intuition about the world we would have probably never arrived at the strange world of Quantum Mechanics, though now that we have we find one experiment after another verifying the theory to remarkable accuracy. So in answer to your original question, I would say that Mathematical Calculations are logical applications of theory to physical observations, but cannot substitute for actual observations done in the lab.

What astounded me was how logical and well thought out most of its tenants were. Rather than being the stuff of crackpots, given the empirical evidence and paradigm concerning the world of that day, the work of Alchemists in theory and logic were almost too elegant and too beautiful not to be true. But of course they were hopelessly far off base.

This statement really strikes a chord with me regarding String Theory and M Theory. One of its major champions, the highly regarded physicist Eugene Wigner, has said the same thing about String Theory being too elegant and beautiful not to be true. And yet after 45 years, where are the proofs, empirical evidence, and applications to vindicate the theory?

Incidentally, I concur with A_Seagull and MazerRackhem's previous posts on this issue.