## Friday, September 28, 2007

### Topos 4

Topos 4
http://arxiv.org/abs/quant-ph/0703060 The topos articles.
http://.arxiv.org/abs/0704.0646

Andre Willers
28 Sept 2007

For Ermeine on request .
Don’t worry . We reach a natural pause soon .

Other Sources:
http://andreswhy.blogspot.com/ : see in general , or search for “mining the Oort” , “Topos ” , “Topos 2” , “ Topos 3 “ etc Transcendent numbers ,etc.

First , a Godel detour .

Arith II :Defined as
The standard axiom-set of 10 axioms that gives rise to our set of numbers .

I here use the usual number-line as learned at school . A line that starts at 0 and continued indefinitely (to infinity) via the property that (x+1) <> x .
Ie that numberline never loops back on itself .
But this axiom is arbitrary .
(The axiom that gives difficulty is usually given as the axiom Number 4)
This is analogous to the parallel-axiom in Euclidean systems that gave rise to non-Euclidean geometry .

Godel proved rigorously that if you have a theory that incorporates ArithII , then you can formulate statements which cannot be derived (proved) from the given axiom set as True or False unless you incorporate at least one extra axiom . In other words , at the heart of our number system lies statements which are both True and Not-True .

This is equivalent to stating that the set of statements represented below cannot be proven complete unless n is an element of ArithII .

But if n is an element of ArithII , then it is infinite . Not just an ordinary infinity , but an infinity where aleph -> omega .

ArithII + A(1) = Arith I(1)
ArithII + A(2) = Arith I(2)
.
ArithII + A(n) = Arith I(n)

Where A(n) is an axiom defining a loopback of the numberline .
As you can visualize , the loopback can terminate on any point of the ArithII numberline . Hence , n must be an element of ArithII .

This is not a very rigorous proof , but true nonetheless .

What does it mean ?
1. No General Unified Theory (GUT) is possible using a finite set of axioms .
This means that mathematics and physics are open-ended . There is no end to new understanding (axioms) . Literally .

2. An entity capable of using infinite sets of axioms would be a Reality Class four entity . Ie strong godlike .

3 . Local groupings of axioms .
These can be found by algorithmic means . At least two rigorous ones and one iffy one are known :

3.1 The Scientific Method
3.2 Transcendand number tunneling (ie numbers like e , pi) . (Note my use of 1/e in previous posts.)
3.3 Direct inspection . (See “Souls” below)

The Willers-Venn diagram .
Ordinary set-theory cannot be used , since elements in the Universum cannot be given a Defineability Axiom .

This is the trick :
Use a window on the Universum . Simple ,eh? But very powerful .

Take a piece of paper and draw a rectangle .
This is a window on the Universum , all the defineable and non-defineable thingies .

Now you do not have to worry that the Universum has no boundaries , as long as your internal Venn diagrams do not touch the sides of the window .

Inside the window , draw the normal intersecting Venn circular diagrams denoting Y and N and not touching the sides of the window . The Intersection being YN .

It is not easy to find YN by just looking at Y or N .

But we can sneak up on it by looking at Not-Y and Not-N .

In Aristotelian systems ,
{Not-(Not-Y)} Intersection {Not-(Not-N)} = YN

but in Non-Aristotelian systems
{Not-(Not-Y)} Intersection {Not-(Not-N)} = YN + Everything outside the Y or N circles .

Conservation Laws and chaos .
If you have a system where nothing has been defined , and no conservation of any kind can be found , regardless of defineability and repetitiveness axioms , then the system can be described as truly chaotic . No internal space or time metrics can be found . In other words , it is a point . But in an infinite sea of such universes , some will be closed and some will interact . The interacting ones give rise to the phenomenon known as vacuum energy .

There is a further discontinuous spread of interaction giving rise to “particles” .

The essential point is that if there is a conservation law in the set Y , then there is a mirrored conservation law in the set N . Most important that there is then a conservation law that can be found in the “pseudoset” ( YN + Everything outside the Y or N )

This means that elements of YN is holographically spread all over the show , regardless of any space , time or any other constraints less than class 4 reality .

Does this remind you of anything ?

Souls have never been proved or disproved after 70 000 years of trying .
Yet they are as real as a car-bomb in the market .

The conservation effect in YN structures means that souls do exist . But our definition of individuals as a traveling standing-wave of memories needs some work , as each wave terminates on going to sleep . The waking is rather a random affair . See previous posts .

Can the soul be destroyed ?
Yes . If a class 4 entity “looks” at you , YN->0 and the elements of personality become fixed . Free will , which is another description of personality , ceases . Of course , the entity can restore the YN state vectors exactly . But why ? If He bothers to Look , you have the Heisenberg Hop with a vengeance .

Class 3 entities or less cannot destroy a soul . Attempts to do so by restricting the freedom parameters of individuals end in tears .This is true regardless .

The inverse is interesting . Increasing the freedom parameters of individuals usually works . but it can badly wrong as with Nazism and Stalinism . Then it results in even larger scale bloodletting .

Ah well .
The rest you will have to work out for yourselves .

Andre

## Sunday, September 23, 2007

### Final warning of War .

Final warning of War .

I am not repeating this .

Andre Willers
17 Sept 2007

Attention all family members .

The probability of a limited scale war of the order of WWI has risen to 95% - 100% .
Time of outbreak : Sept or Oct 2007 .

Scope :Far and Middle East

Scale : Limited nuclear . Limited biowar .

Duration : about 6-7 years .

Effects:
1.Immediate curtailment of tourist industry . (Insurance will not cover flights, planes will be converted to military use .)

2. Volkewanderung .
How bad can it be ?
The sudden cessation of food aid from US/Canada/South America as the ships cease to arrive will cause an immediate food crisis .

A human can survive without food for about 5 days . The wave-front of desperate food hunters is then about 5 x TravelTime x time from a population center . But note that the first arrivals plunder the food supplies very thoroughly . Overland routes become death-traps as both sides battle to extinction .

The front wave is also thin .

That is why fast travel via coast-hugging boats enables the locusts to move faster than defense forces .
This has happened before . During the collapse of the bronze age , the Peoples of the Sea were the only survivors . They could outrace the news of their coming and focus large forces .

In this scenario , the survivors of the desperate food seekers move down the East Coast and plunder lightly defended places like Jeffrey’s Bay . Do not think you are safe . One thing the English and the Vikings showed was that sea-borne attackers can arrive at any moment .

At present moment , the SA Navy cannot defend against this threat . This is not a deep-sea threat , but a coast-hugging threat . U-boats and frigates are no use . You need small boat navy . We can make them , but in the interval the coastal region will suffer .

Do not go near the Eastern Coast (ie Jeffries) during the next year . I am serious . This sort of crisis blows up quickly .Hundreds of millions of starving refugees can be stopped overland , but is impossible to stop in coasthugging mode .The starvation period is 5 days . The pulse is immediate and deadly .

And don’t think it can’t happen to you . That is what the Jews thought when the they saw “Arbeit macht frei”

South Africa:

Will it survive ?
Yes , and quite handily as well .
A result of the above will be a pulse of expansion across the continent . This will be contested by a weakened China , India , US , Russia and EU .

Stirring times .

South African casualty figures from crime alone is larger than the war in Iraq . If you add in the deaths from AIDS , it is much higher .

The AIDS problem is about to be solved . The crime problem can be exported (as the British did) . The resulting explosion will outcompete Chinese and Indian influences in Africa .

Unfortunately , the resultant mix looks more like the Draka .

An extremely aggressive outward pulse through Africa , fuelled by reduction in crime levels (ie we export our crooks) and relative reduction in death rate from AIDS .

The rest of the world .

Andre

### Topos 3

Topos 3

Andre Willers
21 Sept 2007

For Ermeine on request .

Sources:
http://arxiv.org/abs/quant-ph/0703060 The topos articles.
http://arxiv.org/abs/0704.0646

“Physics from Fisher information” by B.R.Frieden ISBN 052163167X
Alternative Topos-type derivation of physical laws .

http://andreswhy.blogspot.com/ : see in general , or search for “mining the Oort” , “Topos ” , “Topos 2” , Transcendent numbers ,etc.

Zero-point Energy , Zitterbewegung and Postdiction .

How to get macroscale effects from quantum fluctuations .

Zitterbewegung : the electron near lightspeeds jitters around . This is derived from the Dirac equations as interpreted by Schrodinger in the 1930’s . The electron moves near lightspeed within an envelope . Tunneling will take place if the electron is seen as a particle .

Puthoff (1989) interpreted that this jitter can represent energy asymmetrically transferred from quantum foam particles .

Further , that the energy of the electron mass equals this nett energy transference .

Thus , the electron can be thought of as a standing wave maintained by vacuum fluctuations .

Postdiction:
This is a YN>0 situation .
But we can make it true by pinching the postdiction in a specific way .
The output is then extra electrons (current) , extra push(EMV) or both in a directly usable form , directly derived from zeropoint energy .

Cheap energy .

But note that there is a hidden cost : Entropy pollution .

Entropy pollution :
By definition , life decreases entropy inside it and increases it outside it .

This causes problems with quantum devices . (Heisenberg’s principle can be seen as a mild form .)

Chernobyl.
See a borderline nuclear system like Chernobyl at the end of the safety test . Containment systems were at a cusp , but previously found safe . Then the night-shift comes on . They understand less , thus their entropy is greater . The higher entropy means higher uncertainty . This bumps the probability of a fission per atom up over the stability level .

Not “boom” , but “sizzle” .

A classical example .

When the typically human fingerpointing started , some did try to point out that this was a routine performed many times before , but never at the phase change between an old shift and a new shift .

Hoist by Heisenberg !

Hopefully , nuclear weapons are more robust .

Entropy Sinks.

Any zeropoint energy device (and here we include lifeforms) require an entropy sink far away from the action to function at Reality Class 1 and 2 levels .

Ignorance is a reasonable ground-level state , but organized religions are much more efficient entropy sinks .

The mass media are also quite efficient at spreading entropy about .

This is why they evolved .

But high-intensity exploitation of different entropy levels (like zeropoint energy) will require specific designs. It is not too difficult , once it is known .

Note that Electromagnetic Waves of any description that passes through the body (ie low frequencies like radio , TV , Sun spots , etc) , increases the order inside the body (increases entropy .)
This is a Bad Thing unless you have compensatory mechanisms .

Increasing order at DNA/Intron level leads to interference with the quantum-level optimization of pathways .

Luckily , we have a stop-gap mechanism for low intensities :
Heat-shock proteins chaperone and mask small folding irregularities due to heat or small mutations . If they are overwhelmed (like big pulse of low-frequency EMP from meteor strike , large volcanic explosion , close proximity to cell-phone tower ,nuclear explosion) , the genetic and protein changes are suddenly released . A pulse of change ensues in the organism . Some think that this is one of the mechanisms driving punctuated equilibrium in evolution .

Negative Entropy Battery.
It is interesting to note that this mechanism operates as a storage battery of change , then releases it at once or slowly depending on the environment . This ties in with introns and repeated strings of genomes .

As expected from evolutionary theory , this system will operate better by orders of magnitude if it fluctuates . A relaxation of stress will cause an explosion of numbers in the most favourable mutations . An increase in stress will weed out the non-survivors . Repeat .

The social systems of human survivors of hundreds of cycles of this have got ups and downs built in .

Civilizations rise and fall .

But they fall jolly well faster if the internal Entropy inside each individual increases rapidly . I refer here particularly to the well-documented fact that social unrest is closely correlated with EMV activity caused by the sun . (1990’s)

The rapid increase of internal entropy forces a decrease in external entropy . Social disorder increases .

In the absence of extreme point-sources of zeropoint energy , entropy can be taken as fairly uniform over large volumes . (Close to a conservation principle)

So , if internal order per individual increases , the external social order decreases .
The more radio , TV , computers , solar flares , the greater the social unrest .
If the EMV pulse goes over a certain threshold , masked mutations are released and the cancer rate goes up .

HIV
The virus is reasonably successful because the mechanisms that would normally choose an optimal pathway to combat it is masked by the increase in entropy .
Their quantum mechanism is disturbed .

Just restoring a Faraday cage is not sufficient , as the balance has already been disturbed .

The internal entropy needs to be increased .

Blasting the organism with really random electromagnetic waves will drastically increase the disorder inside it , in contrast with the ordering waves it is exposed to .
Hopefully , quantum choices of optimal pathways are then made in a MORE noisy environment . Resonance effects come into play .

Really random is extremely difficult .

But how to get really random EM waves economically ?

Applause .

This is the wavefront of thousands of people clapping hands in a semi-random fashion. Fairly random .

Listening to applause for an hour loudly should reset some random counters .

Andre

### Benford's Law and number 11

Sigh .

Accountants should know better .

I refer you to Benford's Law (Google it) .Wikipedia has a good reference .

The frequency distribution of the first digit of numbers to base 10 (not labels , so no use in lotto) is
1 2 3 4 5 6 7 8 9
30.1 17.6 12.5 9.7 7.9 6.7 5.8 5.1 4.6

This has been rigorously proven as a property of numbers , not just a statistical effect . It is also scale and base invariant .

The number 11

So , 11(base 10) = 10(base 11) , and the frequency of the first digit will have nearly the same distribution as base 10 .

The frequency distribution of the first digit of numbers to base 11 is
1 2 3 4 5 6 7 8 9 10
28.9 16.9 12.0 9.3 7.6 6.4 5.6 4.9 4.4 4.0

Why base 11 ?
Because of the hidden assumption in the sampling . No what the mapping is , the sum of the digits are kept smaller or equal to 11 .

This is the same as defining a base 11 .

This is typically Human procrustean sampling . Chop and stretch .

So , on these axioms ,the number 11 will appear about 29% of the time , regardless of the mapping used . Any significance can only lie in a divergence from this expected frequency .

There are numerous scams and faulty analyses based on this property of numbers .
Numerology is one . Elliot waves to a certain extent .
Of special note is the"Bible Code" , which appears impressive . On analysis , it is simply trawling through a large but finite set of human grammar- organised numbers using different bases and finding higher probabilities of some sequences . This is like saying that one horse will run faster than another . True , but of very limited use .
Vibrations , which is merely numerology in another guise .
Quantum physics , the latest human fad of how many true angels can dance on the head of a pin .

Andre

Start Post scriptum.
---
I Quote from the Wikipedia article :
Even more astonishing are the effects of Benford's Law on number sequences. Intuitively, most people assume that in a string of numbers sampled randomly from some body of data, the first non-zero digit could be any number from 1 through 9. All nine numbers would be regarded as equally probable.
But, as Dr. Benford discovered, in a huge assortment of number sequences -- random samples from a day's stock quotations, a tournament's tennis scores, the numbers on the front page of The New York Times, the populations of towns, electricity bills in the Solomon Islands, the molecular weights of compounds the half-lives of radioactive atoms and much more -- this is not so.
Given a string of at least four numbers sampled from one or more of these sets of data, the chance that the first digit will be 1 is not one in nine, as many people would imagine; according to Benford's Law, it is 30.1 percent, or nearly one in three. The chance that the first number in the string will be 2 is only 17.6 percent, and the probabilities that successive numbers will be the first digit decline smoothly up to 9, which has only a 4.6 percent chance.
A strange feature of these probabilities is that they are "scale invariant" and "base invariant." For example, it doesn't matter whether the numbers are based on the dollar prices of stocks or their prices in yen or marks, nor does it matter if the numbers are in terms of stocks per dollar; provided there are enough numbers in the sample, the first digit of the sequence is more likely to be 1 than any other.
The larger and more varied the sampling of numbers from different data sets, mathematicians have found, the more closely the distribution of numbers approaches what Benford's Law predicted.
One of the experts putting this discovery to practical use is Dr. Mark J. Nigrini, an accounting consultant affiliated with the University of Kansas who this month joins the faculty of Southern Methodist University in Dallas.
Dr. Nigrini gained recognition a few years ago by applying a system he devised based on Benford's Law to some fraud cases in Brooklyn. The idea underlying his system is that if the numbers in a set of data like a tax return more or less match the frequencies and ratios predicted by Benford's Law, the data are probably honest. But if a graph of such numbers is markedly different from the one predicted by Benford's Law, he said, "I think I'd call someone in for a detailed audit."
End Post scriptum.

-----------

-----Original Message-----From: Botha, Aniki [mailto:abotha@kpmg.com.au] Sent: 20 September 2007 06:02 AMTo: jade chilvers; Bradley, Angie; Lappin, Renae; Simon O'Malley; Imogen; Craig.Taylor@det.nsw.edu.au; niki.schneider@sasol.com; janebotha@hotmail.com; Kleyn, Johan (JM); karienconradie@hotmail.com; Johnston, Andrew; andre.w@absamail.co.za; 2004007858@student.uovs.ac.za; mpbotha@hotmail.com; Michael.Reid@dpi.vic.gov.au; Ului.Latu@dhs.vic.gov.au; Zubko, Inna; coopster2012@yahoo.caSubject: FW: The number 11
The Secret behind the number 11

Pretty Chilling - read to the bottom. Try it out.
If you are a sceptical person - still read on as it's actually very interesting!!
This is actually really freaky!! (Mainly the end part, but read it all first)
1) New York City has 11 letters2) Afghanistan has 11 letters.3) Ramsin Yuseb has 11 letters. (The terrorist who threatened to destroy the Twin Towers in 1993) 4) George W Bush has 11 letters.

This could be a mere coincidence, but this gets interesting: 1) New York is the 11th state.2) The first plane crashing against the Twin Towers was flight number 11. 3) Flight 11 was carrying 92 passengers. 9 + 2 = 114) Flight 77 which also hit Twin Towers, was carrying 65 passengers. 6 + 5 = 115) The tragedy was on September 11, or 9/11 as it is now known. 9 + 1+ 1 =116) The date is equal to the US emergency services telephone number 911.

Sheer coincidence..?

1) The total number of victims inside all the hi-jacked planes was 254.
2 + 5 + 4 = 11
2) September 11 is day number 254 of the calendar year.
3) The Madrid bombing took place on 3/11/2004. 3 + 1 + 1 + 2 + 4 = 11. 4) The tragedy of Madrid happened 911 days after the Twin Towers incident.
Now this is where things get totally eerie:

The most recognized symbol for the US, after the Stars & Stripes, is the Eagle. The following verse is taken from the Koran, the Islamic holy book:
"For it is written that a son of Arabia would awaken a fearsome Eagle. The wrath of the Eagle would be felt throughout the lands of Allah while some of the people trembled in despair still more rejoiced: for the wrath of the Eagle cleansed the lands of Allah and there was peace."
That verse is number 9.11 of the Koran.

Unconvinced about all of this still ..?

Try this and see how you feel afterwards, it made my hair stand on end:
1. Highlight the Q33 NY. This is the flight number of the first plane to hit one of the Twin Towers.2. Change the font size to 48.4. Change the actual font to the WINGDINGS……………………
What do you think now????
Send this to as many people as you know and in 11 minutes you will get a nice surprise, if you don't you will get the shock of your life in 11 min.

From: Etienne Visser [mailto:etiennevisser@yahoo.com] Sent: 20 September 2007 1:42 PMTo: Adam Hillaby; Andrew Gertge; Botha, Aniki; Dawnelle; Ernesta; Ina Saayman; Jaco Fourie; Jaques Marais; Jerry; Johan Visser; John Rippy; Jonathan; Karen; Marike Botha; NICOLE CLOUTIER; Ray; Ruth; Ryan; Tanya Du Toit; Xiao Shan; Zelda (KIO SIS Human Resources) VisserSubject: Fw: The number 11
You should know that I don't usually send out junk mail ... but this is kind of freaky !!!

Etienne Visser

"There are two cardinal sins from which all others spring: Impatience and Laziness." - Franz Kafka

## Friday, September 21, 2007

### Topos 3

Topos 3

Andre Willers
21 Sept 2007

For Ermeine on request .

Sources:
http://arxiv.org/abs/quant-ph/0703060 The topos articles.

“Physics from Fisher information” by B.R.Frieden ISBN 052163167X
Alternative Topos-type derivation of physical laws .

http://andreswhy.blogspot.com : see in general , or search for “mining the Oort” , “Topos ” , “Topos 2” , Transcendent numbers ,etc.

Zero-point Energy , Zitterbewegung and Postdiction .

How to get macroscale effects from quantum fluctuations .

Zitterbewegung : the electron near lightspeeds jitters around . This is derived from the Dirac equations as interpreted by Schrodinger in the 1930’s . The electron moves near lightspeed within an envelope . Tunneling will take place if the electron is seen as a particle .

Puthoff (1989) interpreted that this jitter can represent energy asymmetrically transferred from quantum foam particles .

Further , that the energy of the electron mass equals this nett energy transference .

Thus , the electron can be thought of as a standing wave maintained by vacuum fluctuations .

Postdiction:
This is a YN>0 situation .
But we can make it true by pinching the postdiction in a specific way .
The output is then extra electrons (current) , extra push(EMV) or both in a directly usable form , directly derived from zeropoint energy .

Cheap energy .

But note that there is a hidden cost : Entropy pollution .

Entropy pollution :
By definition , life decreases entropy inside it and increases it outside it .

This causes problems with quantum devices . (Heisenberg’s principle can be seen as a mild form .)

Chernobyl.
See a borderline nuclear system like Chernobyl at the end of the safety test . Containment systems were at a cusp , but previously found safe . Then the night-shift comes on . They understand less , thus their entropy is greater . The higher entropy means higher uncertainty . This bumps the probability of a fission per atom up over the stability level .

Not “boom” , but “sizzle” .

A classical example .

When the typically human fingerpointing started , some did try to point out that this was a routine performed many times before , but never at the phase change between an old shift and a new shift .

Hoist by Heisenberg !

Hopefully , nuclear weapons are more robust .

Entropy Sinks.

Any zeropoint energy device (and here we include lifeforms) require an entropy sink far away from the action to function at Reality Class 1 and 2 levels .

Ignorance is a reasonable ground-level state , but organized religions are much more efficient entropy sinks .

The mass media are also quite efficient at spreading entropy about .

This is why they evolved .

But high-intensity exploitation of different entropy levels (like zeropoint energy) will require specific designs. It is not too difficult , once it is known .

Note that Electromagnetic Waves of any description that passes through the body (ie low frequencies like radio , TV , Sun spots , etc) , increases the order inside the body (increases entropy .)
This is a Bad Thing unless you have compensatory mechanisms .

Increasing order at DNA/Intron level leads to interference with the quantum-level optimization of pathways .

Luckily , we have a stop-gap mechanism for low intensities :
Heat-shock proteins chaperone and mask small folding irregularities due to heat or small mutations . If they are overwhelmed (like big pulse of low-frequency EMP from meteor strike , large volcanic explosion , close proximity to cell-phone tower ,nuclear explosion) , the genetic and protein changes are suddenly released . A pulse of change ensues in the organism . Some think that this is one of the mechanisms driving punctuated equilibrium in evolution .

Negative Entropy Battery.
It is interesting to note that this mechanism operates as a storage battery of change , then releases it at once or slowly depending on the environment . This ties in with introns and repeated strings of genomes .

As expected from evolutionary theory , this system will operate better by orders of magnitude if it fluctuates . A relaxation of stress will cause an explosion of numbers in the most favourable mutations . An increase in stress will weed out the non-survivors . Repeat .

The social systems of human survivors of hundreds of cycles of this have got ups and downs built in .

Civilizations rise and fall .

But they fall jolly well faster if the internal Entropy inside each individual increases rapidly . I refer here particularly to the well-documented fact that social unrest is closely correlated with EMV activity caused by the sun . (1990’s)

The rapid increase of internal entropy forces a decrease in external entropy . Social disorder increases .

In the absence of extreme point-sources of zeropoint energy , entropy can be taken as fairly uniform over large volumes . (Close to a conservation principle)

So , if internal order per individual increases , the external social order decreases .
The more radio , TV , computers , solar flares , the greater the social unrest .
If the EMV pulse goes over a certain threshold , masked mutations are released and the cancer rate goes up .

HIV
The virus is reasonably successful because the mechanisms that would normally choose an optimal pathway to combat it is masked by the increase in entropy .
Their quantum mechanism is disturbed .

Just restoring a Faraday cage is not sufficient , as the balance has already been disturbed .

The internal entropy needs to be increased .

Blasting the organism with really random electromagnetic waves will drastically increase the disorder inside it , in contrast with the ordering waves it is exposed to .
Hopefully , quantum choices of optimal pathways are then made in a MORE noisy environment . Resonance effects come into play .

Really random is extremely difficult .

But how to get really random EM waves economically ?

Applause .

This is the wavefront of thousands of people clapping hands in a semi-random fashion. Fairly random .

Listening to applause for an hour loudly should reset some random counters .

Andre

## Friday, September 07, 2007

### TOPOS

Topos
Andre Willers
7 Sept 2007

For Ermeine on request .

Sources:
www.arxiv.org/abs/quant-ph/0703060
“Physics from Fisher information” by B.R.Frieden ISBN 052163167X
http://andreswhy.blogspot.com : see in general , or search for “mining the Oort” ,

Topos is simply a new name for non-Aristotelian logical systems .
Gauss saw it , but did not publish , deeming it too controversial . (He hated controversy.)
Russell and Whitehead proved that A and not-A is less than the Universum .
Godel’s work was a consequence of this .

What does it mean?
If you say that something exists (say A) , it means it must be defineable in some way , separate . In other words , the person talking about A plays a role , he defines it . Even using a symbol like A makes it separate .

But there is then always something left over . The indefinables . In other words , A and not-A is not the Universum .

This has been rigorously proved . It is obvious from the above .

True is defined as existing . Existence is defined as defineable . Something that is not defineable then is true and not-true . The essence of quantum systems .

If you have read and understood what I wrote before , you know more about these systems than the Topos authors .

Unless a Wright-proof (ie an undeniable physical gadget ) results , these theories become froth on the gales of history .

Andre

PS
Topos is a typical publish or perish phenomenon . Dress up old , known things in a new guise . Some quotes from the Topos paper :
“Intuistionic logic” : what does not fit , gets swept under the carpet . They should get a fuzzy logic Roomba .
“Heyting algebra” : fuzzy logic , as used by your fridge or microwave , but a neat term .
“Sets” is used in the argument : sets? Sets are a number of similar identifiable items , these being identified and counted by the hypothetical observer . This directly contradicts the basic assumption of Topos .
Notice how classical set theory warps if you add the hidden assumption of somebody doing the defining and counting .

Topos is not a very good attempt . Frieden did better .