We should never forget that the human brain is perhaps the most complicated system in the known universe; if we are to build something roughly its equal, open-hearted collaboration will be key.

Researchers like Josh Tenenbaum, Anima Anandkumar, and Yejin Choi are also now headed in increasingly neurosymbolic directions. Large contingents at IBM, Intel, Google, Facebook, and Microsoft, among others, have started to invest seriously in neurosymbolic approaches. Swarat Chaudhuri and his colleagues are developing a field called “neurosymbolic programming”23 that is music to my ears.

Artur Garcez and Luis Lamb wrote a manifesto for hybrid models in 2009, called Neural-Symbolic Cognitive Reasoning. And some of the best-known recent successes in board-game playing (Go, Chess, and so forth, led primarily by work at Alphabet’s DeepMind) are hybrids. AlphaGo used symbolic-tree search, an idea from the late 195

No single AI approach will ever be enough on its own; we must master the art of putting diverse approaches together, if we are to have any hope at all.

Belittling unfashionable ideas that haven’t yet been fully explored is not the right way to go. Hinton is quite right that in the old days AI researchers tried—too soon—to bury deep learning. But Hinton is just as wrong to do the same today to symbol-manipulation.

For at least four reasons, hybrid AI, not deep learning alone (nor symbols alone) seems the best way forward:

n 1990, Hinton published a special issue of the journal Artificial Intelligence called Connectionist Symbol Processing that explicitly aimed to bridge the two worlds of deep learning and symbol manipulation.

When deep learning reemerged in 2012, it was with a kind of take-no-prisoners attitude that has characterized most of the last decade. By 2015, his hostility toward all things symbols had fully crystallized. He gave a talk at an AI workshop at Stanford comparing symbols to aether, one of science’s greatest mistakes.

Warren McCulloch and Walter Pitts wrote in 1943, “A Logical Calculus of the Ideas Immanent in Nervous Activity,” the only paper von Neumann found worthy enough to cite in his own foundational paper on computers.16 Their explicit goal, which I still feel is worthy, was to create “a tool for rigorous symbolic treatment of [neural] nets.”

Symbolic operations also underlie data structures like dictionaries or databases that might keep records of particular individuals and their properties (like their addresses, or the last time a salesperson has been in touch with them, and allow programmers to build libraries of reusable code, and ever larger modules, which ease the development of complex systems. Such techniques are ubiquitous, the bread and butter of the software world.

If symbols are so critical for software engineering, why not use them in AI, too?

s the renowned computer scientist Peter Norvig famously and ingeniously pointed out, when you have Google-sized data, you have a new option: simply look at logs of how users correct themselves.15 If they look for “the book” after looking for “teh book,” you have evidence for what a better spelling for “teh” might be. No rules of spelling required.

our word processor, for example, has a string of symbols, collected in a file, to represent your document. Various abstract operations will do things like copy stretches of symbols from one place to another. Each operation is defined in ways such that it can work on any document, in any location. A word processor, in essence, is a kind of application of a set of algebraic operations (“functions” or “subroutines”) that apply to variables (such as “currentl

it goes back at least to 1945, when the legendary mathematician von Neumann outlined the architecture that virtually all modern computers follow. Indeed, it could be argued that von Neumann’s recognition of the ways in which binary bits could be symbolically manipulated was at the center of one of the most important inventions of the 20th century—literally every computer program you have ever used is premised on it. (The “embeddings” that are popular in neural networks also look remarkably like symbols, though nobody seems to acknowledge this. Often, for example, any given word will be assigned a unique vector, in a one-to-one fashion that is quite analogous to the ASCII code. Calling something an “embedding” doesn’t mean it’s not a symbol.)

lassical computer science, of the sort practiced by Turing and von Neumann and everyone after, manipulates symbols in a fashion that we think of as algebraic, and that’s what’s really at stake. In simple algebra, we have three kinds of entities, variables (like x and y), operations (like + or -), and bindings (which tell us, for example, to let x = 12 for the purpose of some calculation). If I tell you that x = y + 2, and that y = 12, you can solve for the value of x by binding y to 12 and adding to that value, yielding 14. Virtually all the world’s software works by stringing algebraic operations together, assembling them into ever more complex algorithms.

A wakeup call came at the end of 2021, at a major competition, launched in part by a team of Facebook (now Meta), called the NetHack Challenge. NetHack, an extension of an earlier game known as Rogue, and forerunner to Zelda, is a single-user dungeon exploration game that was released in 1987.

A lot of confusion in the field has come from not seeing the differences between the two—having symbols, and processing them algebraically. To understand how AI has wound up in the mess that it is in, it is essential to see the difference between the two.What are symbols? They are basically just codes. Symbols offer a principled mechanism for extrapolation: lawful, algebraic procedures that can be applied universally, independently of any similarity to known examples. They are (at least for now) still the best way to handcraft knowledge, and to deal robustly with abstractions in novel situations.

And yet, for the most part, that’s how most current AI proceeds. Hinton and many others have tried hard to banish symbols altogether.

Among other things, we are very likely going to need to revisit a once-popular idea that Hinton seems devoutly to want to crush: the idea of manipulating symbols

grammar is incredibly powerful, because grammar is this one component of language which takes this finite vocabulary that all of us have and allows us to convey an infinite amount of information, an infinite amount of ideas. It's the way in which you can put things together in order to convey anything you want to

Interstitial journaling, a term and suggestion from Tony Stubblebine , is about writing down what you did after a task, how it felt or went, plus what you intend to do next.

Now we understand why there has to be an inner reality which is made of qualia and an outer reality which is made a lot of symbols, shareable symbols, what we call matter.

Moods: Indicated by the equals sign (=), are for logging feelings. These can be emotional or physical feelings like joy, pressure in the chest, butterflies, anxiety, fatigue, excitement, etc.

iconism

The typewriter was made in Siegmar-Schönau—a suburb of Chemnitz—by Wanderer, an early German pioneer in manufacturing bicycles, motorcycles, cars, and later military trucks and tanks for the Wehrmacht, the armed forces in the Nazi era. In the 1930s, Wanderer’s automotive division was one of four car companies consolidated into the Auto Union AG, which later became Audi. Indeed, one of the four interconnected rings on the Audi brand logo represents Wanderer.

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I'm using LaTeX to create my Zettel notes. .t3_158gy35._2FCtq-QzlfuN-SwVMUZMM3 { --postTitle-VisitedLinkColor: #9b9b9b; --postTitleLink-VisitedLinkColor: #9b9b9b; --postBodyLink-VisitedLinkColor: #989898; }

Chord Labels

CHORD SYMBOLS

Chord Symbols vs. Roman Numerals

The function symbol notation is the least used notational system in jazz. As the namesuggests, this notation specifies the harmonic function of individual chords and evencomplete chord progressions. It has the potential of being useful to notate specificbehaviors of chords that may not—at least, not on the surface level—indicate that theybelong to a particular functional family of chords. As such, function symbols enable theperception of harmonic progressions from a more structural perspective. Function symbolsindicate neither the architecture nor the specific scale degrees of chords. This style ofnotation is more conceptual than it is representative of a specific surface event. The termssurface level and structural level are used to describe musical events and the degree oftheir importance. “Structural” events occur beneath the musical “surface” and areresponsible for the overall tonal, harmonic, and melodic forces controlling the piece.Function symbols use three labels: T for tonic-type chords, PD for predominant-typechords, and D for dominant-type chords.

const requiredMetadataKey = Symbol("required");

I’ve also begun adopting a style loosely based on the approach to introductory signals used in legal writing, where things like See: [[something]] and See also: [[something]] and But see: [[something]] each have slightly different meanings. This gives me a set of supporting, comparison, and contradictory signals I can use when placing links as well.

In paper books I use Cal Newport’s “Morse Code method” placing a dot in the margin by a main point and a dash in the margin by a supporting point.

I agree.After thinking about it for a bit, a common symbol for "the present card/note" is the one I'm most wanting.For the other stuff, I'm thinking:The squigly arrow symbol in latex is probably enough to do fuzziness. Then it could be squigly arrow to the current card or squigly arrow to not symbol current card. And for pen and paper, just use the biochem flat arrow with a squigly body for "somewhat contradicts" or is in tension with.

Are there symbols for 'supported by' or 'contradicted by' etc. to show not quite formal logical relations in a short hand?

No one can say how many symbols Tiro came up with — presumably he wrote it down, but no such key is known to have survived — but successors began adding to it until, according to Isidore of Seville writing around 630 CE, no less than Seneca himself had topped it up to 5,000 symbols.

2 • 3 = 6

Ideally we could use Unicode, 3 2 1 ~ 3 2 1 ≃

I use the asterisk in the conventional way, to indicate a sentence that deviates in some respectfrom grammatical rule.

Symbols might conveniently have been used for woids ofsuch frequent occurrence as: for, in, of, with, as, to, the,bill, statute, footnote.

he Last Rose of

For the leading Frenchhumanist Guillaume Budé (1468–1540), seven volumes of notes are extant, justa fraction of his original output, replete with color- coded inks and marginal sym-bols that remain unexplained;

1. Multiple strong symbols are not allowed○ Each item can be defined only once2. Given a strong symbol and multiple weak symbols, choose the strong symbol○ References to the weak symbol resolve to the strong symbol3. If there are multiple weak symbols, pick an arbitrary one

● Global symbols○ Symbols defined by module m that can be referenced by other modules.■ e.g., non-static C functions and non-static global variables.● External symbols○ Global symbols that are referenced by module m but defined by some other module.● Local symbols○ Symbols that are defined and referenced exclusively by module m.■ e.g., C functions and global variables defined with the static attribute.○ Local linker symbols are not local program variables

die and rise the same

µ

The form of the obelus as a horizontal line with a dot above and a dot below, ÷, was first used as a symbol for division by the Swiss mathematician Johann Rahn in his book Teutsche Algebra in 1659.

To the consternation of some users, 3.x employed Unicode variable names such as λ, φ, τ and π for a concise representation of mathematical operations. A downside of this approach was that a SyntaxError would occur if you loaded the non-minified D3 using ISO-8859-1 instead of UTF-8. 3.x also used Unicode string literals, such as the SI-prefix µ for 1e-6. 4.0 uses only ASCII variable names and ASCII string literals (see rollup-plugin-ascii), avoiding encoding problems.

The abstract shapes in the brackets symbolize the "OK" from the boot up screen, services running inside systemd, and our overall optimistic outlook.

Used injudiciously in these circumstances, mathematics – and especially mathematical modelling – can serve to obfuscate rather than clarify, or at best add nothing at all to the situation other than the illusion of control.

Statistics

The above errors can be resolved by simply adding the ⚡attribute to the <html> tag like so: <html ⚡ lang="en">

<html ⚡>

⚡4email

JSON.parse(json, symbolize_names: true)

the overloaded operators ¬, =, ≠, and abs are defined

Most of Algol's "special" characters (⊂, ≡, ␣, ×, ÷, ≤, ≥, ≠, ¬, ⊃, ≡, ∨, ∧, →, ↓, ↑, ⌊, ⌈, ⎩, ⎧, ⊥, ⏨, ¢, ○ and □) can be found on the IBM 2741 keyboard with the APL "golf-ball" print head inserted; these became available in the mid-1960s while ALGOL 68 was being drafted. These characters are also part of the Unicode standard and most of them are available in several popular fonts.

preceded by an index, ☞like this

This type relation is sometimes written S <: T

a ≺ b indicates the causal relation "b depends on a"

This supplemented the individual's memory and ability to visualize. (We are not concerned here with the value derived from human cooperation made possible by speech and writing, both forms of external symbol manipulation. We speak of the manual means of making graphical representations of symbols—

ಆವ ಜಾತಿಯಲ್ಲಿ ಹುಟ್ಟಿದವನಾದಡಾಗಲಿ,ಶ್ರೀಮಹಾದೇವನ ನೆನೆವಾತನದ್ಥಿಕ ನೋಡಾ.ಆತನಿಂದದ್ಥಿಕ ಕಂಗಳು ತುಂಬಿ ನೋಡುವಾತ.ಆತನಿಂದದ್ಥಿಕ ಕೈಮುಟ್ಟಿ ಪೂಜಿಸುವಾತ.ಅದೆಂತೆಂದಡೆ, ಶಿವಧರ್ಮೇ-``ಲಿಂಗಸ್ಯ ದರ್ಶನಂ ಪುಣ್ಯಂ ದರ್ಶನಾತ್ ಸ್ಪರ್ಶನಂ ಶುಭಂ |ಶಿವಲಿಂಗಂ ಮಹಾಪುಣ್ಯಂ ಸರ್ವದೇವ ನಮಸ್ಕøತಂ |ಯಃ ಸ್ಪøಶೇದಪಿ ಪಾಣಿಭ್ಯಾಂ ನ ಸ ಪಾಪೈಃ ಪರಿಲಿಪ್ಯತೇ ||''ಎಂದುದಾಗಿ,ಅಂತಪ್ಪ ಶಿವಲಿಂಗವನು ಹೆರೆಹಿಂಗದೆ ಅಂಗದ ಮೇಲೆನಿರಂತರ ಧರಿಸಿಕೊಂಡಿಪ್ಪಾತನೆ ಎಲ್ಲರಿಂದದ್ಥಿಕ ನೋಡಾಅಖಂಡೇಶ್ವರಾ.

Take for instance the case of Matt Bonner’s yellow mule.

Doubtless, if things themselves be under-stood, it docs not seem material what names are assigned them.

But because he makes use of words only, as the signs of emotions, which it is impossible they can represent; and omiL<; the use of the true signs of the passions, which are, tones, looks, and gestures.

“symbolic anthropology” (Geertz 1974 [1971]; 1977 [1973]; 1988).

Before I knew it, I found myself on a street I had never been to, in a city I had never been to, about to head into a room full of people I had never met before, all united by one simple symbol... 1 A penguin. An hour before, that penguin had seemed so inviting and friendly. It was a symbol that encompassed everything about the movement it represented, a movement that came together in spirit and mind to build a system that drove a new generation of technology and freedom... a movement that celebrated this drive by forming user groups in unknown streets, in unknown cities, and with unknown people.