Exactly. Observation of physical phenomena is at the root of science, not maths. Rpenner put it very eloquently I think in another thread, when he observed that "the map is not the territory". We make mathematical models but it is dangerous to assume that the models are the reality, however closely reality appears, today, to conform to their predictions. The constants of physics have to be measured: there is no mathematics that can derive them all without measurement. And then, as I have been saying, most of science is too messy and complex for mathematics to account for it completely.
IMO, Mathematical functions have always existed! Even before there was anything physical the mathematical function existed as an abstract potential. It is how the universe functions dynamically. *Cause and Effect* is a natural universal *mathematical* abstract constant. A specific cause will result in a specific effect. The only possible way this can happen is if there is an underlying natural function which is inherently mathematical. Else there would be only chaos. Seems to me we are in agreement on this. I hope this clears up this misunderstanding.. If we go back in history we can clearly see that the earliest understanding of universal mathematical functions was incomplete. We only need to look at the evolution of the science of chemistry, which started as alchemy. Example: the attempts to make gold by mixing stuff together. At that time it was unknown that the mathematics of creating gold require enormous heat and pressure, as can only be found in nature as a result of a star gone nova. Today we know this and we are in fact able to create gold, it just cost much more to make it than its worth, because we have to simulate the heat and pressures necessary by artificial means. Yep, until we get the maths just right there will be many failures. But we arenow able to create self-replicating synthetic DNA (XNA), which are the mathematical instructions for cell growth and functions. Hazen made the point that biomolecules may be formed by a range of methods, yet all have a common denominator in that the process is mathematical in essence. Yet, our knowledge of AI is evolving at an incredible rate. We are already considering the possibilities of quantum computers. To use the term "meaning" is irrelevant to the mathematical function. It applies only to humans, however tests show that a Lemur (a very distant cousin) can abstractly count by recognizing the difference between *more* and *less*. but more remarkably, the Lemur can be taught to select a lesser quantity, in order to receive a reward. A mathematical calculation. Why would you consider this "weird". Seems to me that any other hypothesis would be much weirder than the orderly processing of information by consistent mathematical functions, which are apparent at many levels from spiral galaxies to daisies, from the mass of a star which predicts what its final state will be when it dies . Example: We know that it is mathematically impossible for our sun to go Nova. That Pi (a ratio) shows up in all wave-forms and seems to be part of the universal mathematical function. All our known Natural Laws are mathematical in essence, else we would not be able to translate them into human mathematics, which btw. is considered man's greatest achievement. The translation of universal mathematical values and functions into a symbolic language gave birth to the physical sciences which has proved some philosophical hypotheses and disproved other philosophical hypotheses. Once we *believed* the earth was flat. Once we *believed* in many gods which created different events by some miraculous act of will. Today we *know* the earth is not flat and that thunder and lightning are not caused by the god Thor. Again I ask if anyone can come up with an example which is not mathematical in essence.
If anything, I would consider that *promising*, if not sufficient. Can you come up with a more accurate system? With respect, this sounds that you are contradicting your earlier statement; "This is untrue. Science did not invent mathematics. Mathematics existed, independently of science, for a long time". I agree with the latter. But I also agree with Rpenner, that it takes observation of recurring patterns, before we can quantify them. But again, the patterns were there long before man came along and observed their consistency and was able to translate these observations of the inherent mathematical aspect of universal functions into mathematical language. The two are not mutually exclusive. As confirmed by cosmologists who claim to experience a feeling of discovery. A Eureka moment, if you will.
From a philosophical logical POV one could make an argument that all things in the universe are subject to the same general rules of mathematical permission or restriction. If this is true, it would suggest that all things share universal *common denominators* in the propagating of information (which is an abstraction itself), and that information propagation occurs in the form of mathematical functions. The processing of specific information *values* is a natural *quantification* of that information.. If not true, then we would not be able to recognize these functions and be able to quantify anything. But humans are made from stardust, we have that in common and we are part of this Wholeness. Why should we not be able to recognize the mathematical order of the universe, when every atom in the universe can and does (must) function in accordance to its inherited mathematical values and potentials?
You'll need to explain to me how claiming that mathematics cannot derive the values of physical constants without measurement contradicts the entirely separate assertion that mathematics had an existence independent of science. It seems to me they complement each quite naturally, both indicating that mathematics and science are distinct things - which is my contention.
I made no such claim. Perhaps you missed my agreement with Rpenner's posit. I think we have a semantic problem with the word "mathematics". If you may have noticed, whenever I speak of *universal mathematical functions*, the way the universe seems to behave in accordance to an abstract but orderly process and NOT human mathematics, which is the human shorthand translation and accounting (quantifying) of these discovered and observed orderly functions. So a human might say the universe works mathematically, the universe itself just functions as it must by a hierarchy of abstract orders, from the very subtle to expression in reality. Another example where human mathematics were used predictively; We have even succeeded to synthesize several *undiscovered* elements which were missing from the standard Table of Elements, but which undoubtedly exist somewhere in the universe; we just haven't found them yet. They must be very rare elements. So to fill the empty squares on the Table we made them. And we could because of our knowledge of the mathematical structures of elements, as well as its components and values. It turns out that,
You said: " With respect, this sounds that you are contradicting your earlier statement [ that science did not invent mathematics] ".
If I did, then I misstated it, but does not change the fact that our current mathematics are constantly augmented by new discoveries. And some of our maths seem to be extremely accurate symbolic representations of the behavior of observed universal mathematical functions.
I really, really, hate the way you continually misuse the word "function" in the context of maths. You cannot observe a function. It is an abstract concept, the "f" in f(x). For example if f(x) has the form ax² +bx +c, then it can be graphed as y= ax² +bx +c and the graph will be a parabola. Galileo discovered (science) that objects in free fall under gravity follow a parabolic curve, but, as this Wiki article explains: https://en.wikipedia.org/wiki/Parabola , the mathematical object was known for a thousand years before Galileo's time, apparently without any recorded scientific application.
I see several problems with that. First of all, I'd rather say that we assume that physical reality has behaved regularly for as long as there has been physical reality. Presumably the regularities in how physical reality behaves have always been as we know them and the same mathematical functions would have always served to model them. (But we don't actually know that.) In other words, I'm talking about the so-called laws of physics, assuming that they have always applied in the physical universe and have always been the same as we presently know them. But that's an assumption. And second, I really don't want to say that "before there was anything physical the mathematical function existed as an abstract potential". That's the assertion that the "laws of physics" predate the origin of the physical universe, and that's just a metaphysical speculation as far as I can see. We have no way of knowing it. And I want to reiterate that if the 'laws of physics' predate the origin of physical reality, then the origin of physical reality wouldn't be the initial something-from-nothing event. The origin of your "abstract potentials" would be. If we try to argue that the 'laws of physics' are eternal, have no origin and hence their existence needs no explanation, we are just recycling an old theological dodge to including God in the scope of the cosmological theistic arguments, except with 'mathematical functions' in the place of 'God'. Even if an eternal being requires no temporal cause, the question 'why is there an eternal being rather than nothing at all' still applies. 'God' has the advantage over 'mathematical functions' in that the 'God' concept allows the introduction of intentionality, teleology and purpose. Many medieval and early modern thinkers (including Isaac Newton perhaps) would probably have identified the 'laws of physics' or your eternal 'mathematical functions' as the rational structure of God's ideas, his 'logos'.
I am glad we agree that the word function is an abstract human concept of the way things interact (perform work) to produce a result. A function does not need to be active to exist as a latent universal potential. Example: Light, the propagation of a set of photons, functions at a constant rate *c* . We don't know exactly how or why photons are restricted to *c*, but we do know they function that way, even at different wave-lengths.. We may not be able to see this function at work, but we can measure the results and from these consistent results we can deduce that photons function @ *c*. Even in the absence of light this function exist as an abstract mathematical potential of the universe (a constant). And so it is with all known universal constants. and functions. They exist in the abstract until expressed by the action or event. As to the parabola, it is a mathematical expression (object), resulting from a combination of work done by a set of other universal potentials (such as mass, momentum, density of surrounding medium such as air resistance, and gravity), on the object in motion.. Take away gravity and a parabola cannot form, the object continues in a straight line away from the point of origin. Take away (or equalize the resistance of the medium on the moving object and all things fall at the same exponentially increasing rate. It all seems to follow strict mathematical rules which produce verifiably consistent results. Question, why would dynamical actions always follow some "unwritten" mathematical universal rules and functions, unless these mathematical rules were already present in the abstract?
This is why I believe Bohm was correct in his hypothesis of a hierarchy of (mathematical) orders. Same answer as above. Physical laws became expressed when the first physical particles became manifest. Before then, they existed in the abstract as (latent) universal *potentials*. I never claimed an eternal being. I agree with Bohm on "a hierarchy of (mathematical) orders. Yes, IMO, that was the original idea of a causal power. But we know now that was incorrect. All gods ever invented are the imagined causalities by scientifically ignorant (no offense intended) minds. Personally I would have no problem visualizing God as a mathematical quasi intelligence which permeates the universe. But the common concept of God is that It has human motivated intent (purpose), which to me disqualifies the term and context, as used to explain the existence and functions of the universe.. In the grand scope, the proposition that there is an eternal supernatural being with human emotions is not an advantage, but a scientific disqualification. The fact that most religions are not consistent in their teachings demonstrates the inherent flaws of believing in a motivated god or gods. Religions are not mathematically consistent or compatible, therefore cannot scientifically be considered as True. OTOH, the adoption by science of universally consistent mathematical functions as implacably dictated by universal constants is compatible with real world events and is therefore True or at least a close functional approximation. IMO, the universe functions by a set of implacable mathematical rules, some of which science has been able to identify and quantify and have named "universal constants", which do not require intent, but are an abstract potential (latency) of the universal spacetime fabric itself.
@ exchemist, Recently read an article which claims that *c* is the limit imposed by the quantum function (QM). p.s. Please don't let you emotions cloud your judgment. As always I qualify my posts as probative, even if my posts sometimes come across as trying to be authoritative. I make no such claim and as always consider your posts carefully and have learned in the process.
But my challenge still stands. Can anyone cite an example in physics which does not involve a mathematical value or function? For me that would be a game changer.
I did, several posts ago (post 33). But you ignored it and instead started wittering on about the Higgs boson.
"I'm glad we agree"? When, in post 20 I explicitly said that work done is nothing to do with something as woolly and vague as "interaction" between "values"? Furthermore you have totally ignored the point I was making about parabolae, which is that the concept predates its scientific applications by a thousand years.
OK, so you are just equivocating about the word "function". There are many mathematical functions regarding light in which a specific constant plays a factor, sure. But that is not the purpose ("function") of light. Nor are these descriptions in physics necessarily how light operates ("functions"); it is our best description of how light operates. I'm not saying that this description is horribly wrong, but the many functions that we use to describe light (almost always to a degree of approximation) are not the light itself, nor are they metaphysically inherent in the light itself.
Yes. Again. Qualia. That's kind of the definition of qualia. What does a sugar in your coffee taste like? What is the feeling of someone brushing their fingertips across your arm?
