I wish to explore this because we have come up with many mathematical formula that describe how the universe operates from the famous formula such as e=mc2 which has practical applications to many others.
Or is maths completely independent of the physical universe and it just so happens that some mathematics is good at describing some aspects of the physical universe and in fact supersedes it? — simplyG

Math was created within a closed system. Think of a language written in symbols. We came up with math because we need to describe the physical world predictably and reliably. We could have come up with a whole different numbering system than the one we have now.

I feel that your question is similar to saying that the periodic table of elements has always been embedded in the universe waiting to be discovered.

And if so does it point to a creator ?

Is maths embedded in the universe ?
And if so does it point to a creator ? — simplyG

No and no. As @L'éléphant notes, it is a language made up by humans, although there is evidence that the capacity for numerical thinking is hereditary in humans and perhaps other animals.

And if so does it point to a creator? I wish to explore this because we have come up with many mathematical formula that describe how the universe operates from the famous formula such as e=mc2 which has practical applications to many others.

But even simpler than that take for example 1+1 = 2 this can correspond to reality. Though in itself a simple mathematical calculation one apple and another apple means you have effectively applied the math to the real world.

The question is what came before? maths or apples (or the universe) and if maths can theoretically describe anything does that mean that reality is a subset of mathematics made manifest ?

Or is maths completely independent of the physical universe and it just so happens that some mathematics is good at describing some aspects of the physical universe and in fact supersedes it? — simplyG

Mathematics is only useful insofar as it applies to reality.

You could create a plethora of equations and none would have any bearing on our existence. The laws of math precede existence because they do not abide by time.

Math just as any tool is an idea first.

It seems to me like this is partially right, and partially missing something. Sans some interpretation of consciousness where mind does not emerge from or interact closely with nature, it would seem to me that our descriptive languages have a close causal relationship with nature.

Moreover, as points out, basic mathematical and logical reasoning appears to be a trait of many animals. I would add to this that it shows up in human babies before language, and as an emergent property of insect "hive minds," instantiated across what we take to be "individuals." Thus, it seems like there should be some causal tie in between our evolution and our ability to develop the descriptive languages we do. In the more immediate sense our descriptive languages are based on our experiences of the world.

A child locked in a room alone learns no human language and such abuse results in profound mental retardation, although there is a lot of plasticity if people are removed from these settings. In the event that you cut off essentially all sensory inputs, as well as you can without immediately killing an animal, mammals tend to die, and thus don't develop any reasoning abilities.

Hence, it seems like there is an essential way in which the world shaped how we even view our closed systems. Pace Wittgenstein, I would say that it's not a mistake to take "necessity as cause" as fundemental, vis-á-vis the "pure necessity," of logic. If anything, it seems like such "pure necessity," is simply an abstraction of the causal necessity we live with, something we create based on experiences of necessity as cause.

The periodic table is an interesting example because it is in ways arbitrary and in others not. It seems likely that any sufficiently advanced aliens should recognize the table, even if they have moved beyond seeing it the way we do.

In this sense, there are ways logic and mathematics are "out in the world" to the extent that it seems we learn about the systems from the world as much as we describe the world in terms of the systems. I mean, there is a reasons we "teach" mathematics, draw diagrams, make sensory analogies, etc. Bidirectional causality in essence.

Incompleteness and undefinablity made philosophers retreat into deflationary theories of truth and abstractly "closed systems," in the 20th century, separating logic from psychology and ontology, and I think this might be a mistake. It's a sort of fear of error that becomes a fear of truth. Seeing that there might not be an easy answer, any one system that was isomorphic to the world in all cases and yet hewed to our familiar tools of "the laws of thought," we decided that logics and mathematics must simply be "closed off" sui generis abstractions. I'd argue that simply can't be the case. The very limits of our thoughts about such systems themselves are enshrined in nature. Take a hard blow to the occipital lobe, the area used to process vision, and you can lose a lot of the ways you're able to described the geometries of mathematics. Our understanding rests on perceptual systems.

I also think it's interesting that a lot of non-neurotypical people make big breakthroughs in mathematics, Mandelbrot, etc.

In At Home in the Universe, a book about self-organization, Stuart Kauffman wrote:

We will be showing that the spontaneous emergence of self-sustaining webs is so natural and robust that it is even deeper than the specific chemistry that happens to exist in earth; it is rooted in mathematics itself.

Mathematician Eddie Woo showed photos of a river delta, tree, lightning, and human capillaries, which all have remarkably similar patterns, and said:

There's a mathematical reality woven into the fabric of the universe that you share with winding rivers, towering trees, and raging storms.

You could create a plethora of equations and none would have any bearing on our existence. — chiknsld

I agree with you, but it has always amazed me how often some obscure phantasmagoric math ends up being useful in the real world.

Good, thorough post. Extra point for using "sui generis."

At Home in the Universe — Patterner

I've been reading a lot of science lately - switching from my usual fiction. I'll add this to my list. It was written in 1996, do you think it's out of date? Do you know any good, more recent books.

Mathematics is only useful insofar as it applies to reality. — chiknsld

When non-Euclidean geometries were invented (discovered?) they were considered parlor games. It was only later, when it became known that astronomical spacetime is not Euclidean that their use became evident. The description of this reality depended on what seemed to be a useless game.

Or is maths completely independent of the physical universe and it just so happens that some mathematics is good at describing some aspects of the physical universe and in fact supersedes it? — simplyG

I view Mathematics as the meta-physical structure (inter-relationships, ratios, proportions) of the physical universe (objects, things). In other words, Mathematics is the Logic of Reality. In that case, the math (logic, design) is prior to the material implementation (stars, planets, plants, animals). Math doesn't "supersede" the matter, but it necessarily preceded the Big Bang execution of the program of Evolution that produces the Reality we see around us. Hence Math/Logic may be the abstract invisible essential ding an sich that makes concrete substantial things what they appear to be to our senses. :smile:

Right, there is a strong tendency for the mathematical patterns "at work in," or "describing" natural phenomena to be similar at very different levels of scale. For instance, large overlaps between how earthquakes, the timing of fire flies blinking, and heart cells work.

To be honest, it surprises me how stubborn different fields are about acknowledging this. "Neurodarwinism" was viciously attacked because "natural selection can't involve intentionality, it is random." First, it's unclear if this is even the case (the whole EES debate), and it seems motivated more by philosophical concerns about teleology or pseudotelology creeping into explanations. But moreover, it seems silly because there simply IS a huge mathematical and conceptual overlap between how neurons are pruned, how genes undergo selection, how lymphocytes are selected, etc.

This doesn't mean "x and y are the same thing." It means they are isomorphic in key ways. It seems to me that it's important to recall how things are different, but also to look at how they are the same across scales. The general tension with the rise of information theory and chaos theory as the two biggest paradigm shifts in the sciences I can think of in at least a century, is that the new advocates of complexity like to look across silos, while academia as a whole is still quite siloed. And unfortunately, the silos are sometimes defended, not as useful synthetic organizing principles, but like fortresses.

That's the only book on Complexity I've looked at.

Not sure why anyone worries about teleology. The universe has certain characteristics. It has structure. That structure seems more conducive to certain relationships and ratios.

... And if so does it point to a creator? — simplyG

No.

The question is what came before?

This question doesn't make sense.

... if maths can theoretically describe anything does that mean that reality is a subset of mathematics made manifest?

I think a subset of mathematics usefully describes subsets, or aspects, of reality and the rest (most) of mathematics does not. As suggested by Max Tegmark (David Deutsch, Seth Lloyd, Stephen Wolfram et al), the universe might be nothing more than a lower dimensional mathematical structure (i.e. a reality, n. naturata) imbedded in higher dimensional mathematical structures (i.e. the real,, n. naturans).

Or is maths completely independent of the physical universe ...

Not insofar as physical systems are (Quantun Turing) computable.

... and it just so happens that some mathematics is good at describing some aspects of the physical universe ...

I agree as I wrore above.

... and in fact supersedes it?

I don't understand what you mean here by "supercedes".

:up:

Even pure mathematics might open unexpected doorways into reality.

And if so does it point to a creator?
— simplyG
No. — 180 Proof

If we take pure math to be a product of pure consciousness (whatever that is). Then these eternal concepts/abstractions/calculations/numbers which precede the physical universe are only evokable so via consciousness otherwise what would exist then? Just dumb matter.

Mathematics is the language in which God has written the Universe
— Galileo

Just leaving that quote by Galileo there as seems apt to my first question….

Just dumb matter. — simplyG

:ok:

It seems to me like this is partially right, and partially missing something. Sans some interpretation of consciousness where mind does not emerge from or interact closely with nature, it would seem to me that our descriptive languages have a close causal relationship with nature. — Count Timothy von Icarus

This is a good starting point for a new thread because I was trying to discuss with @schopenhauer1 in the Kit Fine thread about what is existence without an observer.

So, I will respond to my comment that " without an observer, the world is a two-dimensional existence". And I know this will take a lot of argument but just as a start, I say that because without an observer (without us), there's no more vantage point at which we view the reality or the world. Think about "no point of view", but only the universe. All points of location can just be two-dimension.

So maybe a thought experiment about what would go away if sentient observers disappear.

It is the other war around; the universe is embedded in mathematics. pi is a geometric proportion but it can, with infinite precision, be expressed as infinite series -

https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80

Numbers are eternal objects and the universe is designed around them.

Numbers exist by purely abstract means. Namely iteration and partition (Set Theory)

Start with /
iterate //
again ///
etc //////////////////////////////////////////...

Partition each step: {/} {//} {///}...

= 1, 2, 3,...

Now set them in proportions as in Leibniz's formula-

1/1, 1/3, 1/5, 1/7,...

And, very simply, we go from set theory to pi to space. Now add time and you've got the basis for a universe. Numbers are the 'atoms' of spacetime.

It is the other war around; the universe is embedded in mathematics. pi is a geometric proportion but it can, with infinite precision, be expressed as infinite series -

https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80

Numbers are eternal objects and the universe is designed around them. — EnPassant

This is true. The universe is designed around numbers. But who designed the scientific concept of ‘universe’ such that mathematics meshes with it so conveniently? Perhaps mathematics and the logic on which it’s based rest on presuppositions about the world rather than the world itself. This would mean that logic and math are derived forms of thinking or grammars.

Perhaps mathematics and the logic on which it’s based rest on presuppositions about the world rather than the world itself. — Joshs

Mathematical truth is not a supposition. It is logical independently of what we think.

Mathematical truth is not a supposition. It is logical independently of what we think — EnPassant

I think I’m going to put that on a T-shirt

I'm not sure if I see the direct relation. Here we're talking about a universe that has observers in it. The question seems to be: "can we say math exists in nature objectively?" Put another way, we could ask: does mathematics exist "out in the world," as opposed to being an "artefact of the sensory system and cognitive processes."

This question doesn't seem that hard to me. Objectivity as a concept only makes sense in terms of observers. Without observers the entire concept of "objectivity," becomes contentless. In an observerless context it becomes a term that applies to everything equally, thus conveying nothing. Something's being "more or less objective," is only meaningful in the context of the possibility of thing's being "more or less subjective."

And it doesn't make much sense to say "what does the world look like without eyes," or "how would we think about the world without minds."

Objectivity then is about descriptions that smooth out the differences that arise from variances in subjects' phenomenal experience. You view the same phenomena in many different ways, using tools, experiments, etc., and identify the morphisms between all perspectives.

Of course, objectivity ≠ truth, but in terms of objectivity I would say "math existing out in the universe," as an objective fact is about as secure as anything. We can see the same ratios at work across a huge range of phenomena, while looking at them in all different ways. The instantiation of mathematical patterns in the world seems to me to be on more sure footing than even bedrock concepts like mass or energy, both of which have shifted over time.

I think the reason this question even gets any traction is because of some common conflations that are easy to fall into.

First, conflating objectivity with truth, such that the truth of the universe is "as seen without eyes and thought of without a mind," which leads to all sorts of conceptual difficulties.

Second, the idea of the world of phenomena as somehow illusory, as opposed to a noumenal world where true causal powers lie. In a lot of ways, this division seems akin to that made by Plotinus, Proclus, and Porphery about the relations between Nous, Psyche, and the material world.

In this view, only the higher, noumenal realm can be causally efficacious, or at least there is only downwards causality from the noumenal onto the phenomenal, not the other way around. To my mind, this creates an arbitrary division in nature that many don't really want to defend, but which it is nonetheless easy to accidentally fall into.

The second point might take us too far afield, but it does shine some light on a third conflation, that the distinction between subjective / objective is essentially the same thing as the distinction between phenomenal / noumenal, treating them as synonyms. They aren't synonyms though, the second distinction comes with far more baggage.

If we avoid these conflations then it's easy to see that the observation of mathematical patterns that describe and predict the world are among the very best established empirical facts.

Math was created within a closed system. Think of a language written in symbols. We came up with math because we need to describe the physical world predictably and reliably. We could have come up with a whole different numbering system than the one we have now.

To this point, I would argue that thinking of math as a "closed," system can be misleading in this context. Obviously our development of mathematics doesn't appear to be causally closed off from the world.

The idea that mathematics is a closed system is a fairly modern invention. To be sure, prior to the use of this language there was a strong tradition of "mathematical Platonism," but people also generally thought of math as simply the discovery of relations that obtained due to necessity. For example, Euclidean geometry was thought to be the only valid geometry and it was thought to be a prime example of how the world (necessarily) instantiated mathematical principles.

I feel that your question is similar to saying that the periodic table of elements has always been embedded in the universe waiting to be discovered.

There obviously is a sense in which the periodic table always was waiting to be discovered. Barring conciousness being non-natural, it seems obvious that living things must incorporate within themselves descriptions of nature that are isomorphic to nature. Such descriptions might be highly compressed, based on heuristics that make them prone to error, etc., but this doesn't preclude the fact that they are to some extent accurate descriptions of nature. And, to the degree they are accurate, I don't see any problem with saying something like "what the periodic table describes exists in the world." It's a claim that can be supported better than many empirical claims.

Math is a continuation of the dualistic nature of concepts in general, there are only ambiguous and foggy dividing lines between language, its syntactical rules and math, each of these things supervenes on the human ability to apply negation on several predicates at once (mutual negation of predicates/identities), which upon phenomenological analysis can be found to happen spontaneously within phenomenal limits, or simply: in everyday experience.

Math is imbedded in the universe non-computationally through its many proportions, if you mean the universe which we refer to inside experience, but the concepts we invent in our minds does not exist in that universe apart from us, just like how the laws which describes its behaviour does not exist inside it, the concepts of our minds can never be abstracted from these proportions alone, instead we must apply dualities onto these proportions to describe them in terms of a language thinkable to us, there is no reason to believe that this language applies to those proportions independently of the process we go through to think in terms of that language.

I feel that your question is similar to saying that the periodic table of elements has always been embedded in the universe waiting to be discovered. — L'éléphant

"Discover" - Middle English (in the sense ‘make known’): from Old French descovrir, from late Latin discooperire, from Latin dis- (expressing reversal) + cooperire ‘cover completely’. So, to uncover or make clear something previously unknown. A great deal of scientific discovery concerns things that are 'embedded in the Universe waiting to be discovered', the Periodic Table of Elements being one.

But even simpler than that take for example 1+1 = 2 this can correspond to reality. Though in itself a simple mathematical calculation one apple and another apple means you have effectively applied the math to the real world. — simplyG

Of course. Numbers are fundamental artifacts of reason, they are basic to the means by which rational thought is able to analyse and predict events and establish causal relationships. Further, mathematical statements are true in all possible worlds, not just in the world we've happened to experience.This universality and necessity cannot be accounted for if mathematics is merely a generalization from experience. Indeed there is a sense that they possess a kind of logical order which is assumed by empiricism.

there is no reason to believe that this language applies to those proportions independently of the process we go through to think in terms of that language. — Julian August

One of the most interested popular articles on philosophy of maths is Eugene Wigner's essay The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Wigner emphasizes how mathematical concepts and equations often prove extraordinarly apt in describing and predicting physical phenomena. He marvels at how mathematical structure can correspond so closely to the behavior of the real world and points out that mathematical concepts have often been developed before they find any application in the physical sciences, where they turn out to be very powerful. There is the famous case of the discovery of anti-matter. In 1928, Paul Dirac formulated a relativistic quantum mechanical equation (now known as the Dirac equation) to describe the behavior of electrons. This equation incorporated both the principles of quantum mechanics and the theory of special relativity, describing electron behavior at relativistic speeds.

However, the equation had solutions that implied the existence of an electron with positive energy (which was expected) and another set of solutions that implied an electron with negative energy (which had never even been considered). Initially, this negative energy solution was a conundrum. Instead of discarding it or considering it a mere mathematical artifact, Dirac proposed that it could correspond to a particle that had the same mass as an electron but with a positive charge - purely on the basis of the mathematics. In 1932, just a few years later, Carl Anderson discovered the positron (or positive electron) in cosmic ray collisions, which was the exact particle Dirac's equation had predicted. The discovery of the positron, the antiparticle of the electron, marked the first evidence of antimatter and validated Dirac's groundbreaking prediction. Many analogous discoveries came out of Einstein's discovery of relativity theory, which often made mathematical predictions well in advance of the means to empirically validate them (hence the oft-repeated headline, Einstein Proved Right Again.)

Wigner concludes by suggesting that the deep connection between the mathematical and physical worlds is something of a miracle. While there might be no definitive explanation for this connection, the fact remains that mathematics serves as an invaluable tool for understanding and describing the universe. (In fact, the word 'miracle' occurs a dozen times in the essay.)

Does this 'point to God', as the OP asks? That's a moot point. But Wigner points to the relationship between mathematical insight and empirical discovery as compelling evidence of the deep ties between the mathematics and the workings of the physical universe. And I think it's safe to say that this relationship transcends naturalist accounts of mathematics - it truly is a metaphysical, not a scientific, question. (See this great CTT interview with Roger Penrose, Mathematics - Invented or Discovered?)

I was just watching The Bit Player, which is about Claude Shannon, who I’m learning is a pretty important person. (Literally never heard of him until a couple months ago when I started reading about semiotics, which I also never heard of until I started hanging out here.) One thing it says is:

“Normal English, though, I calculated was over 50% redundant. You know certain words follow each other, and there’s grammar rules. When you learn a language, you inherently know the statistics. That’s why you can drop letters, and even words, and still understand the message.”

Looking at the redundancy in English gives Shannon his Big Thought #2. Compress your information. Eliminate the redundancy. Just send what you can’t predict.

And then he asked a question that nobody had really thought of before. Is there a minimum size, a minimum number of bits, that I can shrink my information to, and not lose anything essential? He discovers there is a minimum. And he shows how to calculate it. His formula is based on the probabilities in the message. It has a very intriguing form. It’s almost identical to a fundamental quantity in physics called entropy.

He discovers there is a minimum. And he shows how to calculate it. — Patterner

That's why Shannon's work is fundamental to data compression on digital devices. It lead directly to the ability to greatly reduce the number of bits required to encode data.

His formula is based on the probabilities in the message. It has a very intriguing form. It’s almost identical to a fundamental quantity in physics called entropy.

Shannon, the pioneer of information theory, was only persuaded to introduce the word 'entropy' into his discussion by the mathematician John von Neumann.

The theory was in excellent shape, except that he needed a good name for ‘missing information’. ‘Why don’t you call it entropy’, von Neumann suggested. ‘In the first place, a mathematical development very much like yours already exists in Boltzmann’s statistical mechanics, and in the second place, no one understands entropy very well, so in any discussion you will be in a position of advantage’. — Source

To this point, I would argue that thinking of math as a "closed," system can be misleading in this context. — Count Timothy von Icarus

I don't know how to define "closed" in this context, but I agree. With over 26,000 Wikipedia pages, and counting, mathematics continues to expand its realms, especially into abstractions and generalizations. I suppose "closed" could mean based on axiomatic set theory, which it normally is, although frequently some distance from Cantor's creations.

Further, mathematical statements are true in all possible worlds, not just in the world we've happened to experience — Wayfarer

A nice post. But I'm curious about this statement. How do you know this? :chin:

How do you reckon a world would work out, if 2 did not, in fact, equal 2, of if 9 was less than 7? The law of identity, A=A, is an example of something that is true in all possible worlds. That is an element of modal logic referring to what are otherwise known as 'necessary truths'.

If a statement is necessarily true, it means that there is no possible world in which the statement is false. It holds true in every conceivable scenario or possible world. An example of a necessary truth might be a tautological statement like "All bachelors are unmarried".

Conversely, if a statement is possibly true, it means that there is at least one possible world in which the statement is true. However, there might be other possible worlds where the statement is false. An example might be "There is a planet entirely covered in water." It's possible, but it's not necessarily true across all possible worlds. It's contigent as distinct from necessary.

Lastly, if a statement is necessarily false, it means that there is no possible world in which the statement is true. For instance, "A square has five sides" would be considered necessarily false.

I think there's a relationship between this and basic arithmetical logic - I can't see any other way for it to be. That's why I'm generally of the 'maths discovered not invented' school - I think it rests on a foundation of the discovery of necessary truths (although with mathematical ability, also comes the ability to create imaginary number systems and so on, which muddies the waters somewhat.)

Sadly, I know nothing about any of this, so I’m already lost. But I thought it fit the topic nicely.