
The Universe Is Made of Mathematics - zoltz
http://disagreeableme.blogspot.com/2013/12/the-universe-is-made-of-mathematics.html
======
westoncb
Lets say you select all the aspects of a person's life that you consider to
have any relevance to anyone and write down a description of every one of
them—is that person now 'made' of words? That's how ridiculous this is.

I think what this is missing is a justification for thinking the universe
somehow 'uses' mathematics in this sense; being /describable/ by it, is not at
all the same as actually being generated by it.

There is a mistaken assumptions here that consistent rules from /within/ the
universe would apply to its own operation. It's like assuming that because
some rules must always hold when Monopoly is played, that the rules governing
its physical constitution must be drawn from the same set.

"Confusing the moon with the finger pointing at it" —is a simple concept to
understand, but seeing all the subtle places where we actually make the
mistake in our mental lives requires another level of effort.

~~~
zbyte64
I think mathematics and physics sets the bar higher then subjective relevance
when formulating descriptions. If you did manage to create a description that
would accurately predict every response of a person then you would have a hard
time (if not impossible) discerning the difference between the two agents.

~~~
westoncb
But one of them wouldn't be something anyone would call an 'agent.' One would
be a description of an agent, or a recipe for producing one—but at the end of
the day, one is meat and the other is a set of symbols.

~~~
goldenkey
But aye..that's the rub. Is there any difference between meat that appears to
operate _EXACTLY_ the same as different meat (constructed using the symbols)?
Computationally, no. But if two things in an information-theoretic world, are
informationally equivalent, then for all intensive purposes, they are
equivelent. Quantum physics says this with regard to quantum states, there's
no meat to differentiate electrons, only informational states.

You guys basically complemented each-other, and came back to the beauty of the
question.

I'd say what's more pressing is, does the information match the
implementation. That is, is there any glimpse of external forces (that
implement our universe) inside of it.

See
[https://en.wikipedia.org/wiki/Brain_in_a_vat](https://en.wikipedia.org/wiki/Brain_in_a_vat)

If our whole reality is more of a rouge, rather than an accident, then it's
possible our reality has almost nothing to do with the parent-verse. And well,
everything we seem to value as good models for the true implementation, are
well, garbage.

~~~
westoncb
I think you have a mistake here:

> ...the same as different meat (constructed using the symbols)?

Your answer is talking about a comparison between, e.g., a human and an
essentially identical human /constructed/ using a set of symbols that encodes
our understanding of the human's constitution.

The original question is comparing, e.g. a human and a set of symbols which
describes the human.

I consider each of the following to be meaningfully separate questions:

Reality is mathematics.

Reality can be created with mathematics.

Something equivalent to reality can be created using mathematics, if
'informational equivalence' is the equivalence relation in question.

~~~
goldenkey
True reality is ineffable. The subjective does not equal the objective.

The nature of consciousness is a black box. Therefore the nature of
measurement, of assurance that mathematics matches reality, is only within the
context of conscious observation, which is therefore subjective.

The objective truth will not be found within subjection.

~~~
zbyte64
> The nature of consciousness is a black box. Therefore the nature of
> measurement, of assurance that mathematics matches reality, is only within
> the context of conscious observation, which is therefore subjective.

Consciousness has a track record of taking a black box and deducing what is
going on inside.

> The objective truth will not be found within subjection.

Wouldn't you need to understand the nature of subjective processes in order to
stipulate such a limit? If you don't understand consciousness then you do not
understand its limits.

~~~
goldenkey
Yes, but it all rests on a foundation that the inside of the black box is
similar to the outside of the black box. And that, may be totally false.

------
DCKing
The reasons presented in favor of a mathematical universe read somewhat like
rehashed arguments used by deists/theists.

> For something to be physical it must be present at some time and place
> within the universe, and for something to be abstract it must exist outside
> of space and time.

No. He is redefining words here. 'Physical' is not usually defined as "exists
in space and time". Abstract thoughts or concepts do not exist outside of
space and time. Abstract thoughts are the results of the modeling capabilities
of brains and exist very much in the physical world. It isn't even known
whether "existing outside of space and time" is a coherent concept.

> but if the universe is a mathematical object, it needs no creator (on
> Platonism at least),

Firstly, this is the Kalam argument all over again. It isn't clear at all that
the Universe _needs_ a beginning or whether the 'beginning of the Universe' is
a coherent concept at all.

Secondly, even assuming mathematical platonism is true, and even if 'creation'
was a prerequisite for the universe, mathematical platonism has no construct
to go from 'describing a universe' to 'creating a universe'. That seems to be
quite an important thing to miss.

> Our universe is fine-tuned because it is one which has the ability to
> support conscious thought selected from an infinite multitude of
> mathematical structures, most of which are lifeless.

This is very problematic. Once you start thinking about "different
mathematics", you lose all foundations upon which you can reason. Logic does
not work anymore. Even if it were true at all, no human could possibly have
meaningful thoughts about it. Besides, if we abandon the concept of our
'mathematical structures' in other universes, what do the words true and false
itself even mean?

There's lots of handwaving with (very) incoherent concepts and dubious logic
in this post to make the argument for a mathematical universe.

~~~
yongelee
Concepts can indeed exist outside physical brain matter. Such as the concept
of math. The idea that 1+1=2 does not need a physical human brain to exist. If
humans never existed the concept of math would still exist "beyond space and
time". Abstract thoughts cannot exist outside space and time for human
comprehension but those same concepts do not need humans to exist.

~~~
DCKing
I'd love to have some evidence that such things as 'concepts' and 'ideas' can
exist independent of brains. You can't just assert it and make it so. All
concepts and ideas I've ever heard of were the results of brains attempting to
model or describe.

By the way, I'm not talking about physical human brains. I'm talking about
_any_ brain, which includes human brains, dolphin brains, computers, and
whatever other modeling machines exist in the universe.

~~~
goldenkey
The thing is, the definition of a concept, is the axiom that it exists outside
of human understanding. Concepts are informational objects. Anyhow, the
question you really ask, is does information exist outside of conscious
humanity. And it might not. It might just be an interpretation.

~~~
DCKing
> The thing is, the definition of a concept, is the axiom that it exists
> outside of human understanding.

I don't agree with that definition of a concept.

Idea = mental representation of an object, or a set of objects and their
interactions.

Concept = generalization of an idea.

wherein 'mental' justifiably implicates the working of a brain. It is very
much tied to what we call brain understanding. Sorry for taking this
discussion to the definition of words.

------
ching_wow_ka
I'm not much of a mathematician, but I found "Mathematics: The Loss of
Certainty" by Morris Kline ([http://www.amazon.com/Mathematics-Loss-Certainty-
Oxford-Pape...](http://www.amazon.com/Mathematics-Loss-Certainty-Oxford-
Paperbacks/dp/0195030850)) very insightful in regards to the development and
current state of mathematics. A brief synopsis:

From Amazon: "This work stresses the illogical manner in which mathematics has
developed, the question of applied mathematics as against 'pure' mathematics,
and the challenges to the consistency of mathematics' logical structure that
have occurred in the twentieth century."

From goodreads.com: "Most intelligent people today still believe that
mathematics is a body of unshakable truths about the physical world and that
mathematical reasoning is exact and infallible. Mathematics: The Loss of
Certainty refutes that myth."

Edit: This was also interesting:
[https://www.youtube.com/watch?v=RlMMeqO7wOI](https://www.youtube.com/watch?v=RlMMeqO7wOI)
, a video by Stephen Wolfram. I know he is often criticized for various
reasons, but much of what he says makes intuitive sense.

~~~
eellpp
> Most intelligent people today still believe that mathematics is a body of
> unshakable truths about the physical world and that mathematical reasoning
> is exact and infallible.

I had always thought of mathematics as the language of science. (Instead of
saying i want more apples, i can say as i want 5 apples). Physics and other
sciences use mathematics to explain the physical world or make predictions
about them. Is there something more to it ?

------
ccvannorman
1) All mathematical objects exist abstractly and independently of minds
(mathematical Platonism)

Without a mind to understand, interpret, and define mathematics, does it
exist? This is a core philosophical problem at the intersection of science and
feeling. Without observation, no mathematics exists (for the observer). By
proving it exists, you must also have an implicit observer.

2) The mind is a computational process (The Computational Theory of Mind or
CTM)

Pretty big assumption, considering we still have no idea how the mind works
(e.g. quantum fluctuations that lead to patterns and thoughts, the origin of
which are not known to us or predictable by us.)

3) The universe behaves according to laws of physics which are expressible
mathematically (metaphysical naturalism)

What about where those laws break down, such as inside a black hole or at the
beginning of the Big Bang? Do those places and times extend beyond our
Universe? If so, where exactly do you draw the line between where our Universe
ends and something else exists?

These arguments feel quite tenuous to me, another attempt by an intelligent
person to say, "Ah, I've figured it all out, THIS is how everything is."

~~~
kazinator
> _Without a mind to understand, interpret, and define mathematics, does it
> exist?_

Unquestioningly so. For instance, there is a number 2 and a number pi which
are not caused by thinking. Beings which evolve on separate planets (or
whatever) in separate universes have to to come to the conclusion that the
ratio between the diameter and circumference of a circle is a certain number.
Those numbers will be found to agree, though there is no causal link between
the two. You can define what constitutes a circle, and define the question of
the ratio of its parts, but you don't get to define pi.

Or, if you define "composite" and "prime", you don't get to decide which
integers are one or the other, or facts like that two is the smallest prime
and the only even one.

The question is: what is the difference between _your_ existence and the
existence of pi? Maybe there isn't any.

~~~
thaumasiotes
> facts like that two is the smallest prime and the only even one

I see the fact that two is the only even prime brought up from time to time as
if it's inherently interesting. Why is it more interesting than the identical
observation that 37 is the only prime which is a multiple of 37?

I guess this bothers me because 2 being the only even prime isn't a
consequence of the definition of "prime"... it's _part_ of the definition.

~~~
kazinator
You're right in that evenness is divisibility by two by definition. For any P
which is prime, P is the smallest divisible by P.

It is probably that divisibility by two (evenness) is interesting.

For example, it has the property that if we know the evenness of two integers,
then we know the evenness of their sum or product.

Division of cases by even versus odd occurs regularly; in few circumstances do
you have to separately reason about cases corresponding somehow to the
elements of the congruence modulo 37.

~~~
thaumasiotes
As regards your third line, I feel compelled to note that if we know the
equivalence class of two integers (mod 37), we also know the equivalence class
(mod 37) of their sum and product. ;)

~~~
kazinator
Indeed, it just the mod 37 congruence doesn't correspond to nice Boolean:

    
    
      odd(x + y) = odd(x) XOR odd(y)
      odd(x * y) = odd(x) AND odd(y)
    

There.

------
vezzy-fnord
In very broad terms, this is part of an age-old debate in the philosophy of
science about how mathematics should be interpreted - instrumentalists
(manipulating symbols) versus realists (mathematics underpins objective
reality).

Realism is obviously popular because any viewpoint which attaches grandiose
"meaning" and "purpose" to things is bound to be more popular over what is
seen as "colder" and analytic.

There's actually several sides, but those two are the main ones.

EDIT:

In addition,

 _For a creator God, we are left to ask who created the creator - but if the
universe is a mathematical object, it needs no creator (on Platonism at
least), so this is a very satisfying answer to that eternal question. It has
always existed and will always exist outside of space-time as a mathematical
construct._

No. In fact, a lot of people who subscribe to creationism make the exact same
argument - that God has always existed outside of space-time and requires no
creator. Your handwaving this in the same fashion is not a satisfying answer
in the slightest.

------
outofcuriosity
If the universe was "made of mathematics," then there would necessarily exist
a Grand Unified Theory. But, Hawking asserts that Gödel's Theorems imply that
not only does a Grand Unified Theory not exist, but that the formulation of
one is impossible ([http://www.hawking.org.uk/godel-and-the-end-of-
physics.html](http://www.hawking.org.uk/godel-and-the-end-of-physics.html)).

The author stresses that all of reality is mathematical in structure, but this
is at odds with the fact that all mathematical systems containing self-
reference are necessarily incomplete. Physics is a self-referential system.

If the structure of the universe is mathematical, it is probably a very
different math than humans are used to. Insert your favorite flavor of
metaphysics here!

~~~
nemo1618
Hmm. That's an interesting counterpoint.

Suppose we discover our universe is a simulation. This would imply that the
universe is Turing-computable. Would there not therefore exist a "Grand
Unified Theory" that simply described, with absolute precision, the operation
of the simulator? Or would it be impossible to produce such a specification?

~~~
jameshart
So if you Gödelized the universe - mapped every conceivable state to a number
(proving that that is possible left as an exercise for the reader) - then
created mathematical operations on those numbers that transitioned the
universe from one state to another 'physically possible' successor state.. I
guess Gödel would be able to give you a number representing a universe such
that you could not prove whether its state was possible or not?

Then all you have to do is demonstrate that we live in such a universe, and
all the philosophers can retire because we've found the ultimate answer to the
ultimate question.

I think we all know exactly what the Gödel number for our universe would be...

~~~
ursus_bonum
420?

~~~
outofcuriosity
My money's on 69.

Rudy Rucker had some interesting conversations with Gödel about a
deterministic universe in which (because time is illusory) backward time
travel exists: [http://www.rudyrucker.com/blog/2012/08/01/memories-of-
kurt-g...](http://www.rudyrucker.com/blog/2012/08/01/memories-of-kurt-godel/)

~~~
jameshart
Thankyou - fascinating account.

I particularly like how, in describing Gödel's office, he mentions "On the
empty desk sat an empty glass of milk." The paradox seems appropriate.

------
kazinator
Every result in physics hitherto has been some sort of mathematics: an
equation or a constant (measured or otherwise established to some digits of
precision). What is a particle? A collection of mathematical properties. So is
a wave. If we extrapolate from the past to the future, we can expect more of
the same: no "non-mathematical bottom" will be found. Nobody is even looking;
the researchers expect all new results to take the shape of math. So the
notion that "maybe it's just math all the way down" is actually quite
rational. One day we may hit bottom, the way a (terminating) recursive
function does, and realize; this is it: there is nothing more going forward,
and if we look back, it's just a collection of math.

~~~
DCKing
You're just describing the fact that we can make up _descriptions_ of physics
all the way down. If current mathematics is unable to describe physics, then
new mathematics is invented [1]. Just because the descriptions work rather
well does not mean that those descriptions are somehow more than mere
descriptions. It just means that they are very good descriptions.

You're making the same category error as mentioned in the blog post.

[1]
[https://en.wikipedia.org/wiki/Mathematical_physics](https://en.wikipedia.org/wiki/Mathematical_physics)

~~~
kazinator
> _If current mathematics is unable to describe physics, then new mathematics
> is invented_

Now suppose that this process stops. One day, mathematics describes physics.
What does that mean? It means that some pencil-and-paper mathematics
descriptions hint at an abstraction, and that abstraction _is_ physics.

The mathematics which was used prior to that point was not the right one. That
mathematics still corresponds to a universe, just not this one.

The idea is that every mathematical object is a universe (not to be confused
with some representation of that object, like a definition in plain language,
or a diagram, equation).

The world may be exactly the same _category_ of thing as _dodecahedron_ or
_pi_. (Not in the category of pencil-and-paper description of such things; the
category of those thing themselves.)

~~~
ursus_bonum
Now suppose that it doesn't stop. Suppose it can't stop.

Suppose no mathematical system is sufficient to describe any universe. It's
always just a rough approximation.

Either could be true, I guess.

------
Strilanc
If the universe we find ourselves in is a result of post-selecting for
mathematical models where life can exist (i.e. by the anthropic principle),
why is the universe _so large_ and _so rich in neg-entropy_? Shouldn't
minimally-viable-habitat universes be vastly, _vastly_ more numerous (and
don't forget about Boltzmann brains!)? Shouldn't we expect to be in one of
those, instead of here, and be forced to penalize the hypothesis by a
corresponding amount? [1]

> _So, as cosmologists, we have an issue to address — why was the entropy of
> our early universe so small? If high-entropy states are “natural,” why don’t
> we live in one? You might think to appeal to the dreaded anthropic
> principle, and argue that life couldn’t exist in a state with really high
> entropy. But that turns out not to be good enough; the entropy of our
> universe is much much lower than it needs to be to support the existence of
> life. So we are faced with the “arrow of time problem.”_

1: [http://www.preposterousuniverse.com/blog/2004/10/27/the-
arro...](http://www.preposterousuniverse.com/blog/2004/10/27/the-arrow-of-
time/)

~~~
jameshart
The problem with these kinds of arguments-from-probability is that they are
valid arguments _even in highly improbable universes_. So yes, maybe on
average, most sentient life forms that ponder these questions are living
inside tiny simulated universes created as undergraduate term projects for
passing credit. But we happen to be in a really big universe. Maybe ours is a
grad student lab project. Or an exhibit in a museum. Or maybe we hit the
jackpot and ours is _real_. Point of such arguments is you can't really tell
from a sample size of one.

------
eludwig
"A map is not the territory"

~~~
kazinator
In this case, it may be. The territory is never observed other than through
maps, and the maps are all math. That is to say, the maps may be of the same
"stuff" as the territory, and as the differences between the maps and the
territory are erased, eventually you arrive at the map being the territory.

At least, they are all math beyond those subjective observations that are
possible through the human senses. You might think that some hot gas is
"glowing blue", and that this is not "math" to you in any sense, but a more
advanced understanding of the light emanating from it gives us a spectrum, and
that is just a math function.

Of course when we look at an actual map of some place, we know that the place
isn't a picture with symbols denoting its features. It's not so clear for
features of the universe. When you're far from the bottom, the descriptions
look like maps. The mass and acceleration arrows on a free body diagram of an
automobile aren't the automobile; it's all just a diagram.

But the more detailed you make the description of something, the less of a
distinction there is between the description and the thing! At some point, the
description must be the thing. (If it isn't then just alter whatever is
different between the two and patch the description; then repeat.)

Another thing to keep in mind is that math _itself_ has map/territory
descriptions. The formula or graph representing a mathematical object isn't
that object.

When we say that the universe may just be math, we don't mean that the written
math is the universe, but rather that the abstract math described by those
representations is identifiable with what is real: the map isn't the
territory, but those two territories are identifiable with each other!

~~~
DCKing
> The territory is never observed other than through maps, and the maps are
> all math.

Be careful with words here. The universe is observed through other means than
maps all the time. In fact, it is what everyone is doing all the time.

The universe is _described_ using maths. It is also often described by neuron
firing patterns in brains or less accurately using English or Russian. Just
like territories are described by maps or less accurately using English or
Russian.

> But the more detailed you make the description of something, the less of a
> distinction there is between the description and the thing! At some point,
> the description must be the thing. (If it isn't then just alter whatever is
> different between the two and patch the description; then repeat.)

That doesn't follow. At the limit to infinity, the description is the perfect
description. There is no reason to believe it becomes the thing itself.

The line segment representing the radius of a circle perfectly describes a
circle. That does not mean a line segment is the same as a circle.

~~~
kazinator
_The line segment representing the radius of a circle perfectly describes a
circle. That does not mean a line segment is the same as a circle._

Aha, but there is a territory here: the abstract circle. Now suppose we equate
that territory with another territory: something in the real world. Then we
have a description of a circle (the map), but two different territories. If we
say those are the same, it's not a map/territory confusion. At best it is a
territory/territory confusion.

The description of the math will never be the math; but the correct math may
in fact coincide with reality.

If a mathematical model of the world is completely accurate, then the math
which it describes _is_ the world. The world doesn't have any properties which
the math doesn't and vice versa; it doesn't "do" anything which the math
doesn't.

------
ArekDymalski
I don't understand why people still believe in this concept. For me it's quite
simple:

1\. Our nervous system has quite narrow and well defined capability of
receiving signals from the outside world. Every of our senses has own
limitations. We can't see UV or IR etc.

2\. Our body has a specific way of interacting with the world : we have
specific size, strength, have to operate as one, undivided entity etc.

3\. With such input coming from the above points, our brain creates a specific
model of the outside world to function in it, interact, count apples and lions
etc.

4\. Part of this model is this cool toolset containing math and logic. It's
very useful for us to predict and analyze the world and it's so flexible that
we can expand and bend it according to our will in face of mismatch between
observable reality and math.

So there is no surprise that we keep seeing math around us. We created it as a
result of interaction with the world.

But to insist that math is the real way the world works is ridiculous. It's
like saying that there's nothing beyond the visible spectrum of light because
we can't see it.

I'm quite sure that any creatures with significantly different bodies than
ours would come up with different "math" and different view of the universe.

EDIT: I was trying to imagine such creatures but gaps in my knowledge and
limitations of my homo sapiens mind are hard to escape and imagine something
unimaginable. But I'll give it a try: Think of a creature built of 100
autonomously moving clouds of particles, sharing one consciousness. The clouds
can change their sizes in the ping-pong - planet range and communicate by
radio waves. I think that just the ability to watch specific event from 100
perspectives would give this alien completely different psychology and
approach to the logic, truth etc.

------
qCOVET
Here is the documentary if you don't want to read the blog post:
[https://www.youtube.com/watch?v=IuGI6pQFZC0](https://www.youtube.com/watch?v=IuGI6pQFZC0)

------
a3voices
Maybe the universe is a user interface for your consciousness, and physical
objects don't really exist.

