Does mathematics describe reality?

[Graeme M]

I hope this isn't a dumb question. It might be, given my utter lack of knowledge about the subject. Still... here it is. Something I read in a magazine the other day got me thinking. I can't find the statement again, but it went along the lines that the only real thing we can know about the universe is mathematics. Or something like that. I understood this to mean that math explains genuine relationships and properties of the universe.

That seems unlikely to me, so I'm curious to see what the more knowledgeable forum members think of that. I suppose I don't quite get it.

When I think about this, it seems to me that all we can ever know is what our senses present to us. Our sense of the universe is purely representational - that is, both sensory knowledge and factual knowledge can only be encodings in neural patterns. We also cannot observe any facts about the universe to which our sensory apparatus are not tuned. Even the instruments we build to measure the universe can only deliver to us representations that are sympathetic to our sensory apparatus - they must perforce "interpret' the universe.

It follows then that mathematics - an inner symbolic language of representational content - can only describe relationships between neural encodings. Doesn't this mean then that mathematics is no more "real" than any other internal representative state? That is, mathematics describes inner states and relationships, not external ones. Sure, there will be substantial coincidence between the two as our perceptual systems and neural machinery are "tuned" to deliver a reasonable facsimile of the world about us, but there is a finite bound to this.

How can mathematics objectively describe true arrangements and relationships of the external universe?

[mitchellmckain]

Do toasters break rocks?

When a function is not a part of the definition of a thing then it seems bizarre to me to ask a question like this. Is it possible that such a thing could happen? Sure, but it seems very much beside the point to me. One day we very well have toasters incapable of breaking rocks.

Describing reality is not the function of mathematics. Of course mathematics is a very useful tool for describing many aspects of reality. But this is not its function. And while many things in mathematics can describe things in reality, it is not the case that all things in mathematics describe something in reality.

[Athena]

How can mathematics objectively describe true arrangements and relationships of the external universe?

You might enjoy this...

Max Tegmark: "Our Mathematical Universe" | Talks at Google

https://www.youtube.com/watch?v=VlbJoW9Rty0

I might add there is an opinion that our knowledge of matter is not knowledge of reality because matter is in a constant state of change and reality is not.

Here is a theory for you...

'It proves that measurement is everything. At the quantum level, reality does not exist if you are not looking at it,' said Associate Professor Andrew Truscott

Read more: http://www.dailymail.co.uk/sciencetech/ ... z4bEx5kHEz
Follow us: @MailOnline on Twitter | DailyMail on Facebook

This is a shorter youtube about math and how our brains process information and our consciousness.

https://www.youtube.com/watch?v=GzCvlFRISIM

[neuro]

I am not clear about what the question is.
Is the point about the fact that mathematics can "objectively" describe reality, i.e. when you turn to mathematics then your "subjective" view becomes "objective" (ontologically, and not only epistemologically, tenable)?

If this is the question, it certainly looks as a stupid question to me.
If the question is another one, would you please state it more clearly, please, Graeme?

[Graeme M]

Neuro, it was just idle curiosity about the idea that mathematics can describe real things. Does mathematics describe relationships and properties about actual things in the world, or rather between responses to things in the world? If the latter, which seems more likely to me, then we should find that as we extend mathematical concepts and reasoning, we very quickly enter a sort of internal feedback loop in which descriptions of inner experience generate further inner experience. If such were the case, then after a time, any apparent relationship between real external things and inner representations breaks down.

Put another way, all facts, all mathematics, can only be physically instantiated as arrangements of connections between neurons. Math, or any body of conceptual thought, can not represent directly the external world. Rather, such conceptualisation consists of internal physical arrangements. The more complex the concepts, the more complex the inner representational state. But given that inner representational states only represent the real world via perceptual input, how can pure mathematical reasoning have any true correspondence to external things given that such doesn't require perceptual input? The inner state that implements pure mathematical reasoning is self-generating, self-reinforcing.

[Braininvat]

But is it the case that pure mathematical reasoning doesn't require some prior perceptual input? Could I understand numeracy if multiple physical objects had not presented themselves to my senses and I was called upon, in some way, to count them? If there were 17 ducks on the pond and all intelligent observers were wiped off the planet at that moment, would there still be 17 ducks? Internal descriptions that correspond to an external reality have survival value for biological entities that have the neural capacity to develop those correspondences. If math didn't describe real things, we would all be dead. Math can't help but describe true states of affairs in the world, if we're talking about basic math that has a descriptive function that is practical. Accuracy and validity is reinforced by successful interactions with external reality.

[Forest_Dump]

Accuracy and validity is reinforced by successful interactions with external reality.

That is, of course, assuming there is an external reality and you are not just some, um, brain in a vat

[Graeme M]

Braininvat, I agree that there is coincidence between external events and our conceptual models of these. But how confident can we be that all external features are available to our perceptual apparatus and hence that our conceptual models truthfully reflect external reality? But more to the point, once mathematics or any conceptual modelling process begins to operate largely in the absence of perceptual features, tending more to proposing features of the environment and then identifying these, what is the likelihood that we are no longer describing an external reality, but an inner one? The more our conceptualising process operates on internal models and features, the less it might conform to an external reality. What I'm suggesting is that as we abstract away from perceptual features in favour of modelled or logically entailed features, do we start to experience a divergence away from describing a real world (or at least, a world of clear property relations). Put more bluntly, if all "thought", and hence mathematics, are relational arrangements of neurons, how can we be certain that mathematics describes real things in all cases of description and that we aren't just making shit up? I just can't see how any of our conceptualising systems, especially mathematics which by definition is entirely couched in inner symbolic representation, can express any truth about external features. it can only express truths about internal features that coincidentally accord with external features some of the time.

[Braininvat]

Well, as I was stirring in my vat this morning, it crossed my mind that the square root of minus one is not a value I can count on my toes (er, I mean my virtual toes). It does seem to stray a bit from what we call external reality, though quantum mechanics find it useful. Some math can be a convenient fiction. Will ponder further.

[Graeme M]

Hehe, yes I guess. I am not trying to argue that mathematics or any such school of thought is necessarily mistaken and hence all wrong, just that when I read this claim that math is one of only two real things in the universe, I took that as suggesting mathematics has a reality that underpins the universe in some way. That is, that mathematics somehow has an independent... I don't know what - existence, substance, presence... in the universe. That the human mind discovers or accesses this independent quality that of itself constitutes the universe's structure and behaviour. I just can't quite see that, for me it can only ever be entirely internal, and can only ever describe internal relations. Luckily, through our perceptual capacities, those inner relations reflect external relations.

Mind you, perhaps I misread what was said in that article. I haven't been able to find it again, so my memory might be faulty. And perhaps I should watch that video linked above!

[vivian maxine]

Graeme, some time in the past week, Science Daily had an article titled something like "Is the Universe Mathematics? I didn't read it, just noted the title and remembered someone on this forum talking about the universe being mathematics. . Could that have been what you saw?

[Dave_Oblad]

Hi all,

Graeme.. Vivian asked a similar question last June, prompting me to post a thread exploring the concept that Math doesn't just describe our Universe, but rather, our Universe is composed solely of Math.

I don't want to take over this thread.. so I'll just post a link to the answer I supplied that was asked by Vivian here:
http://sciencechatforum.com/viewtopic.php?f=51&t=30776

It is a tricky transition to move from the perception that Math is only a tool to Describe something.. to the Reality that Math can also Create something just as easily (such as a Universe). It's an easy concept for me because I've used Math to create Realities that I can then explore. This isn't your "run-of-the-mill" type Math (like 1+2=3) but Relational Math, Boolean Algebra, Fractals and Cellular Automatons etc.

Anyway, as I said, I don't want to take over this thread nor do I have a lot of time. But I will answer questions posted here.. or.. over on that thread (linked above) that I created specifically for this purpose.

Regards,
Dave :^)

[someguy1]

Math is math, it has no necessary connection to reality. It's useful to physics like hammers are useful to building houses. But houses aren't hammers and the universe isn't "made of math." Tegmark's just wrong. He's confusing the map with the territory. If the universe is made of math, where'd the math come from? To me math comes clearly from the mind. What's "out there" might be random, in the same way we used to think the constellations were animals and people having adventures in the sky.

Math has historically been influenced by reality in the same way abstract art is. Math and art are both free to transcend reality. Math and art inform our understanding of the world by virtue of not being bound by it.

[Braininvat]

Though I tend towards S.G. view, that the map is not the territory, I would say that Tegmark and members like Dave Oblad are saying something a little different, which is that some aspects of mathematical logic are like ground rules for constructing any universe in which organized matter and biological life can arise. What they mean by math is somewhat different from the common definition - they follow in the footsteps of John Archibald Wheeler and his famous "It from bit" concept: that the universe is fundamentally grounded in information, in digital zeroes and ones stuff, in a sort of Ur-structure that requires reality to flow through logic gates in order to "happen."

The question remains: what is the substrate? what is this software running ON? For me, there has to be a level below that, which is pre-logical and pre-mathematical and somehow provides a platform for "It from bit" to be coded and run.

[someguy1]

The question remains: what is the substrate? what is this software running ON? For me, there has to be a level below that, which is pre-logical and pre-mathematical and somehow provides a platform for "It from bit" to be coded and run.

Perhaps the universal program is an algorithm that executes without a substrate ... by analogy with light, which is a wave that propagates without a medium! Deep thought :-)

[Dave_Oblad]

Hi Guys,

There is certainly a substrate and it has Rules. Initially it was called an Aether. M&M didn't understand the rules and couldn't prove its existence. So the idea of an Aether lost face. Later, Einstein found that without a Substrate, he was blocked from further progress in his Field Equations. Distance had to have Scale for anything to hold together or make sense at Atomic Scales. So he introduced a substrate concept, but the word Aether had gotten a bad rap, so he called it Space-Time. This substrate has Scale, described in Planck Units.

This underlying Scale is what makes Atomic Particles compatible. We don't have an issue with combining one tiny Oxygen Atom with two gigantic Hydrogen Atoms to produce Water. We don't get a 19% Spin, it's always evenly divisible. Energy levels don't climb like a straight Line, but more like a staircase with discrete steps.

Matter responds to Speed in the same way it reacts to Gravity. The cyclic nature of Matter slows down, clocks slow down, aging slows down. Gravity and Speed have the same effect on Matter. How can Matter KNOW how Much to slow down.. unless it's sensitive to its personal velocity. How does Matter KNOW how fast it is moving?

This Substrate is the Computer itself. The best Model I can offer is a Neural Network made of Cells, with each Cell doing its own private task of processing information that passes through it. We are that Information. Or more specifically, Matter/Energy is the information being processed by that Network, not unlike how your Brain processes Thoughts.

If it helps, think of the whole Universe being one Giant Quantum Computer and the program is embedded into every single Cell of that Quantum Network as a simple set of rules for the processing behavior of any given Cell. This set of Rules is passed on to every New Cell the Universe Creates. The Creation of New Cells is literally the Expansion (growth) of the Universe. Our concept of "Now" is because we exist on the surface Growth of New Cells.

The Arrow of Time is because New Cells are always being Created at the Speed of Light on the previous surface of this Substrate. The Information that is you (Matter) always propagates into the New Cells from the previous Cells and we call that "Time".

So.. if You and I and everything we can Touch, Smell, Taste or Experience is just Information, like thoughts through a Brain.. Then this substrate is the only Real thing that can be said to Exist. Everything else is purely Informational, not unlike your Thoughts.

So if your Brain is a clump of Cells and the Universe is a clump of Quantum Cells, then what are these Quantum Cells made of?

That's the Million Dollar question.

In my book, these Quantum Cells are a discrete packet of Rules, with inputs and outputs that connect to Neighbor Cells. Thus the Whole Universe is a Quantum processing Machine and it is composed solely of Logic Rules.

Thus, in my Book, the whole Universe is purely composed of Logic (a branch of math).

For every variation in the Basic Rule Set, a completely different Universe results. Most are pure trash, but ours is among a few unique ones where the rules can form enough complexity to establish Chemistry, Life and self-aware beings.

You will never understand this.. as long as you keep trying to force what I've said into your own personal Model of Reality.

I started from scratch and figured it all out because that's what I'm good at. Others, like Max Tegmark, have drawn the same conclusions independent of each other. We have an advantage in that Max is a skilled Mathematician and Physics Major and I am just a Programmer. I've built VR Realities and I understand them and how they work. Some of you have played inside these Mathematical Realities in the form of Computer Games. Killed Dragons, evil minions, and saved the Princess or whatever. Granted those games cheat a lot via shortcuts, because we don't have the resolution that our Universe has.

Bottom line: Your existence is Virtual, mathematically speaking. In fact, the whole freaking Quantum Universe is Virtual.

But if the Quantum Universe is a massive Quantum Computer then is it self-aware? That question is far more interesting in my book. But rather off Topic here by the OP.

Again, I prefer you read the Thread I linked to above. I've answered almost every conceivable question there as simply as possible.

But, for those too lazy to do so, I will answer questions here, until Ron accuses me of snagging another thread on my favorite topic. Honestly, if someone posted a thread saying God Doesn't Exist because there is no Proof.. I doubt even Ron could stay his hand.

I mostly enter such Threads because there are always new readers browsing through these great halls, and they don't have the Time to Browse every Thread on a given Topic. So exposure to these ideas can be very New to many. To capture new readers one must Hook them. Get their Interest. Via advertising, they are paying the bills to support this great site, that I call Home.

Regards and best wishes,
Dave :^)

[mitchellmckain]

Well, as I was stirring in my vat this morning, it crossed my mind that the square root of minus one is not a value I can count on my toes (er, I mean my virtual toes). It does seem to stray a bit from what we call external reality, though quantum mechanics find it useful. Some math can be a convenient fiction. Will ponder further.

Uh.... actually....

The square root of minus one is part of something called complex mathematics that is quite useful in describing many things in reality. Not only has it long been used to explain and describe things in electronics but it is also part of techniques that solve quite an array of real world problems. Counting your toes just isn't the limit of either reality or the practical usefulness of mathematics, and the result is on such terms this number is just as realistic as any of the other numbers/things in our mathematical methods.

[Athena]

Some people confuse arithmetic with math. In fact, Pythagoras did not have Arabic/Indian numerals for math. Yet we know Pythagoras thought everything was math and ...

The idea that all matter is made up of tiny, indivisible particles, or atoms, is believed to have originated with the Greek philosopher Leucippus of Miletus and his student Democritus of Abdera in the 5th century B.C. (The word atom comes from the Greek word atomos, which means “indivisible.”)
Atomic Theory - Infoplease
www.infoplease.com/ipa/A0905226.html

A study of reality Socrates rejected because the attempt to understand the elements lead to studying smaller and smaller things.

This thread requires are board understanding of math.

https://en.wikipedia.org/wiki/Discrete_mathematics

Research in discrete mathematics increased in the latter half of the twentieth century partly due to the development of digital computers which operate in discrete steps and store data in discrete bits. Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations are significant in applying ideas from discrete mathematics to real-world problems, such as in operations research.

[mitchellmckain]

When I think about this, it seems to me that all we can ever know is what our senses present to us. Our sense of the universe is purely representational - that is, both sensory knowledge and factual knowledge can only be encodings in neural patterns. We also cannot observe any facts about the universe to which our sensory apparatus are not tuned. Even the instruments we build to measure the universe can only deliver to us representations that are sympathetic to our sensory apparatus - they must perforce "interpret' the universe.

It follows then that mathematics - an inner symbolic language of representational content - can only describe relationships between neural encodings. Doesn't this mean then that mathematics is no more "real" than any other internal representative state? That is, mathematics describes inner states and relationships, not external ones. Sure, there will be substantial coincidence between the two as our perceptual systems and neural machinery are "tuned" to deliver a reasonable facsimile of the world about us, but there is a finite bound to this.

No, it does not follow. Just because books are composed of paper and ink does mean that these confine what a book can communicate. DNA demonstrates how the encoding of information can vastly transcend the limitations of its own substance, and the representational capacity of human language far surpasses the abilities of DNA. Nor to the origins impose any such limitations because this is not a mechanical extension but part of the highly creative process of life which constantly learns, adapts and tries new things.

How can mathematics objectively describe true arrangements and relationships of the external universe?

It does this by testing the precise agreement between description and the reality in a way that is independent of a particular person. Anyone can follow written procedures to verify for themselves how much they agree.

[Athena]

When I think about this, it seems to me that all we can ever know is what our senses present to us. Our sense of the universe is purely representational - that is, both sensory knowledge and factual knowledge can only be encodings in neural patterns. We also cannot observe any facts about the universe to which our sensory apparatus are not tuned. Even the instruments we build to measure the universe can only deliver to us representations that are sympathetic to our sensory apparatus - they must perforce "interpret' the universe.

It follows then that mathematics - an inner symbolic language of representational content - can only describe relationships between neural encodings. Doesn't this mean then that mathematics is no more "real" than any other internal representative state? That is, mathematics describes inner states and relationships, not external ones. Sure, there will be substantial coincidence between the two as our perceptual systems and neural machinery are "tuned" to deliver a reasonable facsimile of the world about us, but there is a finite bound to this.

No, it does not follow. Just because books are composed of paper and ink does mean that these confine what a book can communicate. DNA demonstrates how the encoding of information can vastly transcend the limitations of its own substance, and the representational capacity of human language far surpasses the abilities of DNA. Nor to the origins impose any such limitations because this is not a mechanical extension but part of the highly creative process of life which constantly learns, adapts and tries new things.

How can mathematics objectively describe true arrangements and relationships of the external universe?

It does this by testing the precise agreement between description and the reality in a way that is independent of a particular person. Anyone can follow written procedures to verify for themselves how much they agree.

I favor Graeme M's line of reasoning. The argument against it appears to me like the scholastic argument that the church knows reality because it has been argued by well-educated men who agree in the end about God's truth. Those men greatly prided themselves in their skills of argumentation as they argued such serious matters as if babies would be born small adults if Eve had not eaten the forbidden fruit, or how many angels could stand on the head of a pin. Our truths, no matter what they are, drag a mine field of false notions. Like what are we checking to validate our truths, but our own ideas of what is true and how we came to that conclusion? Our perceptions are limited. Math and language can expand them, but not past our ability to perceive truth.

[Athena]

Quote Dave... To capture new readers one must Hook them. Get their Interest.

And may I add to this, respect them, and make them feel good about being a part of the discussion because if they don't feel good about being here and if they feel constantly attacked and put down, they will stop logging in. Has anyone seen Revolutionary lately?

[neuro]

my overall impression is that mathematics essentially is the set of all possible symbolic systems, where a symbolic system is defined as a set of rules and relations that define the role and possible functions of each symbol in the system itself.

Many mathematical systems have been developed that had nothing to do with perceptual reality, far before it (at times) happened that they turned useful to model physical aspects newly discovered thanks to technological and scientific advances.

An intriguing article was published by Rovelli a few years ago: Michelangelo's Stone: an Argument against Platonism in Mathematics.
The author faced there the problem of whether mathematics possess an ontological status in that it exists per se. His conclusion was that as long as mathematics is comprized of all possible sets of symbolic systems (i.e. logical systems, as described above) it doesn't "exist" as such, and it rather is built along the road every time we think of any new symbolic/logical system which intrigues us or can be applied to some purpose.
In a sense, it is as if we defined the desert as an extensive landscape in which one can walk along any path they can imagine, and then one came about claiming that "the desert IS the set of all possible paths on the sand", and another guy finally claimed "the set of all possible paths on the sand ontologically exists on its own".

I would conclude then that mathematics is a set of logical tools to help us "understand" reality (epistemology).
However, since it allows us to model any real as well as unreal/impossible system, it does not add any ontological (actual existence) value to the conclusions we reach by examining reality through such tools.

[Braininvat]

That Rovelli paper has been more cited here than any other. Hyksos just gave the paper its own thread, a couple days ago.

Platonism is what people do when they want to sneak dualism back into modern philosophy.

[neuro]

sorry BIV (and everybody else),
I had been absent for a while, and I realized after posting that the thing had come up once more...

[Athena]

my overall impression is that mathematics essentially is the set of all possible symbolic systems, where a symbolic system is defined as a set of rules and relations that define the role and possible functions of each symbol in the system itself.

Many mathematical systems have been developed that had nothing to do with perceptual reality, far before it (at times) happened that they turned useful to model physical aspects newly discovered thanks to technological and scientific advances.

An intriguing article was published by Rovelli a few years ago: Michelangelo's Stone: an Argument against Platonism in Mathematics.
The author faced there the problem of whether mathematics possess an ontological status in that it exists per se. His conclusion was that as long as mathematics is comprized of all possible sets of symbolic systems (i.e. logical systems, as described above) it doesn't "exist" as such, and it rather is built along the road every time we think of any new symbolic/logical system which intrigues us or can be applied to some purpose.
In a sense, it is as if we defined the desert as an extensive landscape in which one can walk along any path they can imagine, and then one came about claiming that "the desert IS the set of all possible paths on the sand", and another guy finally claimed "the set of all possible paths on the sand ontologically exists on its own".

I would conclude then that mathematics is a set of logical tools to help us "understand" reality (epistemology).
However, since it allows us to model any real as well as unreal/impossible system, it does not add any ontological (actual existence) value to the conclusions we reach by examining reality through such tools.

Are fathers real? Are the letters f a t h e r epistemological or ontological? Aren't our words only symbols for concepts, just as math is symbols for concepts? There is at least one tribe with no word for father, therefore no concept of fathers, therefore fathers can not be real to them, however, in our culture a pregnant woman with no concept of who a father is, needs educating. Both words and math are symbolic of concepts, not tangible reality.

[neuro]

There is at least one tribe with no word for father, therefore no concept of fathers, therefore fathers can not be real to them

You are right, fathers cannot be real for them: they have no epistemological access to fathers.
I imagine you realize how important is the fact that fathers do not exist for them, rather than not existing per se: the owner of the sperm that contributed to generating the son does exist, he is real, ontologically, and his biological link with the son is a fact, a real fact.

This is exactly the difference between ontology and epistemology: the real thing vs. the concept we conceive to indicate, interpret, understand it.
I am afraid you are being carried away by the Platonic perspective, which implies that the TRUE reality (ontology) stays with concepts (idealism), and not with their actual instantiations.
Chairs exist (ontologically). The concept of "chair" does not exist (ontologically).

However:
You can build any kind of concept to address any kind of "entity", whether it exists or not (see, e.g. the concept of a unicorn).
You can then believe once you have conceived it the concept will exists (ontologically). However, it has no actual existence (per se) other than as a product of our mind, i.e. a by-product of reasoning (a product of epistemology).
Even if you were to argue that, once you have thought of it, the concept exists, it did not exist before anybody thought of it. Neither unicorns nor the concept of unicorn existed before anyone conceived that idea for the first time.

And this is exactly the issue in the article at hand. Platonism: the existence of concepts (and maths) a priori.
The concept of imaginary numbers, or trigonometry, did not exist before someone first thought of them: they are two among the infinite possible epistemological approaches to understand relations among entities, exactly the same way as a dream is an instance among all possible dreams you may dream of.
Even if you claimed that your dream exists (ontologically) because you dreamt it, this does not imply that all possible dreams you might dream exist per se (ontologically).

[Dave_Oblad]

Hi All,

We must not confuse Discovery with Invention. One can invent almost anything, but one can only Discover that which Existed prior to its Discovery. We can invent the symbols used in Mathematics but we can't invent the Functions those symbols represent.

We may someday meet an Alien Race. If such a Race is as advanced as ourselves, then it is extremely probable they understand Math as well as we do, but may have different symbols for the Functions we both subscribe to.

Math is a form of Absolute Truth. You can't invent Truth.. You can only Discover such Truths.

Math is not Subjective.

Regards,
Dave :^)

[neuro]

Dave,
Michelangelo did not discover the shapes of his statues in the stone.
He claimed he could see them in the stone, that is true and it is nice and poetic.
But he actually IMAGINED such shapes in the stone. He did not discover them.

I this this all discussion is meaningless.

One might just say "I am an Idealist".
This implies that they attribute ontological existence to ideas. And will obviously attribute ontological existence to mathematics and all the mathematical relations one may know, discover or invent (yes, invent, because for an idealist there cannot be invention de novo, and invent can only mean discover). They will also claim that no chef can invent a new recipe, because all recipes exist as ideas a priori to be discovered.

Or one may say "I am not a hard idealist".
This implies that they may or may not attribute ontological existence to ideas, but they will claim that if ideas do ontologically exist they exist only once someone has thought them. The same way as cooking recipes exist only once someone has though of them, and do not live their independent and absolute life in some undiscovered eternal ideal world.