Now he uses:

for “negation” concept, ![enter image for judgdescription here

for “judgment”…

for “existential quantification” concept in his book.

So if we are privy to choose any symbol as “mathematical” unit, what if I chose a single line drawing of a “parrot perched on a stand” to represent concept “parrot perched on a stand” or P.

Or we use an image of single line robot to stand “All is in Robot” or R.

The point of “a single stroke” thought is used to cast doubt on reader’s mind about notion of “separability” and “space” assuming we are not technically cognizant of topology.

So if we imagine an infinite Turing tape, and we allot the first symbol of denoted by R as the visual display of Robot, and the P as (not the symbol but the drawing of ‘parrot’) then we conceive of an imaginary language like ideograms.

Point being, if Frege uses any arbitrary symbol to denote mathematical objects why not use these? Furthermore, can a mathematical knowledge such as Continuum Hypothesis’s state of validity be encapsulated by a single concept L or a random children’s drawing?

Taking this concept further can a symbol such as Ω be conceived of a constant that encapsulated the entire historical recording of universe?

Furthermore, if a ‘writing’ (that too given the carte blanche of [boustrophedon of Eastern Island glyphs rongorongo) DEFINES a mathematical concept, I can arbitrarily define this image T as one state, but doing so automatically defines “an alternate state”.

Thus, consciousness requires non-consciousness. Paradox. And conception or this Soul called Atman by Hindus exist as One or Non-dual.

So we assume nothing. Nothing assumed, we are sile…

This reminds me of Taoist attitude: Those who know, don’t speak//Those who speak, don’t know”.

Point being, we if assume a poetic metaphor that “universe is everything” then this invokes the notion of space(and time). But going back to Frege, he uses a single stroke concept…

This brings to information theory. Forget about “symbols”. Assume a state X. This is opposite to **X**. So this vibration is result of consciousness. But blank state is what exists which is actually a blank state as in Nothing.

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Let above be x.

- Can x exist?
- Is x prime or composite?
- How to ‘measure’ x? How to measure x raised to x raised x….?
- How was x ‘created’?
- Wrap your head arou…wait! wrap a number like x…only bigger…around Earth, Milky Way, Universe and so on. If x is prime, how do you compress it?
- Does x exist? Sure. Can a number like x exist which is infinitely large yet finite? Sure. Can that number be prime? Yes.
- When a number becomes so large, does questions, machinery regarding it or analysis become “meaningless”?

One time, a young scholar named Kun Chung-ni came to the library to ask Li Erh about an obscure ritual. (Kung Chung-ni would later be known as Kung Tzu, or Confucius.) After answering the young man’s questions, Li Erh told him, “You need to file down your sharpness and put away your sword of ambition. The great sage often appears dull and dim-witted, and those with true learning do not display their knowledge.”

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By the by: What IS RH?

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Concatenate them 2357. Either it is a prime or not. If it is a prime then…

Now is there a name for this? What is Smarandache prime? Are there infinitude of them? What can they tell about primes themselves?

But most interestingly. Suppose we take 2357111317192329… Then when will the first pattern appear such as it would read

2357111317192329

OEIS

Numbers n such that the concatenation of the first n primes (A019518) is a prime.

n a(n)

1 2

2 3

3 7

4 719

5 1033

6 2297

7 3037

8 11927

[2,3,7,719,1033,2297,3037,11927]

So is 23771910332297303711927 a prime? Yeah.

So it only remains to ask if an ouroborian [sic] capture is possible or not. Can the beginning of the sequence come back to itself at it’s tail?

Are there infinite of such beast?

Can Smarandahce numbers help us prove RH? Why can’t we prove that there are infinite of such Smarandache or not?

[Puzzle]

How to conceive a large Smarandache prime number? Can a prime number be so tall that once one finds a suitable totem one sees infinite extension to both ends and everything becomes meaningless.

]]>Then from automorphism – non-technically speaking- 2 was created which enables one to say G is not good. From duality came triad. Then we can say God is neither good or bad. When four is created, we can say God is good. Good is bad. Good is netiher good or bad. God is good and bad.

Point being, as each number is created it gives us more utility tools to express ourselves. Now we all know there can be no end to prime numbers. But as each primes are created introducing phenomenal universe where mind-boggling space is there where anything goes.

Stronger, weaker… theory. Suppose it takes x-digit number to come with a proof of RH and a disproof of RH. On “higher realms” whatever that may be, we need x+Δ – digit number to see if all the following cases exist:

RH is trueRH is false

RH is true but unprovable

RH is false but unprovable

RH is true and false but unprovable

Question now immediately becomes how many possible cases exist and how to use infinitary logic to examine all possible cases. Does Kripke frame and modal logic help? IDK. Never rigorously studied Craig Smorynski or for that matter Smullyan volume on combinatory logic.

Now how do we apply these? Is it provable that RH is provable and if THAT is provable, can *that* be provable? Infinite regress anywhere?

You see there are infinite possibilities. And ω-sphere can model all the possibilities EVEN the ω-sphere that does not contain the ω-sphere.

So basically ω-sphere is a generalization of Quine atom. It contains itself. And it doesn’t contain itself. It contains itself which does not contain itself…etcetera.

Task: Figure out a way to model things that are not even ‘modelable’.

And then try to see how phone number problem relate to this? Is there a form in phone numbers? For instance, how do we denote: 214-556-2000 has similar form as 214-445-5000. But how to use a language to describe their identical core form?

When I was stoned on synthetic weed, I saw a vision whose meaning I couldn’t take until later time. It was akin to the boards that chess master sees…a taxonomy…where he decides which program controls which program or rather the different avenues where games branch out in different quantum states.

Pic is worth a lot. Here it is sideways taken from hierarchical temporal memory (HTM) from Wikipedia.

And when I was reading about Diophantus it clicked immediately that Matyiasevich’s work may be a possible approach where the archetypal vision gave me a message from sub-conscious. Hoping it is my benzene I read the master’s paper on RH from a logician’s p.o.v.

His paper basically tried to combine number theory with computability. But ultimately I got the hint from above that may be one way to look at RH should be via Diophantine equations. Where each modules and sub-modules are governed in turn by other sub-programs and so on. That is why I had that image flash in my mind under influence of substance.

]]>

To recapitulate from where we left off yesterday, can one write a number so large so as to the entire concept of writing that number becomes meaningless?

But trifles aside, we will investigate the philosophical problems of induction. Do note: a paper stating if RH can be proven by induction does exist.

Our approach would be different. Before we tackle transfinite one we have to understand mathematical induction itself. Immediately the fact that jumps up is that why should induction work on numbers of arbitrarily infinite length? Suppose our entire history of the universe were binary coded and a tape started reading it. It has infinite length at each ends and the tape when reaches the time universe ends, we assume, that the time starts traveling background. So as the number in the meter of an Unbreakable wrist-watch shows that billions of years elapsed, and then a la Asimov/Hawking, time starts traveling back while the wrist-watch numbers keep increasing. Isn’t this an example of paradoxical event from…say, “overflow”.

Induction is related to entailment. Now one can easily devote tomes on the latter, but I will put the shortest disproof of entailment:

Consider *modus ponens*

if p entails q

if p

then q

or this can be rewritten as ( ((p → q) → (p))→q).

Now bear with me. Now all of mathematics can be rewritten in formal language of symbolic logic, where entailment glues and litters the proofs like broken shells and weeds in a sandy beach.

Now I have another problem.

Take MP. Take an invalid MP. Now send them as message to outer space as sample of logical thought. Suppose they receive the invalid MP first:

if p entails qif p

then p

It is an invalid form of MP. So they receive the second batch and unpack to see

if p entails qif p

then q

which is of course the valid form of MP.

However, the aliens will be terribly perplexed! So they had the wrong one first and they put a chip in their brain programmed with that form to evaluate life differently.

So every time a match strikes and fire is seen, they see the correct form of MP.

Then they are given the wrongful form of MP in their brain.

So every time a match strikes and fire is seen. But if a match is struck, then match is struck. That’s it. No fire. Nothing happens.

Now we come to the fun part. Suppose there are two envelopes. One has the correct form another the incorrect form. Tell the alien to randomly choose one. Be advised the chip in his brain is blank. So if he picks the invalid one, then he programs the chip the schema”

if p then qif p

then p

Now to confuse him we tell him to open the second one. He is still wearing the “wrong chip”, whose program is if p then q, p, then p. Thus, when he reads the correct one:

if p then q

p

q

Well, but the way his mind works is different. He is programmed with the invalid form ( ((p → q) → (p))→p)

So let’s run through this. Basically the form is if p then p, if p, well then p. Now reading second envelope, he reads if p then q, then if p it could be either p or q. It could be p because that is the wrong program in his chip.

My question is who is to say the first MP is valid than the second one. These are all arbitrary MAN MADE symbolic manipulations and not handed down in Stone Tablet but taught at schools and colleges with papal authority as if it is “IT”. Ultimate word of God embedded in Bible of logic which everyone has to take by belief.

If we lived in an alien planet where a man could penetrate wall and bring out stuffs from other side, then the logical structure of that reality would be very different. Or if Jesus did his miracles, again the mathematics would be 1=1+1+1+1…… if you want to model how he pulled all loaves of bread from a single container.

But math IS a religion. It is magic. It is founded on beliefs and axioms which are peer-reviewed. In class I read Pojman’s (West Point grad) book and I can relate to what he said that ultimately we may come to a realization where everything in this life is maya or facade (my description). We have been lied to. Senses lied to us.

For more of my motivation and where I am coming from click here.

]]>Let us **not** solve Riemann Hypothesis. Let us instead bring the child like wonder – one which I had trying to decipher a pattern among prime numbers or to prove the infinitude of primes by myself. So we shall tackle problems involving how to think of primes when they become large… REALLY large? Or why cannot we predict the next prime number? We will consider the big picture and try to dissolve the problem in an outer framework as Grothendieck might’ve expected in his creation of architecture of mathematics.

Well, Euclid dealt the first blow by proving – constructively? – that there are infinitude of prime numbers. I already wrote a paper trying to express the fact that it is a tautological proof. Here is Euclid’s proof:

ProofLet us suppose that

p 1 , p 2 , p 3 , … p nare prime numbers. Multiply them together and add 1, calling this number a new integerq. Ifqis a prime number, then we have a new prime. Ifqis not a prime, it must be divisible by a prime numberr. Butrcannot bep 1or any other from our original list of prime numbers, because if you divideqby any ofp 1 , p 2 , p 3 , … p nyou will get a remainder 1, which means thatqis not divisible by any of these prime numbers. Soris a new prime. Whichever way you choose to look at it, either you have found a new primeq,or ifqis not a prime, than you have found that it has a new prime for a prime factor.

The paper I wrote was a very informal one and during writing of it I knew nothing of Brouwer or Kleene or even the details of intuitionist. But I raised two objections:

- How to define prime? Because the definition of primality is predicatively dependent on their meanings? I used the car example. If there are infinite chasis then there must be infinite cars, for no car can be constructed out of the form of chasis. But by definition, prime numbers include 2 and not 1 and it seems we’ve put a seed that describes the so-called pseudo-pattern. Primality is an adjective and denotes the characteristics of a number. Just like ‘redness’. Now if one knows there are infinite number of apples all red, then
*ipso facto*‘redness’ is infinite. I have not studied set theory but it is about one set containing another. Set of natural numbers embed prime numbers. Intuitively, if there are infinite numbers, and if prime numbers belong to sub-set of natural numbers, then it follows automatically that there are infinitude of primes. Common sense. Yet, Euclid’s proof is is a convolution of eye-wash to give an illusion of ‘proof’ when it is circular in nature. - My second objection was how do we even count? If you scroll up and check then you shall see that we already assume a finite collection of primes exist. I looked at translation of elements but Euclid defines terms in terms of another resulting in vicious circle. What is divisibility? Euclid uses line segment and other primitive analogies but modern problems do not go away.However the purpose of this brainstorming is not to debate about circularity of the proof nor about the constructive nature of the proof. What I am more interested in what happens when numbers become large…. REALLY large?

Currently, the question posed above exists in the following form in philosophy.stackexchange.com: How to understand numbers that become really large?

But we are interested in the algorithmic compressibility of large numbers. Or to state a bit formally the Kolmogorov complexity of primes.

To give a taste of just exactly what kind of numbers we are dealing with here is a link. At naked glance, basically it’s a page full of random digits. But the number is a prime. Sure if you are Ulam you may seek patterns such as Ulam spiral:

Stare you may at this mandala of dotmatrix pattern but God’s face won’t show up. So although it gives us a sense of capturing of large numbers it doesn’t elucidate anything else.

Magritte, a favorite painter of mine, Belgian, wanted to paint ‘unthought of thoughts’ and as the image shows it’s his way of attempting the impossible which we shall emulate. albeit logically.

Since it is an informal treatise of brainstorming here are some concepts that bothers me. How to transcend or go beyond predicative? Or as I asked:Does the concept of predicativity need to be formalized to go beyond Feferman-Schutte ordinal?

There is also the problem of Ω which Cantor declared as the ultimate logical limit and may even be called “God”. Absolute logic of Cantor. Also, Woodin’s pursuit of L: **Ultimate Logic**. Also related problems in mathematics, in spite of Peano’s axiom and Lambda calculus, is the fact of entailment. Does R resolve the paradox of entailment?

And of course, in terms of set theory there is Kunen’s inconsistency theorem is at top of Cantor’s attic. But why? Why is Kunen inconsistency at the top of Cantor’s upper attic?

So we are just putting scraps of notes and puzzles here and there and finally we will attempt to combine and connect all the thoughts. Another problem is mathematical formulation of Indra’s net, paradox in relevant logic, etcetera.

Unless we tackle the foundational issues regarding number theory I am afraid the task will not be solved at all.

What is a proof? I mean if I tell you to prove that 2+2=4, will you show me the paleontological treatise of Russell-Whitehead? Cannot 2+2=3 if we define 4 as 3 and vice versa? Who comes with these arbitrary laws?

You will stop my nonsense at this point immediately saying well they are symbolic representations of quantities. I perfectly understand the mouthful but that is just a veil of circular talk. Sorites permits us to ask “what constitutes a quantity?”

Intuitively speaking, Riemann Hypothesis deals with prime numbers, zeta function, complex plane and induction.

Can induction be used to prove RH? Let’s back up a bit. I was opposed to Euclid’s proof for a long time as I did not understand it. In deep depression I realized that the reason why average people don’t understand complex math problems is not because they are stupid but because of the carefully camouflaged circularity in mathematical argument. If Euclid began by saying there there be prime numbers: p1,p2….. I would stop him right there.

But let’s accept Euclid. So that means there is an infinitude of prime numbers. Loosely, a number with so many digits that they can easily outnumber the particles in universe. Skewes. Now Hardy managed to give a description of Skewes number which I am reproducing here:

Hardy thought it ‘the largest number which has ever served any definite purpose in mathematics’, and suggested that if a game of chess was played with all the particles in the universe as pieces, one move being the interchange of a pair of particles, and the game terminating when the same position recurred for the 3rd time, the number of possible games would be about Skewes’ number.

But one caveat from that same article:

One last thing before we move on: the Skewes’ number we’ve been talking about is the

smallerof the two. There’s another Skewes’ number that the mathematician demonstrated in 1955. The first number relies on something called the Riemann hypothesis being true – it’s a particularly complex bit of mathematics that remains unproven but is massively helpful when it comes to prime numbers. Still,ifthe Riemann hypothesis is false, Skewes found that the crossover point jumps all the way up to 10^10^10^963.

Let us however return to the “intuitive feel” for the problem. What do we know? Well we know that there is a concept of primeness, and we can manufacture limitless mathematical structures from that concept of primeness. But what happens when a new prime is found or discovered? It enables us to build bigger and bigger building blocks or numbers. What of dimensions? Say a person lives in 2-dimensional flatland; what will happen when he moves up to third dimension or fifth or seventh or eleventh….It’s as if one is unlocking or jail-breaking the universe from it’s hidden contents. It’s like every step up is an opening of new world or strata. If each levels are prime numbers then as one reaches the ultimate prime found so far, then she will be propelled to another new world when a new prime, say, P, then P helps us to launch to new dimension where the world may be very different.

But these are just sci-fi thought experiments and not maths.

In Logical Dreams set theorist Saharon Selah casually mentioned about his “dream”. User **Junkie** replies quoting Shelah here *( I copy-pasted the image as I am still learning how to LaTex the posts here in wordpress).*

I know forcing is a relatively difficult concept to master which requires hours of devotion and I do not know much about it. But doesn’t the fact that what we intuitively thought has a semblance of his dream? Consider that the universe is a compilation of marble like particles. And on each particle you write down a symbol. It could be anything. Chinese characters, Egyptian hieroglyphics, Mayan glyphs….. Then it immediately becomes clear that there could be a finite list or infinite list. It’s finite because we are humans and we have finite collection of symbols. But they can be infinite. I can just create a new one, such as, |! , to signify “a 3rd degree murder” where the line is a symbol or sword or spear or stick and the exclamation mark a danger sign. Thus logical symbols are also creative outputs. As technology evolves, we can compress many complex ideas in a single glyph. Korean glyphs already have such encapsulation as well as ideograms and Mayan glyphs. What if we were to create our own number glyphs where arbitrary symbols will encapsulate, say, a consistency strength of a proof or a large prime number. Now, can we create a system where we take all the symbols of the world, start permutations, and produce one proof of another.

In simpler terms, what are the odds that if a deck of cards with mathematical symbols were to be uncovered one by one, it’d spell out the proof of RH?

Now back to Shelah. In short his dream is that RH is unprovable in Peano Arithmetic but possibly provable in some higher theory.

I am smelling a Godelian self-reference application somewhere if we were to pursue this.

Why?

Because no matter how complex, convoluted, succinct, algorithmically compressible, or a large finite number of symbols are used to prove RH, the number of notations and symbols to be used in that infinite Turing tape will be far,far, faaaaar less than the large primes which are not discovered yet. You see, this is the danger of Euclid’s proof. He did deal the first blow, and it seems that no matter how we try to come up with a proof of RH theory, unless self-reference is used, we cannot make any statements about that RH, because the number of digits in a prime can be soooo large as if to encode Britannica.

Suppose this is a prime number spread out: 231248233489278482947239797523497593427999………………..

89435735973457034905734907530447503475340573405730975034750347530750347

I basically typed some random numbers from keystrokes. It may or may not be prime. But that’s moot. We are not interested in the number itself rather the ellipsis. Can a prime be so large as if to have an ellipsis where the entire length of universe is just a speck in that stream?

And that’s exactly where the problem lies. May be it’s meaningless. Indescribable or a badly worded problem. Think about it. There are layers of planes, let’s call them astral planes, and as you move upward from one plane to another you realize there is an infinite planes. But then you want to know if the framework that supports the plane is in 1-1 correspondence, then if the planes extend to infinity, will there be a 1-1 correspondence between the astral planes and the framework that supports it. While it may appear true if trillions of digits are in accordance, it could also be false. Assuming that is true (say, due to sheer statistical evidence) we cannot claim that it is true for all astral planes. Because the next plane that is discovered has already opened up and exploded another new world ie new numbers and that cyclically involves more numbers or astral planes and then when one reaches the highest plane, since there can be still higher plane, one needs to step out of that system or construct higher theory. And when one invents new language or mathematical manipulation of symbols, no matter what higher theory one comes up with, it cannot talk prove anything about RH in PA because, those metatheories would require further proofs.

But I want to get back at the card-flipping thought experiment. Suppose you are really lucky and throw random symbols on a canvas that stretches to infinity in all direction, and poof! those symbols fall into perfect places magically to create the proof of Riemann Hypothesis. And it proves that RH is true. So what exactly happens when RH is true? That means that all non-trivial, zeros of the zeta function all lie on the critical line.

**But whatever proof one uncovers, that proof is still within a system that can be considered marginally small in terms of sheer amount of digits in a prime number.**

This is a subtle point. Because although people are hard-nosed skeptical about quantum theories and what not, my major motivation to asking that large number question in the philosophy forum was if “laws of logic” “break down” “at any point” when numbers come large. There is of course, Poincare Recurrence Theorem but that was a sore subject and got subdued, edited and vanished because of so power the minority mods wield in such forum.

Now I can boldly proclaim in my own turf: CAN A NUMBER BECOME SO LARGE AS FOR THE LAWS OF PHYSICS TO BREAK DOWN WHEN ANYTHING APPROACHES SUCH BOUNDARY? Okay, it’s really not far-fetched because straight from that question this is what I also found:

It all started after reading *The Unimaginable Mathematics of Borges’ Library of Babel* and the review of it here. The problem arises when one sets to catalog the books as the number of the different books become approximately 10^10^6 (yet smaller than googoolplex), justifying the term “unimaginable”. Susan Stepney points out in the review that when one wants to catalogue the number of books in Library:

[…] the problem of finding a “short” description of the book to put in the catalogue: there are not enough short descriptions. For the Vast majority of the books in the Library, the shortest description (that distinguishes it from other books) is the book itself. Most books cannot be “compressed” to a short description.

And then comes the punchline:

Or,as Bloch puts it, **the Library is its own catalogue**.

Library is its own catalogue(!). Some concept there. Or like** Ω ={Ω} **like a Quine atom of Non-well founded set theory.

A contains B. B contains A. Paradox! Ah! My terrain. Law of Excluded Middle and the whole enchilada.

Here is a question: How to axiomatically build up from an axiom that is self-referential or paradoxical?

Another problem I am wrestling with is w-consistency. If T is This is true. And if ~T is This is not true, then : *T* is **ω-consistent** if it is *not* ω-inconsistent.

Apparently, there exists a generalization of ω-consistency to Γ-consistency which Leon Henkin used. I do not understand the latter at all as I couldn’t get my hands on sufficient resource but I was thinking more in terms of Indra’s net or.. if you will permit, an ω-sphere.

It’s an abstract generalization of ω-consistency. Basically, like de Finetti’s theorem, it is a sphere that contains all possibilities including the possibility of a non-possibility or non ω-sphere. Analogy would be again L, ultimate logic, Cantor’s God, or multiverse. This tool will help us model any model.

]]>I often wondered if it is possible to create glyphs (pictorial representation) of all combination of telephone numbers that can be decoded at glance. Unless the number consists of familiar patterns, form, sequence it becomes frustratingly difficult to commit them to memory driving at 65mph on freeway.

First let us introduce the glyphs for base (0,1,2….9):

Following reveals the whole spectrum of numbers with a specific BASE (in this case 2):

Of course the various types of niche or arches represents different form relative to “BASE 2”. If the same arches appear at the upper-right or left corner (depending upon pattern) then it will denote different numbers per BASE.

These are all very arbitrary; so we can use any general form for any specific arch. We shall use the special case of Magritte’s man for the sequence which are all of the same digit.

Let’s us now consider different variations of a 3-digit number.

It can be *increasing*. Such as 123

Or *decreasing*: 321

If neither, then we can have a *palindrome *like 323.

*Form *of 323 reversed can be 232. Call it *reverse* or *obverse* palindrome.

We may have all *same* 333.

We can also have a double double unit such as 662. Reversing it gives 266.

Enough rambling; let’s play with some random 3-digit numbers. Using some random random generator from internet I get a list whose general form I have verbally described:

206 = Turns out we do not have a convention yet. But a guiding factor is 0 which *splits* a 26. Now this 26 can be thought of as 13×2. What does 13 do? Well it’s is 1 less of 14, or *sub-base* minus 1 of 714, my city area code. Note: We will try to think backwards to this CODE of 714. Since we are yearning to be as intuitive as possible, feel free to derive it to a pattern based on your area code.

312 = Again, it has not been defined yet. But to me a pattern that may strike out is that it is a *increasing *sequence which has been *shifted to the right*.

422 = This one we have in the bag. It is a unit double double *form*.

534 = This is an increasing sequence shifted to the right.

653 = It is decreasing sequence.

305 = This has the same form as 206.

844 = Unit double double pattern.

304 = It is 1 minus 305.

852 = Decreasing pattern.

968 = This one is a weird one. We will return to it later.

*Okay, so how do we generalize to an algorithm given any sequence of 3-digit number?*

Well, let’s see. Right now, word count is 490. This can be thought of as 7 squared zero, giving us 7 for the first digit of my area code 714. But how to verbally pin it down forward?

STEP 1: UNIT(BASE)

STEP 2: SQR(R)

STEP 3: ADDZERO(R)

which roughly translates as take the unit of BASE which I am redefining to be 714. Note, previously we talked of a different base. So, take the unit of BASE and SQUARE the R(esultant), then adding a zero to the end result.

How to represent 094? Simple. Call the first algorithm BUTTERFLY. And then use the function REVERSE.

Or REV(BUTTERFLY).

Things are quickly getting muddy. So let us back-out a second, and get a random 7-digit number. Certain plumber in a certain state has a number 439-3407.

What pattern seems to jump out (bearing well in mind it may vary individually?). It can be grouped to: 4,39,34,07 because the 3-digit sequence has no basic pattern.

Although it is of different state, I will affix it to my area code. Then we will create an algorithm. First , it’s time for some terminologies. If we take the CODE 714 and call it BASE, then there are components called UNIT or 7. DBLUNIT or 14. Singleton or 1. SUBUNIT or 4. SUBBASE or 71.

To unleash an inner Bhaskara, here is the algorithm. Extracting SUBUNIT, subtract 1 to get and putting it at the end, then reverse it around 9 ending it in add-1 of it and sub-2 of it.

Quite a mouthful. To formulate it in steps:

STEP 1: SUBUNIT(BASE)

STEP 2: SUBUNIT(BASE),SUBUNIT(BASE)-1

STEP 3: WRAPAROUND(SQUARE(2,2), {here (2,2) denotes step 2, position 2]

So far we have BASE or 714 and then SUBUNIT of 714 is 4. Then we write it as it is comma “as it is” minus 1. Or 4,3.

“Wrapping it around” 9 gives us: 43,9,34 where 9 is actually square of step 2, position 2.

A caveat: the grouping has changed now: It is (43)(9)(34). We definite 9+1 as 0m where 9-2 obviously gives us 7.

Where does the picture fit in? We are getting there. Since it is a BASE 4 game, we can use the glyph of 4 with the various arches representing different forms or patterns.

Before it gets further confusing, let’s harken back to the medieval lady with arches. So there are 24 different patterns for the number 2 as the SEED VALUE. Furthermore, we decide that putting the arches to the left side will give different values. So 48 different patterns.

Difficult part is memorizing all the 24 different patterns. Then one can mix and match and generate any number. Theoretically speaking of course.

For 7-digit number sequence there are 10 million permutations. But we only have 48 different forms for each number and there are 10 of them giving us 480. This barely scratches the surface.

Is there a taxonomy of forms of 7-digit phone numbers? Can we at least force a pattern? The thing is each glyphs by themselves represent all of the same digits. So the Egyptian scribe, if written by itself, gives us 111-1111.

Adding the thinly bordered ogee arch of the first character in the spectrum gives us a random pattern of an algorithm. Basically what it’s saying is take BASE-1 and perform a familiar operation. And when it’s on the left, it will perform a reverse operation.

Admittedly of course, the ornamental arch may not be quickly grasped driving at 65mph highway; but, due to the visual nature it will stick to memory more easily.

Another possible representation can be using the skeletal form of the following:

Bubbling in the nodes will give either number. Open or closed. And shading in segment will give a sequence. Do visual tangrams exist for all permutations of 7-digit number? How about 123-4567? May be an acyclic graph for 1/2?

We have reached a cul-de-sac. Introducing a new glyph, hopefully will help resolve the missing pieces of number forms.

Thus I ponder how much can we lasso the focus to scrawl an equation on blackboard that will enable predicting a car accident before it happens. Surprisingly, Google seemed to have a good match for the searches and it took me precisely to a link which has discussed this issue: *The numbers behind NUMB3RS: solving crime with mathematics*

Now admittedly, I am not a big fan of the show, simply because I feel that it has tried too hard to popularize the sober art of mathematics for lay audience. Not everything must be edutainment and while Scott Free productions has some excellent visuals, it has very much watered down the mathematics insulting audience intelligence. But my intention was not a critique of the show and it seems there is an episode which aired titled *Manhunt* that dealt with Bayesian Inference.

As the afore-cited free link of Google Books shows that apparently 9/11 attack on the Pentagon was predicted on May 2001 via a software called Site Profiler utilizing Bayesian network (also known as belief network). The term Bayesian is named after Reverend Thomas Bayes, a Presbyterian minister, who composed two works in his lifetime, the first one of which was on theology *Divine Benevolence, or an Attempt to Prove That the Principal End of the Divine Providence and Government is the Happiness of His Creatures* (1731).

Bayes’ Theorem which has wide applications from Artificial Intelligence to drug testing, figuring out guilty party in taxicab accident (see here) to aiding entomologist identify a “rare subspecies of beetle” (frequentist example) can be best appreciated with the following example (Wikipedia):

If someone told you he had a nice conversation in the train, the probability it was a woman he spoke with is 50%. If he told you the person he spoke to was going to visit a quilt exhibition, it is far more likely than 50% it is a woman. Call

Wthe event he spoke to a woman, andQthe event “a visitor of the quilt exhibition”. Then:P(W) = 0.50, but with the knowledge ofQthe updated value isP(W|Q) that may be calculated with Bayes’ formula as:in which

M(man) is the complement ofW. AsP(M) =P(W) = 0.5 andP(Q|W) > >P(Q|M), the updated value will be quite close to 1.

Returning to the original topic, can Bayesian inference from a mathematical model aid in assisting a car accident before it happens? Research does not predict accidents at will; they only reconstructs model of past accidents. *Journal of Transportation and Statistics* has a paper by Marjan Simoncic of Slovenia titled A Bayesian Network Model of Two-Car Accidents along with Gary A. Davis’s Bayesian reconstruction of traffic accidents, the abstract of which has been reproduced below from Oxford Journal:

Traffic accident reconstruction has been defined as the effort to determine, from whatever evidence is available, how an accident happened. Traffic accident reconstruction can be treated as a problem in uncertain reasoning about a particular event, and developments in modeling uncertain reasoning for artificial intelligence can be applied to this problem. Physical principles can usually be used to develop a structural model of the accident and this model, together with an expert assessment of prior uncertainty regarding the accident’s initial conditions, can be represented as a Bayesian network. Posterior probabilities for the accident’s initial conditions, given evidence collected at the accident scene, can then be computed by updating the Bayesian network. Using a possible worlds semantics, truth conditions for counterfactual claims about the accident can be defined and used to rigorously implement a ‘but for’ test of whether or not a speed limit violation could be considered a cause of an accident. The logic of this approach is illustrated for a simplified version of a vehicle/pedestrian accident, and then the approach is applied to four actual accidents.

Clearly the question posed in the heading doesn’t seem that much in the realm of sci-fi as given by first impression. For an additional resource see the paper

PREDICTION UNDER BAYESIAN APPROACH OF CAR ACCIDENTS IN URBAN INTERSECTIONS