Theo Verelst Diary Page

Fri Jan 11 2001, 1:10 AM

I've decided after good example to write some diary pages with toughts and events.

Oh, in case anybody fails to understand, I'd like to remind them that these pages are copyrighted, and that everything found here may not be redistributed in any other way then over this direct link without my prior consent. That includes family, christianity, and other cheats. The simple reason is that it may well be that some people have been ill informed because they've spread illegal 'copies' of my materials even with modifications. Apart from my moral judgement, that is illegal, and will be treated as such by me. Make as many references to these pages as you like, make hardcopies, but only of the whole page, including the html-references, and without changing a iota or tittel...

And if not? I won't hesitate to use legal means to correct wrong that may be done otherwise. And I am serious. I usually am. I'm not sure I could get 'attempt to grave emotional assault' out of it, but infrigement on copyright rules is serious enough. And Jesus called upon us to respect the authorities of state, so christians would of course never do such a thing. Lying, imagine that.

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Fri Jan 11 2001, 1:10 AM

It's been some time since the last page, though there were some good and as it seems influential subjects in there.

Tonight, I plan to write about at least the following: making a clock with digital circuits, the vending c.q. coffee machine, internetworking basics (should be good, and remember, I have official enough top level basis for this), permutations and voter district logics, is holland lost? (sounds like a type of magazine I don't like), christian logic.

I'm thinking about throwing in some text about some scriptural findings and thoughts, too. What is that about christ getting in some later heaven scene:

                "Saying with a loud voice, Worthy is the Lamb that was slain to
                 receive power, and riches, and wisdom, and strength, and honour, and
                 glory, and blessing."   (Rev 5:12)

Lets see: power, ok, riches, fine, wisdom, evidently, strength, that too?, what is that exactly? honor, allright, and glory, how does one get glory, and blessing, I would think he would give that, but ok, understandable, he needs it, too. I'll peek at the greek. I just did a search on 'strength', because I remembered the word from reading in revelation, actually in church. Nothing wrong with that, except I have the habit of doing so straight through worship and service without regard for the outward routines such as standing up and sitting down at specified occasions. Then again no not-even-bachelor (as far as I know) good for nothing much whatever needs to address me as if I selected that one pope itself and think they can get away with that uncorrected. Enough freemasons, brittish israel and other non sense and/or secret organisation followers and unfortunately probably illuminati kind and generally bad around already to curse the place for, on top of generally shooting down every unsacret idolatrous spiritual image of mary, crying or not, and actual spirits of the antichrist to be put down or commanded away to have some peace. The latter department to some degree seems to have been succesfully taken over lately by others, but then again, I regulalry go there on sunday evening which probably isn't very representative of the average.

I just looked up 'ischus' in the Scott Liddel greek lexicon, which indicates it means:

   strength of body
   might, power
   brute force
   in Tactics, the main body of troops


As is the whole passage, I'll quote it here for those with interest and a threshold to pick up a bible copy or type or altavista or lycos or yahoo or google or whatever with some sufficient search term. The copyright expired in the second century I guess, so lets quote freely.

Which is funny enough even permitted, those (I had a strong word in mind, but then again) whoevers at the I think positivily NIV (new international version) bible translation group (it wouldn't be commercial I think) have a pretty well drawn out quoting policy which is printed in the actual word of god, something like quote without changes, mentioning the source, and no more than two chapters, and then something like and no more in total than so and so. Well well. Copyright ...

Revelation 5

Quoted from the above, King James version:

                        Rev 5:1
                                 And I saw in the right hand of him that sat on the throne a
                                 book written within and on the backside, sealed with
                                 seven seals.
                        Rev 5:2
                                 And I saw a strong angel proclaiming with a loud voice,
                                 Who is worthy to open the book, and to loose the seals
                        Rev 5:3
                                 And no man in heaven, nor in earth, neither under the
                                 earth, was able to open the book, neither to look
                        Rev 5:4
                                 And I wept much, because no man was found worthy to
                                 open and to read the book, neither to look thereon.
                        Rev 5:5
                                 And one of the elders saith unto me, Weep not: behold,
                                 the Lion of the tribe of Juda, the Root of David, hath
                                 prevailed to open the book, and to loose the seven seals
                        Rev 5:6
                                 And I beheld, and, lo, in the midst of the throne and of
                                 the four beasts, and in the midst of the elders, stood a
                                 Lamb as it had been slain, having seven horns and seven
                                 eyes, which are the seven Spirits of God sent forth into all
                                 the earth.
                        Rev 5:7
                                 And he came and took the book out of the right hand of
                                 him that sat upon the throne.
                        Rev 5:8
                                 And when he had taken the book, the four beasts and
                                 four [and] twenty elders fell down before the Lamb,
                                 having every one of them harps, and golden vials full of
                                 odours, which are the prayers of saints.
                        Rev 5:9
                                 And they sung a new song, saying, Thou art worthy to
                                 take the book, and to open the seals thereof: for thou
                                 wast slain, and hast redeemed us to God by thy blood
                                 out of every kindred, and tongue, and people, and nation;
                        Rev 5:10
                                 And hast made us unto our God kings and priests: and
                                 we shall reign on the earth.
                        Rev 5:11
                                 And I beheld, and I heard the voice of many angels
                                 round about the throne and the beasts and the elders: and
                                 the number of them was ten thousand times ten thousand,
                                 and thousands of thousands;
                        Rev 5:12
                                 Saying with a loud voice, Worthy is the Lamb that was
                                 slain to receive power, and riches, and wisdom, and
                                 strength, and honour, and glory, and blessing.
                        Rev 5:13
                                 And every creature which is in heaven, and on the earth,
                                 and under the earth, and such as are in the sea, and all
                                 that are in them, heard I saying, Blessing, and honour,
                                 and glory, and power, [be] unto him that sitteth upon the
                                 throne, and unto the Lamb for ever and ever.
                        Rev 5:14
                                 And the four beasts said, Amen. And the four [and]
                                 twenty elders fell down and worshipped him that liveth
                                 for ever and ever.

The search is also interesting enough:

                         KJV English Concordance for strength
                                                              Go to Gen 1:1
                 strength occurs 242 times in 232 verses: Page 10, verses 226 - 232
                 Hbr 9:17 For a testament [is] of force after men are dead: otherwise it is of
                 no strength at all while the testator liveth.
                 Hbr 11:11 Through faith also Sara herself received strength to conceive
                 seed, and was delivered of a child when she was past age, because she
                 judged him faithful who had promised.
                 Rev 1:16 And he had in his right hand seven stars: and out of his mouth went
                 a sharp twoedged sword: and his countenance [was] as the sun shineth in his
                 Rev 3:8 I know thy works: behold, I have set before thee an open door, and
                 no man can shut it: for thou hast a little strength, and hast kept my word, and
                 hast not denied my name.
                 Rev 5:12 Saying with a loud voice, Worthy is the Lamb that was slain to
                 receive power, and riches, and wisdom, and strength, and honour, and
                 glory, and blessing.
                 Rev 12:10 And I heard a loud voice saying in heaven, Now is come
                 salvation, and strength, and the kingdom of our God, and the power of his
                 Christ: for the accuser of our brethren is cast down, which accused them
                 before our God day and night.
                 Rev 17:13 These have one mind, and shall give their power and strength
                 unto the beast.
                 You are on page 10 of 10. To view other pages, select page number. (Verse
                 range also shown)

There must be good reasons to use such word, though I didn't double check the greek, maybe I should install all the server and search stuff I did a few years ago on a machine and get all the searching and manipulation stuff on a machine of my own, at least as it is, it should be worth working on such things, though probably the idea of bringing forth simple enough basic truth is worth while and maybe more important, for certain audiences.

For instance the simple idea of some iranian superclass jew leaving babylonic type of surroundings (I guess) to go to a new land and ofspring while having a wife of high age, because (_semi gang voice on_) 'God sent me'. Yeah right. Realy? Aged, no children, no idea of what the people living in the target country are actually like, oh you don't even know where you are going exactly? Just pack your maybe nomad type of tents, get your cattle and household, and go sort of west.

I guess he was crazy enough to thing that some nude woman peeking and wedlock born offspring, though lines of whores and world top famous kings of seed of his loins would live like a sort of bohemian speaker of Gods law and claim to be the son of God, too, like there was also promised one in babylon, though probably that father of his own son with the same wife (cybele, the predecessor of the statue-mary) construction was probably more exotic.

He was crazy enough to start a people who were promised to be uncountable like the stars in the sky or the sand near the sea who were supposedly 'gods chosen people'. They have a country again nowadays, I hear.

The digital clock

I bet there are more than a few, also normal people, who like to put on a little digital clock on a computer screen, or maybe simply around their wrist, simply for the love of having a little device tick away time, and see the letters change according to fixed, understandable, but oh so complicated to built logic. At least the latter I knew when I had one of the first red led digital watches the size of half a matchbox in 4th grade dutch primary school I think it was. I had a teacher who seems to have sighed with my parents that he didn't understand me, though that never bothered me much, and he uttered the theory that notes who as audio waves had longer wavelengths than the space they are supposed to sound in, cannot sound in such a space at all. As if his long bass recorder (flute) would be the same concept as a speaker for instance producing a bass note. Tsk tsk, bad physics. Reminds me of my physics teacher in highschool who sustained in my opinion somewhat stupidly that deflection coils around a Cathode Ray Tube such as the tube in an ordinary television set are electrostatic deflection devices, while in my opinion such only happens in oscilloscope type screens, because I'd seen too many curled up wires acting very convincingly as if they were magnetic coils to me in actual tv set insides. And I read my (public) library books, of course, Alexandria couldn't have been that wrong.

Anyhow the former teacher didn't spoil my appetite for audio, I continued two (I think) of his recorder courses, even though I had a simple plastic normal sized one, and a few years later I wrote a good piece on the physics of sound as an essay which ended up in the school paper, which was fun, and for another reason: at the the Hague communion museum we visited a presentation on sound. I knew sounds travel quite some faster through metal or water, and that standing waves are because of fixed end reflections, that sort of stuff. Loved that, too, when I was 11 or so.

Anyhow, my thoughts were indeed probably where such limited spirits probably couldn't realy go, I had my watch and wanted to know how that worked, and I meant no shit, for real.

I think a few years later my interest and seach for such knowledge was about to get satisfied enough to start to arrive at the point where I'd at least built the sort of circuitry needed to make a digital clock myself, even in actual fact. I got this book on 101 digital circuits or so and read it cover to cover in record time, under the blankets probably faster than anything else, and I got some books on microprocessors, but also on (ttl) logic circuits, including the basics of those, and the fundamentals of all basic circuits such as gates, selectors, decoders, flip flops, counter sections, memory cells and arrays, shift registers, and complicated synchronous designs. The first book included info on surrounding subjects such as stable 5 volt supplies and the way to prevent high frequency crosstalk and interference, to, just like I learned in amplifiers, prevent ground loops and make continent power supply wire plans, the practicalities of driving little leds (electronic lamps) by strong enough pull down totempole ttl outputs, how to prevent clock jitter, crosstalk and slewrate underlimits, and of course I learned by acting as good consumer where the parts I wanted were cheap in which electronics stores, which breadboards would fit which wires, and all such stuff.

And by the time I was 12 or 13 I would find building a clock-type circuit in basic digital form boring, though fun, especially if I'd have had the simple money to buy some more counters and quality led 7 segment displays. Realy, I'd think about designing all kinds of computer and game circuits, and serious ones, actually, such as hardware decimal to hex and (important) back conversion supported in hardware. Such as multiple datapad machines and handcrafting various arithmetic and logic circuits.

A favorite clock like circuit which my part stock could easily enough support was a reaction tester, where a counter would start counting and a light flip on, and the operator would have to immedeately press a button, and the time when that button goes down gets recorded as the response time of the guinnypig person. Major good stuff that was, though simple enough: two counters limited to 10, two decoders (in my case one one to 10 line and a 7 segment decoder, check TI databooks from around 75 all that stuff is in there, and in fact some university courses would do better having a good and long look at them and how they are put together, and why, because people actually want to built working machines with them), a carry connection between the counter sections with the right edge sensitivity, and a quick, preferably calibrated clock generator circuit of for instance 100 Herz (cycles per second), which can be made by a pair of cross coupled 7400 Nand gates and two capacitors in the 100 nF range).

A bit of techtalk to at least make clear to the experts what I was talking about, I want to put some significantly lesser capable persons in high university position out of the alledged credibility, and I mean business, I am for real, and some of them are not, and I want that to be evident, because I don't belief in first taking a trip to auschwitch to belief nazis are bad and must not receive power over my or other peoples life, and like to beat them before mein kampf ever makes into anything at all exept fire place food. Too important stuff, can't play games with that anymore, thank you very much, not this time, no can do, sorry to say.

Anyhow, one would have these little chips, lets see if I can come up with an image somewhere, hang on.


Isn't it pretty? I just grabbed in from some circuit board picture, its in a socket, that's where the 14 lins pointing down are hidden in, and the socket in turn is soldered into to pertinax kind of circuit board underneath. This version is a mitsubishi one, see the little pictogram and the 'M' in front of the so well know circuit number 7400, with or without LS, which nowadays would be HC, for CMOS in instead of Low power Scotty. In electrical engineering courses, I remember using these and circuits in chip packages like it with banana plug fitted small sigare box like aluminium or metal enclosures, which lets electrical engineers to be without the experience of handling a few hands full of such black boxes the length of a small match (the pins are 1/10th of an inch apart, so the whole thing is about .7 inch or about 2 cm long), being carefull not getting an unpleasant tin/lead dangerous row of wounds in a finger when the thing unexpectedly comes loose from its socket when peeling it without proper tools.

Anyhow, such packages also carry counter circuits good enough to make nice and very capable digital clocks with. Lets see if I can examplify, to make clear what my mind was doing at the mentioned ages, instead of learning what mother mary in her oh so limited demonic wisdom is trying to get mankind to belief, acknowledging that it is good and according to the alledged neon gods will that the rich who abuse children should at all cost stay in charge, be unexposed, taken legitimate guides of mankind just because they happen to have been born filthy rich, and that we all will be better of surrendering our lives to the initiation rites into their circuits which will never end until most are even dead in their graves. And the second circle may be only for those willing and capable to sacrifice things even more profound and _holy_ such as sacret _capital_, and maybe, though not certainly, more sacret and to be praised for quite long and longer, the incredible concept of _power_ and authority over others. When they're stupid enough to belief the demomic or human liars who promise them their sacrifice or betrayal or giving over is indeed going to make those rich and dark ones claiming to be light inclined to actually give them something, while probably they have a laugh at best or completely ignore the whole idea, because why would a rich ass like that even give a shit to think about it. Except of course when acting such is going to give him or her of such wanted commodities. Money and power. Hm. Gmph. Seriously, I'm going to work my but off to fulfill some demonic doctrine and make sure some pomous rich ass gets satisfied, yeah right. I'll work for pay. Or an ideal. Or power. Or to learn, or simply to live, but not for that non sense.

Anyhow, against those circuits in general without question, there where these chip manufacuturers who poored out thousands of quite cheap instances of the fruits of quite some research and work, and I profited by using greengrocer buyer logic. Fine, loads or mercy and even grace in there in comparison with just about everything else, taken by the system, not freely developed and thought about, or generally not produced for at least reasonable enough purposes.

And I loved thinking about the possibilities with them, like a clock, but also thing about programming such a clock, and making one cheap and easy enough, to take not a major project circuit board with lots of error possibilities and room heating supply units, and of course more dollars worth of circuit parts. I remember quite vividly the first circuit like a microprocessor core which would add numbers of one digit which I would feed it, at herz range clocks that went step by step, and the displays would display load of relevant start track bridge like control sequences, wand in the end the sum would appear and the machine come to the programmed stop. Wonderfull. Later on? The maze on a tv screen with dual pot XY real time control built as non-processor ttl based circuit. Draw a maze, flip some wires, and move through it without touching the walls, or the light goes off, major fun in 1983 or so. The circuit included a complete TV signal generator made by conventional ttl parts alone, and then more, ha, that was good, getting it stable and reliable of course draws on various analog and digital circuit design, built and test techniques not known by a single of my peers in a project which was ambitious in computer design with me, ai, major error. Their designs didn't work well. Wonder why, they kicked me out when I projected they'd need me a lot more than they projected. I never thought they'd outwork me, so I was right, betrayal was the only way for them to squirm themselves away from my obvious first position. But I don't give that authority away, not even when I'm threatened, those capabilities are mine, not theirs, and they can die before I give them away in the same game that is supposed to wrape, abuse and oppress children, and which is without question nothing of the God I do want to serve. It is to be hated, dispised, put aside, and exposed, and is worth nothing.

Counters are made of the master slave flip flops (actual electronics terminology, you may prefer 'bi-stable multivibrator', idem), in various possible constellations, and one can use sections of 10 and six counter units in a row, in series, to make a clock. The counters feed decoders which for each segment of a 7 segment display and for each counter value determine the logical value, so that when a counter holds the binary coded value 3, all but the left two segments of a display are on. When the highest bit of a counter section goes from 1 to 0, when reaching and stepping over the highest value, 5 or 9, that signal can trigger the next higher counter to count 1 up. The lowest section is then fed with a signal changing every minute or second, and in principle the machine works, minus errors, circuit imperfections or chip defects. A signal generator can be made from a 'blinker' circuit of the right frequency, or from one with a higher frequency and a number of frequency divider steps in between, which is also a common application of counter circuits. There are circuits with a quarz crystal which are pretty accurate in ticking at a specified frequency, which also drive watches, computers, measurement machines and such who need accurate time bases.

Another option is to electronically convert a mains signal from 50 or 60 Herz into a digital pulse, which is then divided by 50 or 60 to get a long term accurate clock drive seconds signal.

Today I saw two pepsi machines which reminded me of that principle. They had flashing displays just out of sinc, but with as it seemed a fixed on-off timing relation, which when based on anything but radio time signals, which is completely unlikely, a local network between them, also out of the question, or a mains based clock will change gradually with time, unless they get switched on and off, of course.There are serious embedded linux projects aimed at giving such machines a linux operating system on a computer, would then the number of coins thrown into the slow impact the display blink rate a touch? Every time the mechanism is polled and a little bookkeeping is done, program execution traces in the computer could be a bit different, effectively changing the average on and of time of the blink routing a little every time, unless it would be accurately timed, for which there is no real need. What a complicated world. And in fact, when you're a up to date and even quite hip ATM network builder or designer, such an issue is of major importance. Those object pushing computer wannabee expert probably don't understand the first thing of what I'm talking about. Oh boy, work to do. Was I challenging here? No, in fact, I don't feel like it, I just remember what a lot of computerists were like, and decided I don't like that sort of attitude enough, so I want that out of the way, that's all.

A better one is how to do correct and decent and honorable composition of two strictly functionally operating units and arrive at a non-functional memory cell with just the one next to simplest circuits: a flip flop with two nand gates which are the most standard digital parts there have ever been, and numbered as such, a problem that from the start undermined any effort a whole section (I was in) took to make a correct by design logic design system, worth millions of my tax money in investments. Seriously. And I even mentioned it, sort of neatly at the time I didn't know who I was dealing with. No response. And they want to built competing computer circuits in the world as it is and even be better overall designers of them. Tsk tsk.

My game later on was to do a multiplexed counter circuit which would store all digits of a for instance 6 digit counter in memory, take on out at the time, load it in a single 4 bit counter unit, count up once, remember the carry, store back the result, and proceed with the next digit, in circle. In 1979 or so, the circuits, including a small memory chip, would have been up to doing all that up to 10 or 20 Mega Herz, which long before even the 4 MHz 8086 computer became known was at least serious computer circuit stuff.

Lately, I've been into nano biology, wanna guess at the games I have in mind with that, 20 years and at least a decade of serious science (I did use my sources) later? Aha, you're catching on. I hear they count and shift too, those nanotubulin molecules wrapped into tiny cilindres, flipping a number of tens of degrees to both sides of their on-equilibrium position. Probably a sort of non-linearly coupled harmonic oscilations. Of a few hundred in a row. What music would they make? I'm sure that no matter what kind, my mother wouldn't understand it, and that my judges from the past are unqualified to even speak about it.

Later on I thought about the multiplexed clock principle to do play back more than one sample at the same time, for instance to make an organ with, and used a seperated data and address memory which later became known (not through my scientific article or something, I was just filling boring physics hours at high school with a notepad and a battery of circuits at home) as the harvard architecture. The principle was to make the bandwidths of the busses reading samples and fixed fraction update factors match so I could get as much polyfony as I liked, have the dynamic refresh larger memory needed and the easier to control static memory for the increment factors on the other side. That sort of stuff I waited long for in university, and I don't think I ever saw much of it, except for some of the better (usually foreign) books, and some well chosen HP remarks and machines. 10 years later. Tsk.Oh chips are made object oriented nowadays? Wel tell me when the java chips take over serious scientific computing, and I'll tell you why having garbage collection in a fragmented memory with actually effective memory translators and even effective virtual memory circuitry can solve all that a lot better, fundamentally right, and without ever running out of handles. But, then you must learn your computer architecture lessons others learned when I was a kid. Preferably in an academically valid way.

My fun in computers, including some of my long surviving as top preferences, was for instance reading about the connection machine, from I think thinking machines, I think they were prototyped or used at the university of berkeley, california.What happens when a nice number of xectors start to do an associative job on thousans of nodes containing symbolical indirect or even better associatively addressed data or xector partner candidates, that sort of stuf, and then of course have a fundament language like lisp to drive the thing, and a decent and actually effective high bandwidth (for the time, I think about 85) driver mini connected. That's fun enough. How is that with traveling salesman problems, degree and np completeness non-sense again? Well that is about probing networks handily and preferably getting away from the intrinsic memory access bandwidth and linearisation of most algorithms, and get as much work as possible in done in simple parallel fashion preferably, probably using a decent, data analysis based network partitioning algorithm. Let's mind our academics, and not forget that math is there to serve us and maybe elevate a bit, not to swamp us with meaningless seemingly important equations no one ever wanted to lay eyes on in the first place. As physicist of about a century ago about such ideas and see if it shouldn't be so that they can look at electrical engineering hotshots or at least serious workers and have an idea of what might be interesting in the future, too, instead of feeling deflated by century old theory being not even applied properly.

I'll see if I get bwise running here to do an impression of a time clock circuit, maybe even with some simulation, or just a drawing. First there are some more sections to be written.

The vending c.q. coffee machine

The amazing lesson I heard copied badly by someone who should be more interesting for their projected position (which indeed that one didn't obtain) from a decent enough book on communicating sequential processes was that you'd have a machine, and you'd throw in a coin, and then you might actually have to wait a little while before the selected commodity would tumble out into the 'out' box.

The question some mathematically minded researchers have posed themselves decades ago was how to model or capture in mathematical language the idea of having a coin dropped in a machine, and getting some candy out, and everything in between, and preferably when more then one thing can happen at a time. We would have Coin --> Candy as main interaction, and for instance  series (parallel (coin --> coin box ; candy --> retrieved) ; candy --> out-tray) as possible refinement, making clear the candy will hit the out-tray only after in some order the coin has dropped in the coin box and the candy has been retrieved from its storage location.

In fact, we could have another coin put in in the meanwhile, or require more than one coin for certain goods, and we'd be into making a state diagram with all possible transitions to make sure for every possibility at every time the machines' control circuits behave perfectly. That is not an easy, but overseeable job, one sits and thinks about all possible events at all times, and draws the right lines for them is a diagram accumulating possible states, of which there can be quite more than a few when multiple coins can be thrown in in any order, and there are more than a few goods. Then one tries to abstract by for instance dividing the goods into price classes, and not distinguishing between individual goods in a price class, and one probably will like the idea of being able to refer to several fixed sets of events as a sort of routine, for instance to simply call of all actions except throwing back all coins untill zero balance before anything else to correct all kinds of possible errors, including being out of chance.

Vending machine exist in quite a variete, and I'm sure most work fine, and are not made by consulting a medium, clairvoyant or medicinman equivalent before they are put into production, put lets say by mainly bachelor level engineering and decent enough work, so there is no need to proove the possibility of actually making mechanics or electronics to do such job right enough, and as theoreticist, one will be forced to take those existing skills into account and at least master them before being taken serious at all. And ones' theories will have to at least add some insight or interesting rule to be taken as relevant.

The theory which also can describe the events in a vending machine called communicating sequential processes (after Hoare) for instance at least is a decent enough definition language, and can be used to base completeness and existance proofs on to see for instance if a certain sequence of events is predicted to exist or where it would lead to and wether that is accurately enough defined. The theoretical value lies in the realisation that communication as an indivisible event between two parties can be used as the basis for an algebra on the various ways of how such events can be composed into a certain combined behaviour. And defining a system which such algebraic representation can be fed to a computer program in a meaningfull way.

The main point to notice in this sort of network approach is the same as in many other network considerations (I am after all a graduee in network theory), also in the well known and of course still hard traveling salesman problem: faculty is a very fast growing number, and directly related to many exhaustive or enumerating network operations or basic computation schemes.

Lets say we put all our fingers on a row and draw 9 lines connecting them, in any order where we make exactly one path, including all fingers in some order. Easy enough? The first finger gives us nine choices, the second 8, etc, in total : 362 thousand 880 possibilities. Well well. At 10 seconds a piece that takes us 42 (no kidding, I think the calculator did the *10/(3600*24) right) days to complete. At 10 per A4 it takes of course quite a pile of paper, too. Suppose we want to make all possible of such ordering graphs of the names in a phonebook of a one million people city. Takes forever. It would seem inpossible to simply try all possible orderings and choose the right one, even for a modern computer, one million faculty is an astronomously huge number, thousands and thousand, in fact millions of zeros, impossible. And that is a simple network, just one link per node, and simply ordering. Suppose we'd want to compare ancestral riches for each possible pair and then order that result in ascending order, that is something else as a computer job. Suppose we don't mind when people aren't sorted in their street, so that only the streets need to be ordered. Many will remember that after the 69th street, we'll run into possible orderings of more then 99 zeros, which is idiotic, also for computers running a few billion (9 zeros) of computations per second.

So if we want to have a 'sort of' correctly ordered result with achievable effort, we'd have to do a not so good sorting job, we'd forget about a lot of possibilities and hope the end result is good enough to work with given the existing list of phone numbers and names, and live with an imperfectly but reasonable sorted phonebook. For instance each name at least sorted per group of a few letters, that should be possible to trace trying all possibilities.

Or one has to be smart, and think of an algorithm which does the perfect sorting job in less operations then the faculty of the number of addresses. As some will know, one can quite decently sort anything using in the order of n times logarithm n comparison operations, where n is the number of phone numbers, which is for instance 6 million for a 10 based logarithm and a million phone numbers, which is completely doable and a second rate PC. One can proof mathematically than one can indeed arrive at the perfect sort for any input order, so the method is fine and of course highly relevant. Less relevant but sometimes important additions are the using of certain statistially or otherwise known information about the input data, which may speed up sorting.

Is this relevant for computer builders or programmers? Yes, completely. It is clear evidence that a good and mathematically founded theory is a major gain over a brute force lets try everything and hope the best method, and the one even can be sure that there will be no errors or imperfections as a result of using the theory correctly. That is something. I remember finding sort routines in a C library for my early atari computer, and liking that I could sort thousands of items per second, even the way I wanted it, because someone even did the effort of making such aids available in programmer ready form. Nowadays, one can get a multitasking operating system officially for free, it even works, and includes the (mostly C) sources to have a look at it internals and rebuilt the whole thing according to one's own ideas. Major grace, bonus points deserved. Somewhere in the Clib, there is still the sorting routine, I'm sure. I tried the command line grep from the also free and open source cygwin, which is sort of (though it is just to get an idea) linux development tools on top of windows, which used half a second to perfectly scan a 7 megabyte (7 million bytes), 12 thousand line long database file for a specified pattern anywhere in it. I don't remember what happened with sort some time ago when I tried it, but it certainly worked.

One can imagine that overseeing all possible sequence of events in a vending machine where there are for instance 10 possible states is quite hard even for a simple machine, 10 states gives us over 3 million possible orders of events to draw by a single line per event to the next. And when there is more than one transition possibility per event, the number is even bigger. That means that a computer program which has to check every possiblity to search for possibel errors or inconsistencies for instance may not take forever, but is strained by such small example already. Unless we find ways to drastically decrease the number of possibilities to get a friendlier number of test to perform which form preferably mathematically provably a superset of all other tests, rendering them useless to perform.

When one uses algebraic expressions sort of like the above, one can reason on the basis of them, for instance to make the possible combinations of events in all possible orders, which after good physical practice can be defined well enough mathematically. One would have two possibilities for listing options withing the equations given above, where the second is only a specialisation, so we don't need the weaker top level transition equation, being coin drops then get candy then candy available, or the first two reversed: candy released ; coin drops in drawer; candy comes out. There could be a rule that the coin always drops before the candy is found, which could during test of the above rules with that new rule point out that the first two rules give possibilities which are limited by the third rule, or be proven to give a unambiguous sequence of events, and only one, without contradictions.

In a network with many computers and many complicated possible programs exchanging a lot of possible messages, such logic may safe or break the network and is very hard to compute unintelligently, though can probably be specified in a closing and provably working and verifyable way. That is a challenging task, and a usefull, and scientifically at least potentially interesting one. 'Make a package of it, put it on the ftp server and see if anyone has interest'. 'Give it a challenging enough interface and let students play around with it with real world examples preferably'.

Internetworking basics

Last day, I thought about phrasing some of the basics of the internet lets call it that, simply because there seems to be such desire to 'be' or 'have a name' in that game, and claim power and the right to rule in the world which has access to that net.

The first thing is that at the lowest level, apart from the coding, what the internet and just about every other network does is transfer strings of bits, zeros and ones around. The physical layer of a network may encode those bits as changing frequencies or phases such as in a modem, the bits may be voltages or symmetrized current pulses, or light pulses of certain properties, but in essence, rows of bits are being transfered.

And in just about every network at most points, bits are transfered between nodes in the network or pieces of software in packets of a certain size, for instance 8 x 256 bits ( a quarter of a kiloByte), usually between a number of bytes (midi going even down to one) and maybe a hudred thousand bytes, not usually outside those bounds.

Packets usually start of with a known number of bits forming the header, followed by what is called the payload or data part of the packet of bitstringed information. The header contains fixed portions contianing digitally coded addressee, sender, kind and subkind, packet number, checksum and time to live information. For instance there could be a sequence of 4 times 8 bits containing the destination IP address as in xx.xx.xx.xx .

Nodes in the network receive the packet, or even just the header as it comes in, and decide of what to do with the packet, drop it, consume it and maybe store in or give it to some program it is running, or forward it to some another node based on information it has in for instance it routing table or adres interpreting routines.

A connection often is made to carry packets on a row in both directions, and there are ways for nodes to make sure that (virtual) connection between its peer is reliable, that means that all data put on it on one end, no matter in what way, for instance bit for bit encoded in little packets or in major sized chuncks, pops up in a program on the other end the same way it was transmitted, that means the same bit sequence. In the meanwhile packets may be lost or mutated and the nodes taking place in the communication must make sure they ask for retransmission of packets if they have reason to believe something went wrong. Packets can take alternative routes based on traffic density considerations, and in tcp they are numbered and confirmed by a number indicating the number of outstanding, as yet unconfirmed packets, which has a maximum after which no more packets are transmitted, and return packets may have confirmations piggybacked on them for efficiency, while tcp also contains flow control functions such as slowly trying to increase transfer rates.

We have the OSI model to at 7 abstraction levels deal with all data transfer components from the physical leven up to standard high level data transfer applications such as ftp or telnet, and the networking and tcp and ip intermedeate transfer and security software take the physical level and impose the packeting, the packet numbering the addressing and routing, up to the 'socket' application program interface level, where a transparently reliable connection is offered at software library interface level.

In the meanwhile a route must be discovered and followed to a certain destination to setup or rerout a virtual connections content, packets must be transfered around sensible enough and gathered up and retransmitted when possible or needed, rerouted without causing network trafic density to explode or posing a security threat, and bookkeeped for cost tracking parties.