Vasarely

Googology Wiki

Googology Wiki

the large number encyclopedia

How many counting numbers are there,
if there is an infinite number of them why are they all finite?
—Sbiis Saibian

Googology Wiki is a free online encyclopedia and community about numbers large and small.
(But mostly large.)

http://googology.wikia.com/wiki/Googology_Wiki

This is a great website to see what's going on in the large number community.

It is worth remembering that large numbers are not so much about magnitude but more about information patterns and colourful uses of language.

There is a surprising amount of information on the Googology Wikia.

Another place that has a lot of information, discussion,
comparison, discovery and invention is the forum game
on the xkcd website, known as My number is bigger!

So much creativity and thoughtful energy has gone into this enigmas and diversions forum game

So I just want to say a warm thank you to all the contributors and supporters.

It is a site I browse every now and then and it is fun to see the mixture of styles and approaches to the topic including some pretty serious and well informed contributions as well as some more light hearted forays into the topic, so many ideas, impossible to find the winners for this game.

On the Eretrandre website I have explored mostly the information patterns associated with large and complicated numbers, but they are only indirectly to do with the forum game, and are more an artistic and accurate idea (modulo well defined interpretations) about how to find a system of patterns, that can be used to understand generalised recursion, especially via COH expressions, where functional composition and hyperoperations come together. COH = Compositions Of Hyperoperations.

The quote above from Sbiis Saibian is actually quite profound for the truth about finite numbers and the concept of infinity, my understanding is, it is saying that considering, or if, there are an infinite number of finite numbers, isn't it a kind of common sense that to describe all of them as finite is glossing over the genuine variety of finite numbers that really exist in conceptual reality.

One of the important scientific contributions has been to clarify the notion of domains of discourse in mathematics. I have tried to elaborate this with my description of the four main realms or regions of the natural numbers or counting numbers (details on the Eretrandre website)

Briefly speaking, the first is the normal everyday realm, the second is the realm of most of number theory, large prime numbers, and combinatorics, the third realm are some of the non trivial stages of the Fast Growing Hierarchy, and the organic information patterns associated with COH expressions, the fourth realm being the numbers such as Graham's number.

Amateur and professional mathematicians can find this new distinction a useful and practical way to classify the natural numbers, complementary and supplementary to the important classifications by Robert Munafo.

www.mrob.com

Professionals and amateurs should mutually recognise each others ideas and let the quality and durability of the ideas be the characteristics to influence and inspire future mathematicians.

username MikeSmith

www.eretrandre.org

transference (hyper9, ordertype9)

Logos ~ cssmiley, ebcard, yinyangart

silly 12-),4 =,',> 24-),25

quagmire

camouflage98

9 dreamy ways

third realm trio ~ peanuts, spice39, 8almost8

 

 

quilt

tweedeedum

amica ~&~ amore

nebu1ou8

trip 227

digicontour ^and* serene60

The light in a bulb

         graph the answers to n^n=a  where  a=d^(e^f)  from the sets  {2,3,4},  {2,3,5}  and {3,4,5}

Functional Type Shifting Patterns - FAQ

Functional Type Shifting Patterns

FAQ  for mathematicians and scientists

I am happy with the nice and easy ( … ) Why did you have to complicate it when the numbers produced are too esoteric to be useful?
My answer is like this, if mathematicians accept Graham’s number, then it is reasonable to accept compositions of hyperoperations. The ironic thing is, understanding compositions of hyperoperations seems to make Graham’s number look even more unreal. As far as the linear notion of ellipsis ( … ) this is fine and the best way to do most of the normal problems of maths, so mathematicians don’t need to fear about interference with the usual techniques and notations.

But the formulae are useless as far as I can see.
They are mostly too unwieldy for the arithmetic used in number theory. Some borderline examples are laddered exponents (Conway and Guy) where comparisons can sometimes be made. The more complicated examples exist as well-defined concepts, and are constructible, and information flow patterns can be compared. They have their own internal logic and character, and can be studied from that point of view. The logic uses the natural continuation of the principle of iterated exponentiation on smaller natural numbers that leads to tetration and so on. The patterns are number classes, and the visually displayable patterns form a metaclass of classes of numbers. The number classes are interesting to understand and imagine, and usually one has the feeling of peering into math infinity via these number representations.

Is it math or pseudomath?
If you are a strict ultrafinitist and think that numbers beyond a googol or a googolplex are silly to consider there’s no need to take an interest in the topic. If you like big numbers you probably could like the pattern concept. If you are a set theorist, it is interesting to see a new kind of understanding of hyperoperations beyond the already known recurrence relations and current information on Wikipedia about hyperoperations. In a way, the patterns are a conceptual exploration of the so-called Frivolous Law of Arithmetic which says that almost all numbers are very, very large.

Are the patterns arbitrary with respect to their geometric form?
No. To fully explain the specific details about the patterns would take a lot of explanation, and the settled-upon form is the most common sensical and extensible.

Are there new results to do with these patterns?
Yes. The new results were discovered from a careful analysis of the properties of these patterns.

Should the patterns be taught at all?
They could be taught to postgraduate students with an interest in the foundations of maths.

Why do you need 19 animations?
The 19 animations cover aspects such as syntactical components, folding patterns, computational pathway, syntactics of pattern extensibility, pattern-formula correspondence, number class boundaries, transitional sequences, coordinate systems, relation to epsilon numbers and compositions of patterns.

Online Papers are on the Eretrandre website  ( "Mike Smith" )

 

B3 or 21B

Naropt -^ & -> Caropt

mopics 4 doh

abstract @ art $ pics

 

Ambient music from Wikipedia.

Ambient music from Wikipedia using the beautiful Lucida Calligraphy font.

http://en.wikipedia.org/wiki/Ambient_music



Ambient music ,
  unlike other forms of "background music" ,  is intended to
   enhance acoustic and atmospheric idiosyncracies in the sound environment .


Whereas conventional background music
        is produced by stripping away all sense of doubt and uncertainty
     ( and thus all genuine interest )  from the music ,
            Ambient Music retains these qualities .


And whereas their intention is to "brighten" the environment
                 by  adding  stimulus  to  it
      ( thus supposedly alleviating the tedium of routine tasks
          and levelling out the natural ups and downs of the body rhythms )
     Ambient Music is intended to induce calm and a space to think.


Ambient Music must be able to accommodate many levels of
           listening attention without enforcing one in particular ;
      it must be as ignorable as it is interesting .


As a genre ,  it originated in the United Kingdom at a time when
       new sound-making devices such as the synthesizer ,
         were being introduced to a wider market.
Brian Eno was an early pioneer of ambient music.
The Orb and Aphex Twin gained commercial success with ambient tracks.
Ambient compositions are often quite lengthy ,  much longer than more popular ,   commercial  forms of music .
   Some pieces can reach a half an hour or more in length .

Homage to Georges Perec novel “A Void”.

Homage to Georges Perec novel “A Void”. Some pretend reviews I made up with no letter “e”.
( Note: The letter “e” is certainly not in the least redundant or useless in English being the most frequent letter in everyday reading matter, such as novels, magazines, poetry, newspapers, science articles, etcetera, however, it is surely quite entertaining to contemplate a written passage, sentence, question or anecdotes that have no “e” in whatsoever! The evidence for widespread employment of the letter “e” is overwhelming indeed! I hope your desire for enlightenment is to be discovered yet once more and you get a few chuckles from this attempt at a homage to the wonderful Georges Perec. Let the pretend reviews of the novel “A Void” commence… )

A joy to my cat !

Toad and frog find it amazing !

Why did I think it was so lovingly found upon my pillow ?  God only knows !

This book is my fav book of all books in my cupboard.

An amazing and fun book to think about.

I could think about it again if I had a will of mind that might work

This man who actually put ink to words on book has thought of a book to bright up my days and so many folk will nap happy during night although it has rain on occasions

You should buy it now

I wish it was classic food in midst of all minds

So much fun in so tiny amount of room

Dayvan Cowboy by Boards of Canada is a good comparison for flavour of this book

It warms pants off bottom part of my body and my foot swings in rhythm and sympathy

Around all nooks and cranny of our world you will find a similar cry of yay yay for this cunning book !

My pals all told my brain softly this book would spark off fantastic mystical trips of cloudy imaginings and okay, aha, right on, bang on, many thanks to this author J

Music do good things for your mind and so do good books, this is as if six books for cost of two books Good fun, buy now quickly, as soon as you can.

Point of fact: this book is nothing short of a brilliant story about amusing goings ons.

This book is a trusty companion for ordinary car trips and if going by train you should own four that is also for your many pals who will accompany you. Many good thoughts in this book. A must buy.

I couldn’t find a word or paragraph to thoroughly suit this magnum opus. Congratulations !

My lizard at back of bathroom is sitting on this book. Soon I will want it again. So off you go lizard!
I want my book back now!

On cold days this book lights up warmth in your body. It is highly thought of for many flights of fancy that you can find by flicking through from start to finish.

Mostly amusing, droll in parts, funny in many parts, round about now I would say it rocks !

I couldn’t put it down. So many ribs in my body with vibrato I laugh and laugh with no control.

Many books can pass your mind as you focus on day to day tasks. This was not such a book. It had my full and unanimous synaptic synchrony so I could not do anything apart from word to word, paragraph by paragraph, from this thought to that thought, follow this book from front to back.
I am a class instructor and always say to my kids this book will haunt your mind in a good way.
“It flows as a brook from plant growths to rocky outcrops” as said famous William Wordsworth.

In my silly and idiosyncratic fashion I want to talk about this fascinating book as I am looking at it right now and also say a bit about my odd family so I shall start now…
I am sitting comfortably on a plastic barstool with my lackadaisical goldfish swimming around its liquid surroundings with fluffy moss lightly touching this dirty glass bowl and soon our adoring, purring cat is waking up from a long nap, and our dog is barking and woofing as usual, and our studious and dutiful mum and charming good old dad around this “wood oval thing” as I usually call it, laughing at our mutually ridiculous situation, I try not to goofball too much, and hold onto my dignity, and by and by, for this, first food of day, I slowly swallow chunks of hot yummy toast with warm apricot jam and sip cool coca cola and all during this usual activity I casually look at this book with clarity and cautious optimism and I grin a lot, for it is not arduous at all, my nostrils flaring with anticipation, and I brush my slightly long chin and facial hair away from my mouth to avoid crumbs from spilling on top of it, trying not to distract my thoughts away to various crucial tasks that should also occupy my stamina and waking hours of advancing morning, but strong sunlight through shiny window is surprisingly stifling and muggy hot for spring so I stay sitting in my chair nibbling crusts of toast, and doing what I want, which is gradually making my way through this sad, almost sorrowful but still absorbing and captivating and thankfully occasionally funny and hilarious story.

I’m sorry, today my mood is not so good or arrogant.  I want to outsmart my unfair family who say abruptly “you don’t know a trick that could kill you” so I must play tiddly winks with gusto and aim to win at all cost. At conclusion of this parlour activity I can sigh victoriously for without a doubt I won round and fair.  Why don’t you try your hand with us at Backgammon or Go if you still drunk with victory air? It’s not that fair. I am all of human history tiddly winks primo conductor and obviously world champion and this I cannot fathom.  So I hastily gulp light brown alcoholic liquid in my glass to bottom, not spilling a drop and my spirits automatically flow with radiant pinkish flush to my skin.  I turn my thoughts to a classic book known as “A void” that is famous for living without a particular typological symbol … surprisingly, various voluntary linguistic constraints imply I cannot truly say or shout out this symbol … and as I am now totally worn out and my luck has probably run out and my brain is going to cloudy mush … and so taking a longish vacation or holiday as usually said in Britain is now a good thought for my mind body and spirit.  At last, hip hip hooray, for my family finally saw a sad clown in my mind so my family did a mindful  u-turn and justly said “okay not guilty, no kill you today” and grin a bit at my stupid and amusing antics.

Well I hope these pretend reviews garnered some guffaws   J

thought hope wish peace and goodwill

Review of Fields of Dreams by Theta Realms

When I heard this, the first time I thought, this is interesting, it sounds new age but more melancholy and introspective, it has wavery sorrowful sounds and beautiful touches of soundwashes that combine in a language of it’s own, the music defines it’s own language as it progresses and although often slow moving and breathing peacefully it finds a way to reassert itself with grace and tenacity, every sound and timbre is masterfully positioned to enhance the motifs and variations the gradual building up to cascading sounds of a most beautiful character I haven’t heard in other music and that’s a sincere complement, because since The Cure wrote their subliminal masterpiece All Cats Are Grey from the Faith album I haven’t heard such deep reflection on how to peacefully cope and transcend daily struggles of life with a heart full of acceptance kindness and sharing goodness. This is a composition that is so subtle in musical style that it helps to be listened with headphones at the correct volume as Theta Realms suggests. It also shares with The Cure the art of simple and effective melodies that softly rise above the etherreal timbres. I wish Theta Realms future success and to journey well and I hope that this composition can be seen as not only wonderful binaural beats but picturesque ambient drum and bass and moreover I hope some classical afficianados can appreciate and give international recognition to this world class electronic music composition.

MULANEPT patterns.

EPT = Exponential Power Tower
NEPT = Nested Exponential Power Towers
LANEPT = Layered Nested Exponential Power Towers
MULANEPT = Multi Layered Nested Exponential Power Towers

Compositions of hyperoperations are very big and complicated natural numbers.
They can be represented in terms of exponential power towers.
These number representations are called MULANEPT patterns.
It is interesting to create mulanept patterns.
All you need is a spreadsheet such as Excel with a color palette.
My papers are on the website www.eretrandre.org
Mostly, eretrandre is about tetration and complex numbers.
My area of interest is how to represent the most complex of all natural numbers
in terms of the exponential function on natural numbers.
This is via the hyperoperations:
tetration, pentation, hexation, heptation, and octation, that is
hyper4, hyper5, hyper6, hyper7, and hyper8
and compositions of these hyperoperations.
It's awkward to describe and talk about these numbers,
but with practice, they are understandable and fascinating.
These number representations use a system of non-standard tiling patterns.
Alister "Mike Smith" Wilson.