I chose some logic/Philosophy/Hellenismos quotes to begin: 'Γνωθι μαθων' (Gk., 'Gnothi mathon;' 'Know what you have learned,') 'Σοφιαν ζηλου' ('Sofian zelou;' 'Long for wisdom,') 'Φιλοσοφος γινου' ('Filosofos ginou,' 'Be a seeker of wisdom,') 'Τεχνη χρω' (Tekne chro,' 'Use your skill')--Apollo; Delphic maxims.
    '... examine all things well. Leaving thyself always to be guided and directed by the understanding that comes from above, and that ought to hold the reins.'--Pythagoras (transl.: Firth,) or '... Consider all things well, let reason, the gift divine, be thy highest guide.'--Pythagoras (transl. whom I have not found is known.)

    Mathematics-algorithmics is the combination of trivium #1 (grammar) & 2 (logic,) and (in the case of teaching, I assume,) 3, as well as quadrivium 1 through 4: arithmetic (#1, now perhaps 'algebra,') and the two that use it, geometry and music (in the case of Fourier analysis and also, in certain ways, other temporal math, including algorithmics) and the culmination, astronomy (which is a definition or part of Platonic physics--so-called 'metaphysics,' both spatial and temporal.)

    I have always liked (art, then architecture,) Geometry, which is here first. I also like algorithmics, (which led to my interest in) algebra (which I took long before) and math. analysis.

TOC (Algebra will likely be added: maybe my undergraduate paper on coordinate systems)
1. Geometria
  1.1. Q-dimensional Geometria.
    1.1.1. Polytopes
2. Algorithmikos
  2.1. Introduction from A Demoscene Viewpoint
  2.2. A Short Dialectic (for 'religious' Pythagorean-(neo-)Platonists, or those who are curious about them.)
  2.3. General Ideas And Usage: Unix/GNU-Linux (POSIX) systems (NetBSD and Slackware/Slamd64)
    2.3.1. Programs It Would Or Could Help to Learn
    2.3.2. Practical Notes
    2.3.3. Files It Would Or Could Help to Save Or Pre-install
3. Epilogue (art section that Philosophy may be added to)
  3.1 GNU/Linux art

    Polytopes (Gk. 'many forms' or something) include (linear) poly- 'nomials' (numbers,) 'gons' (shapes,) 'hedrons' (solids,) 'chora' (cells or rooms,) 'ktiria' ('buildings,' which is descriptive, though a non-descriptive name exists,) etc..

Polynomials Are Polytopes

    The polytopes which are polynomials are described by f:N->R s.t. f(x)=x⁰ in any one dimension of R-space, because such lines or segments of them are straight, i.e. regular. Of course, if you generate bounded segments rather than a line or segment, one might prefer to define it to be several scaled versions (or whatever the vectter terminology is) of the unit segment.

    Polytopes (at least polyhedra) are associated in some/many cases with the following.

for dodecahedron-based polytopes: the universe
for tetrahedron-based ones: 'fire'
icosahedron-based onees: low melting-point minerals (with relatively medium evaporating point and high temperature-point of becoming plasma,) often gaseous
octahedron-based ones: medium melting-point minerals (with relatively high evaporating point,) often liquid.
cube-based ones: high melting-point minerals, often solid.

    It is true that water (often liquid) molecules or arrangements often have forms that certain regular polyhedra model, and some other mineral molecules and arrangements have polyhedra (not necessarily regular) forms. Other mineral or mixture forms often seem to be random/entropic bodies, but in (neo-)Platonism, which uses classical elements, it is irrelevant that there is such difference to 'disordered' modern elements--those may be chaotic and dynamic, which is mathematical. Many people know not classical elements may be (if Sokrates or Plato discovered them or maybe were taught) often relevant to physical, not necessarily only 5-dimensional material or 11-d, reality. Clearly some facts exist that only modern elements may explain, which have relatively little explanation; that does not mean classical ones are illogical: in fact they explain the general states and particular structures of modern ones, and people should not dismiss that classical ones exist in ways people do not know, nor should they presume reality did not and will not exist. I.e., they should not assume that if/since they cannot sense all a dimension (such as the 4th, or 11th or almost) it does not exist, because if they do someone else will not and will make that not be the case, because one can define n-dimensional objects with n-1-dimensional objects.

    The following are my ideas of polychora unfolded, with their perspective (and 120-cell also without it,) into 2-space. Actually, the 5-cell must be corrected, and everything but the 8-cell may be sections (or not) of larger ones.

120-cell section?

120-cell section?

not a 5-cell

24-cell section?

8-cell

    Some regular polychora diagrams may seem asymmetric in 3-space, so maybe some of these sections should more. The possible '120 cell section' above of 8.5 regular (non-perspective) unfolded cells at the origin and a quadrant seems to define a 120-cell: one need only rotate it so each quadrant is the same and there are 120 cells. The possible '120-cell section' above of 13 unfolded cells is what I thought is the regular dodecahedra-celled polychoron, but it may be the geometric centre of the actual regular one: 120-cell. The 5-cell is incorrect above; to fold a face under for sunwheel-type symmetry, it must be done differently. The possible '24-cell section' above of 9 cells is what I thought is the regular octahedra-celled polychoron, but it may be the geometric center of the actual regular one: 24-cell (OTOH, 24-cell unfolded in 3-space may be as asymmetric as a tesseract.) Of course the 8-cell exists and (AFAIK) can be unfolded, with perspective, as shown. (Perspective may not really change the topology, but used with diagrams using regular polytopes, it may help visualization.)

    I had only said Q-dimensional (it includes N-dimensional) because unless one is doing transformations or programming, (s)he is likely to consider axes rays rather than lines.

    This is mostly about Unix/GNU-Linux (POSIX) on personal PCs (and is not very updated but may be slightly useful.) Good ways to start are by trying Slamd64 (powerful) and NetBSD (secure :) and by reading fsf.org, and linuxquestions.org, opengroup.org, comp.unix.shell & comp.unix.programmer FAQs, maybe comp.electronics newsgroups. For DOS/9x/me help see Cubic.org, crest.untergrund.net, and maybe (if you like demoscene) M. Schmitt's Gravis ultrasound plug & play faq. NetBSD.org (the most secure OS,) Slackware.com (a most classic OS besides DOS,) Slamd64.com (the easiest most powerful OS,) and presumably OpenSolaris.org (originally such a pain to get and install that I could not and may not) have docs. Help I seek is: kde xinerama, realloc() for getline() (maybe,) unix midi->trackers (maybe), compiling NetBSD kernel (but I probably could by now) and (maybe) doscmd, ksh.kshrc info that makes BSD usable (I might have lost ksh info), simply compiling simplekde.

    Sokrates: 'E Eirene einai me esas' (or something like that.)
    David: 'einai me esas e eirene, Sokrates Master Megas.'
    sofist: 'Hi. Why can't we have our operating system Windows.'
    Sokrates:'... I guess you could.'
    David: 'Would you say if people use it... society needs more information technicians?'
    Sokrates: 'Clearly.'
    sofist: 'Why can't we operate Windows?'
    David: 'who knows?'
    sofist: 'I want Windows and IT--and meat-eating and doctors!' (paraphrased, except 'Windows and IT--and' from Plato's The Republic)
    Sokrates: 'I still disagree, but let society have extra [IT and] doctors.'
    David: 'There is filosofy of science of operating systems of forms.' (i.e. Platonic systems of ideal forms.)
(EOF)

    2.3.1. Programs It Would Or Could Help to Learn

what you should learn about in POSIX (if you use it) (approximately in order :)
* installing: sh, fdisk, grub, mount

* exploring: man, info, adduser or useradd, ls, cp, mkdir, cat, more, most, less
* editing: ed, vi or vim, emacs, pico or nano or (mostly the best 2 of the 4) SETedit & rhide, maybe xedit, kate
* installing more or compiling: ftp, installpkg or pkg_add, tar, gzip, bzip, make, 'configure' and similar sh scripts, gcc, ln, and, on Slackware: either swaret or maybe slapt-get
* using CD(VD)s: cdrtools
* using a GUI (graphical user interface, i.e. something like Windows or MacOS :) X, xorgconfig or XF86Config, or xorgsetup or XF86setup, or xf86config or xorgcfg, xwmconfig, kde, (and to run most windows programs:) konqueror, wine

what you could learn about in POSIX:
* edit: emacs/TeXmacs (text process, email, newsgroups, programming), kwrite/kedit/kate or SETedit/rhide (both groups are tolerable as Borland and Microsoft text edit,) open office (like MS office,) pico/nano (fast but limited)
* sci./math: GNU plotutils, gtkmathview, labplot, maxima, Octave, some geometric graphics apps (below,) and (highly recommended) BOINC, and possibly much software in Debian (which was very time-consuming compared to Slackware,) which there are many programs similar to at gnu.org's directory now.
* printing: cups (though for any computer, the best printers have problems: HP ones bend the paper, preventing cardboard use, and IBM-based ones, Lexmark, are mostly unsupported on GNU/Linux: unfortunately, Lexmark left IBM before they used GNU/Linux. HP ones work for it and non-POSIX computers, but maybe bent cardboard is not good, and maybe non-POSIX, except DOS/9x... is not computing.)
* time management: cron or kcron
* email & Usenet: sendmail & saslauth, fetchmail (still easier than getmail,) maybe pine or mutt, thunderbird
* file manager ('explorer:') maybe mc, konqueror (tolerable as file manager; ftps)
* graphics: gimp or gimpshop (like photoshop,) kcolourpaint (faster but limited,) sane or xsane (for scanning), povray and kpovray (3-dimensional raytracer), blender, fractint, maybe kiconedit
* chat, IRC (internet relay chat :) irssi (Do not irc as root. If you want '/root' for your home folder, chown it to your username, but then you probably cannot run X/KDE as that user.)
* chat, IM (instant message chat :) pidgin
* kde (possibly the best GUI)
* www: lynx/links, firefox, quanta editor
* music: audacious (play MODs, MIDIs, MP3s like mod4win, winamp,) milkytracker ((X)MOD/S3M/IT MIDI electronic music composition & production)
reading pdfs: xpdf (and Adobe and firefox ones, which crash)

    2.3.2. Practical Notes

    The above and especially below are notes I wrote in case of system crashes where I must reinstall (if you want to find out about undeleteing, look elsewhere, and you will find it is too labourous on POSIX, so you should just back everything important up as often as possible.) If the below is difficult, read tldp.org and netbsd.com before the below.

TOC
discs: mount; /etc/fstab
network: resolv.conf
shell scripts; time management: cron
X/KDE (on BSD)
printing (a note maybe just for BSD)
the BSD disadvantage (as of NetbSD 2.01 or 3.n :) shell (vt100) terminals
the other big BSD security advantage (compared to many more general less major advantages on GNU/Linux)
BSD package system
system files to keep saved and copy into new OS installations before booting

discs
    AT&T and BSD commands are occasionaly different (mount is.)
For this example, disc names now start 'sd,' not 'hd' on GNU/Linux and maybe BSD. gldiscs (like the disc GNU/Linux is on) are '/dev/hd(letter)(number)' (literally except omit quotes and parentheses,) fs (file systems) are: ext2, ext3, ffs, iso9660, vfat. Vfat is Windows 9x/ME and most external storage media. BSDdiscs are '/dev/wd(number)(letter),' fs are: ffs, ext2fs, ext3fs (?,) cd9660, msdos (including windows.) On Linux (AT&T format, IIRC :)
#mount -t gldisc fs directoryname
On BSD:
#mount -t BSDdisc fs directoryname
directory names are whatever you think you can use, like:
GNU/Linux# mount -t vfat /dev/hda1 /mnt
BSD# mount -t msdos /dev/wd0a /mnt

    This is an '/etc/fstab' note: type the partition, path, filesystem for each partition, ro or rw for read 'only' or 'write,' and 1 as anything that has a 1st number number except '/swap' (I think I meant 'anything that should mount 1st. Check though.')

network
    Edit resolv.conf and type 'nameserver' and the number, for each gateway and dns server. (Dialup modem use is easiest after reading 1990s ppp howto.) If you use a BSD and a certain dhcp, you might need to add the line 'dhclient=YES' in /etc/rc.conf, and then you probably need the lines

'make_resolv_conf(){
echo "doing nothing to resolv.conf"'

in /etc/dhclient-enter-hooks.

shell scripts
    Scripts that you make can be put out of the way in a directory. BSD needs it listed in .profile; or /etc/ksh.kshrc if it works. Cron: if you make an alarm clock script, redirect chime to /dev/null /dev/console.

X/KDE
    Kde makes X look and work better. To use it in BSD change every occurence of xdm in /usr/X11R6/lib/X11/xinit/ or etc/X11/xinit/xinitrc to startkde.

printing (maybe just BSD)
nbsp;   (Maybe just on BSD; I forgot;) try to enable groff, nroff, or troff; whatever is the manpage reader on the installation CD(VD) so it is easy to use. Otherwise, print out an editor's help text, to be most futile instead of more futile.

a BSD disadvantage
    BSD (as of NetbSD 2.01 or 3.n) can have more screens only if /etc/ttys and /etc/wscons.conf are edited like:
screen 0 can only be 80x25. Switch to another after reboot by Ctrl Alt Fn (F1, F2,F3 etc..) '/etc/ksh.kshrc' can enable del; maybe home; and end keys to ksh. Search for such keys at os site and a couple .kshrc will come up

a BSD advantage
    An advantage of BSD over GNU/Linux, which has more, may be that in BSD if you alias 'rm -rf' to a shell script to ask you if you really want to delete everything, it might work--it will not on GNU/Linux! So, sometimes every several years I lost (or will lose, but hopefully every many years) most of my hard disc data. Many people say to usually use an account other than root and then do not explain how to do it on a personal PC (examples above.) I know from experience there are things I can only do in root, not a wheel account, though some people disagree and even imply 'make a user and home folder besides '/root' where you run X/KDE and even elsewhere login root every time you want to do something necessitating' on your personal PC, and they never explain much: that is just utterly ridiculous.

BSD software package system (I forgot what I meant here; one or the other.)
    Try not to leave /usr/pkg instead of replacing with standard /usr/local because the only way to pkg_add software where you want is change the BSD os.

    2.3.4. Files It Would Or Could Help to Save Or Pre-install

/etc/dhclient-enter-hooks (BSD) (if you use the related dhcp client)
/etc/genericstable (if you use sendmail)
/etc/fstab (if you want to be able to access the record of what is on your hard disc)
/etc/group (if you want to be able to access the record of users' status and setups)
/etc/ksh.kshrc, /root/.kshrc (BSD) (if you want to type)
/etc/rc.conf (if you do not want to type... everything in when you start)
(BSD :)
/etc/ttys (if you want to type)
/etc/wscons.conf (if you want to type)
/etc/X11/XF86.conf (if you want to ever run X/KDE again when X crashes--'when,' not 'if.' Check this version of the name; it has been a while since I used BSD at home.)
(GNU/Linux :)
/etc/X11/xorg.conf (if you want to ever run X/KDE again when...)

personal files to save: if you use '/root' for home folder, then save its mode (i.e. generally back up your data onto a POSIX filesystem.)
~/.emacs (if you use emacs)
~/.fetchmailrc
~/.firefox (it has the add-ons)
~/.pidgin (if you IM chat with pidgin)
~/.gnus (if you mail with emacs)
~/.kde or ./kderc (whatever they do?) ~/.links (if you read www with links)
~/.lynxrc (if you read www with lynx)
~/.mozilla (if you use firefox)
~/mbox (if your email program saves here)
~/.newsrc (if you use Usenet)
~/.profile (Find out how to add aliases in it to simplify commands, and copy it into new installations before booting.)
~/.ircrc (if you chat with irssi or maybe an older app)
(BSD:)
~/.kshrc (if you want to type)
~/.login (re-check this one)
/etc/X11/xinit/xinitrc (if you want to ever run X/KDE again when...)
(GNU/Linux)
/usr/X11R6/lib/X11/xinit/xinitrc (if you want to ever run...)

    There was a contest to make Slamd64 (Slackware AMD64) logos, and I guess mine were too big, but otherwise they would not have been humourous: