Franz Kafka’s In The Penal Colony

keywords: Franz Kakfa, existentialism, short story, Joseph K, cruelty, commandant


Kafka turns the world we know upside down and inside out with this strange tale of reversed fortunes.  He plunges deep into unsettling psycho-philosophic issues on the nature of society, its members and technology.


In this story we are introduced to four principal characters: the officer, the explorer, the condemned man and the soldier.  These characters emerge like chess pieces in this drama to become stronger or weaker as the story unfolds.


From the beginning of the story, we are given a context that is understood to precede its commencement: the explorer has traveled to an island for convicted men at the invitation of its resident Commandant.  As is his method, Kafka shocks his readers with a casual depiction (via the officer character) of a world where, tortuous execution is the preferred mode of discipline.  The explorer is to witness the execution of a prisoner that has disobeyed one of the stipulations of the Colony.  A condemned man has been strapped to an unusual machine for performing executions.  A soldier is attending to the condemned man, making sure he’s strapped down properly, and keeping him quiet by stuffing a felt rag in his mouth during a 12-hour ordeal of execution.


The task of carrying out this execution has fallen to a zealous disciple of the method whom served under the previous Commandant.  He not only wants to do the job, he wants to make the explorer understand the depth of his devout belief in the Colony’s code of governance and most of all the machine that enforces it.  The reason for the cruel act-to-be is appalling.  The prisoner has failed to salute the Commandant’s door hourly as he was ordered to do.  What is even more astounding is the Officer’s almost religious passion for the device that will execute the condemned man.  He fawns over it and marvels at its technological achievement in tortuous murder.  He is a man that believes in excruciating detail.  Like any precisian, he shows the explorer the mechanical drawing from which the machine was constructed with pride.  He tells him that the prisoner neither knows he has been convicted of a violation, or that he is condemned to die.  This unnerves the explorer and begins a rift that will in short order lead to an odd reversal of fortune for the officer.


The machine is a three-part device consisting of two rectangular layers, one called the Bed, where the victim is laid and the other called the Designer keeps him in place. A large steel needle called the Harrow moves back and forth between the other two components through the use of a controlling steel ribbon (the word Harrow is used in the archaic English sense of cutting or tearing). This horrible instrument can write in the flesh of its victim any phrase the operator desires.


The explorer and officer are speaking French, which is not spoken in the Colony.  So, the soldier and condemned man watch uncomprehending, as the officer explains to the explorer the enormous killing power the machine possesses.  This machine engraves on the body of the convict, the reason for his execution.  While the explorer and officer grow more apart, the soldier and prisoner become more acquainted.  Once the explorer understands what the officer intends to do and why, he is repulsed.  The officer senses this revulsion, and tries to convince the explorer through his slavish devotion to the machine and the cruel culture of the Colony, what he will do to the prisoner is somehowright.  He realizes this form of social retribution is dying out.  The new Commandant doesn’t support it.  In fact, we learn the officer believes that is why the explorer was invited to the island.  He wants the explorer to help him revive this cruel form of punishment.  He believes the explorer; a prestigious foreigner with the respect of the Commandant can convince this man to restore the fame and glory of the machine.  He wants the device maintained and improved.  He longs to see public executions returned to their former status as grand spectacles.  When the explorer rebuffs him, the officer is driven to extreme despair.  The condemned man and soldier are so chummy at this point, they are eating rice together.  The officer cannot endure what the explorer’s refusal to help him implies.  He makes the decision to release the condemned man and replace him on the device.  He has himself strapped down and the machine begins of its own accord, but malfunctions and instead of an inscription written on the officer’s flesh, he is impaled.  He is murdered not tortured.  Now, the condemned man has become a free soul witnessing his former tormentor’s death, and seeming to replace him, as the soldier begins to defer to him.


This story is remarkably similar to Kafka’s other famous work about an evil social system with devoted, though mindless operatives, The TrialIn the Penal Colony is much more positive in some senses.  It is implied that the officer is out of touch with a world, which has outgrown barbarity, by the new Commandant and the explorer’s attitude toward this execution.  We are given a sense that this may be the last time this torture device is used.  The convict is at the story’s end virtually emancipated, and the explorer leaves a place that may be passing the gateway to a more humane society.


What is disquieting in this work is the officer.  The officer is symbolic of the individual who is willing to destroy himself to keep his way of life.  We see Kafka is not far-fetched in depicting this idea in fiction.  You just have to think of the millions of drug addicts in our real world, doing exactly what this tale tells us; wanting with all their minds, hearts and blood to preserve their compulsions.  Or consider the armed conflicts raging worldwide now, to maintain one nation’s power over another.  Worst than this, the officer shows an Hegelian subversion of himself to that of the device and its operation.  It was more important that the machine be allowed to continue exquisitely killing, than preserving his life.  That the officer sacrifices himself because he refuses to accept a changing world is disturbing.

Other Articles of Interest

We live in a world of lies we tell ourselves, without realizing it. I look at a concept that Sartre developed in his Existentialist philosophy that is so very true, yet so damn difficult to control.

Self Deception and Jean-Paul Sartre.

Criminal justice in America is a juridical process many believe to be fair. The guilty are determined by public trial, then judgment is rendered by their peers (in the sense of fellow citizens, not intellectual equals). The article below shows how lamentably wrong that idea is. It may let the guilty go free and punish the innocent. The idea that innocent persons may have been put to death is unconscionable to most of us. Yet it may have happened in this country and perhaps worldwide, if other countries follow this model. I believe these decisions should be taken out of the hands of humans beings.

Flawed Jurisprudence

Before the Law, is one of Kafka’s most thought-provoking narrative discourses. It covers aspects of the human condition via his favorite character “K”.

Before the Law


The words high and low are misused in formal and informal writing and speech. Why do we connect geometric concepts with things that have nothing to do with them?

The Words High and Low

Tzameti 13 is an incredible film by a new director (Gela Babluani) from the former Soviet Republic of Georgia and is set in France. It involves a strange game of Russian roulette that groups of men participate in for larges sums of money. But, as you will see in my review, it is not only a stunning film, but has deep mathematical concepts that can be examined.

13 Tzameti

Kenadid Robleh Wais 9/9/03


Reflections on English: Nicknames and Word Making



Author: Ken Wais

In past articles I’ve considered aspects of English and language in general that are quaint and rarely studied.  For instance in one article the process of compounding in English was examined. I found it had the curious quality of being able to reverse words and form new meaning when applied.  In another essay, I looked at the possibility of allowing persons to choose their names at some point after birth.  In this review we’ll look at word creation and nicknames in English.


Mathematical and Linguistic Aliases

Nicknaming or alias creation is a general process that is not limited to English or human languages.  But, it is a process particular to languages.  Aliases are used in formal computer programming languages like Visual Basic, SQL, Python, PERL, Java, etc. Nicknames share some qualities with their formal counterparts called codes that you might be tempted to think of nicknaming as just a form of encoding names or code names for given names.  But, this is not the case.  An information theorist would not envision the huge set of nicknames that people are given in any language as equivalent to what is done when a source code is transformed into processed code.  The rules for the latter are complex and well-defined, not such with the former.  Though, both processes accomplish something similar: they take a given name (word) and map it to another name (word). Two areas of mathematics are concerned with creating aliases for any set of objects: cryptology and information theory.  Cryptology is primarily focused on transforming one set of objects into another that obscures or hides the original set from detection by intruders.  Information theory is a broader field that is focused on mapping one set of objects to another in a variety of ways.  It primarily studies taking objects of source code and reproducing them in object code as shorten forms of the original code.  This of course can be seen in compression of any source code for data transmission through sound and video.  Or take compressing bank monetary transfers to foreign branches as an example of name encoding.  I could go on with examples like color in video transmission, or even how the code for this Word program is read as examples of a strange form of nicknaming, but let’s not.  In information theory, nicknaming is less important than in cryptology. The questions we would be concerned with in this form of nicknaming are accuracy of the code name to the original. Is it a good representation of the original?  Will it not be confused with other alias names? Are the code names retrievable to their originals?  We have a different set of questions for linguistic nicknaming.

Nicknames are common in our everyday world.  We know of a large numbers of people and objects with nicknames.  If you don’t think so, stop and consider of all the nicknames you have catalogued in your lifetime.  Not just people, but places, geographic names—the Big Apple for New York, objects—money becomes dough, even feelings—feeling sad isblue. Nicknaming is a random process.  Nicknames spring up because of an event or a characteristic of the object to which they are applied.  There is no set of well-defined rules used to create a nickname as there are with compression of a source code.  Questions we might ask of linguistic nicknaming are different than those we would ask of the mathematical form of nicknaming we discussed above.  Here are few:

  1. Do most people have nicknames?
  2. Should nicknaming or alias creation be made a formal process in human languages?
  3. Can the process of nicknaming be reverse?

These are some interesting questions no doubt and we should look at them in depth. Doesn’t it seem most people DO have nicknames?  There are constructive models for forming nicknames in English and several other languages.  For instance, shortening the word or dropping certain letters and adding others.  Example: Franklin can be shortened to Frank or Frankie.  But, there is not a naming rule for creating nicknames.  This answer addresses question 2 to some extent. But, let’s consider question 1.  The only way to determine this number is by census.  In fact, there may be an attempt to assess the size of nicknames in the U.S.  Have you noticed that many forms you fill out virtually or on paper have a category for AKA or aliases?  It is conceivable that if a concerted effort were made to assess how many people had nicknames it could be easily done, especially today with the growth of computer networks.  I believe most of us have nicknames.  It would be interesting to know with certainty if this is true.  Let us suppose this is true in this country and others.  Now we can address question 3.  This question is asking if we have a nickname can it become our socially recognized birth name?  In effect, the process of naming is reversed.  A nickname once contrived replaces our given name.  This process is loosely equivalent to iteration in applied mathematics.  With iteration the output of a function is replaced as the input in the function, and the output is reevaluated.  In the case of a nickname becoming a given name we don’t seek to reevaluate the name simply replace it.  This process invokes the question why?  That is why do this?  The answer is simple.  Since nicknames evolve from given names, they are more applicable to the subject than their given names.  What I mean by the preceding sentence is a name that is associated with a subject synchronically (in time) as a nickname has its meaning rooted in the experience of the subject’s life. An example will illustrate the point.  Let us say a person whose given name is Lawrence is gradually named Don because he coincidentally looks like a deceased person in his neighborhood whose name was Don.  It happens because so many people that meet him remark on the resemblance and some even refer to him as Don in error.  In this story it would appear that the name Don might assume more significance to the person whose given name is Lawrence because it is connected with the oddity of his looking like the dead person named Don.  He can understand why he is called Don, better than why he is named Lawrence.  All names are assignments of identities to objects in human language.  Their meanings are fleeting and without substance in the sense of a law of science.  Personal names in cultures outside that of English speakers often are designed to show family heritage.  Even here nicknames arise. It seems nicknaming is endemic to human culture  To go back to the question—Can a nickname replace a given name?—Yes is the answer.  It happens all time.  It is seldom if ever formalized in the sense of having a person’s given name legally changed to their nickname, but what one is called during their lifetimes most often IS their name.  This is an important point.  If your nickname is uttered, written and used to refer to you during a majority of your life then which name should we consider to be your real name?  Clearly the nickname if it was used predominately during the person’s life.  What happens in reality is what determines meaning.  Regardless of the name you are given at birth, the name that attaches to you as you experience life is your real name, whether memorialized or not.  And this leads directly to the second question.  Should we not inaugurate a process whereby the nickname can be recognized as the formal (birth given name) name of a person?  The answer should write itself.  Sure we should do this.  As I alluded to above steps in this direction seem to be already afoot.  Look at how many formatted documents you encounter in the business world that also request alias names and wonder on how this interest may be a trend toward accepting nicknames as formal names.


Word Creation

Words are created in English and others language routinely.  Some become staple parts of the language and others die out or never take off.  I have begun to play with creating new words in English.  I have 4 candidates; I don’t believe any of these have been invented yet, though my last one may have been.  I will list and define these new words and then ask some questions about how to have them become English words.


Four New English Words

Upgift: To give or receive a present of more monetary value.

Downgift: To give or receive a present of less monetary value.

Futurehistory: This oxymoronic word expresses a subtle idea.  It is referencing events that will occur and then become a part of the subject’s past.  In this sense it skips the present moment to connect the future and past.  This idea could also be expressed as Futurepast.

Bathower: To wash yourself partially by bathing, then complete the bath with a shower.

Clearly these words could be English words.  What is more, the first two can easily be made into verbs.  For example, take this sentence.  Sharon returned the bracelet for her mother’s birthday and felt she could upgift it with a diamond necklace.

Bathower is of course of mixture of two different words Bath and Shower.  Compound admixture of separate words is a common source of new English vocabulary.

How can these invented words be injected into our language?  Should they be submitted to lexical authorities for approval and inclusion in the next English dictionary?  Or should I just start using these words in speech and writing hoping for acceptance by my linguistic contemporaries at large?  Perhaps, a method that uses both these approaches is recommended?  It really doesn’t matter how I attempt to get my new words accepted, if they fit a novel description that current words in the language don’t, they will be accepted and from the spark of perhaps this website article or word of mouth, the new words will become accepted as English words.  Of course, I must check that they are not already in use somewhere.  If these words are superfluous and don’t’ really fit some need for expression in the language they will not become elements of our language.  But, there are other factors that could affect whether these 3 words are adopted into English.  What about their pronunciation?  If we come up with a word that defies the usual vocal tenets of English pronunciation that word is doomed before it starts.  Believe it or not that is the only restriction I’d place on new word creation.  It doesn’t matter if the creator is considered an authority in the language.  It doesn’t matter if the word comes from a less than standard source.  We see this all the time with slang words becoming standard speech and writing.  Who doesn’t use the word cool in speech and writing to mean new and upcoming ideas?  There are other examples any reader could imagine.  I just offered three and I am sure anyone reading this article can think of more.  In fact, wouldn’t it be a grand idea to have a website associated with lexicography that allowed us to submit new words and would interact with us.  It could function as the clearinghouse to word creation.  It could let submitter know if the word was already in use, or why it is not a good choice as a new English word.

Radio Programs, Set Theory and Individuals Part 1



Robleh Wais

The Radio Broadcast Experience

I was listening to a National Public Radio program today, Talk of the Nation, and the hosts were discussing various topics with guests, and encouraging listeners to phone in or email them. The programs motif so to speak is based on allowing listeners to be heard by as the name implies–the whole country at large. But, as I listened to the callers that actually were put on air, an idea of how many listeners actually could be heard on this program began to form in my mind. The fact is very few listeners actually get the chance to speak to the nation. This fact is not very hard to see. Let’s take a fictitious example to illustrate it.

We have a radio called You might get on the air. It has 10,000 listeners. Now let’s see how many of that 10,000 can speak to the nation in one hour.

Radio You might get on the air =10000 listeners

Maximum number of listeners that can speak per minute if we assume the whole hour is devoted to listeners speaking is

10000/60=166 listeners per minute. This is a limit that the program will never reach. It is clear the 166 people couldn’t be broadcasted in series speaking in one minute.


But course listeners aren’t given 1 minute speak each, so let’s say we assume that each listener is given (at minimum) 10 seconds to speak. Ignoring access time, credits (even public radio has beginning and ending credits, though no commercials), we can see that if 10 seconds per call was the limit then we have:

10 sec *6=60 seconds which equals 1 minute, thus 6 callers speak per minute. 6 calls per minute * 60 = 360 callers get to speak on You might get on air.


The percentage becomes 360/10000=4% (approx) spoke on air on Radio program You might get on the air.

These percentages are also the probabilities of your getting to speak. It is undeniably clear from this simple arithmetic that most of the people listening toYou might get on air are never heard when they attempt to call in.  The fact is that most radio programs like this one that are nationwide have many more than 10,000 listeners. Also, note I’m telling the probability if the entire hour were devoted to listeners calling in. Of course, it’s not. If we factor in the time the hosts take running their mouths, the probability is even less. You just have to count how many people you hear on air during a program like Talk of the Nation and do the arithmetic with an appropriate guess of how large the listening audience is, to see–very, I repeat very few are heard by the nation at large. My count is about 6 to 7 at most! I need to qualify these comments.  First, I am sure there are those who will cry no! no! no! He’s wrong.  Suppose only 500 of the 10,000 attempt to call in, then the odds are much better?  I’ve thought of these objections too, and looked at what I project with differing numbers and probabilities, but still the percentage is small and another example illustrates. If only 500 of a possible audience size 10,000 attempts to call, and we assume that say maybe…uh 30 minutes of the 60 are given over to call-ins, then we have the probability of any one of the 30 getting to speak as 30/500=6% per minute. That’s not a good chance again. The only way to increase the probability of a caller getting on air, is to increase the time allotted to call-ins, or a decrement in number of calls coming in. Both changes are unlikely in my opinion. But, on the rare occasions when the topic is uninteresting and there are not many calls, then more are heard. The greatest probability would be if only 30 callers phone in the 30 minutes, then every caller should be heard if we ignore the obvious constraints, access time, the screeners querying you before going on air, etc. But, that is not likely. I have heard on many PBS radio programs that they receive thousands of emails and calls. This is analogous to the numbers of callers phoning in during these programs. So, fiddling the numbers of my above estimation doesn’t change the conclusion: most people are not heard on air.  The producers, hosts, and all others connected with these programs know this! For them to suggest their program as some kind of vehicle for you, the individual to be heard by the whole country is such a lie it makes me angry. And it’s even worst than the simple arithmetic implies, if you don’t play the game their way, even if you are chosen you won’t have the chance to speak to the country If you use profane language or expressing opinions they consider not appropriate you STILL won’t have your cherished chance to speak to their 50,000 or so listeners. It borders on false advertising to me. It is a lie that is foisted upon listeners to tell them to call in and let your voice be heard when the probability at most (drawing from the fictional example above) is 4% that they will be heard. Though I think its deceptive and unfair to make these false attributions to listeners, I am much more interested in what the radio broadcaster/listener experience implies about human relations. It should go without saying that whatever I write about radio as a media will apply to any other one-to-many relationship, such as TV, the Net, magazines, newspapers. We will see using database theory terms and set theory methods, that individuals have a special relationship with the multitude.

The Individual and The Multitude

As individuals we are anonymous to the broadcasting world of radio. Of course, they have all sorts of sophisticated methods of knowing us in general. They typify us by race, age, stations we listen to, income, geography, consumption patterns, sex etc. Yet even with these data the broadcasters (I mean the entire organization by that term) don’t know us as individuals. That is to say, when we tune in a program, there is no person or persons there to see and say… oh that’s X, who is now lighting a cigarette, and okay he told his wife to be quiet, and uh he’s going to take a uh let me see… oh yeah he’s taking a piss before we start broadcasting that’s old X, he always takes his piss before listening to us.  Thank the non-existent God they don’t have that power yet, huh? In fact, there is good reason why they don’t have that kind of power yet: they couldn’t handle the information flow that level detail would require, even with powerful computer monitoring technology maybe in 50 years.  No, we are for them the amorphous, anonymous audience out there. We are theMany dialing into the One. The One has the Godlike power to reach the multitude, while the Many is defined by being a supplicating hoard seeking to speak to the One. Yes if you noticed, this relationship is the same one that is characteristic of religious experiences. When the Many at last finds and can talk to the One, what happens then? This is equivalent in the radio example to a caller having his chance to talk to the nation.

If you’ve ever had the experience of being chosen to give your opinion on a call-in radio show, you’ll no doubt know that it’s an overwhelming one.  When you hear your name announced on some radio program from such and such place, and then the hosts ask you to speak, you are at first shocked to hear your NAME called out and knowing you will be speaking to tens of thousands of people, you are nervous and apprehensive. If you pull it off, you feel a sense of worth and accomplishment. What has really happened in these cases is the many has become a part of the one. You, the individual for those brief seconds, become like the radio show host, touching the multitude out there. You feel something akin to stage fright, your voice may crack, and you might ramble, and completely forget what you had composed in your head, that important point you were going to make, it now seems so small. Or contrarily, you may take control of yourself and speak clearly, and put your point across eloquently. In either case, you feel as if you’ve been given a power: the power to communicate with some many, many others. And you also sense something comes with this. You lose you anonymity in doing this. You are not a private person any longer. This is disturbing to you. And why is that?

We are, all of us private beings. We share the knowledge of our private states of mind, by choice. We think in our heads and have experiences only known to us. Privacy is a part of our existence we have from birth. The child sliding out of its mother’s womb is a child experiencing that occurrence alone. That same child while in the womb, if it has a rudimentary thought process anything like it will have as an adult its still doing this alone. Even its mother carrying it doesn’t know that it might be developing thoughts. So you see, we are by our very nature as living beings in this world-alone. And to be alone means to be private. Not even a most fundamental bond like that of the pregnant mother to her infant can break that necessary divide of being a living thing alone and private unto itself. Is it any wonder that when we are called upon to share ourselves through something like a radio broadcast, we feel a cringing in ourselves?

Then there is this need we feel to communicate with others.  We are unto ourselves a unified agency of states of mind. Still, we do want to know others and communicate with them. I would venture to say, most of us want to touch many others too. We want to be heard, by the many if you will as the one. Most of the time, we only want to communicate as a one-on-one relationship. Again another term from database theory, I’m using. We meet and know others as individuals like ourselves, and are themselves alone as human beings in this world. So what would ever make us want to know more than our individuated experiences can offer? It is the social nature of our being in the world that does this.

We are a mix of several types. Humanity is not one individual or type of individual. We are in our genetic combinations so many types (members) of one set. The human set, which is outward and forming new relationships, and thus forming new sets from its generating set, is a process that defines our social world. This behavior in human beings makes me think we are somehow doing this from something more basic. Let’s see if we can build a model of human communications as a relationship of sets, then apply it to the radio broadcast example above.

 Modeling The Radio Broadcast Experience

If we take the set of integers, {0, 1,2, 3∞}, then the only element of that set that under the operation of + has relation to every other member of that set is 0. And every element of the integer set has a one-to-many relationship with the number 0 called Identity. So, 0 is like the broadcaster above, and we are like the other integers. The problem here, is when we call 0, we get ourselves as the result. This is a very simple set with rules that map in a way that the broadcaster never let’s the members in the set talk to anyone but themselves. Not a very fruitful example. So, let’s consider a set relation that widens the field and somewhat approximates the radio call-in experience. Logarithms of base 10 can capture this idea.

Consider the series below:

It is clear if we keep going on a set integers would be produced from increasing powers of the logarithms of these base 10 numbers.  Now go back to my original example. If we consider the callers as the result of a logarithmic set, then we have the following equation.


F(x) =xlog10

This set would generate every integer to infinity for powers of 10. What does this mean? It means in simple terms, smaller numbers would be mapped to larger numbers. This mapping approximates the one-to-many nature of radio broadcasting.

For example take 4 log 10 = 10000. We could see this as indicating 4 people (the host and a small staff) communicate with 10,000. In this manner, the radio broadcast experience can be said to have a logarithmic relation. Though, to be more accurate about it, we’d probably have to change the base of the logarithm. But, there are other ways to capture the relationship between broadcaster and audience. Few examples will get us started.


Take the equation


F(x) =√x for x≠1 and x is an integer

This relationship is a function for all integers greater than 1. In other words it is a one-to-one mapping. This relationship is said to be isomorphic, since every input begets a unique output within the set of integers. This relationship is more like a conversation between individuals than a broadcast. Though, one person starts all the communicating, that is x starts conversations.

Composite functions also approximate one-to-one mappings, though less uniformly.


Take the equations


F(x) = 2x +1/x2

G(x) =2(f(x)) +1=2(2x + 1/x2) + 1= 4x +2/ x2 + 1= 2/x2 + 4x + 1


Here for every input to F(x) we get a unique output in G(x), often called the image of F(x). These sets are like the above isomorphic mapping and would be another person-to-person sort of communication. However a subclass of composition known as iteration is very much like an exchange in which one speaks and the other responds using the information that was given from the original speaker.


Take the iterative equation

F(x) =

F(F(x)) for F(x)= 1/√x-1. It is a real-valued function beyond 0 and 1

As a non-iterated function this set approaches from the left (that is, decreasing number values for x) the value of 0 as shown below:


F(x) = 1/√x-1 = 0

Lim x->∞

Which means conversation dies off between the two mapped sets. It would be like a one-to-one mapping, where one side stops communicating.


F(x) = 1/√x-1 = 0 and

F((F(x))= 0 also.



Embedding this function in itself and taking its limit leads to again a slow slide to 0. It will take longer no doubt, but the conservation eventually dies off.

 Real Communication: The Individual Meets the Multitude


None of the above set mappings really captures what happens in the radio broadcast I started this article with. But there is way to make the exchange between the broadcaster and audience more symmetric.


We now come back to the one-to-many set mapping we started with using base 10 logs. But instead of base 10 logs we will use base 2 logs. This set relation provides a much more realistic model of broadcasting to a wide audience, for instance look at this:


F(x) = 20 log2 = 1,048,576.


Now that is much closer to the kind of relationship a show like Talk of the Nation has with its listeners. This mapping is saying that a staff of 20 can reach 1,048,576, but they don’t talk back much. Here is what I have been leading up to: why not let groups of listeners form sets that can talk back to the broadcaster as groups. The broadcasters will still decide what listeners will have the chance to speak, but the basis for this decision has more equanimity, and would be representative of the audience. This model can be made with set theory methods. It would be cost-effective in the economic sense of that term. You could dispense with the jerks screening the calls with this model.


We can use the base 2 log above to develop a model that would allow callers to radio programs like Talk of the Nation to voice their opinions in large numbers. The model utilizes the database theory idea of one-to-many, but its converse: many-to-one.  for my model to be realized, the radio shows producers would have to do more preparation to accommodate their mass of callers. It would take an entire week before the broadcast airs for the showsproducers to set-up what my model illustrates. This isn’t asking too much of them. After all, this program is the Talk of the Nation, and it should strive be just that, right?

Go on to next section Sets, Radio programs and Individuals


Radio Programs, Set Theory and Individuals Part 2

We can use the base 2 log above to develop a model that would allow callers to radio programs like Talk of the Nation to voice their opinions in large numbers. This model doesn’t utilize the database theory idea of one-to-many, as I’ve described, but its converse, that is many-to-one.  I must point out for my model to be realized, the radio show’s producers would have to do more preparation to accommodate their mass of callers. It would take an entire week before the broadcast airs for the show’s producers to set-up what my model will illustrate.  I don’t feel this is asking too much of them.  After all, the program I reference to create my model claims to be the Talk of the Nation, thus it should attempt to really allow its multitude of callers to be heard. Right? To use Elizabethean English, Lest it become merely a cheap stage for thine own ends. And thou know not what that may be.


We will assume the following sets H, A, X and R.


H (host and staff) = 20

A (radio audience) = 20 log2 = 1,048,576. (Possible audience size)

X (questions)=3


H broadcasts to A, X questions (for our example we will use 3)

Now we have H○AàX That is, H relates or maps to A with X (which we will replace with 3 for the 3 questions)

X then responds with R.

XßR, means R maps, through the relation A○H. This means A responds to questions X with R responses and is again a mapping of sets.


We can now summary the process as a relation of the 4 sets, H, A, X and R.


H○A=X: Hosts asks the Audience questions X

A○H=R: Audiences answers the Hosts with responses R.

These relations are also a 2×2 symmetric matrix with X and R being their resolutions. In fact, the entire set structure of these relationships could be constructed with matrix alegbra methods, but again the limitations of the IE program makes showing this difficult without special math software. In fact some of the math characters I’ve already used might show up as nonsense figures to some of you. Oh well, it’s only 21st century you know. Now in the 23rd century …etc.etc.


Having developed the set structure we can now apply these relations and show how our talk show could truly represent the Nation.


H○A=X, can take the form of 3 questions as follows:


H asks for instance


B) Why did Hillary Clinton’s campaign for Presidential nominee fail?

C) Will she run as an independent?

D) Will she become Barack Obama’s vice-presidential running mate?


So, H (A)= B + C + Dà H○A=X


And A responses with


E) She was arrogant, or she lacked funds, or she miscalculated her constituency, or she lied during the campaign.  Any response can be given and arbitrary limit set then counted.

F) Yes or No, plus explanations, again this response can be tabulated.

G)Will she run as an independent? Same as F.


So, A (H)= E+F+Gà A○H=R


Here we have a relationship that can be implemented.  That is, the audience can be questioned (via email), responses counted, categorized and finally, output sets can be analyzed and the hosts of the program can choose any number or listeners to speak for the groups of like-minded respondents.  That is once E, F and G have been tabulated, the hosts can call some respondents in each group and choose one to speak for all.  Rather like a representative government in political science, huh?  Also, notice that the One still has omnipotence here, that is, the hosts can pick and choose from the sets of responses, whom will and whom won’tTalk to the Nation.

Go back to first section Sets, Radio programs and Individuals

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Author Kenadid Robleh Wais





Barrow-Tipler Argument against Extraterrestial Life

Barrow-Tipler Argument against Extraterrestial Life:

Note: The Drake Equation has been proposed with different variables by dissenting astronomers. The one I use below is in my estimation, the most popular version.


In Chapter 9 of their book The Anthropic Cosmological Principle, physicists John Barrow and Frank Tipler propose an argument they claim shows that Extra-Terrestrial Intelligent life does not exist anywhere in our Galaxy.


In sections 9.1 and 9.2 they spend some time setting up their refutation.  Not much in these sections does anything to advance this negative thesis.  Actually these sections seem to be trying to illustrate how human life could travel the cosmos and colonize alien worlds.


Finally in section, 9.3 they get to the heart of their argument.


The equation that Barrow & Tipler use to prove there can’t be more than one intelligent species in this Galaxy is:



fp is the probability of star systems with planets

ne  is the number of habitable planets in a star system that has planets

fl  is the probability that life evolves on a habitable planet

fi  is the probability that intelligent self-aware life evolves on a habitable planet

fc  is the probability that intelligent life will attempt interstellar communication within 5 billion years of evolving on a habitable planet.

Ng number of star in our galaxy


It’s called the Drake equation. Its variables are sometimes named differently, but these are the usual ones. As you can see this is a numerical estimate equation based on probabilities and when we estimate the component probabilities times the Ng (number stars in our galaxy), it will give the number of planets where there might be alien species. To support Barrow and Tipler’s thesis, if ne the number of planets in our galaxy is small (as of yet unknown), and Ng the number stars in our galaxy is large (and they are), then the probabilities surrounding these numbers must be small. At least that is what is inferred. Please note this is inference, not implication, in the logical deductive method. It will be important later, as I make conclusions about this weak, very weak anti-alien life argument. One estimate they give is 1/100,000,000,000. One in a hundred billion? If this is a fair estimate, I would most certainly agree that the likelihood of other intelligent life in this Galaxy is very small, and thus we ARE number one! So, the Drake equation is an effective prediction of alien life, if its component probabilities are accurate. But, we can’t make accurate estimates of these probabilities being Earthbound. We don’t know where a planet with species like ours or any other exist. Or where such a planet (or planets) might come into being. Thus, these probabilities are guesses. The predictable numbers we can estimate are the number of stars and planets, but all the rest are guesses.


The other thing to notice is the equation sets a limit on how long it would take intelligent species to go looking for others like it. This is important because we know that the universe has a definite age. By deduction, so do the galaxies. This means intelligent life other than us must evolve, and go searching for others like it within a strict period of time. This is crucial. In fact, the whole argument hinges on this point. They show if we take fc‘s normal distribution as being peaked at 6 billion years and a standard deviation of 1 billion years, this implies just one intelligent species. Of course if the normal distribution is larger, the likelihood is greater, but we won’t split hairs on this point.


In addition, there is an assumption, which this probability must refute: the Principle of Mediocrity.  That is, we are nothing special in the Galaxy, that in all the star systems throughout this Galaxy a similar set of circumstances could have led to the formation of life like ours. There are an estimated 500 billion (this estimate varies widely, I am using the largest one) stars in this Galaxy. If p turns out to be small, then we can negate the Principle of Mediocrity and say, we ARE something special and life did not evolve in numerous star systems in this Galaxy.


The problem with the Drake equation is the fact that fp and ne are experimental and estimates differ.  The total number could be much larger depending on these values.  They admit this.


Now, lets put this probabilistic argument aside.  It contains variables, which are not reliably determined and thus possibly inaccurate.  It would work well, if we restrict it to our Solar System. The real problem with what Barrow and Tipler are arguing is they are rightly showing that if extraterrestrial species exist, then they have not shown themselves to us.  But, this doesn’t prove they don’t exist.  We just have to think of dolphins on this planet, (whom biologists believe to have intelligence near equivalent to our own) to know that intelligent life can exist, but be incapable of traveling or otherwise communicating with species outside their worlds.  That is one GIANT flaw to their argument. They are assuming that extraterrestrial life (ETI) will have both the means and an environment that will be conducive to the desire to communicate with alien species.  We cannot assume that self-aware, intelligent life will take a physical form that allows it to produce devices that can signal or reach us.  In fact, there could be any number of real impediments to ETI’s not contacting or reaching us.  And I don’t mean their killing themselves off.  Believing that they have the answer to those whom say, no evidence of ETI is not proof that ETIs do not exist, they counter that this is exactly what it is!  If aliens exist, why don’t we see them?  They should’ve come to our solar system by now?  Again, believing they have found the right point of attack, they go on to show how intelligent species would have an incentive to explore and colonize the Galaxy.  The incentive could be a dying world, or shrinking resources.   They forget that the physical formation of life in a distant star system could be a major reason why it has not contacted us.  An ETI could exist, but it could still not have the means to contact us, due to its physical structure.  In this case, the ETI would exist, but not have been detected by us, or we by them.  This is an important point.  Barrow and Tipler don’t seem to be excluding life in general from the Galaxy.  Since they have precisely framed their own argument with probabilistic notions, it is easy to say: Can’t there be non-intelligent life in the Galaxy?  Do you think that there are any planets with single-celled or microbial life on them?  And there is nothing in this argument to preclude the possibility.  It is quite easy to imagine a scenario where simple forms of organic life could exist on a planet, and be held in that state for billions of years, never reaching our level of development.  Still this would amount to alien life existing in our Galaxy.

Another fallacious argument about astronomical observations was put forth in the 19th century. It bears striking similarity in method to the Barrow-Tipler conjecture. It used the Scientific Method to make this conclusion. Click below to see how.

Obler’s Paradox



Conclusions and Remarks

Barrow and Tipler are not making a sound inductive argument for the non-existence of ETI in our Galaxy. They are making a speculative argument for this non-existence.  They make an obvious error in believing that not having evidence of ETI in our Solar System implies no ETI in the Galaxy.  Using the probabilistic theory of Drake and Sagan, they believe a valid conclusion is made as to why no ETI exists in the Galaxy.  This is the mistake. I quote:


It is important to note that the above argument uses the observed evidential fact that the ETI are not present in our solar system; the situation is not the one implied by the epigram to this section, ‘absence of evidence is not evidence of absence’.  Rather, the evidence is that ETI are absent from our Solar System, and from thisobserved fact (and other astrophysical observations and theories) it is inferred as a logical consequence that ETI are absent from the Galaxy.


What the above quote is saying in different terms is we don’t see any aliens in our Solar System, so we propose a theory why that is the case.  We form a probabilistic model that should predict not just whether there are life forms in our Solar System, but the whole Galaxy.  That model tells us it is not very likely.  We conclude not only are there no aliens in our Solar System but that none exist in the whole Galaxy.  The error in this conclusion is: the model is speculative and contingent upon large samples.  They try to gloss over this problem with some additional constraints, but I believe them to be insufficient.  So, their conclusion can’t apply to the entire Galaxy.  That is a mistake.


It can apply with ease to our Solar System.  We know Ng and ne in our Solar System.  So, yes they are right, there is one intelligent species in our Solar System, e.g. us.  This is not such an obvious conclusion.  There are many whom have posited alien visitation to Earth.  Others claim that life forms have existed here in the past and created the ancient ruins of Egypt or those in South America.  The Drake equation tells us this isn’t so, and was not so in the past.  And here is where Barrow and Tipler err.  Their conclusion should be reduced to one about the Solar System not the Galaxy.


Both these physicists believe so strongly in their conclusion, because the feel they’ve used the Scientific Method to arrive at it.  Both they and their critics agree, we don’t have much evidence of ETI, here on Earth.  However, unlike those that simply go on looking for it, Barrow and Tipler use a model to account for this lack of alien life.  If the model agrees with reality and tells us no alien life, then we conclude no alien life.  The problem is if the model is wrong or too broadly applied (as it is in this case), you still arrive at a false conclusion.


However, the argument Barrow and Tipler make for the scarcity of ETI in the Galaxy is not completely without merit.  I believe that they are close to correct. Though, their method is weak, they still are on the right track.  To be more exact, I speculate that there may be at most 1 perhaps 2 other species like us in the entire Galaxy.  It does not take a very sophisticated string of inductions to see this. Here is a conservative estimation based on the Drake equation.


Lets take Ng as=the number of stars in our Galaxy


Assume Ng=500 billion stars.


If fp is only 1%, then we have Star systems with planets, Nss=5.0*109*.01=5,000,000,000.


If the probability of these systems having Earthlike planets is .01, then we have, Nearthlike= 5.0*109*.01=50,000,000.


If again the probability of these Earthlike planets having life on them is .01, we have, Nel= 5.0*107*.01=500,000.


Taking the probability of intelligent and communicative life being on this set of planets at .01, we have, Nlc= 5.0*105 *.01=5,000.


We now have 5000 planets in this Galaxy that might have some form of life, that is close to ours, and can possibly communicate with us.   While this may seem like few to the uninitiated, this is way, way too many! Believe it or not, it’s way, way too many!  Remember the Earth is a plenum with life. There are 6 billion people, trillions of insects, many millions of mammalian animals and microbial life that exceeds named numbers.  If we consider life historically, then the numbers are even larger.  We create detectable emissions that reach far out into space.  If we’ve got 5000 sources of this kind of radiation, then we’d be detecting all kinds of life through radio telescopes and other signal collecting devices. Lets add one more probability to this estimation; the probability of the 5,000 planets with intelligent and communicative life having used nuclear weapons.  After all, if there are several planets with this destructive force, a probability of their use is a real possibility.  This time, based on our Earthly experience (meaning we used nuclear weapons) I will up the probability to 5%.


The number of planets of that engage in nuclear destruction is Nnd=5.0*102*.05=250.


If Nnd is 250 worlds, then the original estimate is even more unlikely.  The radioactive fallout of that many nuclear conflagrations, would almost certainly be detected by the low Earth orbit Hubble telescope even across several thousand of light years of space.  So, even if we conservatively estimate ETI, we are bound to speculate that the number must be exceedingly small.


I have noticed since writing this review, that the Barrow-Tipler argument is in fact a prime example of a well-known logical fallacy called Denying the Antecedent. This fallacy is symbolically written as


If A then B.



Therefore ~A.


Applying this to our case we have:


If there is alien life in the Galaxy, then we will detect it.


Alien life has not been detected in our Galaxy.


Therefore there is no alien life in the Galaxy.


This is a simplified form of the fallacy, in most cases it has a major and minor premise, nevertheless it exhibits the fallacy. Why is this argument fallacious? If the consequent of a categorical argument is not fufilled it does not invalidate the premise! For instance: If it doesn’t rain today, I will jog for 3 hours. I did not jog for 3 hours It rained today (applying the algebra of a negative times a negative makes a positive for the major premise). Now, clearly my not jogging for 3 hours couldn’t cause it TO RAIN. The error of this reasoning is eye-rolling clear, right? The consequent of the antecedent doesn’t EVER invalidate it, if the consequent isn’t fulfilled. Here, we find these scientists mixing two very different forms of logic: hypothetical and categorical. In hypothetical logic we propose an explanation, then find evidence to support it. It is inductive in nature and contingent, i.e. it can change and be reworked depending on the evidence supporting it. Categorical logic, on the other hand is deductive and deals with valid forms of deducing conclusions. It is immutable and akin to (in fact the progenitor of) mathematical logic. Arguments are said to be reduced from proposition to conclusion. Its principle model is syllogism from which other models are derived. Barrow and Tipler are mixing these two different forms of inquiry. They want to take an inductive argrument and make it categorical; it doesn’t work. This is why, I can’t agree there are NO alien species in our galaxy. Only a categorical argument can come to an absolute conclusion. However, a hypothetical argument can come to a general conclusion. Which is why I assent that if there are alien species in the galaxy, the number is small. This inductive conclusion is sound and in my opinion likely.




Ken Wais 10/27/03

Other Articles of Interest

In 2001, I wrote a rather lengthy article about a topic that is closely related to the controversy above. This one involves the attempt by computer scientists’ to create an Artificial Intelligence (AI). It is again a search for intelligence, but this time instead of looking cosmologically for an ETI, the quest is to make an AI virtually. I examine how the famous, late English mathematician, Allan Turing misconceived a way to test for an AI. Along the way, we discuss all the subjects that are contained in the Turing Test. Artificial Intelligence Have you ever listened to a call-in radio program and wondered: How many people actually get to talk on this program?

Radio programs, Individuals and Set Theory

In the last 20 years, charlatan scientists have been parading an alternative explanation of the genesis of the universe, that not only excludes the current physics model, but suggests that anintelligent designer could have made the cosmos. The basis for this outrageous claim is an appeal to mathematical probability. I couldn’t help but give an illustration of how absurd their proposition is, using an example from my own life. There are many, but I focus on one: Hugh Ross, a Canadian physicist, and very representative of the whole lot.

Scientists with a religious agenda spread misinformation with probabilistic arguments.

Portal SiteScience, Philosophy, Language, Music and More.

Age Half-Life Immortality


8/9/13, 2:21 AM

Ken Wais

Age, Half-Life and Immortality

Here is an interesting idea concerning two sets of numbers.  One we will call: YourAge.  YourAge is just how old you are, expressed in integer numbers like 1, 2, 3, etc.  The other set we will call: YourHalfLife.  This set will be a set of rational diminishing numbers that is also a convergent set. Unlike the YourAge set which is divergent.  They can be shown as follow:


1, ½,1/4,1/8, 1/16,1/32,1/64….→0

This half-life set decreases by ½ of the original number with every member added. But let’s go back to the YourAge set. It increases by integer values so to show it we have:



Now, let’s say at some point in the 2nd set, how ‘bout 25, which is your real age in time, we could map the first set to the second?  But, I want to go further.  Let us also define that the YourAge set is your real physical age with all the medical-biological implications that coinage means.  The second set, YourHalfLife, is a measure of how much the first set extends.  Here we have an exquisite mapping of sets.  As you age in life from say an arbitrary number, 25 in YourAge set, the second set YourHalfLife is mapped to it.  Here is an example of it.

25→25, 26→1/2, 27→1/4, 28→1/8, 29→1/16….∞

When you are 25 you are 25.  This is your base year.  But as years continue your age decreases by a fraction of that base year. So, when you are 26 you increase in age ½ your age at 25, at 27 you increase ¼ your age at 25, when you are 28 you increase 1/8 your age at 25, at 29, you increase 1/16 your age at 25.

Thus, as you age in real time you actual age would decrease, or should I say your half-life would decrease?

Here we are making what algebraic mathematicians call a surjective map from one set to another.  That is, we are putting numbers from one set to another but not the other way around.  Both these sets have properties.  The set YourAge is an infinitely increasing set.  The set YourHalfLife is an infinitely decreasing set.  But YourHalfLife is decreasing to a value.  Its value converges to 0.  But, that value is 0, and it applies to only part of this set.  Since YourHalfLife is a rational number.  The integer part, 25 stays constant only the decimal is converging to the value of 0.  Which means, the set value YourHalfLife is converging to 25.  Let us show this in a diagram.


YourAge 25 26 27 28 29 30 31 32
YourHalfLife 25 25.5 25.25 25.125 25.0625 25.03125 25.015625 25.0078125


You can see that as your real age increases, your half-life age will never go beyond 25.  In fact it will keep getting closer and closer to your original age of 25.  Notice also, though YourHalfLife does converge to 0, it does it infinitely.  It never actually reaches 0, it just tends toward 0. Of course, this means with such a set mapping you will live infinitely at the age 25.  This could be called immortality I guess, except no one has figured out how to map such age-sets. And man o man, I wish some biologist-geneticist-wizard-scientist-booger would! 

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