For context, one of the main focuses of my early education was in mathematics, and though my career has departed into the semi-related field of computer science, not much has changed about my familiarity and interest in numerical curiosities. As well as that, my university studies led me down the paths of linguistical intrigue, Japanese didacticism, and East Asian studies. So anything that is at the intersection of the Venn diagram of all four topics would certainly call my attention.
I don't know exactly when I first encountered this particular topic, but perhaps it was semi-contemporaneous with my long-ago post on Japanese ten-power numbers in relation to intuition about currency-conversion and various culturo-economic touchstones for how much 一兆円 can get you (answer: probably still a 新幹線 line but I haven't bothered doing any additional research to account for inflation or the like). But in any case, there are certainly much bigger numbers than (一兆 = 一(万万万) = (10 000)3 = 1 0000 0000 0000 = 1,000,000,000,000). For the sake of convenience going forward, I will probably adopt a neutral convention of using direct 10x notation to avoid the need to list both thousand-scale and myriad-scale (fun fact: though used generically to refer to a large quantity and often an assortment, the term 'myriad' specifically indicates 一万 or 104) versions of every large number, especially since we have a long ways to go.
Since I am not wikipedia, I won't go into the full details which, assuming that the ravages of time leave the page unscathed, ought to remain on the relevant page for long enough that future-me doesn't have to reiterate the basics.
This post will be a partial translation, partial exploration, and partial archival post for a resource that has, at some point, become inaccessible due to the impermanence of all things (which is oddly on-topic, and though there probably isn't a notion of the internet in historical Buddhism, is true especially on the internet). The resource in question was hosted at this now-dead URL: http://www.sf.airnet.ne.jp/~ts/language/largenumber.html, but which, thanks to the Internet Archive's Wayback Machine, can still be found here. Even though 100% of my known audience can read Japanese, that same 100% is a native English-speaker and so might prefer that I (viz. they) encapsulate some of the details in a more direct fashion to avoid a language barrier.
I don't know much about the original author 高杉親知 (which, based on Rikai-tan's assessment, is probably read as Chikatomo TAKASUGI), and my interest is not so much in the writer as it is in the post itself, which introduced me to a list of etymologically Buddho-centric Japanese astronomical numbers I had not previously encountered. Since my ability to read through large troves of Japanese is limited severely due to my inexposure and inexperience to such tasks, and my generally stagnant Japanese skills not having been necessarily strong enough even at their peak to read through archaic sources on esoteric topics, I won't really try to claim that I can be sure that the information I am re-presenting is authentic and unbiased, and because the names that we call any given numeral quantity are as much a social construct as most other linguistic conventions (though I do not wish to denigrate any historical significance or importance of the influential origins on words in a languge or from a culture I have no direct personal grounding in), even a misrepresentation of what sequence of characters, what reading thereof, and what etymology they derive from, ought to be relatively innocuous and uncontentious when applied solely to numbers, which are rarely ever victims (except in the case of the famous incident where nine was mercilessly eaten by seven).
Of course, even without the blog-post I am parroting, everyone probably knows by now that the Japanese counting and number-system uses explicit place-markers in the form of fixed-ten-powers as post-positional unit suffixes for any digital scalar (being 1-9, leaving 0 out). In other words, the notation for a number greater than 9 is always the concatenation of each of its significant place-values in highest-to-lowest sequence, additionally omitting the leading 一 (1*) for explicit (i.e. not the unrendered 100) tens-power units up to 千=103. Though there is no direct way of adapting this notion to the standard western conventions in using arabic numerals with purely positional implicit tens-power units, using 0 to fill in the gaps between non-consecutive tens-powers, it is somewhat close to the way that spoken English treats large numbers. "Ten thousand and four" being the way we convey the idea that is rendered orthographically as 10004, rather than reading each digit by itself in sequence like 'one zero zero zero four' (though for pure number-sequences not meant to have place-value associations, like phone-numbers and other pure digit-strings, both Japanese and English fall back on reading the numbers verbatim in sequence without attaching place-value to them, in either respective convention; with some exceptions, of course, most notably that of the emergency phone number in Japan, 110, being referred to in common speech as
I would also like to note for those who either lack the patience or ability (due either to issues relating to the Internet or the task of reading Japanese being difficult or impossible) to read the original post, that the relevant 'values' of large tens-powers are by no means a diachronic immutable, and have had different attributions either between their modern and historical usage, or between multiple 'historical' sources using the same effective kanji-sequence to denote differing tens-power-values. As with many linguistic conventions, especially those that are notational and highly abstract, how big a 'stride' one takes to get from one place-value to the next is entirely a subjective choice when taking an agreed-upon succession of ascending scale to mean a very precise thing, especially when the consequences of making a different choice than someone else are virtually nonexistant, and any choice that at least orders the symbols in the same ascending pattern in an internally consistent and logically sound fashion is basically as 'correct' as any other. So while there are multiple tables even in the one blog-post I am rehashing, with multiple columns denoting sources and the names used for the varying scales, I will try my best to show what is the 'modern accepted' version if multiple interpretations exist, and leave any further digging to whomever reads this and finds it inadequately detailed.
For those tens-power-units that are noted in 'common' usage (though their frequency is almost certainly diminishing the higher one goes up the scale, for understandable reasons), virtually all beyond 万 are effectively raised-powers of 万=104 itself.
子供の頃、算数の教科書で大きい数の単位を知って感動した。日本語は素晴らしいと思ったが、実はこれらは全て中国から来たものだと後に知った。以下は日本語の数の表である。
Which I am, as a rank amateur, choosing to translate as:
As a child, I was moved [tr. emotionally] upon learning the large number-units in an arithmetic textbook. [At the time] I had thought 'Japanese is wonderful', but I later learned that, in fact, these were all Chinese in origin. Below is a table of Japanese numbers.
I am adapting the actual table that follows that opening line into a more compact form, leaving out the additional columns that specify the prefix-scale applied to yield intermediate ten-powers between one myriad-power and the next, and rather focusing on the myriadic powers themselves. I am assuming (perhaps incorrectly) that anyone reading this far is either familiar enough with 一十百千 to not need the additional explainer for these sub-myriad powers, or is in any case only concerned with the big numbers, not those 雑魚 (ざこ/zako). Also note that because all these powers are above 千, when they are actually being used productively to form a proper numeral quantity, a prefix of 一 would be used to denote 1*10x.
(By 'adapting', I really mean translating/editing the original table, as an HTML entity. It's big enough that I would probably want to write a script to generate the HTML from scratch if I were going down that road, and the HTML structure itself is relatively hard to interpret as the IP of the author, since it is very formulaic and merely encapsulates existing facts rather than putting an authorial spin or creative interpretation on them. Not that I am saying 'steal from this person', I just believe that the table itself can't reasonably be designated as a creative opus and consitute what I am doing below as plagiarism. Even the adaptation of the HTML is being done by hand rather than script or, worse-yet, via AI, and is rather painstaking as-is, so I would argue that even if the original is IP, my version is a transformative product.)
| Kanji | Value |
|---|---|
| 104 | |
| 108 | |
| 1012 | |
| 1016 | |
| 1020 | |
| 1024 | |
| 1028 | |
| 1032 | |
| 1036 | |
| 1040 | |
| 1044 | |
| 1048 | |
| 1052 | |
| 1056 | |
| 1060 | |
| 1064 | |
| 1068 |
*: There are multiple notes on this particular entry. The first is that, perhaps due to font or unicode-related issues, the orignal blog-post by Takasugi-shi used a now-dead image link for this character, which I have done my best to find the corresponding Unicode glyph to replicate. The other is that there is an extended aside in the body of the blog itself, that explains that the value of 1024 was originally (and properly, according to Takasugi-shi) designated by the character 「
Now, onto the main point of interest I had in first finding this page, which, like young Takasugi-shi, I was moved upon finding.
無量大数 (muryoutaisuu, lit 'immeasurable large number), at 1068 (or 1088 depending on which system you are employing or what source you are treating as authoritative), is already pretty darn big, I would say. There aren't a lot of things you can reasonably count that high within practical reason, though unlike numbers such as one googol (10100) which are effectively 'monolithic' large numbers without any nearby ten-powers you can ease yourself down to without referencing googol itself, it is just the last turtle in the chain of myriads-of-myriads. But it is by no means the end of the story, and we can go even deeper.
The end of the blog post has a huge ringer in the form of a list of numbers from a Buddhist source that grow unbelievably fast and which quickly outstrip the number of atoms in the observable universe and any other quantity that forms a basic upper-bound on how large a number you would ever need to worry about if you were purely a pragmatist. With the exception of the first number listed in the table that follows,
I might later do a deeper dive into the significance or origins of the names of the numbers given below, which for time constraints, I will merely leave as kanji with hiragana ruby annotations and not transliterate the whole list quite yet (though I might go back and edit this post later for the sake of finishing it more quickly but not leaving it an incomplete product). The majority I believe to be derived from Sanskrit terms with significance rooted in Buddhism, rendered into either Japanese Kanji or Chinese Hanzi (which I may, if I do compile a follow-up post to this one, explore further).
Without any further ado, here is the insane table, this time ripped mostly one-for-one from the revivified blog-page of Takasugi-shi (with the column-headers translated but otherwise unaltered).
| Numerical Value | Lexical Form |
|---|---|
| 105 | |
| 107 | |
| 107×2 = 1014 | |
| 107×22 = 1028 | |
| 107×23 = 1056 | |
| 107×24 = 10112 | |
| 107×25 = 10224 | |
| 107×26 = 10448 | |
| 107×27 = 10896 | |
| 107×28 = 101792 | |
| 107×29 = 103584 | |
| 107×210 = 107168 | |
| 107×211 = 1014336 | |
| 107×212 = 1028672 | |
| 107×213 = 1057344 | |
| 107×214 = 10114688 | |
| 107×215 = 10229376 | |
| 107×216 = 10458752 | |
| 107×217 = 10917504 | |
| 107×218 = 101835008 | |
| 107×219 = 103670016 | |
| 107×220 = 107340032 | |
| 107×221 = 1014680064 | |
| 107×222 = 1029360128 | |
| 107×223 = 1058720256 | |
| 107×224 = 10117440512 | |
| 107×225 = 10234881024 | |
| 107×226 = 10469762048 | |
| 107×227 = 10939524096 | |
| 107×228 = 101879048192 | |
| 107×229 = 103758096384 | |
| 107×230 = 107516192768 | |
| 107×231 = 1015032385536 | |
| 107×232 = 1030064771072 | |
| 107×233 = 1060129542144 | |
| 107×234 = 10120259084288 | |
| 107×235 = 10240518168576 | |
| 107×236 = 10481036337152 | |
| 107×237 = 10962072674304 | |
| 107×238 = 101924145348608 | |
| 107×239 = 103848290697216 | |
| 107×240 = 107696581394432 | |
| 107×241 = 1015393162788864 | |
| 107×242 = 1030786325577728 | |
| 107×243 = 1061572651155456 | |
| 107×244 = 10123145302310912 | |
| 107×245 = 10246290604621824 | |
| 107×246 = 10492581209243648 | |
| 107×247 = 10985162418487296 | |
| 107×248 = 101970324836974592 | |
| 107×249 = 103940649673949184 | |
| 107×250 = 107881299347898368 | |
| 107×251 = 1015762598695796736 | |
| 107×252 = 1031525197391593472 | |
| 107×253 = 1063050394783186944 | |
| 107×254 = 10126100789566373888 | |
| 107×255 = 10252201579132747776 | |
| 107×256 = 10504403158265495552 | |
| 107×257 = 101008806316530991104 | |
| 107×258 = 102017612633061982208 | |
| 107×259 = 104035225266123964416 | |
| 107×260 = 108070450532247928832 | |
| 107×261 = 1016140901064495857664 | |
| 107×262 = 1032281802128991715328 | |
| 107×263 = 1064563604257983430656 | |
| 107×264 = 10129127208515966861312 | |
| 107×265 = 10258254417031933722624 | |
| 107×266 = 10516508834063867445248 | |
| 107×267 = 101033017668127734890496 | |
| 107×268 = 102066035336255469780992 | |
| 107×269 = 104132070672510939561984 | |
| 107×270 = 108264141345021879123968 | |
| 107×271 = 1016528282690043758247936 | |
| 107×272 = 1033056565380087516495872 | |
| 107×273 = 1066113130760175032991744 | |
| 107×274 = 10132226261520350065983488 | |
| 107×275 = 10264452523040700131966976 | |
| 107×276 = 10528905046081400263933952 | |
| 107×277 = 101057810092162800527867904 | |
| 107×278 = 102115620184325601055735808 | |
| 107×279 = 104231240368651202111471616 | |
| 107×280 = 108462480737302404222943232 | |
| 107×281 = 1016924961474604808445886464 | |
| 107×282 = 1033849922949209616891772928 | |
| 107×283 = 1067699845898419233783545856 | |
| 107×284 = 10135399691796838467567091712 | |
| 107×285 = 10270799383593676935134183424 | |
| 107×286 = 10541598767187353870268366848 | |
| 107×287 = 101083197534374707740536733696 | |
| 107×288 = 102166395068749415481073467392 | |
| 107×289 = 104332790137498830962146934784 | |
| 107×290 = 108665580274997661924293869568 | |
| 107×291 = 1017331160549995323848587739136 | |
| 107×292 = 1034662321099990647697175478272 | |
| 107×293 = 1069324642199981295394350956544 | |
| 107×294 = 10138649284399962590788701913088 | |
| 107×295 = 10277298568799925181577403826176 | |
| 107×296 = 10554597137599850363154807652352 | |
| 107×297 = 101109194275199700726309615304704 | |
| 107×298 = 102218388550399401452619230609408 | |
| 107×299 = 104436777100798802905238461218816 | |
| 107×2100 = 108873554201597605810476922437632 | |
| 107×2101 = 1017747108403195211620953844875264 | |
| 107×2102 = 1035494216806390423241907689750528 | |
| 107×2103 = 1070988433612780846483815379501056 | |
| 107×2104 = 10141976867225561692967630759002112 | |
| 107×2105 = 10283953734451123385935261518004224 | |
| 107×2106 = 10567907468902246771870523036008448 | |
| 107×2107 = 101135814937804493543741046072016896 | |
| 107×2108 = 102271629875608987087482092144033792 | |
| 107×2109 = 104543259751217974174964184288067584 | |
| 107×2110 = 109086519502435948349928368576135168 | |
| 107×2111 = 1018173039004871896699856737152270336 | |
| 107×2112 = 1036346078009743793399713474304540672 | |
| 107×2113 = 1072692156019487586799426948609081344 | |
| 107×2114 = 10145384312038975173598853897218162688 | |
| 107×2115 = 10290768624077950347197707794436325376 | |
| 107×2116 = 10581537248155900694395415588872650752 | |
| 107×2117 = 101163074496311801388790831177745301504 | |
| 107×2118 = 102326148992623602777581662355490603008 | |
| 107×2119 = 104652297985247205555163324710981206016 | |
| 107×2120 = 109304595970494411110326649421962412032 | |
| 107×2121 = 1018609191940988822220653298843924824064 | |
| 107×2122 = 1037218383881977644441306597687849648128 |
If any of this stuff is interesting to even one person [other than myself], I'd say it was worth it to keep this list of numbers alive into a new era.
Stay tuned for the announcement of my upcoming incremental idle game where you win if your score reaches 不可説不可説転. /hj.