
The Trouble with Theories of Everything (2015) - dnetesn
http://nautil.us/issue/29/scaling/the-trouble-with-theories-of-everything
======
analog31
In my view one of the puzzles of physics is actually its success over the past
couple of centuries. That we have such precise and comprehensive models of
_anything_ could not have been anticipated.

But this success doesn't guarantee future success or a predictable rate of
future progress. Whenever we agree to work on a fundamentally new question, we
are never sure whether the answer will arrive in 5 minutes or 5 centuries.
Reconciling quantum mechanics and gravity might be a 5 century problem for all
we know.

Likewise, we can never claim with assurance that any non-trivial question is
un-answerable. When problems get hard, books get written about the boundaries
of science.

As I understand things, it took humanity some 1000 years to solve quadratic
equations.

~~~
lisper
Depending on how you count (no pun intended) it took 4,000 years to invent the
number zero.

~~~
mchahn
What are these 1000/4000 year starting points? From when mankind evolved?

~~~
lisper
Actually it turns out I was off by an order of magnitude. The earliest recoded
number systems date back 40,000 years [1]. Zero was invented about 5000 years
ago [2].

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

[2] [https://www.scientificamerican.com/article/what-is-the-
origi...](https://www.scientificamerican.com/article/what-is-the-origin-of-
zer/)

------
themodelplumber
I enjoyed reading the article. This reminded me of my own work, in which I
apply various theories in every interaction with my clients. Some of the
models with which I'm familiar are very detailed and provide some amazing
scaling features such that they work on multiple levels. However, no sooner do
they do that then they begin to require the construction of abstract models
just to understand and leverage them, to say nothing of properly testing them
in depth. Even so, each one of these models gives me a slightly different lens
on a problem, and those lead to new and varied leverage points. For that they
are extremely useful.

As an aside, I was also reminded of role-playing simulation systems like Fate,
GURPs, and Risus--all of which can model entire worlds, but each of which does
so with varying experiential 'leverage points'. GURPS can offer the experience
of quantifying a solar system, if you want that. You can then look at Risus
and maybe it's simple and not substantive in that way, but that doesn't give
due credit to its capability within specific boundaries like time, experience
level, etc. IMO the boundary concept is important to embrace and appreciate in
any theoretical or even any human endeavor, otherwise theories / models can
start to leak leverage, so to speak.

------
stareatgoats
> nature, as Feynman once speculated, could be like an onion, with a huge
> number of layers

Much of this was like woosh to me admittedly, but in between the Greek; happy
to see that even distinguished scientists with degrees seem to think that we
are nowhere near understanding 'the mind of God' as the late Stephen Hawking
once or twice proposed we might be, may he rest in peace.

So, a TOE seems more and more improbable. The most sane and reasonable stance
IMO would then be to _suspect but not know_ an _infinite_ number of layers,
scales and dimensions, be it in terms of time, space or speeds.

Such a position would seem useful in theory-creation as it would free our
assumptions about the universe from our natural human-centered prejudices in a
radical way.

And philosophically, place us in the center of the universe again in a way
(since the center of an infinite universe is everywhere).

And tentatively allow us to get a glimpse of, albeit not understand and
certainly not acquire, 'the mind of God'.

But this is obviously where science ends and belief begins.

~~~
notduncansmith
This has been roughly my position for the past few years and it has, without a
doubt, multiplied my ability to understand new concepts and perceive causal
relationships, among many other positive radical changes.

------
foldr
A similar idea was worked out in more detail by the philosopher of science
Nancy Cartwright under the heading of "the dappled world":

[https://www.amazon.co.uk/How-Laws-Physics-Nancy-
Cartwright/d...](https://www.amazon.co.uk/How-Laws-Physics-Nancy-
Cartwright/dp/0198247044/ref=sr_1_1?s=books&ie=UTF8&qid=1527949009&sr=1-1)

[https://www.amazon.co.uk/Dappled-World-Study-Boundaries-
Scie...](https://www.amazon.co.uk/Dappled-World-Study-Boundaries-
Science/dp/0521644119)

It's interesting to see a physicist suggest something similar. Review/summary
of the second (more recent) book here:

[https://philosophynow.org/issues/28/The_Dappled_World_A_Stud...](https://philosophynow.org/issues/28/The_Dappled_World_A_Study_of_the_Boundaries_of_Science_by_Nancy_Cartwright)

------
vorg
> There is no known physics theory that is true at every scale—there may never
> be

The article mentions how GR and QM have never been successfully combined
together into a testable theory, how SR and QM produce infinities that need to
be "renormalized" when combined together, and how there's no "direct" evidence
that QED and QCD can be combined together.

The article didn't mention Thermodynamics that operates at scales between GR
and QM, and how its reliance on a directed time dimension means it also
doesn't combine with time-reversible GR, e.g. where has the information gone
after a black hole evaporates via Hawking radiation, or what happens at the
Cauchy horizon in a rotating black hole. QM is also time-reversible so I guess
TD can't be combined with QM either.

~~~
kkylin
Not a physicist, but I do not think thermodynamics is a physical theory in the
same sense that QED or GR are: it isn't about any specific physical system or
interaction, but rather a general pattern when one looks at certain properties
of bulk matter on (relatively) long timescales. Feynman had a good explanation
of this, but for the life of me I can't remember the reference right now --
it's either in one of the lectures in the Character of Physical Law (try the
one on the distinction between past and future) or one of the Feynman Lectures
chapters on thermo.

IIRC thermodynamics per se does not have to "change" to adapt to systems where
quantum effects play a role. How to link abstract thermodynamic concepts to
the microscopic dynamics of a specific system in which quantum effects play a
role _would_ require a quantum theory, but for that we have quantum
statistical mechanics
([https://en.wikipedia.org/wiki/Quantum_statistical_mechanics](https://en.wikipedia.org/wiki/Quantum_statistical_mechanics))
which is a fairly well-developed subject.

(This leaves out connections to relativity, special or general, about which I
don't know much.)

------
AndrewKemendo
Every domain of study actively tries to create a unifying Generalized theory.
It's basically implied that research is attempting to completely model a
system into the "Grand Unified theory of [insert domain]."

I think it's a quirk of Humanity to think that systems trend toward stability
and immutability, but I'm not sure if it's possible to say for sure. In other
words, there is a slight possibility that the fundamental "laws" governing
systems could actually change over time. That is not to say that our
perception of them changes with better tools, but that fundamental
interactions may not be immutable.

------
_cs2017_
To summarize the article: maybe we'll never discover a unified theory and will
have to live with approximations for each context. But maybe we will. But nah,
we should be skeptical about that. Probably not.

Just like pretty much any philosophy ever.

------
songeater
Godel's incompleteness is the closest we have come to the theory of everything

------
naasking
If there is no theory of everything, then reality simply cannot be captured by
a formal system of any kind.

I'm not sure that this possibility agrees with what we do know about reality.
Like the unreasonable effectiveness of mathematics.

~~~
danharaj
The integers can't be captured by a formal system of any kind either.

~~~
naasking
Well that's not true. You can't prove every true statement about the integers,
but that's not the same thing.

~~~
yorwba
For every unprovable true statement about the integers, you can find a set of
"non-integers" that has all the properties of integers that are provable, and
in addition the unprovable statement is false.

I don't think a formal system can be said to capture the integers if it also
allows such "non-integers".

~~~
naasking
I honestly don't follow your first claim or how it has any bearing on this
question. Perhaps you could provide a link to the actual theorem you're
describing to clarify.

~~~
danharaj
GP is alluding to the fact that any unprovable true statement about the
integers has a counter-model for which the statement is false which the formal
system cannot distinguish from the integers. Therefore no formal system
characterizes the integers, there are always these false integers lingering.

These objects are highly pathological artifacts of the formal system in
question, but that just goes to show how slippery the integers are.

~~~
naasking
> GP is alluding to the fact that any unprovable true statement about the
> integers has a counter-model for which the statement is false which the
> formal system cannot distinguish from the integers.

Again, do you have a link or a name for the theorem you're describing?

~~~
danharaj
This is a consequence of Goedel's completeness theorem: a statement in a first
order theory is provable if and only if it is true in every model.

The counter models obtained for arithmetic true unprovable statements are
called non-standard integers.

~~~
naasking
Ok, now we're getting somewhere [1]. So various theorems can be used to prove
the existence of non-standard models of arithmetic. I'm not sure why I should
find this compelling.

There are infinitely many possible models of arithmetic, each of which has
different properties. Some of these are isomorphic to standard models in
various ways, some of which are not.

But, if the world is governed by mathematics, then at least one such model
would best match reality. How would we even speak of a world which was not
internally consistent such that it could be formalized in such a fashion?

[1] [https://en.m.wikipedia.org/wiki/Non-
standard_model_of_arithm...](https://en.m.wikipedia.org/wiki/Non-
standard_model_of_arithmetic)

~~~
danharaj
I'm not sure what you're asking. Any formalization of the integers won't be
"the" integers, the totality of which perhaps isn't even a reasonable idea.

Mathematics is a part of the world and does not stand apart from it. There is
no reason why such a "best" model should exist, and by any reasonable
definition, it doesn't. Mathematics is irrefragably incomplete. It is perhaps
the only human discipline that demonstrates its own limits.

~~~
drdeca
What?

Every model of arithmetic has every standard integer though?

Are there nonstandard models of second order ...

Ok Wikipedia says that "the axioms of Peano arithmetic with the second-order
induction axiom have only one model under second-order semantics.", so...

~~~
danharaj
Second order induction could hardly be called a formal system: There is no
complete, effective proof system for it. This is the basically the same
limitation on first order PA. The standard model for second order arithmetic
involves the power set of the naturals which is immediately a far more complex
object than any computable system; it essentially presupposes the object that
you're trying to formalize in the first place.

~~~
drdeca
I don't see why the lack of a complete effective proof system for it should be
a problem.

I do in fact consider the power set of the naturals to exist, so I'm not sure
I see the problem? Is it just that uncountable sets have elements that we
cannot pick out? I don't have a problem with that.

~~~
danharaj
It matters because it means second order arithmetic isn't a finite object in
the same way first order effective theories are where you might have
"infinitely" many axioms but they are packaged up in a finite object, an
algorithm.

The whole point of a formal system, its formality, is that it doesn't require
any semantic notions to describe it. Second order arithmetic with its full
model is no such thing. It is inherently infinitary and therefore not formal
at all.

And it's a treacherous object. C.f. Richard's paradox which demonstrates that
"subset of the integers" is by no means a naive idea.

~~~
drdeca
Isn't it true that the only countable model of the natural numbers (including
ordering) which is computable is the standard model of the naturals?

