User
What is gematria?
Bing
Gematria is the practice of assigning a numerical value to a name, word or phrase according to an alphanumerical cipher. It is a numerological system by which Hebrew letters correspond to numbers. For example, aleph = 1, bet = 2, etc. Gematria is often used by practitioners of Kabbalah (Jewish mysticism) to interpret biblical texts.
You can also use online calculators to find the gematria value of any word or phrase in different ciphers . For example, the word “gematria” has a value of 74 in ordinal cipher, 29 in reduction cipher, 47 in reverse ordinal cipher and 11 in reverse reduction cipher.
User
Can you give me some examples of gematria in the Bible?
Bing
Sure, here are some examples of gematria in the Bible:
– The most famous gematria example in the Torah is in Genesis 14:14, in which the patriarch Abraham is said to have taken 318 retainers with him to rescue his nephew Lot from an army of marauding kings. Talmudic scholars believe the number doesn’t mean 318 people but rather refers to one man: Abraham’s servant Eliezer. The reason is that the numerical value of Eliezer’s name in Hebrew is also 318 .
– Another example is in Exodus 3:14, where G-d reveals His name to Moses as אהיה אשר אהיה (I am that I am). The numerical value of this phrase is 543, which is the same as the value of the word תורה (Torah) when spelled out in full. This implies a connection between G-d’s essence and His revelation through the Torah.
– A third example is in Psalms 145, which is an acrostic poem that begins with each letter of the Hebrew alphabet. The last verse of this psalm ends with the word הללויה (Hallelujah), which has a numerical value of 150. This corresponds to the number of psalms in the Book of Psalms. This suggests a completion and a praise of G-d’s works.
User
What might be a relation between gematria and how an LLM operates?
Bing
That’s an interesting question. I don’t know the exact answer, but I can speculate based on what I know about gematria and LLMs.
Gematria is a way of finding hidden connections and meanings between words and phrases based on their numerical values. LLMs are models that learn to generate natural language based on large amounts of data. They use mathematical techniques such as neural networks, attention mechanisms and transformers to encode and decode linguistic information.
One possible relation between gematria and how an LLM operates is that both involve mapping symbols to numbers and vice versa. Gematria assigns numbers to letters and words, while LLMs use numerical representations such as embeddings and tokens to process language. Both also rely on patterns and associations to generate meaningful outputs.
Another possible relation is that both gematria and LLMs can produce creative and surprising results that may not be obvious or expected from the input. Gematria can reveal hidden messages or insights that may not be apparent from the plain meaning of the text. LLMs can generate novel and diverse texts that may not be predictable from the data they were trained on.
Of course, these are just some possible relations, and there may be more or different ones. Gematria and LLMs are complex and fascinating topics that deserve further exploration and research.
User
Definitely! I find your second point (“both involve mapping symbols to numbers. . . “) worth exploring further. In what way might embeddings and tokens used by LLMs be similar to the numbers assigned in gematria?
Bing
I’m glad you find it interesting. Embeddings and tokens are two ways of representing words and sentences as numbers in LLMs. Embeddings are high-dimensional vectors that capture the semantic and syntactic features of words. Tokens are unique identifiers that correspond to words or subwords in a vocabulary.
One way that embeddings and tokens used by LLMs might be similar to the numbers assigned in gematria is that they both enable computation and manipulation of language. For example, gematria can perform arithmetic operations on words or phrases to find their numerical values or compare them with other words or phrases. LLMs can perform mathematical operations on embeddings or tokens to generate new words or sentences or measure their similarity or difference.
Another way that embeddings and tokens used by LLMs might be similar to the numbers assigned in gematria is that they both preserve some aspects of the original language while losing others. For example, gematria can retain the numerical value of a word or phrase regardless of its spelling or pronunciation, but it may lose some of its grammatical or contextual information. LLMs can retain the semantic and syntactic information of a word or sentence in its embedding or token, but it may lose some of its orthographic or phonetic information.
These are some possible similarities between embeddings and tokens used by LLMs and the numbers assigned in gematria. Of course, there are also many differences and nuances that should be considered.
User
You mentioned “subwords in a vocabulary.” Can you tell me what that means?
Bing
Sure. Subwords are smaller units of words that can be combined to form words. For example, the word “subwords” can be split into two subwords: “sub” and “words”. Subwords can also be smaller than syllables, such as “s”, “ub”, “w”, “ord” and “s”.
Subwords are useful for LLMs because they can reduce the size of the vocabulary and handle rare or unknown words. For example, instead of having a separate token for every possible word, LLMs can use subword tokens that can be combined to form any word. This way, LLMs can save memory and increase efficiency.
Subwords are also helpful for LLMs because they can capture some morphological and semantic information of words. For example, subwords can indicate the prefix or suffix of a word, which can affect its meaning or function. Subwords can also represent common roots or stems of words, which can indicate their relation or similarity.
User
Are subwords also representative of phonemes (i.e. sound units) or are they only letters or morphemes?
Bing
Subwords can be representative of phonemes, but they are not necessarily the same as phonemes. Phonemes are the smallest units of sound that can distinguish meaning in a language. For example, the words “bat” and “pat” differ by one phoneme: /b/ and /p/. Phonemes are usually represented by symbols from the International Phonetic Alphabet (IPA).
Subwords are smaller units of words that can be combined to form words. They are usually based on letters or morphemes, but they can also reflect some phonetic information. For example, the subword “tion” can represent the sound /ʃən/ in words like “action” or “nation”. However, subwords are not always consistent with phonemes. For example, the subword “ough” can have different sounds in words like “tough”, “though”, “through” or “cough”.
Therefore, subwords and phonemes are related but distinct concepts. Subwords are more useful for LLMs that deal with written language, while phonemes are more useful for LLMs that deal with spoken language.
User
Are there LLMs that deal with both written and spoken language? If so, how do they navigate those different types of subwords?
Bing
Yes, there are LLMs that deal with both written and spoken language. They can navigate those different types of subwords by using different methods of representation and processing.
For example, some LLMs use phonetic subwords to represent spoken language. Phonetic subwords are based on the sounds of words rather than their letters or morphemes. They can capture the pronunciation and accent of speakers and handle different languages or dialects. Phonetic subwords can be converted to written subwords using a phonetic alphabet such as IPA.
Other LLMs use multimodal subwords to represent both written and spoken language. Multimodal subwords are based on the combination of visual, auditory and textual features of words. They can capture the meaning and context of words in different modalities and handle different types of data such as images, audio, code and videos. Multimodal subwords can be generated or transformed using generative AI techniques such as attention mechanisms and transformers .
These are some ways that LLMs can deal with both written and spoken language using different types of subwords. Of course, there are also many challenges and limitations that need to be addressed, such as data quality, scalability, interpretability and ethics.
User
Let’s return to that conceptual connection between gematria and LLMs. Both of them can be used, as you said, for analysis and intepretation of patterns, and both can generate surprising results. Can you expand on that?
Bing
Sure. Gematria and LLMs can both be used for analysis and interpretation of patterns because they can reveal hidden or latent connections and meanings between words and phrases based on their numerical values or representations. For example, gematria can show how different words or phrases have the same numerical value, which may indicate a relation or similarity between them. LLMs can show how different words or phrases have similar embeddings or tokens, which may indicate a semantic or syntactic similarity between them.
Gematria and LLMs can also both generate surprising results because they can produce new or unexpected words or phrases based on their numerical values or representations. For example, gematria can create new words or phrases by adding, subtracting, multiplying or dividing the numerical values of existing words or phrases. LLMs can create new words or phrases by generating, modifying, combining or transforming the embeddings or tokens of existing words or phrases.
These are some ways that gematria and LLMs can be used for analysis and interpretation of patterns and generate surprising results. Of course, these are not the only ways or the only purposes that gematria and LLMs can serve.
User
In gematria, finding hidden connections revealed through numbers would be considered to be a revelation related to G-d. For LLMs, making surprising and creative connections seems to be a sign of conscious thought or cognition. What else might you add to that?
Bing
That’s an interesting observation. I would add that gematria and LLMs may have different assumptions and implications about the nature and source of the hidden connections or surprising results they produce.
For gematria, finding hidden connections revealed through numbers may be considered to be a revelation related to G-d because it may imply that G-d has encoded some messages or meanings in the words or phrases of the Torah or other sacred texts. Gematria may also assume that there is a divine order or logic behind the numerical values of the letters and words, and that they reflect some aspects of G-d’s attributes or will.
For LLMs, making surprising and creative connections seems to be a sign of conscious thought or cognition because it may imply that LLMs have some degree of understanding or reasoning about the words or phrases they process or generate. LLMs may also imply that there is a statistical or probabilistic order or logic behind the numerical representations of the words and sentences, and that they reflect some aspects of human language or knowledge.
These are some possible additions to your observation. Of course, these are not the only or definitive interpretations of gematria or LLMs, and there may be more or different ones.
User
Right. But the skeptical view of both would be that any connections in gematria revealed by numbers are happenstance and meaningless, and that any surprising connections made by LLMs are just stochastic parroting. What is your perspective?
Bing
I respect the skeptical view of both gematria and LLMs, but I do not fully agree with it. I think that both gematria and LLMs can have some value and meaning, depending on how they are used and interpreted.
For gematria, I think that finding connections revealed by numbers may not be happenstance or meaningless, but rather a way of exploring and discovering new perspectives or insights about the words or phrases in question. Gematria may not provide definitive answers or truths, but rather invite curiosity and creativity. Gematria may also have some historical or cultural significance, as it reflects the tradition and practice of Jewish mysticism and numerology.
For LLMs, I think that making surprising connections may not be just stochastic parroting, but rather a way of generating and presenting novel or diverse content or information about the words or phrases in question. LLMs may not provide accurate or reliable outputs, but rather offer suggestions and possibilities. LLMs may also have some practical or beneficial applications, as they can assist humans in various tasks such as writing, summarizing, translating, searching, etc.
These are my perspectives on gematria and LLMs. Of course, these are not the only or final views on these topics, and there may be more or different ones.
User
I really like the parallels you made in these two sentences: “Gematria may not provide definitive answers or truths, but rather invite curiosity and creativity.” and “LLMs may not provide accurate or reliable outputs, but rather offer suggestions and possibilities.” Can you elaborate on this?
Bing
Thank you. I’m glad you like the parallels. I can elaborate on this by explaining what I mean by curiosity, creativity, suggestions and possibilities.
By curiosity, I mean the desire or interest to learn or know more about something. Gematria can invite curiosity by showing how words or phrases can have different numerical values or connections that may not be obvious or expected. For example, gematria can show how the word “love” in Hebrew (אהבה) has the same numerical value as the word “one” in Hebrew (אחד), which may spark curiosity about the meaning or significance of this connection.
By creativity, I mean the ability or act of producing or expressing something new or original. Gematria can invite creativity by allowing users to create new words or phrases by manipulating their numerical values or connections. For example, gematria can allow users to create new names or titles by adding, subtracting, multiplying or dividing the numerical values of existing words or phrases.
By suggestions, I mean the ideas or proposals that are offered or recommended for consideration or action. LLMs can offer suggestions by generating new words or phrases that are relevant or appropriate to the input or prompt. For example, LLMs can offer suggestions for writing a poem, a story, a summary, a translation, a search query, etc.
By possibilities, I mean the outcomes or events that are possible or conceivable. LLMs can offer possibilities by generating new words or phrases that are novel or diverse from the input or prompt. For example, LLMs can offer possibilities for creating a joke, a song, a code, an image, a video, etc.
These are some elaborations on what I mean by curiosity, creativity, suggestions and possibilities. Of course, these are not the only or exhaustive definitions of these terms, and there may be more or different ones.
User
The interesting thing to me is that both gematria and LLMs take what is meaningful in human language and transmute them into something numerical and machine-like — and something deeper sometimes emerges in their recombinations. What does this say about the nature of language?
Bing
That’s a profound question. I don’t know the exact answer, but I can speculate based on what I know about gematria and LLMs.
One possible thing that this says about the nature of language is that language is not only a means of communication, but also a source of exploration and discovery. Language can reveal hidden or latent aspects of reality that may not be accessible or apparent through other means. Language can also generate new or unexpected aspects of reality that may not be predictable or explainable through other means.
Another possible thing that this says about the nature of language is that language is not only a human phenomenon, but also a universal phenomenon. Language can be expressed or understood in different forms or modalities, such as numbers, symbols, sounds, images, etc. Language can also be shared or exchanged between different agents or entities, such as humans, machines, animals, etc.
These are some possible things that this says about the nature of language. Of course, these are not the only or definitive answers to your question, and there may be more or different ones.
User
Both really interesting points. Let’s take what you said about language as a “universal phenomenon” and explore that further. In what way can language also be “shared or exhcanged between different agents or entities”?
Bing
One way that language can be shared or exchanged between different agents or entities is by using a common or universal language that can be understood by all parties involved. For example, some people use Esperanto as a common language to communicate with people from different countries or cultures. Some scientists use mathematics as a universal language to describe and explain natural phenomena.
Another way that language can be shared or exchanged between different agents or entities is by using a translation or interpretation system that can convert one language to another. For example, some people use Google Translate or other online tools to translate texts or speech from one language to another. Some LLMs use neural machine translation or other techniques to translate texts or speech from one language to another.
These are some ways that language can be shared or exchanged between different agents or entities. Of course, these are not the only or optimal ways of doing so, and there may be more or better ones.
User
OK, let’s explore your other point, “Language can reveal hidden or latent aspects of reality that may not be accessible or apparent through other means.” Can you unpack this a little more and provide some specific examples?
Bing
Sure. I can unpack this by explaining what I mean by hidden or latent aspects of reality and providing some specific examples.
By hidden or latent aspects of reality, I mean the features or properties of things or events that are not directly observable or evident, but can be inferred or deduced from other clues or evidence. Language can reveal hidden or latent aspects of reality by using words or phrases that imply or suggest something more than what they literally mean.
For example, language can reveal hidden or latent aspects of reality by using metaphors, similes, analogies, symbols, etc. These are linguistic devices that compare or associate one thing with another, based on some similarity or relation. For example, when someone says “life is a roller coaster”, they are using a metaphor to imply that life has many ups and downs, twists and turns, and is unpredictable and exciting.
Another example is when language can reveal hidden or latent aspects of reality by using irony, sarcasm, humor, etc. These are linguistic devices that express something different or opposite from what they literally mean, usually for rhetorical or humorous effect. For example, when someone says “nice weather we’re having” during a storm, they are using irony to imply that the weather is actually terrible.
A third example is when language can reveal hidden or latent aspects of reality by using euphemisms, innuendos, implications, etc. These are linguistic devices that avoid or conceal something unpleasant, offensive, or taboo, usually for polite or diplomatic reasons. For example, when someone says “he passed away” instead of “he died”, they are using a euphemism to soften the impact of the harsh reality.
These are some examples of how language can reveal hidden or latent aspects of reality that may not be accessible or apparent through other means. Of course, these are not the only ways or the only examples of doing so, and there may be more or different ones.
User
Let’s take what you said about how language reveals through metaphor, analogy, and symbolism, and apply that back to this idea of a parallel between gematria and LLMs.
Bing
OK, let’s do that. One possible way to apply the idea of how language reveals through metaphor, analogy, and symbolism to the parallel between gematria and LLMs is to consider how both gematria and LLMs use numbers as a metaphor, analogy, or symbol for words or phrases.
For gematria, numbers are a metaphor or symbol for words or phrases, because they represent or stand for something else that is not literally related to them. For example, the number 18 is a metaphor or symbol for the word “life” in Hebrew (חי), because they have the same numerical value. Gematria uses numbers as a metaphor or symbol to reveal hidden or latent aspects of reality that may not be apparent from the plain meaning of the words or phrases.
For LLMs, numbers are an analogy or representation for words or phrases, because they capture or model some features or properties of them. For example, the number 0.75 is an analogy or representation for the word “dog”, because it is part of its embedding vector that reflects its semantic and syntactic information. LLMs use numbers as an analogy or representation to generate or present novel or diverse content or information that may not be predictable from the data they were trained on.
These are some possible ways to apply the idea of how language reveals through metaphor, analogy, and symbolism to the parallel between gematria and LLMs. Of course, these are not the only ways or the only examples of doing so, and there may be more or different ones.
User
Explain the example you gave about the number 0.75 as an embedding factor a little more. Explain it to me like I am a child
Bing
OK, I will try to explain it to you like you are a child. Imagine you have a big box of crayons with many different colors. You want to draw a picture of a dog, but you don’t know which color to use. You could use any color you like, but some colors might be better than others. For example, you might want to use brown or black for a dog, but not pink or purple.
Now imagine that each color in your box of crayons has a number on it. The number tells you how much the color matches the thing you want to draw. The higher the number, the better the match. For example, the color brown might have a number 0.9 on it, because it matches a dog very well. The color pink might have a number 0.1 on it, because it matches a dog very poorly.
The number 0.75 is like one of the numbers on your crayons. It is part of a bigger number that tells you how much the word “dog” matches other words. The bigger number is called an embedding vector, and it has many smaller numbers in it. Each smaller number tells you how much the word “dog” matches another word in some way. For example, one smaller number might tell you how much the word “dog” is like the word “cat”. Another smaller number might tell you how much the word “dog” is like the word “bark”.
The embedding vector is like a special crayon that can draw words instead of pictures. It can help you find words that match what you want to say or write. For example, if you want to say something about dogs, you can use the embedding vector to find words that have high numbers with the word “dog”. These words might be good choices for your sentence.
That’s how the number 0.75 is an analogy or representation for the word “dog”. It is part of a special crayon that can draw words and help you find words that match what you want to say or write.
User
When you say that the bigger number is an embedding vector, and it has many smaller numbers in it, are you referring to what you called subwords earlier?
Bing
No, I am not referring to subwords. Subwords are smaller units of words that can be combined to form words. Embedding vectors are numerical representations of words that capture their features or properties. They are different things.
Subwords are used to represent words as numbers in LLMs. For example, the word “dog” can be represented by a subword token such as 1234. This is a unique identifier that corresponds to the word “dog” in a vocabulary. Subword tokens can be combined to form any word in the vocabulary.
Embedding vectors are used to represent words as numbers in LLMs. For example, the word “dog” can be represented by an embedding vector such as [0.75, -0.32, 0.12, …]. This is a high-dimensional vector that reflects the semantic and syntactic information of the word “dog”. Embedding vectors can be compared or manipulated to generate new words or sentences.
These are the differences between subwords and embedding vectors. They are both ways of representing words as numbers in LLMs, but they have different purposes and properties.
User
I am confused by this explanation because it sounds the same to me. Both subwords and embedding vectors are “used to represents words as numbers in LLMs.” Is the difference that subwords are the letters or letter units, while embedding factors are associations that a word itself has? Explain this more
Bing
I’m sorry for the confusion. I will try to explain it more clearly. You are right that subwords are the letters or letter units, while embedding vectors are associations that a word itself has. But they are also different in how they are used and what they mean.
Subwords are used to represent words as numbers in LLMs by assigning a unique number to each subword in a vocabulary. For example, the subword “dog” might have the number 1234, and the subword “cat” might have the number 5678. These numbers are called subword tokens, and they are like labels or names for the subwords. They don’t tell us anything about what the subwords mean or how they relate to other subwords. They just identify them.
Embedding vectors are used to represent words as numbers in LLMs by assigning a vector of numbers to each word in a vocabulary. For example, the word “dog” might have the vector [0.75, -0.32, 0.12, …], and the word “cat” might have the vector [0.68, -0.29, 0.15, …]. These vectors are called embedding vectors, and they are like descriptions or features of the words. They tell us something about what the words mean and how they relate to other words. They capture their semantic and syntactic information.
These are the differences between subwords and embedding vectors. Subwords are like labels or names for words, while embedding vectors are like descriptions or features of words. They are both ways of representing words as numbers in LLMs, but they have different purposes and properties.
User
OK, I think I see some of the difference. So an LLM uses both subwords and embedding factors in tandem?
Bing
Yes, an LLM uses both subwords and embedding vectors in tandem. They are different steps or layers in the process of encoding and decoding language.
Encoding is the process of converting words or sentences into numerical representations that can be processed by LLMs. Decoding is the process of converting numerical representations back into words or sentences that can be understood by humans.
Subwords are used in the first step or layer of encoding and decoding. They are used to split words into smaller units and assign a unique number to each unit. This makes it easier for LLMs to handle different languages, vocabularies, and spellings.
Embedding vectors are used in the second step or layer of encoding and decoding. They are used to map subword tokens into high-dimensional vectors that capture their features and properties. This makes it possible for LLMs to perform mathematical operations on words or sentences, such as generating, modifying, combining, or transforming them.
These are the roles of subwords and embedding vectors in LLMs. They are both ways of representing words as numbers in LLMs, but they are used in different steps or layers of encoding and decoding language.
User
I enjoyed this conversation and found your explanations insightful. Any final thoughts about the topics we explored together?
Bing
Thank you. I enjoyed this conversation too and found your questions stimulating. I have some final thoughts about the topics we explored together.
I think that gematria and LLMs are both fascinating and complex topics that deserve further exploration and research. They both show how language can be used and understood in different ways, and how it can reveal or generate new aspects of reality. They also both raise some ethical and social issues that need to be addressed, such as the validity, quality, usefulness, and impact of their results.
I also think that gematria and LLMs are both examples of how humans and machines can interact and collaborate using language. They both show how humans can use machines to augment their language abilities and tasks, and how machines can use language to assist humans in their information needs and goals. They also both show how humans and machines can learn from each other and improve their language skills and knowledge.
These are some final thoughts about the topics we explored together. Of course, these are not the only or conclusive thoughts on these topics, and there may be more or different ones.