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Active: 4286 users

Challenge: Maths isn't all that hard. 

Blogs > Hildegard
Post a Reply
Hildegard
Profile Blog Joined November 2012
Germany348 Posts
Last Edited: 2025-11-02 07:16:12
November 02 2025 05:47 GMT
#1
OK; maybe that's not entirely true. Recently, I found, that my issues with maths wasn't understanding it. The reason I underperformed in maths is that I was too lazy to write down formulas and definitions in a well-ordered way. 
So I started watching a German channel for students to catch-up with formulas, definitions and on things like set theory. Parallelly, I watched videos about things like Bayes's theorem, Hilbert Space or Markov chains and again that is not as hard to understand as it appears at first once definitions are clear. 

That is, of course, until the Laws of Form by George Spencer-Brown enter the arena. Tl.net is one of the places with the most intelligent people on the internet. That's my reason for blogging here, in combination with the ease of keeping up with SC2 while at it. 
Is anyone here who claims to understand the first or even both of the theorems in Laws of Form? The first one is much easier. The second one will transform your thinking once you understand it. I have a way to explain it to 5-year-olds, but actual mathematicians seem to have a hard time with it. So I am curious — anyone around daring to write an explanation of the second theorem? I will post my ELI5 version of the second theorem once I get some answers here.


SC2 and internet issues
A few weeks ago I switched my internet provider and SHOULD have a 1000 Mbit/s connection by now. Sadly, there have been issues and I only have mobile internet at home. So I have time to practice offline games against the AI. But as my hotkeys aren't there any more, I didn't improve much because I am still way too slow with 32–40 APM currently.


Book-writing
My book is progressing well, and I will publish the promo chapter here once it's done. 


Stay tuned: Social Links
Firstly, I hate social media and prefer to call them digital platforms instead. The English internet is mostly a sales platform. I miss the old internet from around 2005. That was a more hopeful time, especially the 90s, up until September 11. Anyway… I have social accounts now, but I won't pester you with them, except for the twitch.tv channel of my start-up Dyadica.AI. 


*****
tl.net humour: https://www.kurtvonmeier.com/blog-1/2018/1/14/on-audio-alan-watts-and-g-spencer-brown-discuss-laws-of-form
JimmyJRaynor
Profile Blog Joined April 2010
Canada17735 Posts
Last Edited: 2025-11-02 14:00:59
November 02 2025 13:59 GMT
#2
ya, that 4 colour problem is obvious.
i had a prof whose Erdos # was 3.
Ray Kassar To David Crane : "you're no more important to Atari than the factory workers assembling the cartridges"
Hildegard
Profile Blog Joined November 2012
Germany348 Posts
November 03 2025 00:15 GMT
#3
A brief spark from a hypomanic moment:

Douglas Adams famously gave us the most iconic joke in science fiction:
The answer to life, the universe, and everything = 42.
But what was the question?

Mathematically, the most elegant path to 42 is 6 × 7.

Symbolically — in numerology and ancient storytelling —
6 is the number of the human, the earthly, the feminine.
7 is the number of the divine, the transcendent, the masculine.

When the two come together, we get:
Love — the bridge between earth and sky.

So maybe Adams’ real message was:

The answer is love.
We just needed to find the question.

(And yes, Douglas Adams did once confirm that “six times seven” was the hidden clue. My AIs cheerfully approve.)
tl.net humour: https://www.kurtvonmeier.com/blog-1/2018/1/14/on-audio-alan-watts-and-g-spencer-brown-discuss-laws-of-form
JimmyJRaynor
Profile Blog Joined April 2010
Canada17735 Posts
November 03 2025 22:25 GMT
#4
What were your most life changing math courses?
For me, it was Life Cons 231 and Applied Combinatorics 344.
Ray Kassar To David Crane : "you're no more important to Atari than the factory workers assembling the cartridges"
KrillinFromwales
Profile Blog Joined March 2022
68 Posts
Last Edited: 2025-11-04 17:19:04
November 04 2025 17:12 GMT
#5
Good post. Good to see you. Bayes' Theorem is the most important in my opinion. For statistical inference (which is a big part of operative mathematics), Bayes' Theorem defines the closed system. There are probably two sides to the imaginary coin: Whether inference is itself achievable (Independent Events) & Bayes' (Updating Statistical Inference).

Logical structure is more complicated and we're trying to achieve the same proofs in logic as we are in mathematics. There's nothing remarkable about using logic to prove what we use math to prove but symbolic notation can be more general for the novice. Personally, I find structural proofs of Completeness / Incompleteness quite challenging and usually refer students to Cantor. In fact, I think the work is similar in construction (Kurt Godel & Georg Cantor). Whether the proof is structural or purely mathematical doesn't matter so long as the language is conveyed to the reader & presented by the author.

edit: As an economist, I don't approach HIlbert all that often, and the Hilbert / Banach / Lebesgue space distinction often escapes me. One, I think is a measure (Lebesgue) while Hilbert and Banach deal with something other than measure. John Von Neumann is the go-to for Economists because of his role in originating the utility transformation. For readers of John Nash and John Von Neumann, there are some symmetries in traditional geometric logic that separate the accounts. I think this is a good approach to understanding Hilbert, but whether the question is intentionally illusive is part of the magic. Someone naturally gifted in mathematics realizes that language is still part of the obstacle course.
Hildegard
Profile Blog Joined November 2012
Germany348 Posts
November 05 2025 03:25 GMT
#6
On November 04 2025 07:25 JimmyJRaynor wrote:
What were your most life changing math courses?
For me, it was Life Cons 231 and Applied Combinatorics 344.


By Prof Dr phil. Stefan Asmus about George Spencer-Brown's Laws of Form. Nothing else comes even close.


On November 05 2025 02:12 KrillinFromwales wrote:
Good post. Good to see you. Bayes' Theorem is the most important in my opinion. For statistical inference (which is a big part of operative mathematics), Bayes' Theorem defines the closed system. There are probably two sides to the imaginary coin: Whether inference is itself achievable (Independent Events) & Bayes' (Updating Statistical Inference).

Logical structure is more complicated and we're trying to achieve the same proofs in logic as we are in mathematics. There's nothing remarkable about using logic to prove what we use math to prove but symbolic notation can be more general for the novice. Personally, I find structural proofs of Completeness / Incompleteness quite challenging and usually refer students to Cantor. In fact, I think the work is similar in construction (Kurt Godel & Georg Cantor). Whether the proof is structural or purely mathematical doesn't matter so long as the language is conveyed to the reader & presented by the author.

edit: As an economist, I don't approach HIlbert all that often, and the Hilbert / Banach / Lebesgue space distinction often escapes me. One, I think is a measure (Lebesgue) while Hilbert and Banach deal with something other than measure. John Von Neumann is the go-to for Economists because of his role in originating the utility transformation. For readers of John Nash and John Von Neumann, there are some symmetries in traditional geometric logic that separate the accounts. I think this is a good approach to understanding Hilbert, but whether the question is intentionally illusive is part of the magic. Someone naturally gifted in mathematics realizes that language is still part of the obstacle course.


Hilbert Spaces felt way harder than the other two.I can explain Markov Chains and Bayes' Theorem, but Hilbert Spaces felt like I understood them after finishing the, but can't recall it in detail currently.
tl.net humour: https://www.kurtvonmeier.com/blog-1/2018/1/14/on-audio-alan-watts-and-g-spencer-brown-discuss-laws-of-form
Hildegard
Profile Blog Joined November 2012
Germany348 Posts
November 05 2025 03:40 GMT
#7
[image loading]


ELI5 version of the second theorem of the Laws of Form

The so-called second theorem is the re-entry. Something enters itself. Sounds hard? It isn't just think of custard or pudding.

If your mum pours the vanilla pudding into the chocolate pudding, you could say that the pudding is re-entering itself. The only difference with Uncle George's re-entry is that it's twice chocolate or twice vanilla re-entering themselves.

Technically it's called re-entering, but that is also easily explained. Just imagine that your mum first empties half of the pudding back into the pot.

Congratulations, if you ever have maths lessons, your teacher probably didn't understand that. So you can be a little bit proud.

Translated with DeepL.com (free version)
tl.net humour: https://www.kurtvonmeier.com/blog-1/2018/1/14/on-audio-alan-watts-and-g-spencer-brown-discuss-laws-of-form
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