Excellent study session! Some fun playing around with Dalle, some new useful glyphs, and some interesting philosophical questions. I wish I could attend live!

Metamathematics is a deep and fascinating subject. For those interested in learning more about the history of these ideas I recommend Logicomix by Doxiadis & Papadimitriou. It’s a biographical graphic novel centered around Bertrand Russell and his struggle with these topics. A one of a kind book.

Combinatorial logic is also a deep and fascinating subject. The foundations of computation were developed at the same time as a revolution was occurring in mathematics. For those interested in a hands on explaination of what this stuff is all about I highly recommend David Beazley’s workshop at PyCon 2019 Lambda Calculus from the Ground Up.

If you would rather read than watch, I adapted the talk into an Observable notebook you can play around with → The λ Calculus

Looking forward to the next session! APL study seems to lead to many interesting topics.

Thanks for the great sessions! About the golden ratio: 1 +∘÷⍣= 1

To enhance my understanding, I tried to make to it more clear how the APL code relates to Python. Posting it here, as I thought it might help someone else also. Note that the compose (∘) defined here in Python is not generic but crafted for this specific problem.

Python:

from math import isclose
# APL: ∘
def compose(f, g):
def _inner(*args):
return f(g(args[0], args[1]), args[1])
return _inner
# APL: +
def add(x, y):
return x + y
# APL: ÷
def divide(x, y):
return x/y
# calculate_phi ← { ⍺ divide_then_add repeat_until_equal ⍵ }
def calculate_phi(a, b):
# APL: divide_and_add ← +∘÷
divide_then_add = compose(divide, add)
# APL: repeat_until_equal ← ⍣=
res = divide_then_add(a, b)
prev_res = float('nan')
while not isclose(res, prev_res, rel_tol=1e-06):
prev_res = res
res = divide_then_add(1, res)
return res
# APL:
# divide_then_add ← +∘÷
# repeat_until_equal ← ⍣=
# a ← 1
# b ← 1
# ⎕ ← phi ← a calculate_phi b
a = 1
b = 1
phi = calculate_phi(a, b)
phi

APL:

divide_then_add ← +∘÷
repeat_until_equal ← ⍣=
a ← 1
b ← 1
calculate_phi ← { ⍺ divide_then_add repeat_until_equal ⍵ }
⎕ ← phi ← a calculate_phi b

In the Python version, the functions divide_then_add and repeat_until_equal should be passed to the calculate_phi function as arguments to make it more equivalent to the APL version, but I thought it would make the code more difficult to understand and decided to omit.

Edit: Posted first accidentally to session 5 thread and moved it here.

∇ {res}←{left} AddMult2 right;local
:If 0=⎕NC'left' ⍝ if variable "left" is not defined already
left←0
:EndIf
local←left+right
res←2×local
∇
AddMult2 3 ⍝ result is "shy"
⎕←AddMult2 3 ⍝ coerce display of result
6
1 AddMult2 3 ⍝ result is "shy"
10×1 AddMult2 3 ⍝ use result anyway
80

That’s a tradfn, which is something we haven’t covered yet (and quite a few APL programmers avoid nowadays, so I’m not sure we’ll get to it in a hurry either).

Thank you! I was just trying to wrap my head around the curly braces and the situations where they’re used. I didn’t realize trad-itional functions weren’t used so much anymore.

I applied for DALL·E 18-April and got acces 18-June. Its been lots of fun.

A tip… the more detailed you are the better. Rather than provide a very general abstract requirement, try to picture a scene as you would describe it to a savant five-year old.

In the context of the course, I thought I would try for something related to machine learning. Sorry I got a bit carried away. (Perhaps there needs to be separate category, with guidelines limiting how often to post generated images (it could be popular).)

Ten detailed tiny copper brains on a printed circuit board connected by copper traces. The brains are very detailed. Photo realistic 3d render.

But I also need more practice to better understand how it will interpret…

Tiny copper brains on GPU chips connected by copper traces across a door in a wall. The brains are very detailed. The door has a lock. A monkey is looking at the lock putting a key into the lock. Photo realistic 3d render.

Photo realistic 3d tender of a gate made out of an array of GPU chips. The gate has a golden lock and border frame. A monkey is putting an ancient golden key into the lock.

A human teacher standing in front of a classroom of robot students. Line drawing viewed from the back of the room. The teacher is writing on the blackboard.

Looking from the back of the room at a classroom of seated robot students looking at a blackboard. The robot students vary in shiny colours. At the front of the room a human teacher wearing a suit is writing the alphabet on the blackboard. photorealistic 3d render.