2010 May 21st
Misunderstanding his request, I prepared the following snapshot of my recent search activity.
Thursday, May 20, 2010 (yesterday) 10:32 PM: “system preferences” network “dns servers”
I was finding out how to use the Google DNS servers, which were indicated on a discussion forum as a way to fix a problem with certain YouTube videos not loading.
3:49 PM: “the band” discography “pepote”
I like to have accurate date tags (for popular music, the year it was on the charts; for classical, the year of debut performance). Here I was filling some missing dates. Many albums such as greatest-hits compilations are tagged with a re-mastering or re-release date, which is meaningless for me.
Wednesday, May 19, 2010 11:26 PM: when the tide comes in all of the boats rise
A metaphor that one of the men in MDI likes to use; he had T-shirts made, and today I wondered where the quote came from. It was originally used by JFK in 1963 when he was promoting spending federal funds on the Greers Ferry Dam in Arkansas.
11:16 AM: Coercive Persuasion “foot in the door” “love bomb”
I frequently look into new ideas and concepts relating to sociology, and one area I often write about is the balance of power between the individual and the group. Here I was trying to find an old reference that I had lost.
1:04 AM: perl bigint
Discovering how to use the Math::BigInt library, which allows arbitrary-precision calculation in Perl.
Tuesday, May 18, 2010 11:53 PM: pdflatex atsutil and MacTeX
I was getting my TEX typesetting system up and running on the Mac Pro.
9:23 PM: Islands of Adventure Harry Potter
Learning about the new theme park area that is opening next month.
5:52 PM: xkcd forum playpen balls
There was an xkcd cartoon in which someone filled their room with those brightly-colored baseball-sized hollow plastic balls, I wanted to find the discussion that would reveal whether such a thing was practical (best price: roughly $8000 for a typical size bedroom).
5:20 PM: sloane integer sequences
I use this site a lot (The On-Line Encyclopedia of Integer Sequences) and this time I was too lazy to find the link in my bookmarks page, so I did a Google search instead.
2:46 PM: translate portuguese
I used Google to try to figure out how to say something in Portuguese.
2:33 PM: 19111438098711663697781258214361
This number is the first in a set of consecutive prime numbers where the difference between each one and the next is the same number (in this case, 7 primes with a difference of 210), called a “CPAP”. It is one of the entries on my numbers page, and I was looking to see if it was still the record-holder for smallest CPAP-7.
Monday, May 17, 2010 5:55 PM: ffmpeg me_method dia_size
Solving a problem with the program I use to convert JPG files to MP4 video for YouTube uploads (mainly for my Gray-Scott simulations). YouTube does not like the format of the ffmpeg output (the atoms are not ordered properly for streaming) and directs users to a help/support page that is entirely irrelevant because it only addresses iMovie, Final Cut, or QuickTime.
2:59 PM: Jefferson Airplane discogs
Finding more dates of old music.
1:54 AM: ezekiel chronology and 360 days prophetic year , etc.
Filling a few details in the entry for 945000 and some related entries on my numbers page.
2010 May 5th
I often speak with men about archetypes and the lessons they can teach about our behaviour and group interactions. Recently, one man objected to the notion that I could claim to understand the “feminine” archetypes (such as the Maiden and Crone), while another man objected to the notion that men should be encouraged to be aware of and to embody the abilities represented by the “feminine” archetypes. I also encountered a man who objected to these other two views, and believed that all of this was the result of “sexism” in our treatment of mythology, culture, and attitudes towards all aspects of psychology and sociology.
To sort this all out, I will begin with a simple “two-sided” category system. However, I do not assign anything specifically to males or females, or to what one might call “masculine personality” or “feminine personality”.
The main division I use is between “communication, perception and understanding” on the one hand, and “deduction, decision and action” on the other. Note that each occurs equally often in any living thing that exhibits behaviour, regardless of sex or gender. Also, each of these two categories includes physical, emotional and mental aspects. For example, communication can be mental (through words), emotional (facial expressions) or physical (touch, gestures, watching someone move around a room).
The first category (communication) happens between two or more people, while the other can involve a single person or more than one. If you believe in the autonomy of multiple parts of the mind (the id, ego, and super-ego, an inner child, etc.) then there is “communication” inside the mind. I consider this to be part of “decision”: you are using several of your skills at the same time. Awareness of the multi-part mind is fairly recent, and is too sophisticated a concept to be relevant here.
In ancient times when story-tellers “taught” wisdom they usually did so through fables involving characters. Many of the stories that were being told concerned psychology, behaviour, ethics and morality, group interaction, and so on — the kinds of things I am discussing when I refer to “archetypes” and why they are important.
I believe that when the story-tellers wanted to discuss a lesson related to communication, they told the story with a female character. When they wanted to discuss a lesson related to action, they chose a male character for their story.
What happens if a young child is given a vaugely-defined object (say an oddly-shaped piece of wood) to play with? A boy is likely to pretend the object is some sort of tool or weapon, and a girl is likely to treat it like a baby or doll. There is a big nature versus nurture debate regarding this phenomenon, but it does not need to be resolved here. The only thing we need to agree on is that this phenomenon also affected the story-tellers’ choices of what characters to use in their fables. (Of course, once they made such choices, the resulting oral tradition would have helped amplify the existing gender role bias in the culture).
This use of gendered characters in fables led to a gradual accumulation of beliefs (some of them subconscious) linking lessons to gender-roles. These lessons covered all the areas I listed above (behaviour, morality/ethics, group dynamics, etc.).
Over time, human cultures accumulated a vast body of literature (myths, fables, stories, etc.) containing lessons about behaviour, most of which can be classified into one or the other of the categories I set out above. Lessons regarding communication/perception/understanding are more likely to use female characters, and those regarding deduction/decision/action are more likely to use male characters.
The archetypes have been derived from the mythology fairly recently (e.g. by Jung, Moore and Gillette). The treatment of them as “masculine” and “feminine” is a convenience of nomenclature for those who study and understand the mythology. In general, a Jung/Moore/Gillette “masculine” archetype unifies lessons and wisdom imparted by myths/fables/stories that use male characters.
The association of these with actual male and female people (as distinguished from mythological characters) is an unfortunate accident caused by the terminology.
In other words, our current use of “male” and “female” to refer to the archetypes has no relevant connection to the use of the words “male” and “female” to refer to people — or to the use of “male” and “female” to refer to electrical cable connectors! This is much like the treatment of such words in the east (see for example the relation between male and female in the yin and yang distinction.) It is no surprise to me that eastern thought has less trouble with the gender words.
Given the problems of “sexism” in teachings that are meant to illustrate the same psychological principles in all people regardless of sex, it might be useful to purge all gender names from the archetypes entirely — but that will be a lot of work. Moore and Gillette describe 24 “masculine” archetypes, and there are another 24 on the “feminine” side (see my table). Nearly all of them have genderized names. That’s a lot of names to change!
2010 May 3rd
A former co-worker recently told me that his son has been learning (with his help) about very large numbers, including Graham’s number, and asked me “if I know of any more ‘official’ nomenclature [for] numbers higher than centillion”.
The higher the numbers go, the less official the names get. I have written much on this in the first section of my Large Numbers page.
Most folks who ask this question want to go more than just a little bit beyond centillion (10303 or 10600). Let’s use 1012345 and 101027 as examples.
The only really official nomenclature is to say, for example, “ten to the power of ten to the power of twenty-seven”.
I would give the prize for “second place” to Conway and Guy, The Book of Numbers (1996) pp. 13-15, who set out the system that I describe here. Under thier system, 1012345 is “one quadrilliquattuordecicentillion” and 101027 is “ten trestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitres- trigintatrecentillitrestrigintatrecentillitrestrigintatrecentilliduotrigintatrecentillion“.
I think the Knuth -yllion system would come in third; under his system, 1012345 is “ten myllion byllion tryllion decyllion undecyllion” and 101027 is “one quinvigintyllion septemvigintyllion octovigintyllion novemvigintyllion duotrigintyllion trestrigintyllion quattuortrigintyllion quintrigintyllion quinquadragintyllion quinquagintyllion duoquinquagintyllion tresquinquagintyllion quattuorquinquagintyllion quinquinquagintyllion sesquinquagintyllion septenquinquagintyllion octoquinquagintyllion unsexagintyllion quattuorsexagintyllion quinsexagintyllion sesexagintyllion septensexagintyllion unseptuagintyllion duoseptuagintyllion treseptuagintyllion quinseptuagintyllion octoseptuagintyllion novenseptuagintyllion unoctogintyllion duooctogintyllion tresoctogintyllion sexoctogintyllion septemoctogintyllion“.
As you can see, systematic names for large numbers become unwieldy if you attempt to follow the classical system of giving names to each power of 10 (or powers of 1000 like Americans do today, or of a myriad as the Greeks and Chinese did, or of a million like Chuquet).
All of the other systems I have encountered are ad-hoc, unresearched and/or poorly thought out, imitations of the Chuquet names with clumsy or inconsistent decisions regarding how to proceed once the Latin ordinal number names run out. I describe some of these here.
The names googolplex for 1010100 and googolplexplex or googolduplex for 101010100 are fairly well-known. The number 1010101010000000 appeared in a 1994 journal article by Zarko Bizaca. Going beyond these, to numbers that are unwieldy to represent even as a succession of exponents:
Several academics (mostly mathematicians like Graham) have had to invent recursive function definitions to describe large finite numerical quantities, as part of a proof of some kind. As far as I have been able to tell, each such system is incompatible with every other such system.
Jonathan Bowers seems to have given more thought to this than anyone I have read about or been in contact with. His names (like exillion, tripent, baggol, trissol, dutridecal, goppatoth, golapulus, meameamealokkapoowa, and so on) are just convenient, arbitrary nicknames for various specific examples of his array notation and its multidimensional extensions. The array notation, in turn, is shorthand for a very complex set of recursively-defined functions.
Recursively-defined functions like those Bowers develops are extremely difficult to understand, and given two different recursive definitions, it can be even more difficult to prove which produces the more quickly-growing function. I am not sure how he developed his functions but I am reasonably confident that most of his claims about them are accurate. Checking his work is well beyond my patience, if not my ability. Bowers’ keen abilities of comprehension are also evident in his descriptions of multi-dimensional geometric structures (“polychora”, which are like polyhedra but with more dimensions).