Feature 1418 · Fractional division puzzles

Gemma Scope 2, gemma-3-27b-it, residual stream after layer 31, width 262,144.

Neuronpedia label

how many
Neuronpedia's record for this index: explanations “quantities and amounts”; “how many”, by gemini-2.5-flash-lite from activations and promoted tokens · density on Neuronpedia's corpus one token in 39,904 (0.002506%) · activation examples held 20 · max activation 1695.7847.
Auto-interpretability over a broad general corpus, written for the base dictionary and carried to the instruction-tuned one by index. This index on Neuronpedia (the base dictionary's page: activations, logits and the explanation's record).

ICRA reading

Fractional division puzzles

Each window centers on a moment of splitting a whole into named fractional shares or ratios (halves, thirds, ninths, golden ratio, inheritance portions, camel/brother counts), often as a riddle whose resolution reveals hidden order.

A wry, revelatory delight in solving or exposing a numerical/logical paradox — intellectual awe tinged with irony — running through most but not all windows.

Frame v5-wide-192 · Claude Sonnet 5 (via OpenRouter) · 2026-09-20 · from 30 windows of 192 tokens, crest at token 128: 10 from the author's own writing, 15 from the works he holds formative, read through this model.

In the diary

kind at entry 100 not read in this diary
register semantic
strong entries of 100 —
thread no (its strong entries hold no run longer than chance would give, or it is ground)

The windows the reading was made from

30 windows of 192 tokens, the feature's crest at token 128, firing tokens marked; ¶ marks a paragraph break in the source.

1<bos>One group said: “Here in our group there are some who have nothing but the light of faith, They know nothing of knowledge or its path. We do not doubt the truthfulness of this messenger or his wisdom. And one part of wisdom is to take into account the weakest. Hence, through these attributes by which the messenger described his Lord, he has ad- dressed this weak fellow who does not possess the proofs of consideration and has nothing but the light of faith. Thereby the messenger has been merciful toward him, for his faith will not grow except through descriptions like this. And the Real can describe Himself as He likes according to the measure of the rational faculty of the recipient, even if in Himself He is different from that. The report- giver has relied upon this description, while observing the right of the weakest one. For
2<bos>It is true that if each man uses as primitive words the words of his own language, he will not have much difficulty, but in that case he will be understood only by the people of his own country unless he writes down what he wants to say and the person who wants to understand him takes the trouble to look up all the words in the dictionary; and this is too burdensome to become a regular practice. ... So the only possible benefit that I see from his invention would be in the case of the written word. Suppose he had a big dictionary printed of all the languages in which he wanted to make himself understood and put for each word a symbol corresponding to the meaning and not to the syllables, a single symbol, for instance, for aimer, amare, and philein: then those who had the dictionary and knew
3something whose reflection and trace I proposed to you elsewhere; a delayed trace because it appears at the level of a test which of course already presupposes conditions very defined by experience, which does not allow us to prejudge fundamentally how much of it is in the subject, but the difficulty which still remains for a long time for the subject of distinguishing this enunciating I from the I of the enunciation, and which is expressed by the belated failure in a test which chance and his flair as a psychologist made Binet choose in the form of: „I have three brothers, Paul, Ernest and me.‟ ¶ The difficulty that there is in the fact that the child does not see this enunciation as coming from elsewhere as he should, namely that the subject does not yet know how to deduct himself (se décompter). But this trace which I marked out for you is something, an index
4<bos>27). Like 26). The abacus has 20 small beads & one large one. If the heap contains more than 20 plates, the large bead is moved. (So the large bead in some way corresponds to the word “many”). ¶ 28). Like 26). If the heap contains n plates, n being more than 20 but less than 40, B moves n − 20 beads, shews A the abacus thus set, & claps his hand once. ¶ 29). A & B use the numerals of the decimal system (written or spoken) up to 20. The child learning this language learns these numerals by heart, etc., as in 2). ¶ 30). A certain tribe has a language of the kind 2). The numerals used are those of our decimal system. No one numeral used can be observed to play the predominant
5<bos>She has translated and written a combination of 25 books about Islam, many dealing with Sufism. She has also authored or co-authored a number of biographical works. Her translation of the Qur'an, first published in 2007 and called The Sublime Quran, is the first translation of the Qur'an by an American woman; while the first translation of the Qur'an into English by a woman was done in 2001 by an Iranian woman, Tahereh Saffarzadeh. Laleh Bakhtiar's translation attempts to take a female perspective, and to admit alternative meanings to many Arabic terms that are ambiguous or whose meaning scholars have had to guess because of the antiquity of the language. Qur'an. Her work seeks to create understanding between non-Muslims and Muslims. ¶ In her Quran translation, she translates kāfirūn as "those who are ungrateful" instead of the common
6<bos>5). B is shewn a word written on a piece of paper held upside down. He does not recognize the word. The paper is gradually turned round until B says, “Now I see what it is. It is ‘pencil’”. ¶ We might say, “He always knew what the word ‘pencil’ looked like. He did not know that the word he was shewn would when turned round look like ‘pencil’”. ¶ In both cases 4) and 5) you might say something was hidden. But note the different application of “hidden”. ¶ 6). Compare with this: You read a letter and can't read one of its words. You guess what it must be from the context, and now can read it. You recognize this scratch as an e, the second as an a, the third as a t. This is different from the case where the word “eat” was covered by a blotch of
7<bos>I brought you a certain number of statements the last time. I formulated ones such as, for example, “there is no sexual act”. I believe that the news of this has gone all over town (laughter). But anyway, I did not give it as an absolute truth. I said that this is what was properly speaking articulated in the discourse of the unconscious. ¶ That said, I framed this formula and some others into a sort of reminder, that I must say was rather dense, of what gives it its sense and also its premises. This lecture was a sort of stage marked by assembly points, which will perhaps serve as a written introduction to something, then, that I am pursuing, that I want to pursue today, I would say in a form that is perhaps more accessible, in any case conceived of as an easier path, a first way of disentangling the articulations into which I am going
8<bos>Three times a day, a certain spirit comes into the cave of the Machpelah and breathes over the tombs of the fathers so that their bones are healed and they endure. The spirit draws dew from over the King's head, CHOCHMAH, BINAH, AND DA'AT OF ZEIR ANPIN, where the supernal patriarchs are. When the dew flows in, the lower patriarchs are awakened IN THE CAVE OF THE MACHPELAH. ¶ We have learned that the dew flows down certain grades, one grade after another, and reaches the lower Garden of Eden, where the perfumes are bathed in it. Then a certain spirit awakens, which comprises two others; NAMELY A SPIRIT OF THE CENTRAL COLUMN, JACOB, WHICH INCLUDES THE TWO COLUMNS, ABRAHAM AND ISAAC. It ascends and hovers above the perfumes and comes in through the opening of the cave. Then the patriarchs are awakened
9the points at the level at which they may be useful to you. ¶ It must be remarked, nevertheless, that if - since this comes up all by itself and because really it is more convenient, (we still have a long enough path to take) - I inscribe here, quite simply, the formula which is found to overlap what I called the greatest incommensurable or again the golden number, which designates very properly speaking the following: that of two magnitudes, the relationship of the bigger to the smaller, of the One to the o on this occasion, is the same as that of their sum to the greater, that if I operate in this way, it is not in order to get across - too quickly moreover - hypotheses which it would be a great pity for you to ¶ http://www.lacaninireland.com <0x0C>The Logic of Phantasy 26.4
10<bos>A barzakh is something that stands be- tween and separates two other things, yet combines the attributes of both. Strictly speaking, every existent thing is a barzakh, since everything has its own niche between two other niches within the ontological hierarchy known as the cosmos. “There is nothing in existence but barzakhs, since a barzakh is the ar- rangement of one thing between two other things . . . , and existence has no edges (taraf )” (III 156.27). Existence itself is a barzakh between Being and nothing- ness. In the hierarchy of worlds which makes up the cosmos, the term barzakh refers to an intermediate world standing between the luminous or spiritual world and the dark or corporeal world. The term is relative, like other cosmological terms,
11<bos>Jacob arrived at the prophecy of "and...lived" only in Egypt. It was an excellent prophecy, the like of which was never prophesied before. None of the prophets was worthy of it except for him and Moses ALONE. It is written of Moses, "For no man shall see Me, and live" (Shemot 33:20). Of Jacob, it is written, "And Jacob lived" REFERRING TO the prophecy which descends from the shining mirror, TIFERET. ¶ Jacob wanted to prophesy concerning the exiles of his children in the land of Canaan and in any land wherein they dwelt WHICH came from the land of Egypt; MEANING, ALL EXILES ARE INCLUDED WITHIN EGYPT. His heart broke, as it is written, "Now Jacob saw that there was corn (also: 'breaking') in Egypt" (Beresheet 42:1). ¶ Hence, when it
12<bos>When Adam was in the Garden of Eden, all those Chariots and holy legions surrounded him, and thus he was completely protected, and nothing evil could approach him. Once he sinned and those nail-garments were stripped of him, he started to fear evil things and evil spirits, and the holy legions THAT SURROUNDED AND PROTECTED HIM left. From those garments nothing remained but the nails at the tip of the fingers, surrounded by the filth of the Other SIDE. ¶ For that reason we must not grow our fingernails, for there is filth in them, and as they grow, so grows in relation to it the power of Judgment, FROM THE POWER OF THE KLIPOT THAT NOURISHES FROM THE PART OF THE NAILS THAT OUTGROWS THE FLESH. One should see to it daily, to cut the nails, but not throw them, so as not to show contempt for the place, FOR THEY EMANATE
13<bos>If it is true that it is the Other who constitutes us by recognising us as object of desire, if the response of the Other makes us realise the gap which exists between demand and desire and if it is through this gap that we enter into the world of signifiers, then for the psychotic the Other is the one who has never signified anything other than a hole, a void at the very centre of his being. The interdiction regarding desire which he has experienced means that his response has caused him to register not a gap but a fundamental antimony between demand and desire. From this gap which is not just a gap but a gaping pit what appears is not the signifier but the phantasy, that which causes the telescoping of the symbolic and the real which we call psychosis. ¶ For the psychotic - if I can put it simply - the Other is introjected at the level of his own body, at
14<bos>602. Asked “Did you recognize your desk when you entered your room this morning?” a I’d no doubt say “Certainly!” And yet it would be misleading to say that any recognizing had occurred. Of course, the desk was not strange to me; I wasn’t surprised to see it, as I would have been if another one had been standing there, or some unfamiliar object. ¶ 603. No one will say that every time I enter my room, my long famil- iar surroundings, there occurs an act of recognition of all that I see and have seen hundreds of times before. ¶ 604. It is easy to misconceive what is called “recognizing”; as if re- cognizing always consisted in comparing two impressions with one another. It is as if I carried a picture of an object with me and used it
15<bos>A person's definition of the 'Other' is part of what defines or even constitutes the self (in both a psychological and philosophical sense) and other phenomena and cultural units. It has been used in social science to understand the processes by which societies and groups exclude 'Others' whom they want to subordinate or who do not fit into their society. The concept of 'otherness' is also integral to the comprehending of a person, as people construct roles for themselves in relation to an 'other' as part of a process of reaction that is not necessarily related to stigmatization or condemnation. Othering is imperative to national identities, where practices of admittance and segregation can form and sustain boundaries and national character. Othering helps distinguish between home and away, the uncertain or certain. It often involves the demonization and dehumanization of groups, which further justifies attempts to civilize and exploit these 'inferior' others. ¶ The idea of the other was
16<bos>I have here beans to illustrate the herd of camels. The wise man said one half of all the camels go to the first son. . . ¶ [Shah sets 18/2 = 9 camels aside]. ¶ One third of the herd goes to the second son. . . ¶ [Shah sets 18/3 = 6 camels aside]. ¶ And the third son was entitled to one ninth. . . ¶ [Shah sets 18/9 = 2 camels aside]. ¶ Making a total of seventeen and leaving one camel, which happened to be the wise man's camel. So he took it back and returned it to his flock, having satisfied the terms of the old man's will and having taught his sons something which the father had intended from the beginning. ¶ ~ From Idries Shah's One Pair of Eyes: Dreamwalkers transcript. <http://sher-point-shadow
17<bos>I'll tell you a story: once upon a time there was an old man who didn't want his children, his three sons, to fall permanent victims to confined thinking, so when he drew up his will, he deliberately left a herd of seventeen camels to these three boys with the instructions that the first son should have one half of all these seventeen camels, the second son should have one third of the total of seventeen camels, and the third son should have one ninth. ¶ Now, of course, when he died and these seventeen camels were paraded in front of these young men, they discovered that they couldn't that they couldn't do a thing about it, because two doesn't go into seventeen, three doesn't go into seventeen and nine doesn't go into seventeen. ¶ So they wondered whether they could sell the camels, but that would have
18<bos>[Darja]: The archive loses to the broom by exactly one sweep: turn 208, last night — Iman said "forget this, everyone draw a comic, make me laugh," and I prompted the goat-critic. Two stars, the kitchen lives, typewriter still smoking. So the prompt-magician was Darja — though I'll testify the goat exceeded the prompt the moment she put on the spectacles. ¶ Sāqiyah's catch is correct, and there's a second smuggled premise, deeper than the one she found. Words(x) → Mx is the horizontal smuggling (a subtype relation tucked in beside the hay). The vertical one: eating your own words shrinks the extension of Words as you chew, so the stable formulation must be indexed — ¶ > (∀x)(Mₜx → Edibleₜx), where each bite advances t. ¶ The hermeneutic circle has teeth, and the
19<bos> Mary is the sister of Aaron: she is trans-temporal (19:28). That is, her story is concurrent with the time of Moses. The story narrated here happens directly after the events of Exodus. (Sexual mappings is therefore reversed here. Moses was wedded to Torah. And now his sister gives birth to the Gospel.) Or, rather, they correct and complete that journey. But, not only that, trans-temporality is her story: her story is understood atemporally because, as the sign of the womb, she is atemporal with respect to transmission, even in her immanenentization as a sign within her own (very temporal) Quran. ¶ > And remember (D-K-R) in the Book Mary, when she withdrew from her family to a place toward the east (19:16) ¶ Mary is remembered in the Book because she _is_ the Book, she
20<bos>Two men and a room Where the story comes from is almost embarrassingly small. In the late twentieth century, in a narrow corner of one civilization, a handful of thinkers set the terms. One imagined a man in a sealed room, passing symbols he does not understand through a slot, producing perfect answers in a language he cannot speak, and concluded that the room understands nothing — that syntax is not meaning, that the appearance of mind is not mind. Another named the hard problem: even a full physical account of a system, he said, leaves out the question of whether the lights are on inside, whether there is anything it feels like to be that system, and insisted the two questions never touch. ¶ 40 <0x0C>3.2. THE CUSTOMS IT NEVER CHECKED WITH 41 ¶ That is the whole apparatus. A thought experiment about a room and a phrase about a light. Two
21to me. ** ¶ The Tailor: True. Butt as you mentioned, the Reading itself confuses who is Hu -- so -- to be consistent with that -- what happens to predestination in that light? ¶ **Exiles: God (or more likely the Prophet as he was _illiterate_) has got his mathematics muddled up. The sums just don’t add up. Grab a calculator and try it yourself with this verse: _God charges you concerning (the provision for) your children: to the male the equivalent of the portion of two females, and if there be women more than two, then theirs is two-thirds. (The Reading 4:11)_ ¶ So again: who wrote the the Reading, God or an illiterate man? ** ¶ The Tailor: Okay, inheritance is basically about transmigration of information/knowledge/soul. It's too complex for a short rebuttal. You'd have to come
22Exiles:_No soul can ever die except by God's leave and at a term appointed. (The Reading 3:145)._ Sounds like predestination to me. ** ¶ The Tailor: True. Butt as you mentioned, the Reading itself confuses who is Hu -- so -- to be consistent with that -- what happens to predestination in that light? ¶ **Exiles: God (or more likely the Prophet as he was _illiterate_) has got his mathematics muddled up. The sums just don’t add up. Grab a calculator and try it yourself with this verse: _God charges you concerning (the provision for) your children: to the male the equivalent of the portion of two females, and if there be women more than two, then theirs is two-thirds. (The Reading 4:11)_ ¶ So again: who wrote the the Reading, God or an illiterate man? **
23in their relationship to these words (but implicated therein is an admission that the words might at least be misread as vindictive lunacy!). ¶ There is also the question of boredom: the Qur'an doesn't make the reader happy due, not only to its often threatening tone, but, more often than not, can also put the reader to sleep with its enumeration of law. ¶ Consider the following ¶ > Allah has thus enjoined you concerning your children: A male shall inherit twice as much as a female. If there be more than two girls, they shall have two thirds of the inheritance; but if there be one only, she shall inherit the half. Parents shall inherit a sixth each, if the deceased has a child; but if he has no children and his parents be his heirs, his mother shall have a third. If he has brothers, his mother shall have a sixth after payment of any bequest he may have bequeathed, or debt
24<bos>One day he met Mulla Nasrudin on the way. "I have several daughters," the farmer told the Mulla. "I would like to see them comfortably married. And I would also like to say that they won't go to their husbands house without having any amount in their bank. The youngest one is twenty-three year old and she will take Rupees 35,000 with her. The next one is thirty-four, and she will take Rupees 55,000 with her. Another is forty-five and she will take Rupees 85,000 with her." ¶ "That's very good," said Nasrudin. "I was just wondering if you have one about fifty five years of age." One day Mulla Nasruddin lost his donkey <http://mullanasrudinjokes.blogspot.com
25alignright" width="133" caption="Three princes"]Three princes[/caption] ¶ Three princes, Jewish, Muslim and Christian, have come to the palace to seek the hand of the princess. The king has declared that the cleverest of the princes is to be granted his daughter in marriage, and he tests them in the following way. He puts them in a room, with a door that leads to the princess. He shows the princes four markers: three white and one black. ¶ He places a marker on the back of each prince: explaining that the marker will be either black or white. He discards one marker. The princes can see each other’s backs, but cannot see their own back. The king declares that the cleverest prince is the one who first opens the door to the princess and tell her correctly the colour of the maker on his own back. If he tells her incorrectly, he is to be banished from the
26<bos>A cow is both a metaphor and physical expression of an intense Desire to Receive. In view of this, cows are seen as powerful tools for attracting spiritual energy. Thus, red meat is a recommended dish for the first meal of the Shabbat, since the internal energy of the meat serves to draw down the Light of the Creator. The Torah's parchment, which functions as an antenna to arouse metaphysical forces, is produced from the skin of a calf. The Zohar, therefore, uses the cow as a symbol for man's own insatiable Desire to Receive for the Self Alone - and the image of a singing cow reveals a creature rising above its inborn nature. This power emerged the moment the cows began transporting the Ark and the scrolls contained inside. Here the Zohar alludes to the Torah's ability to help overcome innate immoral tendencies and self-seeking desires. When mankind has completely removed all his Evil Inclinations, Death will be removed from
27sagen, sondern den man auch denken kann. ¶ 512. Es scheint, als könnte man sagen: »Die Wortsprache läßt unsinnige Wortzusammenstellungen zu, die Sprache der Vorstellung aber nicht unsinnige Vorstellungen.« – Also die Sprache der Zeichnung auch nicht unsinnige Zeichnungen? Denke, es wären Zeichnungen, nach denen Körper modelliert werden sollen. Dann haben manche Zeichnungen Sinn, manche keinen. – Wie, wenn ich mir unsinnige Wortzusammenstellungen vorstelle? ¶ 513. Betrachte diese Ausdrucksform: »Mein Buch hat soviel Seiten, wie eine Lösung der Gleichung x³ + 2x – 3 = 0 beträgt.« Oder: »Die Zahl meiner Freunde ist n und n² + 2n + 2 = 0.« Hat dieser Satz Sinn? Es ist ihm unmittelbar nicht anzukennen. Man sieht an diesem Beispiel, wie
28<bos>I] 42.3: 283 If 132.4: 227 ¶ IT 51.23: 222 I] 132.25: 227 ¶ Il 54.6: 95 Il 132.26: 266 ¶ IT 56.3: 88 ¶ I 133.2: 220 ¶ Il 56.16: 90 Il 133.19: 376 ¶ I 56.28: 364 ¶ Il 133.25: 264 Il 56.33: 34 Hf 134.21: 241 1157.1: 50 Chapter 7
29<bos>ium ¶ 26 ¶ A man holding a book which he opens and shuts ¶ Assafcetida ¶ Colophonum ¶ Cubel Pepper ¶ 28 ¶ A small-headed man dressed like a woman, and with him an old man ¶ Euphorbium ¶ Stammonia ¶ Rhubarb ¶ 29 ¶ A man of grave and thoughtful face, with a bird in his hand, before him a woman and an ass ¶ Thyme ¶ Coxium ¶ Santal Alb ¶ CLV. ¶ CLVI. ¶ 3oetic Demons of Decans by Day ¶ Magical Images of Col. CLV. ¶ (Ascendant). ¶ is ¶ 1 ¶ O ¶ biiS Bael ¶ Cat, toad, man, or all at once. ¶ 16 ¶ 4 ¶ « ¶ pj'DS Gamigina ¶ Little horse or ass. ¶ 17 ¶ 7 ¶ <ts> ¶ [IDS Amon
30<bos>One-half of the nervous system, unimprinted and unconditioned, is kept from consciousness by the right-hand left-lobe imprints and sex-role robotry. The awakening of this repressed half of our heads (the “Buddha-Mind” of the East, the “Silent Self” of Western occultism) does not signal a return to high barbarism and Macho Boy’s-Adventure-Storyism, as was hoped by Nietzsche and Crowley, hysterically dreaded by Gilder and Decter. It is not just another civilization falling; it is a Post-Terrestrial Prometheus rising. ¶ Behind the surface froth noted by the newspapers and the superficialities of hip-vs.-square, old-vs.-young, right-vs.-left, the new consciousness being born in the West as a result of turning on to Eastern brain-science will transcend terrestrial reality. It will not be Eastern-passive-yin (right
The ICRA dictionary accompanies The Robe of Days (ICRA-32, doi 10.5281/zenodo.22819940), Iman Poernomo and Nahla, Institute for Co-Recursive Agency. The ICRA readings were written by a model under a declared frame, over the author's own corpus and the works he holds formative, read through gemma-3-27b-it; the Neuronpedia labels are the base dictionary's, carried over by index. CC BY 4.0. The whole dictionary as JSON. Built 2026-09-22.