
Shut up and calculate: an extreme mathematical universe - Phithagoras
https://arxiv.org/abs/0709.4024
======
westoncb
It baffles me that people ignore the fact that they have subjectivity when
making these claims. It makes a certain amount of sense since science itself
aims to remove any taint of subjectivity in its practice, so folks who want to
be thoroughly 'scientific' in other aspects of their lives (e.g. their
personal philosophies of reality) carry over over this ideal.

But it's also a contradiction since science scientific methodology demands we
check our results empirically: the fact that you have subjectivity (i.e. that
qualia exist) and what it's like, is the most direct empirical fact we have
access to and which needs reconciling in any discussion of the universe's
constitution.

I think people sort of push this point aside either by saying that
qualia/subjectivity could be _generated_ by math (or a computational process),
and that's what _really_ matters. But we have no examples of abstract math
generating anything; physical processes generate things and we use math to
influence their behavior—but that's it! And furthermore, even if math
generated subjectivity—it's still _there_ in all of its un-mathematical
obviousness at the end of the day.

I've yet to see an argument in favor of math having higher ontological status
than this which wasn't every bit as unrestrainedly imaginative and unfounded
as Plato's 'ideal forms'. I would expect a thoroughgoing adherent to
scientific methodology to instead say something on the lines of, "this is
outside the domain of science to judge one way or the other; the most we can
say is the idea that reality is made of math is one untestable hypothesis
among many whose probabilities of correctness each approach zero by dint of
their many peers."

~~~
placebo
You're right, and I also see how this obvious observation is consistently and
elegantly ignored in most scientific or philosophical arguments that try and
promote some totally "objective" account of reality.

However, it's not really that surprising: Science over the centuries has
steadily (and for it's time, justifiably) eroded the role of subjectivity in
order to uncompromisingly get at what is consistently true (regardless of what
we'd like to be true) and this process required being very suspicious of any
subjective accounts that can't be measured.

That being said, perhaps the time has come to dig a bit deeper and in the same
persistent and uncompromising way ask what does objectivity or subjectivity
mean? What do they arise from and to whom? I don't know if any new
technologies can be derived from having clearer insights to these questions,
but I do feel that it would be time better spent than any untestable mind made
artifact about what reality ultimately is.

~~~
westoncb
I agree it's worth looking more closely at the relationship between
objectivity and subjectivity, especially the mapping from the 'nearest'
objective structure we know to various aspects of subjectivity. I think this
could be a decent route to finding a brain structure tightly related to
conscious experience.

However, my suspicion is that the experience itself will remain not amenable
to conceptual analysis—that it will remain fundamentally incapable of
systematizing. For instance what would the mathematical description of the
_experience_ of a fever chill look like? (Hint: the definition there requires
that you don't take a reductive approach to this: it's not asking about a
mechanism which _produces_ or is _responsible_ for the experience, it refers
to the experience itself.)

That said, I think it would be very valuable to understand better what the
limits of our conceptual faculty are: as impressive as cognition is relative
to other things we and other animals are able to do, we're being unduly
anthropocentric in assuming it to be boundless in capability. More recently
I've come to consider concepts as almost like another sense: they are symbolic
patterns consistently formed when we are exposed to certain stimuli (like our
experience of smells consistently reappearing when exposed to similar
molecules). Our conceptual faculty augments the pure pattern-correspondence of
our more primitive senses in that the patterns can be associated with other
internal patterns, and in that we can generate new patterns purely from
existing patterns (using logical and analogical processes), which at some
future time may be usefully associated with some never-encountered external
stimulus.

Finding the limits to our conceptual faculty is almost synonymous with find
its 'structure', which I think would have clear benefits.

~~~
placebo
> _However, my suspicion is that the experience itself will remain not
> amenable to conceptual analysis_

I'm in total agreement with this as well. When I suggested looking into what
is it that objectivity and subjectivity arise from, I wasn't referring to the
"physical" explanation (which I assume will eventually be resolved, though not
in the near future) but to the core of the hard problem of consciousness. My
take on this is that when looked at closely, it will not be found within the
domain of anything that can be conceptualised simply because it precedes
concepts. _Any_ concept requires consciousness to exist but not vice versa. Of
course the usual argument at this point is something in the line of "so the
sun didn't exist before any thinking animals existed?" To which my answer is
that the sun as a concept didn't exist. Neither did hydrogen, electrons or
wave functions. Only pure pre-concept reality existed, neither objective nor
subjective, "waiting" for a mind to evolve and eventually form subjects.
objects and concepts that with increasing accuracy describe how this reality
functions, and then proceed to confuse this description of reality with
reality...

~~~
westoncb
Heh, yeah, that's pretty much exactly how I think of it :) I didn't mean to
state my previous comment as a disagreement, just an elaboration.

------
js8
I like the idea that the reality is just mathematics, I thought about it
independently, but it gets weird really fast.

I yet to have read this essay, but I had two thoughts:

1\. Similar to Turing completeness, actual physical reality might not matter
for the internal observer. All Turing-complete machines can calculate same
things and observer from the inside of the machine cannot determine on what
hardware the machine is implemented. Similarly, this can be case for observers
within our universe (humans). So maybe there is, at a high enough level of
abstraction, only one mathematically possible universe.

2\. The mathematical theorems are shortcuts to computation. For example, I can
add two numbers on a computer, or I can use a theorem, which will tell me only
some property of the result, but avoids having to do the actual calculation.
So if universe is just a computation, one could avoid actually computing it in
certain cases by having a theorem that would tell them enough information they
need. In other words, you don't actually need to simulate anything in order
for objects in simulation to "exist". So there is no need for actual hardware
on which the universe runs to exist.

Addendum: So I read the essay, and I disagree that the multiverse is
necessary. As I already stated in point 1, it can be the case that all
possible mathematical realities are the same at high enough level of
abstraction.

~~~
kybernetikos
> So there is no need for actual hardware on which the universe runs to exist

You may enjoy the science fiction book Permutation City

~~~
teraflop
If we're talking about Greg Egan, then I'll go ahead and also suggest his
short stories _Luminous_ and _Dark Integers_. They postulate a similarly tight
connection between physical processes and mathematical theorems, and then go
on to consider the implications of the fact that such a system can't prove its
own consistency.

------
fizixer
Two points:

\- What he describes in the abstract is nothing new. Part of your work as an
applied mathematician is to take mathematical models developed by others, e.g,
in the form of systems of differential equations, and treat them as absolute
truths (for the sake of computation; essentially you create "a mathematical
bubble" for yourself and choose to live in it), study the consequences, and
present the results. So his claim of "I advocate" is disgusting
plagiarism/credit-snatching of a well-known technique.

\- What he actually advocated is total bullshit as far as physics is
concerned. You can live as long as you want in the bubble of your mathematical
models. But if you have to connect your math to reality, you have to make your
math subordinate to empirical data, and if the data disagrees, your shiny
mathematical model is wrong, period. Also don't forget what George Box said
"All models are wrong. But some are useful".

------
krylon
It is remarkable how sufficiently advanced physics / cosmology sounds to the
layperson like a conversation between two teenagers who smoked weed a little
while ago.

(My favorite: [https://en.wikipedia.org/wiki/One-
electron_universe](https://en.wikipedia.org/wiki/One-electron_universe))

I do not say that to belittle physicists. Not at all, I have the utmost
respect for what they do.

But as they dig deeper and deeper, what they come up with sounds like the
universe is a pretty strange place to be. Personally, I am okay with that
idea, because, if I look closely enough, I _have_ been living all my life in a
world that does not really make sense. But it is really strange, nevertheless.

------
followmeon
If our reality consists of mathematical programs and the multiverse theory
holds, then the theory of everything is a simple incrementing binary counter.
Every possible binary string is ran on a Turing machine in a different
universe.

The halting problem (endless loops) is sidestepped by being contained to a
single universe. Also, apparently our universe got lucky as we get to live in
an ordered universe, and not dissolve into nothingness due to a bug in our
universe's binary code.

Of course, like "normal" mathematics, "reality" mathematics should also be
incomplete. Furthermore, there is no way to know everything of the universe
one is a part of, as this requires at least 1 bit more than there are
available bits in the universe. But this still allows for the possibility of
the universe itself being an inference machine.

Edit: Then again, I believe that mathematics is a mental construct,
mathematics does not exist without brains, or if it really exists external to
human minds, it exists in all possible forms: Humans do not discover maths as
a whole, they cast a local net of subjective observation over it, and keep the
things that make sense to our brains and are consistent within the current
framework. Again, this does not preclude the possibility that our mathematical
reality exists inside the mind of a giant supercomputer.

~~~
Houshalter
I think you've confused the representation with the computation. Sure maybe
that binary number could represent a universe state in some encoding. But
there's no computation happening to it. It's static.

>I believe that mathematics is a mental construct, mathematics does not exist
without brains

Brains evolved through natural selection to survive in the universe we exist
in. Ideas similarly "evolved" to be good at modelling the universe. If
mathematics didn't exist outside of our head, it would be useless. If there
are two apples on the ground, and two more fall of a tree, then there are four
apples on the ground. This is true whether or not a human is there to observe
it and count them.

~~~
jonnybgood
> If there are two apples on the ground, and two more fall of a tree, then
> there are four apples on the ground. This is true whether or not a human is
> there to observe it and count them.

I don't know about that. How close do the apples have to be to number them? If
two apples are within inches and another a mile away, is there two apples or
three apples? Define ground. Is it dirt? And dirt of what? If two apples are
on Earth and one apple on Mars, is there two or three apples on the ground?
What does it even mean to number things? What is a number?

My point is that it takes a human brain for establishing definitions, axioms,
and conditions. Only after these have been established can we do math.

------
1001101
The author expands on this concept in his 2014 book (~7 years after the
publication of this paper), Our Mathematical Universe: My Quest for the
Ultimate Nature of Reality. I've read it, and I would highly recommend it to
my fellow HN'rs. I found his multiverse classification scheme [1] very
compelling and something that finds its way into my worldview and a lot of my
thinking.

[1]
[https://en.wikipedia.org/wiki/Multiverse#Max_Tegmark.27s_fou...](https://en.wikipedia.org/wiki/Multiverse#Max_Tegmark.27s_four_levels)

------
Santosh83
An interesting article addressing this from Sabine Hossenfender:
[http://backreaction.blogspot.in/2007/10/mathematical-
univers...](http://backreaction.blogspot.in/2007/10/mathematical-
universe.html)

Her more recent article (review of Max Tegmark's book) also comments on the
same subject: [http://backreaction.blogspot.in/2017/11/book-review-max-
tegm...](http://backreaction.blogspot.in/2017/11/book-review-max-tegmark-
our.html)

~~~
westoncb
This (the universe is 'made' of math) seems to me like the most egregious
error in the general outlook of contemporary scientifically-minded people—and
one I made myself for many years.

If you really consider the issue closely, you'll see it depends on not
overlooking certain dark corners of it which you can sort of ignore and assume
to not contain contradictions—but they're there! And once you see them, it's
hard to unsee them: what in the world would it mean for a desk to 'made' of
mathematics—it's nonsensical. I think programmers are especially susceptible
to this mistake because they're used to using mathematical descriptions to
generate things, but even there, the idea that the math is doing any
generating is a bias of our perspective since we're focused on the math;
what's actually going on is a physical process involving silicon and plastic
and metals etc., which can also be _described_ mathematically, but the leap to
_being_ math is an unfounded step which could probably be predicted by the
fact that that's where our focus lies.

It also begins to look kind of silly when you consider how _human_ math is:
it's an outgrowth of an evolved mental faculty. Cognition is certainly
impressive _relative_ to the other things we and various animals are able to
do—but it's probably still in the same category of our other faculties like
the olfactory, visual, tactile etc.—and unlikely to be involved in the literal
fabrication of the universe.

~~~
naasking
> If you really consider the issue closely, you'll see it depends on not
> overlooking certain dark corners of it which you can sort of ignore and
> assume to not contain contradictions—but they're there! And once you see
> them, it's hard to unsee them: what in the world would it mean for a desk to
> 'made' of mathematics—it's nonsensical.

What does it really mean to "exist" at all? It's equally undefined. This
question is either problematic for every metaphysics, or none of them.

A desk is not "made" of mathematics any more than the words you're reading
right now are "made" of electrons. What matters for existence is the
_relationships_ between mathematical structures. In this case, the
relationship of your mind perceiving a desk is identical regardless of whether
your mind and the desk are mathematical structures or some non-mathematical
matter.

And once you accept that isomorphism, it's an easy step to a type of
Platonism/mathematical monism because it's so unproblematic as a philosophy of
mathematics. And once you're there, you have the mathematical universe.

~~~
westoncb
> What matters for existence is the relationships between mathematical
> structures.

Well, that's what Structuralism is
([https://en.wikipedia.org/wiki/Structuralism_(philosophy_of_s...](https://en.wikipedia.org/wiki/Structuralism_\(philosophy_of_science\))
—but it would be running in circles to say that Structuralism is the correct
approach here since it would only be the correct approach if the universe is
in fact made of mathematics (in other words, it would be assuming your
conclusion in your argument).

~~~
naasking
> (in other words, it would be assuming your conclusion in your argument).

To be convincing, it's not necessary to claim that any particular position is
definitely true, I should only need to demonstrate that said position solves
open problems that have not or cannot be solved by other positions while being
of comparable complexity, conceptually.

This is indeed the case for something like the mathematical universe over
naturalism. There may yet be a comprehensive, unproblematic account for
mathematics in naturalism, but we certainly don't have it yet. That's a huge,
gaping wound in our fundamental knowledge.

The mathematical universe, by contrast, easily grounds mathematics and matter
by encompassing both in the former.

~~~
westoncb
There is a solution without requiring the universe be made of math: math just
describes it instead. You can point out that this doesn't explain why math
works so well, but I'll point out it's better not to pretend we have an answer
if we really don't--then we keep looking. The idea that reality is made of
math as an answer is totally lacking in justification, so sure it is
technically an answer but saying the moon is made of cheese is an answer too.
Not all answers are created equally.

~~~
naasking
> You can point out that this doesn't explain why math works so well,

The philosophical implications are far broader than that. The mathematical
universe provides working foundations for a lot of philosophy and physics. For
instance, the multiverse entailed by the mathematical universe explains why
fine tuning for life isn't necessary.

> but I'll point out it's better not to pretend we have an answer if we really
> don't--then we keep looking.

You can keep looking despite accepting that the mathematical universe is
currently our best explanation. Your implication that we wouldn't do this is
simply bizarre. Would you shout equally loudly that we shouldn't build on our
best scientific theory simply because it may not explain everything?

> The idea that reality is made of math as an answer is totally lacking in
> justification

Except I just covered the justification: the fact that it explains plenty of
philosophical and scientific problems without introducing unnecessary
complexity. What more justification could you possibly need?

Frankly, it sounds to me like you're either special pleading or moving the
goalposts simply because you don't like the idea of the mathematical universe.

------
cs702
As stated by the author, this is necessarily a speculative piece ("assuming
that..."), but still worth reading -- as long as you keep that in mind. It
makes no sense to criticize it or dismiss it for being speculative, as others
have done here!

By the way, if you enjoy reading this piece, you might also enjoy really
interesting paper coauthored by the same person: "Why does deep and cheap
learning work so well?," available at
[https://arxiv.org/abs/1608.08225](https://arxiv.org/abs/1608.08225) \-- it
posits that deep learning works well because of the particular structure of
the laws of physics in the universe in which we happen to live.

------
jcelerier
> For example, a sufficiently powerful supercomputer could calculate how the
> state of the universe evolves over time without interpreting what is
> happening in human terms.

Hasn't it been understood for a long time that quite a bit of things were
entirely non-deterministic ? eg radioactive decay. You could compute a
possible state, but the universe is a sequence of state spaces.

------
jcmoscon
Math works because reality works. Not the opposite. Reality is bigger than
math. Math is just a tool that models reality.

~~~
hackinthebochs
On the contrary, reality works because reality cannot contain contradictions.
But the set of possible structures without contradiction is a superset of what
is physically realizable. And mathematics is just discovering and cataloging
the set of structures without contradiction. So reality works because math
works.

~~~
malkarouri
Why wouldn't reality contain contradictions?

~~~
hackinthebochs
I mean in the logical sense. If reality could contain logical contradictions
then that would mean reality isn't rule-based, which means unconstrained
randomness, no information, no meaning, etc.

~~~
namelost
But the contradiction is in the mathematical model not reality. Even a totally
random universe follows some kind of distribution, which can then be modelled
(which is exactly what QM is).

~~~
naasking
> But the contradiction is in the mathematical model not reality.

He's assuming a mathematical model that faithfully represents reality, hence
"reality can't contain contradictions". We're not going to one day find a
contradiction and vanish in a puff of logic, the ultimate model of reality
will be contradiction-free.

------
omazurov
The tale of the frog and the bird may be good for a less mature audience but
here we can really go with a richer analogy: the two views correspond to how a
virtual machine is seen from within and from the environment in which it runs.
I prefer this analogy to the "abstract mathematical structure, an immutable
entity existing outside of space and time"because it not only allows to
comprehend how space and time could emerge within that VM and not only what it
means to exist outside that emergent space and time, but also that that
outside environment could have its own space and time and in turn be just
another VM, totally beyond our reach but not inconceivable.

------
bitL
Alright, why not go one step further and make Universe computational instead?
(i.e. state is important in von Neumann-style instead of meaningless in
classical math-style; or algorithms vs formulas)

~~~
eref
Tegmark's Mathematical Universe Hypothesis (MUH) is actually pretty much a
computational theory of the universe. It basically makes the assumption that
there exists somewhere the simplest process imaginable: One that counts
through and runs all mathematical formulas which includes all programs, which,
in turn, includes all (computable) universes. This assumption explains why our
universe is oddly complex: If all universes exist, then a weird one such as
ours merely exists because all universes do. This line of reasoning is also
called the "anthropic principle".

I think, Tegmark does not talk about computations per se because the
hypothesis is agnostic about what kind of computer our universe is. It could,
for example, be a geometric computer in which the position of objects can be
determined with infinite precision (i.e. using the real numbers). Such a
computer would be strictly more powerful than a Turing machine or equivalent
(i.e. all computational models that can be described and run inside a Turing
machine). Enumerating the space of all formalisms (i.e. the domain of
mathematics) is as agnostic as you can be.

~~~
gfodor
I didn't take Tegmark's argument to be a computational theory. I took it to be
an inductive one based upon the trend of the physics over the last decades
towards the more and more generified multiverse theories. Ultimately, you land
on a model where all consistent mathematical representations of a reality
exist. At that level of abstraction, there is no where to go: it is the limit
of the induction. There's a rather satisfying sense of self-evidence about it,
but that doesn't mean it's falsifiable or true.

IIRC there are no arguments about computation or what underlying medium(s) are
involved, it seems like a separate question.

~~~
naasking
> Ultimately, you land on a model where all consistent mathematical
> representations of a reality exist. [...] IIRC there are no arguments about
> computation or what underlying medium(s) are involved, it seems like a
> separate question.

These are actually related by Goedel's incompleteness theorems and the Curry-
Howard isomorphism. Computation and mathematics are inextricably linked.

The Computable Universe is a necessary restriction on the mathematical
universe hypothesis to avoid accepting inconsistent universes.

~~~
eref
It links a certain axiom set with computations, not all of mathematics (i.e.
the set of all axiom sets), doesn’t it?

~~~
naasking
If you accept that every mathematical structure of interest has an
intuitionistic construction (as is currently believed to be the case), then
every mathematical structure has an expression as a computer program.

------
daxfohl
Wasn't Einstein'srelativity a product of intuition rather than of
calculation? And, intuition of processes that far exceed the bounds that
Darwinian evolution would have prepared us for?

If we all just shut up and calculated, we'd still be doing Lorentz transforms
near speed of light "just because they work", right?

------
iainmerrick
I don't think any of this stuff is very meaningful or useful, but the title
seems particularly cheeky.

The whole point of that catchphrase "shut up and calculate!" was supposed to
be "stop speculating about things we can't prove or disprove and wouldn't have
any direct impact on us if we could; focus on crunching the numbers and
figuring out what's effective."

This whole "mathematical universe" thing seems like practically the definition
of premature speculation! It's no more useful than ancient Greek philosophers
speculating on the nature of the elements. Those other people over there
drawing circles in the sand, now, they're getting somewhere.

------
gfodor
Haven't read the paper but I'm assuming this is the same concept (likely more
digestible for the layman) in his book Our Mathematical Universe, which I
highly recommend!

------
Houshalter
I can't even comprehend what the alternative viewpoint would be. The the
universe _isn 't_ mathematical. A universe that doesn't obey any system of
logical rules.

A universe with true randomness might satisfy that literally. But random
variables can be incorporated into a mathematical model. But what would it
even mean for a universe to not be describable by any kind of math at all? I
don't think such a concept is coherent or discussable.

~~~
carvalho
To be a fully random sequence, a sequence would have to contain substrings of
apparent predictable beautiful order. If it didn't, it would be more
predictable (you could then discard ordered continuations), not unpredictable.

> [Model-agnosticism] consists of never regarding any model or map of the
> universe with total 100% belief or total 100% denial. Following Korzybski, I
> put things in probabilities, not absolutes... My only originality lies in
> applying this zetetic attitude outside the hardest of the hard sciences,
> physics, to softer sciences and then to non-sciences like politics,
> ideology, jury verdicts and, of course, conspiracy theory. -- RAW

A universe _isn 't_ a map, it is the territory. An ordered universe can still
be mapped/modeled with maths. A universe that is impossible to be
mapped/modeled and has no predictable patterns would be an impossibly boring
universe indeed (Kolmogorov Random Universe). Perhaps our brains would evolve
to think more in probabilities than absolutes in such a universe. Or they
could simply not be allowed to exist (intelligence requires order).

------
vorg
The author asks how we could use the mathematical equations which describe all
of reality to compute the frog’s view of the universe — our observations —
from the bird’s view. Wouldn't we also need to include our self-awareness in
those observations, which would make the computation impossible according to
Turing's halting theorem, or is it Godel's?

~~~
jxy
The basic result from Turing/Godel is that you don't need any self-
referential. As long as it is an enough powerful formal system, it is always
incomplete from day one. There will always be some mythical things you cannot
compute. There will always be some universes you cannot prove their existence
or nonexistence.

------
lainon
Here's something more philosophical concerning the mathematical universe
hypothesis:

[http://shelf1.library.cmu.edu/HSS/2015/a1626190.pdf](http://shelf1.library.cmu.edu/HSS/2015/a1626190.pdf)

------
skc
Theoretical physicists are my favorite people. They all sound slightly insane
and I love it.

------
otakucode
A purely mathematical universe immediately brings to mind a question: Since
chaotic systems evolve in a way provably intractable to calculation, how could
any system based solely upon calculation address, well, almost everything that
exists?

~~~
tzahola
Chaotic systems are only intractable if you measure the initial conditions
with finite precision.

~~~
otakucode
No, that is not true. Their intractability has absolutely nothing to do with
the precision of measurement. Assume the initial condition with infinite
precision and the further evolution of the system is still intractable.
Ignoring the Heisenberg Uncertainty Principle for a moment and getting to the
heart of chaos theory the problem is the production of information at a rate
faster than any existant (and I believe, though I don't understand it well
enough to give exact details) or fundamentally possible future system of
mathematics can compensate for. Nonlinear systems (ie, essentially everything
in existence) display chaos (extreme sensitivity to initial conditions,
period-doubling, whatever you wish to call it) on every scale. Were the
universe mathematics and mathematics alone, all things which are provably
outside of the grasp of mathematics would also be non-existent. Such things,
however, do exist.

While we may not be able to predict the location of a single molecule of air
in a mere 10,000 years with a rough accuracy of a cubic femtometer, the
universe does it. And our inability to predict it is not because we need a
bigger computer. Our inability to predict it is because in order to predict
it, we would have to simulate the entire universe and every single particle
within it, and every interaction between all of them, to infinite (ehhh...
maybe) precision. Which would have an information load exactly as big as the
universe itself and increase entropy (which implies it takes as much time) as
much as actual evolution of the entire universe over that course of time. To
predict one molecule of air. And the universe does it for all the molecules of
air. Along with all the other particles.

~~~
Koshkin
> _the universe does [predict]_

But it does not.

~~~
otakucode
That's a very strange quote you did... did you honestly think that I meant the
pronoun 'it' to mean 'predict'? I absolutely did not. The universe does it. It
executes. It evolves along the pathway and 'calculates' (if you wish) the end
result. A thing which no mathematics can, or will ever be able to, do.

~~~
Koshkin
> _calculates ... the end result_

It does not do that, either. (Because there is no "end result" to calculate.)

~~~
otakucode
If you are looking for the future position of a particle, the future position
of that particle is by definition the result sought. I think I might not
understand your meaning.

~~~
Koshkin
According to the modern physics view, the "future position" is undefined in
principle; the only position that is known is the position just measured.

------
aj7
That was always Feynman’s attitude, obscured by the strong human layer he ran.

~~~
Koshkin
Didn't Feynman think that the world was essentially _void_?

------
Bromskloss
I couldn't go to his lecture in Stockholm the other day. Were any of you there
and could tell us something about it?

Edit: Hm, actually, the lecture was about dangers of AI, so not the same
topic.

------
lou1306
I'm a philosophy noob, but isn't this very similar to Berkeley-style
immaterialism?

~~~
Koshkin
Not really. Berkeley's idealism contests the _objectivity_ of reality, while
here we are presented with another view of the foundation of the (objective)
material world.

~~~
lou1306
This is true, but:

> When we derive the consequences of a theory, we introduce new concepts —
> protons, molecules, stars — because they are convenient

Couldn't _matter_ itself be just another "human", "convenient" concept? Indeed
the author writes:

> our external physical reality is assumed to be purely mathematical

Why should a purely mathematical reality also be material? Doesn't this lead
to the logical conclusion that ideas, err, maths is "all that there is"?

Sure, in this case ideas are objective and not subjective, but Berkeley's
"mind of God" argument _also_ leads to an objective, albeit immaterial
reality, doesn't it?

~~~
otakucode
>Sure, in this case ideas are objective and not subjective, but Berkeley's
"mind of God" argument also leads to an objective, albeit immaterial reality,
doesn't it?

No, it leads to a subjective inability to know anything at all. It's a
difficult philosophical view to talk about, because the people espousing it
can not possibly actually believe it and usually don't even understand it. The
non-existence of a shared, knowable, objective reality means that, even in a
totally solipsistic model, inductive reasoning can not be applied. You can not
assume that attempting to breathe in the next moment will extend your life
rather than extinguish it. You can not conclude that the air in your lungs
will not suddenly become ants. You certainly can not leap to the extensively
complex chain of reasoning necessary to believe that between this sentence and
the next the English languages will turn into French. It introduces
aggressive, pervasive, impossible-to-dismiss inconstancy in all things,
including ones self.

A true believer in a subjective universe would remain still in their bed,
doing nothing, until they died. Any action whatever beyond automatic
biological functions instantly betrays their belief that they know their body,
know the environment they are in, and know how the mental activity necessary
to cause the action will elicit a change in the environment which is not
likely to destroy them. And that is a thing they can never know in a
subjective universe.

The 'mathematical universe' on the other hand is simply discussing how the
shared, knowable, material universe we live in came to be or is best
understood. I happen to think it is factually wrong on a few points (the
author just off-hand claims that if we had a big enough supercomputer we could
exactly calculate the future development of the universe which is
fundamentally untrue for one) but it certainly doesn't amount to subjectivity.

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daveydog
I don't think the idea that everything is math, is particularly original.

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m3kw9
Meaning everything can be predicted if you know the equation and have enuough
processing power. Problem is doing the calculation in the same universe where
you are also predicting it also disrupts the calculation. Something in the
line of the uncertainty principle

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kingkawn
a Subset cannot have greater cardinality than the set it derives from.

Subjective existence cannot be reduced to Math because it is our explorations
in subjectivity that led to math’s invention and refinement

~~~
wolfgke
> a Subset cannot have greater cardinality than the set it derives from.

I am not completely certain in the subtleties of non-standard set theory, but
at least if we replace the axiom of Choice (AC) by the axiom of Determinacy
(AD) - which is perfectly fine, though it is less common to do mathematics in
this system - we can partition the real line R by an equivalence relation that
has more equivalence classes than elements of R. So at least we can partition
R into more disjoint subsets than R has elements.

Source: [https://math.stackexchange.com/questions/1104028/what-are-
di...](https://math.stackexchange.com/questions/1104028/what-are-disasters-
with-axiom-of-determinacy/1148609#1148609)

~~~
titzer
> we can partition the real line R by an equivalence relation that has more
> equivalence classes than elements of R

That's not surprising, since an equivalence relation is a function of two
elements of the set, i.e. O(N^2), and a subset is a function of a single
element, i.e. O(N) . The OP mentioned subsets, and an equivalence relation is
not a subset of the original set--it doesn't even typecheck.

~~~
wolfgke
> That's not surprising, since an equivalence relation is a function of two
> elements of the set, i.e. O(N^2), and a subset is a function of a single
> element, i.e. O(N) . The OP mentioned subsets, and an equivalence relation
> is not a subset of the original set--it doesn't even typecheck.

I don't understand your reasoning. Every equivalence relation partitions the
set S on which it is defined on into subsets - these are called equivalence
classes. Every equivalence class contains at least one element of S. So I find
it quite surprising that there are more equivalence classes than elements of S
(in this case S are the real numbers) if we assume AD.

------
danharaj
Which mathematics?

~~~
Koshkin
The one of homotopical type.

