4 ms·

The Ruliology of Lambdas

134 points by marvinborner 1y ago

zelphirkalt 1y ago
Most of this post seems like maybe a good intro to lambda calculus, but also endless pointless visualization of nesting depth, which makes me wonder what the point of the post is. The probably invented term "ruliology" is not even explained anywhere, and I am not going to jump through all the other posts tagged with that word, to maybe somewhere find a definition of it. The post would have benefited from explaining what will be found clearly in an initial paragraph, instead of endlessly meandering. As it is now, it feels like wanting to find anything spectacular, but actually finding nothing. Well, except for made up term "ruliology" that is not defined.
- willvarfar 1y ago
  Wolfram has named his concept of the 'the universe is a program' the 'ruliad' and calls the study of it 'ruliology'. He has been using these terms and explaining them - in his long rambling way - for the last few years.
  - dan-robertson 1y ago
    Surprised he didn't call it wolframology
    - block_dagger 1y ago
      A New Kind of Ology
      - sunrunner 1y ago
        20 Years of a New Kind of Ology, even
  - sinfulprogeny 1y ago
    https://wolframinstitute.org/research/ruliology https://wolframinstitute.org/research/ruliology
    - cubefox 1y ago
      > Ruliology [...] examines how simple computational rules can generate complex behaviors.
      - zelphirkalt 1y ago
        Sounds like emergence.
  - bitexploder 1y ago
    It feels to me like someone who is managing their own existential needs. To make a mark. To have done important works. But it always comes off as unauthentic. It is amusing considering how good things like Mathematica and many of his less bloviating thoughts were. Wolfram Alpha was also very useful in the times before the LLM.
  - MangoToupe 1y ago
    I find his obsession with a computable universe a little off-putting. I guess if all you have is a hammer everything looks like a nail....
- munchler 1y ago
  He manages to make himself the actual subject of everything he writes. When I saw the author’s name, I knew the article would make sure to fluff up his own ego, and it took him less than a paragraph to get there.
  - omnicognate 1y ago
    He's insufferable, but I'll take his variation on the theme of "narcissistic billionaire" over most of the others we're currently forced to share the planet with, any day of the week.
  - bondarchuk 1y ago
    It's not just his ego though, it's the way his ego clashes with other egos of internet commenters. Why do so many people feel the need to comment that they already knew Wolfram would write about himself and then confirm that it is indeed so? If you can predict it so well and you don't like it, you could just ignore it. But somehow it triggers people even knowing that he exists and they can't let it go.
    - munchler 1y ago
      I like the lambda calculus and I was intrigued by the title, so I gave the article a shot. Hope springs eternal.
- cjauvin 1y ago
  Counterpoint: I actually really enjoy his style of writing, which I find clear, patient (you must appreciate visual examples and exploration though) and very often challenging and stimulating (recent examples: the posts about the bigger brains, Conway GoL engineering, and biology / evolution). I find he regularly introduces intriguing and useful ideas, like the distinction between "brain-like" computers (which includes neural networks) and more general, Turing-like mechanisms, and I find his overarching concept of computational irreducibility (even though he didn't invent it) quite profound in its implications. I would add that his posts read like an ambitious research program in progress (like a book written one chapter at a time) and that is why I think certain concepts (like ruliology) may appear obscure at first, if you didn't read a lot of stuff that comes before. One tiny nitpick I have: certain language tics, like the constant use of the "And, yes" pattern (he really uses this a lot I wish someone somehow told him).
  - jebarker 1y ago
    I agree. I usually find his posts illuminating. Sure, they’re verbose and self-aggrandizing, but there are way more writers out there online that are also self-aggrandizing but offer no original content or value. Also the rambling style presents a more realistic view of how scientific exploration works than a distilled down paper missing crucial details needed for replication (I’m looking at you ML/AI).
- alphazard 1y ago
  The articles are not necessarily written for a software engineering audience. Going through the lambda calculus would be a necessary prerequisite for the part he actually wants to tell you about at the end. Especially for physicists and mathematicians who primarily study things other than computation. If you found the visualizations pointless, then you aren't the intended audience. This is a straightforward continuation of his existing research into computation, which started with cellular automata. If you're reading a Wolfram blog, then you're in part coming for the pretty pictures. > The probably invented term "ruliology" is not even explained anywhere. The "ruliad" is what he calls the "space of all possible rules" where a rule is like a program that dictates the next state of the system. The ruliad is one of the few rigorous approaches to answering why the laws of physics are the way they are. Stephen's theory is something like "every possible rule for evolving the system is in fact happening, and we are likely to be observing phenomenon that are convergent among more than one rule". His physics project is a good example of what real physics looks like outside of academia. Stephen is financially independent. He can research whatever he wants and doesn't have to worry about tenure, or sucking up to department heads or people with grant money. Even so, he's not a crank, other physicists understand and engage with what he's doing, and all the math involved is very real.
  - Y_Y 1y ago
    Stephen Wolfram has done real worthwhile physics. He's an exceptionally smart dude, even if that doesn't come across in some of his writing. Just to pour some more opinions on the fire, I think he's been descending into crankery slowly, but steadily, since the 80s. Have a sconce at what his output was like before he took m-expressions and built a paywall around them, become a fairly wealthy demigod of science in the process. https://www.stephenwolfram.com/publications/academic/all/ https://www.stephenwolfram.com/publications/academic/all/ The academy (in physics at least), is crusty and traditional, but not to the point of ignoring good work. It's like alternative medicine, do you think if essential oils cured cancer you wouldn't have all the big pharma companies leaping from their high horses? Wolfram does some cool stuff with cellular automata, and has lots of students doing cool stuff too. What he's not done, neither with NKS nor anything since, is make some contribution to understanding the physical universe that was significant in eyes other than his own.
bubblyworld 1y ago
I really liked this. It's a nice meander through the basics of lambda calculus. It's striking to me how much insight you can get by visualising stuff, even if it's not a great visualisation and you're doing something super abstract. Perhaps a lesson to take into my own programbles...
tromp 1y ago
Wolfram's exploration of longest lifetimes of lambda terms of a given size is carried out more systematically in my functional busy beaver https://oeis.org/A333479 https://oeis.org/A333479
- ngruhn 1y ago
  Is this easier to analyze than Turing Machine based Busy Beaver?
  - tromp 1y ago
    The first 5 values are FAR easier to determine, since there's only 1 lambda term of at most 5 bits:-) And the next few unknown values, BBλ(37).. BBλ(39) will be easier to determine too since the search space is smaller and no so-called cryptids have been identified yet (terms whose halting behaviour is closely related to unsolved math problems). But if the effort that is being applied to researching BB(6) and BB(7), is applied to researching BBλ(37) and beyond, then we expect to run into similar difficulties of having more and more unsolved terms which do not lead to a normal form in any reasonable number of steps and also defy known techniques for proving them to lack a normal form. There's some hope though that we'll be able to identify BBλ(49) before identifying BB(7). And while the former is known to exceed Graham's Number, the latter is only conjectured to do so, and I made a large bet with the people conjecturing it saying it won't be proven within 10 years.
    - ngruhn 1y ago
      Very interesting, thanks!
- Xcelerate 1y ago
  Would love to read a HN-tailored blog post of your work or an overview of the binary lambda calculus if you ever have the time btw
  - nswanberg 1y ago
    A walkthrough would be nice, but he's got a lot of understandable material linked on that page. For example, here's an overview of the binary lambda calculus: https://tromp.github.io/cl/Binary_lambda_calculus.html https://tromp.github.io/cl/Binary_lambda_calculus.html And here's a readable and fascinating post on "the largest number that's representable in 64 bits": https://tromp.github.io/blog/2023/11/24/largest-number https://tromp.github.io/blog/2023/11/24/largest-number. If you go through these and find some interesting things, it'd be worth posting to HN.
pjmlp 1y ago
And this is what lambda calculus is all about, during a few months.
deviation 1y ago
This was a great coffee read. Very insightful.
20wenty 1y ago
I have never made it to the end of a Wolfram post, or a David Foster Wallace book. I'm envious of people who can read AND understand these tomes.
- antonvs 1y ago
  I really don't think there's any need to be envious.
antonvs 1y ago
[flagged]
theGnuMe 1y ago
I may be wrong but it appears that he rediscovers the Church-Turing thesis in this work.
pcfwik 1y ago
Re: visualizations of lambda terms, also see "To Dissect a Mockingbird" https://dkeenan.com/Lambda/ https://dkeenan.com/Lambda/
- bntr 1y ago
  The most complete catalog I've found: https://github.com/prathyvsh/lambda-calculus-visualizations https://github.com/prathyvsh/lambda-calculus-visualizations
the__alchemist 1y ago
This guy streams on Twitch btw. If you need a break from E-Sports, E-Girls, and video game actors stumbling through abandoned hospitals.
russellsprouts 1y ago
Related video showing animated lambda diagrams: https://m.youtube.com/watch?v=RcVA8Nj6HEo https://m.youtube.com/watch?v=RcVA8Nj6HEo
- bntr 1y ago
  Another notation showing the construction of the predecessor function: https://www.youtube.com/watch?v=CWzn2ucPMdg https://www.youtube.com/watch?v=CWzn2ucPMdg

134 points by marvinborner 1y ago

Most of this post seems like maybe a good intro to lambda calculus, but also endless pointless visualization of nesting depth, which makes me wonder what the point of the post is. The probably invented term "ruliology" is not even explained anywhere, and I am not going to jump through all the other posts tagged with that word, to maybe somewhere find a definition of it. The post would have benefited from explaining what will be found clearly in an initial paragraph, instead of endlessly meandering. As it is now, it feels like wanting to find anything spectacular, but actually finding nothing. Well, except for made up term "ruliology" that is not defined.

willvarfar 1y ago
Wolfram has named his concept of the 'the universe is a program' the 'ruliad' and calls the study of it 'ruliology'. He has been using these terms and explaining them - in his long rambling way - for the last few years.
- dan-robertson 1y ago
  Surprised he didn't call it wolframology
  - block_dagger 1y ago
    A New Kind of Ology
    - sunrunner 1y ago
      20 Years of a New Kind of Ology, even
- sinfulprogeny 1y ago
  https://wolframinstitute.org/research/ruliology https://wolframinstitute.org/research/ruliology
  - cubefox 1y ago
    > Ruliology [...] examines how simple computational rules can generate complex behaviors.
    - zelphirkalt 1y ago
      Sounds like emergence.
- bitexploder 1y ago
  It feels to me like someone who is managing their own existential needs. To make a mark. To have done important works. But it always comes off as unauthentic. It is amusing considering how good things like Mathematica and many of his less bloviating thoughts were. Wolfram Alpha was also very useful in the times before the LLM.
- MangoToupe 1y ago
  I find his obsession with a computable universe a little off-putting. I guess if all you have is a hammer everything looks like a nail....
munchler 1y ago
He manages to make himself the actual subject of everything he writes. When I saw the author’s name, I knew the article would make sure to fluff up his own ego, and it took him less than a paragraph to get there.
- omnicognate 1y ago
  He's insufferable, but I'll take his variation on the theme of "narcissistic billionaire" over most of the others we're currently forced to share the planet with, any day of the week.
- bondarchuk 1y ago
  It's not just his ego though, it's the way his ego clashes with other egos of internet commenters. Why do so many people feel the need to comment that they already knew Wolfram would write about himself and then confirm that it is indeed so? If you can predict it so well and you don't like it, you could just ignore it. But somehow it triggers people even knowing that he exists and they can't let it go.
  - munchler 1y ago
    I like the lambda calculus and I was intrigued by the title, so I gave the article a shot. Hope springs eternal.
cjauvin 1y ago
Counterpoint: I actually really enjoy his style of writing, which I find clear, patient (you must appreciate visual examples and exploration though) and very often challenging and stimulating (recent examples: the posts about the bigger brains, Conway GoL engineering, and biology / evolution). I find he regularly introduces intriguing and useful ideas, like the distinction between "brain-like" computers (which includes neural networks) and more general, Turing-like mechanisms, and I find his overarching concept of computational irreducibility (even though he didn't invent it) quite profound in its implications. I would add that his posts read like an ambitious research program in progress (like a book written one chapter at a time) and that is why I think certain concepts (like ruliology) may appear obscure at first, if you didn't read a lot of stuff that comes before. One tiny nitpick I have: certain language tics, like the constant use of the "And, yes" pattern (he really uses this a lot I wish someone somehow told him).
- jebarker 1y ago
  I agree. I usually find his posts illuminating. Sure, they’re verbose and self-aggrandizing, but there are way more writers out there online that are also self-aggrandizing but offer no original content or value. Also the rambling style presents a more realistic view of how scientific exploration works than a distilled down paper missing crucial details needed for replication (I’m looking at you ML/AI).
alphazard 1y ago
The articles are not necessarily written for a software engineering audience. Going through the lambda calculus would be a necessary prerequisite for the part he actually wants to tell you about at the end. Especially for physicists and mathematicians who primarily study things other than computation. If you found the visualizations pointless, then you aren't the intended audience. This is a straightforward continuation of his existing research into computation, which started with cellular automata. If you're reading a Wolfram blog, then you're in part coming for the pretty pictures. > The probably invented term "ruliology" is not even explained anywhere. The "ruliad" is what he calls the "space of all possible rules" where a rule is like a program that dictates the next state of the system. The ruliad is one of the few rigorous approaches to answering why the laws of physics are the way they are. Stephen's theory is something like "every possible rule for evolving the system is in fact happening, and we are likely to be observing phenomenon that are convergent among more than one rule". His physics project is a good example of what real physics looks like outside of academia. Stephen is financially independent. He can research whatever he wants and doesn't have to worry about tenure, or sucking up to department heads or people with grant money. Even so, he's not a crank, other physicists understand and engage with what he's doing, and all the math involved is very real.
- Y_Y 1y ago
  Stephen Wolfram has done real worthwhile physics. He's an exceptionally smart dude, even if that doesn't come across in some of his writing. Just to pour some more opinions on the fire, I think he's been descending into crankery slowly, but steadily, since the 80s. Have a sconce at what his output was like before he took m-expressions and built a paywall around them, become a fairly wealthy demigod of science in the process. https://www.stephenwolfram.com/publications/academic/all/ https://www.stephenwolfram.com/publications/academic/all/ The academy (in physics at least), is crusty and traditional, but not to the point of ignoring good work. It's like alternative medicine, do you think if essential oils cured cancer you wouldn't have all the big pharma companies leaping from their high horses? Wolfram does some cool stuff with cellular automata, and has lots of students doing cool stuff too. What he's not done, neither with NKS nor anything since, is make some contribution to understanding the physical universe that was significant in eyes other than his own.

bubblyworld 1y ago

I really liked this. It's a nice meander through the basics of lambda calculus. It's striking to me how much insight you can get by visualising stuff, even if it's not a great visualisation and you're doing something super abstract. Perhaps a lesson to take into my own programbles...

tromp 1y ago

Wolfram's exploration of longest lifetimes of lambda terms of a given size is carried out more systematically in my functional busy beaver https://oeis.org/A333479 https://oeis.org/A333479

ngruhn 1y ago
Is this easier to analyze than Turing Machine based Busy Beaver?
- tromp 1y ago
  The first 5 values are FAR easier to determine, since there's only 1 lambda term of at most 5 bits:-) And the next few unknown values, BBλ(37).. BBλ(39) will be easier to determine too since the search space is smaller and no so-called cryptids have been identified yet (terms whose halting behaviour is closely related to unsolved math problems). But if the effort that is being applied to researching BB(6) and BB(7), is applied to researching BBλ(37) and beyond, then we expect to run into similar difficulties of having more and more unsolved terms which do not lead to a normal form in any reasonable number of steps and also defy known techniques for proving them to lack a normal form. There's some hope though that we'll be able to identify BBλ(49) before identifying BB(7). And while the former is known to exceed Graham's Number, the latter is only conjectured to do so, and I made a large bet with the people conjecturing it saying it won't be proven within 10 years.
  - ngruhn 1y ago
    Very interesting, thanks!
Xcelerate 1y ago
Would love to read a HN-tailored blog post of your work or an overview of the binary lambda calculus if you ever have the time btw
- nswanberg 1y ago
  A walkthrough would be nice, but he's got a lot of understandable material linked on that page. For example, here's an overview of the binary lambda calculus: https://tromp.github.io/cl/Binary_lambda_calculus.html https://tromp.github.io/cl/Binary_lambda_calculus.html And here's a readable and fascinating post on "the largest number that's representable in 64 bits": https://tromp.github.io/blog/2023/11/24/largest-number https://tromp.github.io/blog/2023/11/24/largest-number. If you go through these and find some interesting things, it'd be worth posting to HN.

pjmlp 1y ago

And this is what lambda calculus is all about, during a few months.

deviation 1y ago

This was a great coffee read. Very insightful.

20wenty 1y ago

I have never made it to the end of a Wolfram post, or a David Foster Wallace book. I'm envious of people who can read AND understand these tomes.

antonvs 1y ago
I really don't think there's any need to be envious.

antonvs 1y ago

[flagged]

theGnuMe 1y ago

I may be wrong but it appears that he rediscovers the Church-Turing thesis in this work.

pcfwik 1y ago

Re: visualizations of lambda terms, also see "To Dissect a Mockingbird" https://dkeenan.com/Lambda/ https://dkeenan.com/Lambda/

bntr 1y ago
The most complete catalog I've found: https://github.com/prathyvsh/lambda-calculus-visualizations https://github.com/prathyvsh/lambda-calculus-visualizations

the__alchemist 1y ago

This guy streams on Twitch btw. If you need a break from E-Sports, E-Girls, and video game actors stumbling through abandoned hospitals.

russellsprouts 1y ago

Related video showing animated lambda diagrams: https://m.youtube.com/watch?v=RcVA8Nj6HEo https://m.youtube.com/watch?v=RcVA8Nj6HEo

bntr 1y ago
Another notation showing the construction of the predecessor function: https://www.youtube.com/watch?v=CWzn2ucPMdg https://www.youtube.com/watch?v=CWzn2ucPMdg