Combinators: A 100-Year Celebration

100 years after combinators were first presented, Stephen Wolfram shows how the computational paradigm moves closer to the idea of combinators through a series of examples and an eye to the future. See the announcement blog: writings.stephenwolfram.com/2...
Combinators and the Story of Computation: writings.stephenwolfram.com/2...
Where Did Combinators Come From? Hunting the Story of Moses Schönfinkel: writings.stephenwolfram.com/2...
Originally livestreamed at: / stephen_wolfram
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Check out the announcement post: wolfr.am/physics-announcement
Find the tools to build a universe: wolfr.am/physics-tools
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[@avramcs]

why the hell do i just wakeup and my phone or computer is playing wolfram videos

[@ufointrovert]

Right? Last time it was structures of black holes in wolfram physics💀

[@fluxmebaby]

Me too!!

[@eyeLie]

LOL same that's how I got here

[@rowbart3095]

ahah same, i was watching shit about space idk wtf a wolfram or a combinator is

[@musewinter9369]

But im not upset by it

[@monocles.IcedPeaksOfFire]

Great Teacher, eyes opening - it's personally. To go down to basic underlying computational structures and to get a' kick' by getting connected to Life's expressions of Nature (!) To start to vibrate with, what a gift! Another aspect: A Man of Power in science,who managed to survive and to succeed . A marathon runner of personal scientific intuition , an Athlet of dignity. How becoming is it for S.W. to celebrate this historical milestone of sense-of- life field -the combinators(!) I ' love' both - the content and the feeling! Of course, nothing should escape an acid of criticism. Nevertheless it's one of triumphant moments of life! Somehow, a Justice of Nature... Congr.(!) ❤❤❤

[@parmenides9036]

Woah! Thats Henk Barendregt! (Lambda calculus syntax and semantics) Dana scott was here as well!!

[@pascalbercker7487]

Big fan of Raymond Smullyan's logic puzzles! Nice to see his book briefly discussed!

[@firSound]

Stephen is the ultimate Senpai.

[@parmenides9036]

It's heartwarming to see Schonfinkel was so excited to got to Gottingen and talk to David Hilbert 😊

[@eleonorapasazhova7436]

this is embarrasing to say, but you are my favorite teacher and voice on youtube, Prof. Stephen. i'm sure if half of the world spent time to listen to your livestreams, everyone will be a lot brighter, creative and composed, as a result. thank you! (i am hard to give a positive criticism lately because my standards have been rising because of the sea of fake news, science, public figures, products and data, so i am really honored to have found your podcasts this summer. all the best to you!)

[@meepinboy8857]

😅

[@JemingMyang]

same

[@goddamn4012]

In the Upanishads, the absolute reality Brahman is defined by the phrase "Neti, Neti" which means "Not this, not that". Sounds pretty close to NAND which is also a universal generator of logic.

[@Beanchristine]

Waking up to this was so random

[@Earzone63]

I "skimmed" the 150 page blog post in 1hr30. Takeaways: Genuinely I LOL'ed when Stephen started introducing novel ways to visualise and escalated the investigation to plotting the number of bracket pairs IN 3D, how could that ever be useful, how wrong I was! Also the parallelism with hypergraphs (for the Fundamental Physics computation) were intriguing, sort of like introducing a new mechanics framework a la Lagrangian Vs Newtonian Vs Hamiltonian ; BTW my skimming rate was inversely proportional to my comprehension rate; If I understood more I would have spent longer

[@TheMemesofDestruction]

::Tiny Toons Theme:: “We’re combining relations, all across the nations! And in this presentation, we’ll help to show you why!” ^.^

[@Anders01]

Interesting that combinators are still fairly obscure. Combinators seem to be a powerful and fundamental construct. For example I wonder if it's possible to compile computer languages into combinators as a general foundation instead of into specific machine code.

[@dts5184]

Yes: D. A. Turner, A new implementation technique for applicative languages, Software Practice and Experience 9:31-49 (1979).

[@LorenzLeutgeb]

Maybe the Lambda Calculus (see en.wikipedia.org/wiki/Lambda_calculus ) is what you are looking for? Closed expressions (terms without free variables) in Lambda Calculus are essentially combinators. And Lambda Calculus (and its extensions) inspired many programming languages (Haskell, Coq, Agda, Idris). AFAIK there is no computer hardware to directly implement lambda calculus though. But the idea to use this for programming certainly is very present.

[@Anders01]

@@LorenzLeutgeb I'm not an expert, but it seems that combinators are more fundamental than Lambda calculus. My idea was to compile computer languages into combinators as a general abstraction layer, and then have specific translation compilers from that general layer down to any hardware implementation. That would allow any programming stack to run on any hardware.

[@Anders01]

@@dts5184 That sounds interesting. I found the abstract: "It is shown how by using results from combinatory logic an applicative language, such as LISP, can be translated into a form from which all bound variables have been removed. A machine is described which can efficiently execute the resulting code. This implementation is compared with a conventional interpreter and found to have a number of advantages. Of these the most important is that programs which exploit higher order functions to achieve great compactness of expression are executed much more efficiently."

[@dts5184]

@@Anders01 There is a lot of later work, but that paper was the starting point in doing what you suggest. See for instance chapter 16 of the book "The implementation of functional programming languages" by Simon Peyton Jones, www.microsoft.com/en-us/research/wp-content/uploads/1987/01/slpj-book-1987-small.pdf

[@uku4171]

My favourite part about this stream was watching all the facecams lol

[@nicholaskuebelbeck7184]

this was on when i woke up late today. im on new meds and have noooooo idea how i got here, yet i definitely belong. I have some anxiety as several of my "pots are simmering right now". im taking a screenshot for later research. ahhh uuughhh so good though.... so so so good though. ouchie

[@alan2here]

If combinators are turing complete then you should be able to build things like iterating down a binary tree shaped data structure following a binary sequence of directions? or for something like a hash-map. But maybe time complexity works differently for combinators.

[@NightmareCourtPictures]

Turing Complete systems can literally build anything. So if something as basic as a combinator (which you can abstractly think of as a 0,1 binary language.) Then you can literally build any system you want.

[@santerisatama5409]

Do you mean like Stern-Brocot Tree? Which is much about time complexity, as Brocot was a clock maker. A search gave article 'The Stern-Brocot Tree' by Gammie and Lochbihler.

[@viii3233]

​@NightmareCourtPictures 🎉🎉 oooo oooo o ooo o o😊😊😊ooooooooooooooooooooooooooo😊oooooo😊oooo😊ooooooooooooo😊oo😊😊

[@viii3233]

​o😊😊ooo😊😊😊😊

[@viii3233]

😊 aku adalah aku ii oi😊i😊io o ooo o 😊😊 o i😊😊ooo😊oiooo 😊o oi

[@merigetasenaysenshaw9152]

great explain

[@thespacemathematics3762]

love u sir

[@ryoung1111]

The two ostensible Rule 30 diagrams (short and extended version} at <a href="#" class="seekto" data-time="2005">33:25</a> don't agree about the binary caption. The "30" only seems to work for the short version.

[@barfyman-362]

This is amazing. I can just barely understand the gist of what he’s talking about

[@alan2here]

I was bobbing along on the surface as well, maybe there are some pages of NKS that will help, then again maybe nobody quite gets how to sit down and code up a big app with combinators.

[@rishabhkaushik22]

Only if I knew enough maths and physics in addition to my CS degree, I would've understood it better... Too late to learn now gotta do my office work lol

[@stefanwullems]

It’s never too late. I have a software engineering job that takes up my weekdays and a wife that I want to spend time with, but I still study on some nights and sometimes a day in the weekend. It’ll take a lot of effort to get into the flow of it but after some time you’ll find a schedule that works for you. Focus on a specific goal and make sure you have a way to measure your progress towards that goal. You can do it if you want it enough and you set your mind to it.

[@afriedli]

@@stefanwullems Very true. I'm retired now, but even when I had a very demanding job and a young family, I still found time for formal study. Even busy people can find 20 hours a month easily if they put their minds to it, and I often set aside twice that. And I made it a rule to take my wife on a date once a week (an investment of time that over the long term is paid back with interest).

[@alan2here]

You can do this playfully too, try drawing out all the small examples of a type of mathematical object, build intuition, talk to people who like math, work out when one type of object behaves like and therefore is another, etc… {}, {{}}, {{{}}}, {{{}}, {}}, …

[@alan2here]

You could have combinator code, but also have variables and name things?

[@zoltang1660]

At <a href="#" class="seekto" data-time="64">1:04</a>:37 in the presentation the graph looks like the Local Void and the Great Attractor in our Universe....

[@ranam]

I miss understood it as a school computation as puting some values and getting return aime numbers but a computational system should be able to return anything sometimes string numbers booleans any information that can be computable and also great power of lambda calculus is you can construct any gate function theory or any computational system and also you can get any booleans arithmetic results or any computational information that can be computed please correct me if iam wrong not only numbers but every thing computers can do from simple arithmetic to 3d gta to rocket launching or any computation by the power of constructing function and getting results as function too And turning logic into computation

[@MRTACPANS]

ABC=6.0, ABCD=10.0 BCD =9 ...ABC/1+2+3=6.0, ABCD/1+2+3+4=100.0 BCD/4+3+2=9. Rotation in Ten is 6/9 or 33 as 3x3=9, 3+3=6.... What is 1 4 7 Numbers or Words.. One Four Seven.. Seven Months Thirty One Days Four Months Thirty Days One Month 28 days with the Fouth Year at 29 Days.. What is 7/24/365, 366.. Math Alphabet Geometric Shapes words The are a Skeleton peices of Parts of Creation..... One 34 Four 60 Seven 65 The DIce Cube Has 6 SIdes THere are One Dot Through SIx Dots on the Cube equalling to 21. COmpare the facees to Rubix Cube or the Calculator. There are Nine Per side, 6 Sides 9x6=54...... Rubix Cube Has 26 CUbes total 54 Area Space Per Cube or 104 DOts Plus the Cor area or the CUbe is 3x3x3=27 CUbes BUt the Calculation is 3+3+3=9+27=36.0 1458 Area Spaces 1 2 3 4 5 6 7 8 9 TWO 58 Five 42 Six 52 Number to Earth 52 These Numbers Create all 8s math wise 2x2=4 2+2=4+4=8 2x5=10 2+5=7+10=17/1+7=8 2x8=16 2+8=10+16=26, 2+6=8 5x5=25 5+5=10+25=35/3+5=8 5x8=40 5+8=13+40=53/5+3= 8 17 Q The reverse on the CUbe is SIx as 2+4=6/5+3=8 Pick up two Dice Cubes. Now it Says F O X 666 HQZ 888 Moon Diameter is 6x6x6=216.0 6+6+6=18+216=234, 432 Hz Earth Vibration 1440 Minutes a Day x 1.5= 2160. 6 Days of Creation 1440x6 days= 86400 Seconds in a Day SUn Diameter 86400.. Million 8640x 3 =25920 Mayan Long Cycle.. MRTACPANS Keeping it Short. Game S Words Everything in a Nut SHell Explains all

[@lawofuniverserealityanalyt3199]

the causal wave which explores multi way hyper-graph potentials is the natural candidate for P=NP-complete calculations! simplest algorithm with the greatest effect, no need for quantum computers. inspired by Dijkstra's shortest path algorithm an example of David Bohm's subtle implicate order. The way the brain works.

[@benrayfield2153]

If you can always know in finite time, if a tree of only s will halt, that proves s alone is not turing complete. you need s AND k. If you're looking for a universal combinator, churchPair(s)(k) is the iota combinator.

[@dr.alangomez4039]

What about Lambda calculus, isn't fundamental also this way?

[@user-tx4wj7qk4t]

Combinatory logic is lambda calculus without abstraction

[@dr.alangomez4039]

@@user-tx4wj7qk4t thanks!

[@nobody7817]

You have a large percentage of combinators present? What, both of them?

[@ranam]

So now iam able to understand what you people are talking about is lambda calculus in which everything is an function and any operation or operator can be created and AND GATE which returns what ever it gets and hence it ca n return any thing as a result from simple arithmetic to 3d games like gta its all about construct hence a computational systems power relies on constructing any function and doing any operation on it hence AND gate explains all and we are usually used to substituting numbers directly but the concept of numbers are set here in peano arithmetic where we convert logic inti computation but with no numbers but my doubt is weather it grammar in it but the below one tells the connection between group theory and this theory but there is no connection because inversion is not allowed here in combinators or lambda calculus I guess hence computation I don't ni weather it has context or context free or it has grammar or doesn't have grammar and mathematics also has grammar or does not have grammar or does it have context or context free and that's why and gate and nor and nand gate are important ingredients that make the system turing complete hence nand and nor gate has AND inbuilt it as negation With the symbols of these basic rules which creates an pattern in the same way we can create or make an analogy to group theory patterns I guess iam correct if not please correct me the element of truth is filled and false is empty which is given as an input to an axiom or an predicate logic sentence creates these patterns am I correct if any one watching this video correct me 🙏🙏🙏

[@goddamn4012]

Can you derive relativity or quantum mechanics using combinators? Wake me up when you are able to.

[@ConnorMcCormick]

Dana looks upset, why? <a href="#" class="seekto" data-time="102">1:42</a>:44

[@existential_turtle]

You're right. Why are they upset?

[@goldnutter412]

Hmm.. clever chap huh😂

[@ditironeito9815]

Ko ooo. Olo Kokomo okkn