
A Python implementation of formal systems from the book “Gödel, Escher, Bach” - geospeck
https://github.com/alexprengere/FormalSystems
======
ehudla
My implementation of M-I-U, more than 30 years ago, as a kid, in Turbo Pascal.

[https://github.com/ehud/MIU](https://github.com/ehud/MIU)

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mixmastamyk
Didn't the original PC have lowercase? I thought I programmed TP in mixed-
case, but can't remember.

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defined
I definitely programmed TP 1.0 in mixed case on a TRS-80 Model II running
CP/M.

~~~
ehudla
Sure. It was a style thing!

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intrasight
For those not in the know, the first book ever bought from Amazon was Douglas
Hofstadter's "Fluid Concepts and Creative Analogies : Computer Models of the
Fundamental Mechanisms of Thought"

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gech
Did he get that right or do neuroscientists dispute his models?

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intrasight
Most neuroscientists don't try to tackle such philosophical topics,
unfortunately.

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sirodoht
Here is an introduction to the MIU formal system for someone who hasn't read
GEB.

[https://sirodoht.xyz/blog/the-miu-formal-
system/](https://sirodoht.xyz/blog/the-miu-formal-system/)

~~~
DanielRibeiro
Thanks for sharing. This is also a nice answer to the MU puzzle, mentioned at
the end of the article:
[https://en.wikipedia.org/wiki/MU_puzzle](https://en.wikipedia.org/wiki/MU_puzzle)

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pge
On a related note, if you are interested in learning more about Godel and the
Incompleteness Theorem and its significance, I recommend the book
Incompleteness by Rebecca Goldstein.

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Y_Y
I remember doing this with pen and paper ages ago when I read the book.
Somehow it clicked with me a lot better than my Abstract Algebra lectures.

~~~
tluyben2
I did that too; I remember the squares paper in the book. I see it in front of
my eyes still. Good memories at some Portugal vacation with my parents in the
80s.

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alexprengere
Author here! Thanks for the post :)

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tdumitrescu
Here's some more Python related to the book (by a coworker):

[https://github.com/Quuxplusone/TNT](https://github.com/Quuxplusone/TNT)

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gergoerdi
I once did an introductory talk to Agda that was structured around solving the
MU problem, i.e. proving that MU is not derivable in MIU:
[https://unsafePerform.IO/projects/agda/sg-
meetup/SGMeetup.pd...](https://unsafePerform.IO/projects/agda/sg-
meetup/SGMeetup.pdf) (the MIU bit starts in Part III, slide 46)

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bluefox
Nice, I wrote code for MU as well. What about BlooP and friends?

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schoen
There's only one of those "friends" (FlooP): Hofstadter explained that there
is no more powerful "GlooP" language, because FlooP turns out to be as
powerful as any computing formalism that can be implemented on a computer.

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

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dnautics
I'd be interested in seeing implementation of the machine learning systems
from "fluid concepts"

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lucastx
Fluid Concepts and Creative Analogies is a wonderful book. I wouldn't call the
systems they build upon (such as lMetacat [1] and Tabletop [2]) "machine
learning"...

[1]
[http://science.slc.edu/jmarshall/metacat/](http://science.slc.edu/jmarshall/metacat/)

[2]
[https://deepblue.lib.umich.edu/handle/2027.42/105891](https://deepblue.lib.umich.edu/handle/2027.42/105891)

I'd also like to see FARGonauts / Center for Research on Concepts and
Cognition style software implementations around... I have run with success
this python implementation of Copycat:

[https://github.com/ajhager/copycat](https://github.com/ajhager/copycat)

~~~
emmelaich
A link on the book for other ignoramuses like me. Dunno how I've never heard
of it.

(It's also by Douglas Hofstadter.)

[https://en.wikipedia.org/wiki/Fluid_Concepts_and_Creative_An...](https://en.wikipedia.org/wiki/Fluid_Concepts_and_Creative_Analogies)

~~~
dnautics
Its maybe a matter of taste but I find his other work to be rather
pretentious, although geb is entertaining and somewhat useful (I half liked le
ton beau de marot).

I really think k there's something useful.in _fluid concepts_ that maybe can
help with low data learning. I think geoffrey Hinton hints at it in his
lecture about trying to do pca on learned neural states to find manyfold
correlations which in high dimensional states are stronger to be nonrandom.

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castle-bravo
Where's typogenetics? :D

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kleer001
It'd be great to get all of DH's code online. Even the scratch and mistakes
and half baked ideas and notes and...

heavy-breathing

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nthcolumn
I am not a mathematician but are there any others who have problems with
Godel's 'Theorem'?

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milesrout
Why would you have problems with Gödel's incompleteness theorems (which are, I
assume, the ones you are referring to), and why do you put 'theorem' in quotes
as if they aren't actually theorems?

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nthcolumn
A sort of uneasiness about their symbolic basis to start off with, nothing
subsequent - I can follow it. Lack of understanding. That 'it smells' feeling.
I'm not suggest they are wrong, just asking. Its okay to ask?

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scandox
Well perhaps you have the same problem as Whitehead and Russell? In GEB
Hofstadter IIRC is quite harsh on them for their intellectual timidity in not
being able to face the paradox inherent in Godel's Theorem...Paradoxes can
"feel" uncomfortable.

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mirimir
That sufficiently capable logical systems are necessarily incomplete can be
uncomfortable, especially if the beauty of completeness has been your lifelong
goal.

But on the other hand, it's very cool that this provides an opening for
consciousness and free will to arise.

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castle-bravo
How are consciousness and free will implied by incompleteness of formal
systems?

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mirimir
I defer to Douglas Hofstadter:

[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach](https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach)

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

