
Would aliens understand lambda calculus? (2018) - signa11
http://tomasp.net/blog/2018/alien-lambda-calculus/
======
whatshisface
I think the answer is kind of obvious if you understand the foundations of
mathematics. Any alien that was smart enough to manipulate written symbols
according to rules would agree that our induction rules applied to our axioms
would lead to our theorems, because proofs are a purely symbolic game that
even a computer can do. Aliens might not agree on the axioms or induction
rules except by pure coincidence, because even within our own species there is
disagreement over which axioms (choice for example) or induction rules (the
excluded middle in intuitive mathematics for example) are self-evident.

The law of the excluded middle might seem obvious to you, but not to these
guys:
[https://plus.maths.org/content/intuitionism](https://plus.maths.org/content/intuitionism)

~~~
BadThink6655321
A lambda calculus of two variables requires the law of the excluded middle, or
it won’t work. The alphabet of the calculus has to be distinguishable and
unambiguous.

~~~
voxl
The law of the excluded middle is about the truth status of any proposition.
The fact that the alphabet of the language has to have a decidable equality
does not mean the law of the excluded middle is true for any theory built from
the lambda calculus. (Or true in general)

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VLM
The problem with the Sapir-Whorf hypothesis as an argument against academic
knowledge is it may be true for the general population, however, the entire
purpose of STEM academia is to subvert the Sapir-Whorf hypothesis. Teaching a
kid quantum mechanics or calculus inherently has little to do with the general
population's belief in religion or astrology or virtue signalling, for
example.

The average Joe_6_Pack Arrival movie heptapod might culturally have an easier
or harder time learning lambda calculus; its certain that the only people
(well, heptapods) who would matter, the CS academics, would be quite familiar
with lambda calculus.

STEM has a dependency chain such that its hard to do quantum mechanics without
something like statistical thermodynamics and basic probability theory. Thus,
cultures without statistical thermodynamics, like Ancient Rome or non-European
cultures in general never developed quantum mechanics, therefore no nifty
MOSFET transistors therefore no electric cars or industrial VFDs therefore no
solar non-petrochemical energy industry therefore they die out or are replaced
with more advanced cultures before interstellar travel is reached.

We don't know the dependency chain for interstellar travel but the more
complicated things are, the more fragile they are, always, so its HIGHLY
likely any two interstellar cultures would have identical dependency chains to
pass various gates along the path. You can play games with early steam engines
burning lignite or peat and it won't matter terribly much at the time or in
the long run, but it seems there's only one way, using metal catalysts, to
"invent" your first organic chemistry hydrogenation process, for example. You
can make steel in a low tech medieval blacksmiths shop, but transistors have
tighter constraints. Most of advanced civilization is a mask over fragile,
complicated, and delicate dependency chains.

We'd like to think we're on the path to interstellar travel rather than self
destruction, so obviously all interstellar aliens would have lambda calculus
much like ourselves, because the gates we have to pass thru only pyramid and
narrow as the task gets more complicated. And interstellar travel seems likely
to be complicated.

~~~
ordu
You are relying on implicit assumption that quantum mechanics is the only
possible theory that could lead to an invention of MOSFET transistors. Maybe
this assumption is true, but I do not know it to be proved. Of course QM is
the only known to us theory that had led to MOSFETs, but it doesn't mean that
one couldn't invent some completely different way to describe reality which
would enable him to invent MOSFETs.

~~~
theamk
In order to build a MOSFET, you need to know how do electrons react in the
presence of thin barriers, and how thick should the gate oxide be to prevent
breakdown while still keeping the field strong.

Does a civilization know this? If no, they cannot make MOSFETs. If yes, than
whatever branch of physics and math describes this is called “quantum
mechanics”

Can it be different, can you do QM without Schrödinger Equation? Sure, but it
will still be QM. One can rearrange terms on formulas, use different units,
work with voltage instead of energy, introduce various metrics and so on.
Physicists do it all the time, it is simply theory reformulation.

~~~
ordu
_> In order to build a MOSFET, you need to know how do electrons react in the
presence of thin barriers, and how thick should the gate oxide be to prevent
breakdown while still keeping the field strong._

Here you are speaking using words like "electron", "thin barrier", "oxide" and
so on. So you are thinking in a framework of our culture and our variant of
STEM. Doing so you are trying to prove that there is no way to invent another
variant of STEM. I believe, that such an approach could achieve nothing.

I mean, to speak "electron" you need to rely implicitly on a whole mountain of
theories about reality. So even if you proved that one cannot build MOSFET
without QM, it would mean that he cannot do it while relying on this mountain
of theories. It wouldn't prove that there are no other mountains allowing to
invent MOSFET.

 _> Can it be different, can you do QM without Schrödinger Equation? Sure, but
it will still be QM._

It is a trivial proposition. "QM without Schrödinger Equation" is QM by
definition. The question is if it possible to build some other models of
reality that allow to invent MOSFET. As I see it you are trying to remove QM
from the mountain of theories and to think what could replace QM. It is
completely possible that nothing but QM could replace QM in such a setup. But
what would happen if you remove _all_ of the mountain of theories and start
from scratch?

I do not know. To see what would happen I need to design an empirical research
that would involve some millions of people and a few millennia. To be sure I
would need to repeat this at least 50 times.

~~~
afiori
The fact that the electron exist is not culturally dependent. As much as the
fact that stars exists.

Any alien civilization capable of studying the behavior of atoms must also be
able to express concept that are compatible with ours.

Maybe the do not use numbers, calculus, or maybe they do not even use unit of
measures. Yet the result of our experiments will have to be the same and since
we can develop experiments that show specific operations they must also be
able to express those operations.

~~~
ben_w
Electrons are a perfectly adequate model for reality. I do not read the
previous poster as disputing this point.

Instead, they appear to be asking, “is there another model for reality which
would also work well enough to build a MOSFET?”

I do not know either.

That said, people keep telling me that both QM and GR are known to be
incomplete, so perhaps electrons are no more real than phlogiston? I would
certainly be surprised, but that’s besides the point, and even if someone is
currently rolling their eyes and preparing to explain why I am wrong and
electrons can’t possibly be “like phlogiston” (not a position I actually hold
so don’t waste your time), an alien civilisation _could_ make an analogous
mistake and fill the electron-shaped gap in their physics model with something
completely different _analogous to the way phlogiston filled the oxygen-shaped
gap in chemistry_.

~~~
theamk
The good thing is, it does not matter. It is entirely possible the electrons
are not "real" \-- so what? The electric field is not "real" either (in the
sense that there is no corresponding physical object), and the magnetic field
is even less "real", it is just a change in electric field.

As long as there is predictive power, we can use a theory. And once we
discover there are unpredicted cases, we can update the theory.

In particular, the reason phlogiston theory was discarded was not some
philosophical reasons -- it was because it made bad predictions (specifically,
that things always lose mass when burned).

There is a beautiful exercise in where you take two very basic physics rules
(electrostatic force between two individual charged particles and speed of
light equation), and derive basically entire electromagnetic theory from it.
Really drives the point that underlying physics is simple, and most of the
formulas, especially introductory ones, are just shortcuts to make reasoning
and computation easier.

------
Traubenfuchs
I bet even the majority of relevant STEM graduates (CS, math, Philosophy (?),
etc.) do not understand lambda calculus beyond the bits and pieces they
remember from "that dreadful class about formal logic or something like that"
they had in their first college semesters.

I learned to calculate/reduce (are those the right words?) lambda calculus
expressions where one line would span multiple lines on wide paper for
college. I don't think I ever understood much of it. Thinking back on this
makes me so, so glad I will never have to study this ever again.

------
BadThink6655321
First, the answer to whether or not an alien would understand the lambda
calculus is no different than whether a dog or a dolphin can understand the
lambda calculus. It depends on the wiring of their brain. The lambda calculus
is recursive; perhaps then self-awareness/self-reference is a prerequisite to
understanding.

Second, the claim that the lambda calculus was discovered but all programming
languages are invented does not take into account LISP, which was both
discovered and invented (cf. Paul Graham's "Roots of Lisp"
([https://sep.yimg.com/ty/cdn/paulgraham/jmc.ps?t=1564708198&](https://sep.yimg.com/ty/cdn/paulgraham/jmc.ps?t=1564708198&)).

------
theknarf
> The naive argument that computer scientists often make is that lambda
> calculus is at the heart of the isomorphism between logic, computation and
> category theory and this suggests that it refers to some eternal truth. This
> is a Platonist view of mathematics which is just one of several positions.
> The main problem with it is that it cannot be tested and so it is more a
> religious belief than a scientific claim. However, it also ignores the
> social, cognitive and cultural aspects of mathematical knowledge.

I still feel like this Platonist idea somewhat holds. Eventually you'd land on
some isomorphic variant of logic, computation or category theory.

~~~
mannykannot
Indeed - if/when we meet aliens that we can communicate with, I suspect that
they will have their own theory that we can all agree is also part of the
isomorphism.

------
Sysreq1
So I think the fundamental problem with a lot of the arguments I am seeing
presented here is this fascination with logic and thought as being a universal
truth. We are, in fact, no different than Flatlanders.

If we walk through the evolutionary history, we can see a clear pattern of
each advancing step slowly creeping into further and further dimensions. First
it was single cell protobacteria being able to detect light or dark above
them, and gradually growing more and more complex. A dog, while a 3
dimensional construct, is really little more than a 2 1/2 dimensional being.
Humans, by extension, are really the first fully realized 3 dimensional being.
And also one of the first to take steps into the perception of the 4th
dimension. And as evolution continues to advance, there is no reason to
suspect our ability to perceive the 4th, or even 5th dimensions won’t continue
to advance. Soon our ability to manipulate those dimensions will follow suite,
and with it, will come a fundamental shift in how that creature conceptualizes
the physical world.

To say that a 4th or 5th dimensional creation would still use a binary logic
system equal to true or false, on or off, is nonsense. And as such, any
mappings of our current logic systems would fall relatively flat.

Our world is still flat, confined by the limits of our own physical hardware.
In a billion years what ever comes after us will be completely different.
Confined by its own limited hardware.

------
Qwertystop
I'm not sure I follow the argument at the end. The author has given a good
explanation for why our current metaphors describing the lambda calculus might
not be applicable to aliens (requiring the concepts of direction and
containment), but I don't see why, for example, the gas-planet aliens might
not have their own metaphors relating to wind patterns or aerial acrobatics or
something we wouldn't understand at all. There can be multiple metaphors for
the same math.

------
tromp
Perhaps, if our symbolic notation would appear "alien" to them, the simple
graphical notation in [1] could help them understand.

[1]
[http://tromp.github.io/cl/diagrams.html](http://tromp.github.io/cl/diagrams.html)

------
ncmncm
Any article that congratulates hyoo-mons on their uniquely superior capacities
instantly disqualifies itself from representing anything fundamentally
correct.

Either (1) fundamental mathematical principles are universal, and every
society that incrementally improves will converge on them, or (2) our
mathematical principles are socially constructed, and other societies will
evolve their own structures that may be closed to us. There is no middle
ground.

There is, however, a third possibility: some of the universal fundamentals may
be inaccessible to humans because of innate limitations in our savanna-evolved
monkey brains, where aliens need not be so restricted. In other words, we (and
everybody else) have access to the basics, but not everybody gets beyond the
basics.

We can reasonably conclude that we have thus far only touched on the basics,
because we have only just started looking. Whether we will progress beyond
those basics has yet to be demonstrated. If civilization collapses as the
natural world breaks under the strain put on it by industrial society, we
might stop at this level. Or, if the number of people with mental capacity to
comprehend increasing levels of sophistication declines, eventually it will
reach one, and then zero.

Our only hope might be inventing machines that can progress beyond us, but
they would then supplant us. The aliens might see no value in talking with us,
but only with our machines, and we would never understand what they were
saying to one another.

All of the above is the natural progression of the Copernican revolution: any
assumption of specialness is flawed in exactly the degree by which it flatters
us.

------
ccalf
I just found this week's blog posting by RJ Lipton:
[https://rjlipton.wordpress.com/2019/10/21/a-polemical-
overre...](https://rjlipton.wordpress.com/2019/10/21/a-polemical-overreach/)

The Mackenzie book chapter discusses both the Fetzer and DeMillo Lipton Perlis
controversies.

It's really interesting that the debate got into the questions like, can one
formally verify a bridge?

------
ducaale
What would happen if this question was reformalated as "If there was another
civilization, would they have invented lambda calculus?"

As for the question of "is mathmatics discovered or invented", if two or more
people can discover the same branch of mathmatics, wouldn't that mean that it
is a universal truth that could even be discovered by aliens?

~~~
lkbm
Not if they're both building on top of a shared body of mathematics (or even
shared sensory organ evolution and brain structure). Aliens may be working
from an entirely different foundation, resulting in entirely different
mathematics.

~~~
ducaale
So you are saying that there could be aliens that would percieve 1+1 as 3, how
would that even make sense?

If our society is built by mathmatics that can be seen as wrong by aliens, how
would they percieve our reality and how would they explain the complicated
structures we have built using our mathmatics?

~~~
lkbm
> So you are saying that there could be aliens that would percieve 1+1 as 3

Nope. More likely they'd skip the concept of "1" and "+" and "3", but that's
also more specific than what I'm saying.

What I said was that your stated evidence doesn't support the claim you made.
Multiple people didn't come up with the same branch of mathematics completely
independently. They did so from the same foundations.

[EDIT: Oh yeah, also said that aliens may be using compeltely different math.
See below for explanation of that.]

> how would that even make sense?

I've no idea. That's the point.

> If our society is built by mathmatics that can be seen as wrong by aliens,

There's a difference between wrong and incomprehensible.

Think about some of our foundations:

\- We think of numbers as deterministic. We've come to understand that the
universe is probabilistic.

\- We think of numbers as continuous. We've come to understand that the
universe is discrete.

\- We think of a table as a distinct thing. It's actually a bunch of atoms
bonded together that are constantly shedding and gaining atoms. Oh, and that
table over there is welded to the floor, so it's actually bonded to the floor
in the same way, yet we think of the floor (and entire building) as a
different distinct object.

These new ideas are comprehensible to us, but kinda weird and foreign. Suppose
instead of starting with the naive view of determinism, continuous space, and
distinct "platonic" objects, you start with the weird reality where those
aren't true. What will your mathematics look like if your foundational
mathematics is based on that?

Do you think in terms of "1" and "1" and "2", when you don't think of two
tables as two items? Do you think of deterministic addition when your
perception of the universe is non-deterministic?

And these are just variations I thought up using my human brain based on
things that human brains have managed to understand. I'm saying "hey,
completely differently structured brains could think in a way our human brains
don't understand". "But that makes no sense to my human brain" is pretty
clearly not a refutation, and asking for an explanation of it also misses the
point.

------
mapcars
All the things we are discovering and inventing are only result of how we
fundamentally see the Universe (which is strongly connected to how our
perception organs work), not other way around.

I would say they might understand anything we understand on a basis that we do
so it is possible and it is equally possible that they might not understand us
at all :)

------
danharaj
This philosophical approach to mathematics is still rooted in conceptions of
mathematics from the beginning of the previous century, perhaps even earlier.
This may very well be because professional philosophers have not really
engaged with mathematics since then and so don't have the experience required
to ascertain its current philosophical undercurrents. Even more, most
mathematicians _also_ understand the philosophy of mathematics from this
outdated point of view, perhaps because most professional mathematicians have
not engaged with philosophy since then.

For a philosophical exposition of recent mathematical activity, I don't think
there's any book other than Synthetic Philosophy of Contemporary Mathematics
by the mathematician Fernando Zalamea. The translation reads a little clumsy
to me, but the ideas are very much worth it.

[https://www.urbanomic.com/book/synthetic-philosophy-of-
conte...](https://www.urbanomic.com/book/synthetic-philosophy-of-contemporary-
mathematics/)

------
MikeTaylor
Yes, but no amount of explanation and analogy would enable them to understand
what the heck a monad is.

------
ducaale
A relevant video that discusses if math is invented or discovered
[https://youtu.be/AmySxYHqQCQ](https://youtu.be/AmySxYHqQCQ)

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bregma
TIL I may be an alien.

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bobloblaw45
Not if they were equally as smart as me.

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mannykannot
If a conjecture is true, but no-one has proved it yet, is it still true?

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ouid
of course they would.

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DKEYBOY
Cool

