That would seem to apply in the physical universe, once it's up-and-running. Physical events in that universe do seem to conform to regularities that can be described by mathematical functions. (The so-called "laws of physics".) I don't understand that. Can you explain the "simple logic"? Here's how I'm conceiving of these things: If the 'nothing' before the Big Bang was true unadulterated nothing, and if the Big Bang was an absolute something-from-nothing origin event, then that nothing couldn't have had any properties at all. (Using the word 'it' to refer to it is a matter of grammar rather than ontology.) So there couldn't have been any "permittive conditions" or laws of physics before the big bang, since nothing was before the Big Bang. But if we want to imagine laws of physics and "permittive conditions" that can be appealed in hopes of explaining the Big Bang, then the Big Bang couldn't have been an absolute something-from-nothing origin event. It wouldn't represent the origin of the principles of physics that supposedly explain the whole thing. Once again, I think that it's important to emphasize the difference between 'vacuum' and 'nothing'. Vacuum is space unoccupied by matter. But space is certainly something rather than nothing, especially if we want to ascribe fields, geometrical properties and things like quantum pair-production to it. Cosmology even likes to claim that space is expanding. Space (or space-time) is definitely part of the inventory of physics. Nothing is more of a logical concept. It means not-something, or perhaps more accurately not-everything. It's saying (for all x)(not-x) where x is allowed to range over all of existence. 'Nothing' wouldn't seem to "forbid" anything, except perhaps the possibility of explaining the origin event. The logical problem there is circularity. If the origin event is the origin of everything, including your mathematics and "permittive" functions, then it would be circular reasoning to base the explanation of the origin event on its products. That's why I think that physics is completely out of its depth in trying to answer the something-from-nothing question. 'Nothing' means no physics and no mathematics, nothing left that could provide the explanatory principles. (This is the ultimate metaphysical question and I don't think that human beings will ever know the answer.) Don't apologize for being philosophical. It just means that you are smarter than most people. I can't really comment intelligently on Tegmark since I haven't read his book. I do suspect that he might be on to something, though. (I'm thinking of structural realism now.) But I don't think that his kind of mathematical ontology provides a satisfactory answer to the something-from-nothing question. My target in my remarks is less Tegmark than Krauss. I think that Krauss makes exactly the error that I just described. Not only that, he makes it knowingly and intentionally with hopes of misleading laypeople, something that I think is dishonest. https://www.amazon.com/Universe-Nothing-There-Something-Rather/dp/1451624468 http://www.nytimes.com/2012/03/25/books/review/a-universe-from-nothing-by-lawrence-m-krauss.html https://blogs.scientificamerican.co...krauss-a-physicist-or-just-a-bad-philosopher/
*Mathematics* as the symbolic representation of natural values and mathematical functions was invented by man. In nature there are only values and functions which are translatable by mathematics. The universe functions mathematically, but it does not know that, we do. I'll take the blame for that poorly constructed and inexact quote of Tegmark's actual statement. My bad! I disagree, the universal mathematical function permits some actions (work) and forbids other actions (work). That is the essence of mathematical functions and workings. Please consider the message, not the semantics. But at that level we can only speak in woolly terms, such as *quantum foam*. Can you come up with a less woolly term? But I don't understand why you seem to be arguing against the scientist who agrees with you and is trying to prove that your statement; "Mathematics existed, independently of science, for a long time", is in fact true. And this is a verbatim quote from Tegmark " some people say that the universe has some mathematical properties. I say that the universe has only mathematical properties." Do you disagree with that? p.s. Sagan did a wonderful job selling his work, was he a jerk?
This does not specifically address *vacuum*, but makes the case for a *mathematical universe*. https://www.youtube.com/watch?v=JOtAFiI39_I
You persist in talking nonsense. There is no "universal mathematical function". So the "message" is junk. "Quantum foam" is a pure speculation. But it has a defined meaning, as per Wheeler's development of this idea, cf. Wiki article here:https://en.wikipedia.org/wiki/Quantum_foam I am saying that science did not invent maths. It was you who claimed it did. If you now say some scientist or other says this is crap, then I wholeheartedly agree. So why did you say the opposite, eh? Anyone who says the universe has only mathematical properties is an idiot or a charlatan. The universe is physical. Mathematics is abstract. Physical properties may , if we are lucky, be expressible in mathematical terms but the properties themselves are physical and exist irrespective of any mathematical relationships we may attach to them.
OK, I'll remember that statement and will refer to it later. I agree, so does the phrase *mathematical functions* Seems that mathematical functions are also well-defined , no? Science did invent the symbolic language which we call "mathematics". Science invented the symbolic representations (numbers, equations) by observation of the naturally occurring mathematical functions, patterns, and actions. Tegmark agrees with you, but just goes one step further and proposes that all physical properties are expressible in mathematical terms, with sufficient information. Human maths are only useful to humans. But *mathematical functions* are essential to the existence of physical reality, no random miracles, only mathematical probabilities. IMO, it makes for a very elegant argument, because a mathematically functioning universe, does not contradict an abstract hierarchy of mathematical orders, thus agrees with Bohm on the self-referencing aspect of universal constants, either expressed or as latent potentials, all of them mathematical in nature and function. The *mathematical function* is a fundamental essence of our universe with or without man whose existence was once only a mere probability. Lucky us!
So the argument is that to be real means to be quantifiable? Anything that isn't translatable into numbers can't be real? That's a very strong metaphysical proposition that I'm not ready to embrace. Science certainly makes use of mathematics. And I think that an argument can be made that mathematics got its beginning in rules of thumb (like 3-4-5 right triangles) employed by cultures like the Egyptians for practical ends. That's why geometry has the name 'geometry' which means 'earth measurement'. I believe that it was the Greeks (particularly Euclid) who first organized this practical mathematics into a deductive system where the various traditional rules of thumb were derived logically from a small set of primitive axioms. And once they had hit on the idea of proofs, they started applying that new methodology to all kinds of mathematical ideas and issues and mathematics as we know it was off and running as an independent subject. And for centuries, the ideal of "scientific method" in the rest of human thought was an Euclidean-style deductive system and countless thinkers tried to force every idea with aspirations to be "science" into that procrustean bed of axioms, lemmas and deductive conclusions. Without notable success. But ignoring some precursers like Archimedes and medieval geometrical optics, it wasn't really until the 17th century 'scientific revolution' that physics became thoroughly mathematized in a brand new way. These physicists didn't try to spin reality out of their heads by elaborate proofs. They observed reality with the Renaissance artist's/craftsman's eye and recognized that very simple physical systems (planetary orbits, pendulums, falling objects) displayed regularities that lended themselves to mathematical description. And it wasn't long before the kinds of problems faced by physicists forced new developments in mathematics. It was the obvious need to mathematically describe rates of change that forced Newton to invent his system of calculus. So the history of physical science and mathematics have been mutually interactive and each has influenced the other, but they aren't identical. And just as the concept of proof had once led to an explosion of mathematics (but not so much physics), once the new mathematical physics was up and running, it expanded to address no end of new and more complex physical and dynamical questions and spun out all kinds of new and highly abstract ideas in just a century or two, as vectors, least-action principles, conservation principles, Lagrangians, Hamiltonians, phase-spaces and all kinds of new concepts elaborated and multiplied. Part of the difficulty lay people have in understanding theoretical physics today is that so much of it is expressed in this highly abstract, mathematical and unfamiliar conceptual vocabulary. Certainly the number of possible mathematical relationships/functions/structures is essentially infinite. Those of practical importance in physics is only a small subset of abstract mathematics. I certainly don't believe that there is ever going to be some purely mathematical criterion internal to mathematics, that distinguishes the mathematical relationships with physical application from all the rest that only have abstract mathematical interest. I don't think that physics (even mathematical physics) can ever turn its back on empirical observations of the real world and from its attempts to mathematically model that world, and turn itself into a purely rationalist system.
I think the argument is that for anything to exist or interact in our physical reality, it has to have a value. We may not always be able to quantify this value, but we have come a long way in our quest for knowledge of "how things work", and in a relatively very short time. We have our maths and equations to prove our depth of understanding. I'm curious, can anyone come up with a scenario which does not involve a value and/or a mathematical function?
Why would you want it to be irrational? The universe went through that hierarchical state during the inflationary epoch, when there was only pure unbound energy. and http://www.vision.net.au/~apaterson/science/david_bohm.htm
Well of course all physical properties are expressible in mathematical terms, with sufficient information, (though often the requisite information is not available). You can in principle model anything mathematically, if you have enough data and computing power. So what? That does not mean that the things you attempt to model are mathematics. All you seem to be saying - once the Shapiro/Tegmark bullshit is stripped away - is that there is order in the universe. As long as there is order, i.e. a discernible pattern, to something, you can model that pattern with mathematics. That is obvious and not much of an insight. The trouble with this whole line of thought is that it strikes me as the worldview of a rather arrogant and not-very-thoughtful physicist. In fact, all the systems that physics models are idealised and simplified subunits of the physical world we see around us. In that physical world, there are a myriad entities in interaction all the time. This effectively precludes mathematically exact modelling in all but some specialised classes of phenomenon. Most of physical reality is messy and inexact - hence the approach in the physical sciences to reduce it to artificially simplified situations that can be modelled exactly. Thus it is that just about any mathematics we apply to the physical world is a mere approximation to the actual state of affairs. Theologians have often seen the fact that there is order in the universe as an argument in favour of a deity (e.g. the Genesis account of creation, which is partly a story about imposing order on chaos). Some I think even argue that this order is the deity. Others of course just say well that's the way the universe is, and don't see the need to draw any further conclusions from the existence of order. But I do feel it is a huge error to elevate mathematics, which is just a human creation based on applying logic to numbers, to the status of being the actual fabric of reality. It is a tool for understanding the order in it, no more than that.
The bit about empty space containing huge amounts of energy is crap. Attempting to estimate this is something that physics notoriously cannot do. This is known as a "vacuum catastrophe": https://en.wikipedia.org/wiki/Vacuum_energy Current theories are unable to agree on this at all.
Thanks for the link! I have been toying with the idea of a collapsing vacuum which might have been causal to the BB.
I can mention many things in the physcial world which are the subject of well-developed scientific theory but are not usefully described quantitatively. Take physical geography, say, the theory of the features of a glaciated landscape and how they arise. What meaning or purpose is there in ascribing a "value" to a hanging valley, a truncated spur or a misfit stream? Or what about the theory of Continental Drift and Plate Tectonics? People certainly model mathematically individual parts, of idealised versions, of some of the processes involved, but to describe the theory you need words, not mathematics. This sort of thing is why I contend that the maths-is-everything notion looks like the product of a narrow-minded physicist who is too far up his own arse. There is a lot more to the physical world than sub-atomic wave-particles and astrophysics.
Precisely, if somehow there would have to be no more than a mathematical imperative (a singularity with an inherent mathematically causal potential) to get it all started, what more would we want to know?
This question does not appear to make much sense. - I don't understand what is meant by a "mathematical imperative". Mathematics does not force anyone to do anything. - Many simple models in physics use singular potentials (e.g. Coulomb potential surrounding a "point" charge, as used in the QM model of an atom). What has this to do with the notion of an "imperative"? - And "getting it all started" means what? What is "it" in this context and what is meant by "started"?
I am not assigning meaning to any of this, but, yes, IMO, all these things are mathematically quantifiable. That may be so, but one thing is pretty sure, they seem to fit nicely with our current mathematics. For example, the Higgs boson was mathematically predicted, even though no one had ever observed one. Yet, when we asked the *mathematical function* nicely (by smashing two particles together at near SOL, there it was .....as predicted by abstract theoretical mathematics. Rather than "narrow-minded", it seems to me an example of *thinking outside the box* at a very deep level. This why I like Bohmian Mechanics, they provide the bridges, the hierarchies fom the infinitely subtle unfolding into expression in reality.
You are refusing to engage with my point. The Higgs boson is not what I was talking about. How does glaciation or plate tectonics "fit pretty nicely with our current mathematics"? You seem hung up on particle physics, as if that is all there is to the physical world or to science. That is exactly what I mean by a narrow minded physicist up his own arse. My examples were designed to show how ridiculous this attitude is.
That's kind of the very definition of qualia. Qualia are the things we experience that can't be quantified. What a headache feels like, the taste of wine.
I was employing a bit of philosophical jargon there and contrasting 'rationalist' with 'empiricist', not with 'irrational'. http://www.philosophybasics.com/movements_rationalism.html In particular, I was rejecting the idea that there is some purely mathematical (or logical) criterion, internal to the mathematics taken as a self-consistent deductive system, that establishes which mathematical functions, relations or structures will apply to physical reality and which won't. To establish whether mathematics applies to physical reality, and if so, which bit of mathematics that will be, inevitably requires that somebody actually observe how physical reality is behaving. In other words, I'm arguing against the idea that physics can be spun like a huge endless proof out of some basic set of fundamental mathematical axioms, scattering physical principles along the way as lemmas.
How do "maths and equations... prove our depth of understanding"? There seem to be all kinds of deep questions about theory construction, confirmation, and the nature of explanation hidden in that idea. A lot of biology, arguably. What is 'life'? I suppose that somebody might try to reduce life to a set of functions, describe those functions in quantifiable terms, then apply mathematics to it. But that's going to be awfully cumbersome. The meaning of linguistic words and phrases. Again, I suppose that somebody might try to reduce this to computational linguistics of some kind, but again that's going to be difficult. Mathematics might conceivably be applied to almost anything and all of reality might conceivably be modeled in terms of mathematics. But that's often just a hypothesis at this point, little more than a research program. To argue that the hypothetical possibility demonstrates that reality is mathematics in some weird metaphysical way, is little more than speculation in my opinion.
