Topos and Topos2

Topos
Andre Willers
7 Sept 2007

For Ermeine on request .

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


“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 .

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Topos 2
Andre Willers
10 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 ” , Transcendent numbers ,etc.

Topos (plural topoi) is simply a new name for non-Aristotelian logical systems .

Perhaps I should clarify a bit , as my previous post could do with some expansion .

The Aristotelian system . Binary logic .
Definition : Something is true or not-true . The middle (ie something that is both true and untrue) is excluded .

Our purest expression of this is in computers : binary language (1 or 0) .
Now translate this into reality .
Current flow is equivalent to 1
Non-Current flow is equivalent to 0 .
But how are we to distinguish between a string of 0’s and somebody cutting the wire ?

We cannot , except by way of a third signal . In computers , timing is used (pulses of current at varying times .)

Can you see the uncertainty inherent in this worldview ?
Using two variables to describe a 3-variable environment . There is always uncertainty . Hence quantum systems .

Try to construct different ways . It is not possible . There is always a different third state , denoting no-signal .

For example , (+1) + (-1) = (0) … three states .

The reason is in (A) U (~A) < n="1" yn="0" yn="1" yn="any">1
Y+N+YN=any . Strong godlike . YN>1

For example , to describe a real thing we have to say:
Reality(Class =1, Y=1) for our traditional Aristotelian reality.
Reality(Class =2, Y=0.9 , N=0.02 , YN= 0.08) for our Quantum reality.
Reality(Class =3, Y=0.7 , N= 0.1 , YN=0.3) for our creative , bootstrap,weak godlike reality.
Reality(Class =4, Y=0.7 , N= 0.1 , YN=5) for strong godlike intervention reality.

Why the Classes of Reality ? Because of the phenomenon known as “wave-function collapse” . This is a Procrustean human system whereby the Y,N,YN of Class 2 realities are summated and then selected : the lowest summation of YN value is selected as the “wave-function collapse” . High N values are ignored . This is called quantum physics –Copenhagen interpretation . (This is already breaking down from experimental evidence. )

The “reality” is that there is no wave-function collapse . The thingies happily keep on being what they are . Humans pick the creamy , chocolate ones and ignore the rest . Typical .

Topoi as formulated do not take the observer into account . This limits them to distributive-logic systems . The Mathematician plays the role of the observer .

Unfortunately , science requires replication of experiments by different observers (ie distributive-logic . )
.
Yet we routinely use quantum devices with a high degree of certainty . The trick is in two parts :
Expand the quantum bubble (ie , move closer to macro-state)
Quantum-tunneling is a transfinite process found everywhere , on macroscopic scale as well .
See :
http://arxiv.org/abs/0708.0681 : photon tunneling of up to 1 meter was experimentally verified , using very simple apparatus . See also New Scientist 18 Aug 2007 p10 “ Light seems to defy its own speed limit.”
Tunneling seems to play a role in fusion and fission processes . Indeed , if tunneling over macroscopic distances is routine , why does cold-fusion not occur regularly ? Maybe it does/did . Ref natural Okra fission reactor in North Africa .

Jupiter’s energy budget seems to indicate that some low-temperature fusion reactions are occurring because of meson-tunneling between large crystals formed in the atmosphere and sheared in two by violent storms .

The Sun’s energy output is too high for its temperature . This crack is papered over by postulating additional energy formation in the corona . But this is exactly where heightened fusion because of tunneling would be expected . This layer is also very susceptible to magnetic effects from the planets . Thus , Earth’s weather, via the Earth’s magnetosphere can have an effect on the sun’s surface fusion energy production . The effect is non-linear , so even small changes in earth’s magnetosphere can have large effects on the surface fusion on the sun .

Consciousness : quantum effects have long been postulated . The general prevalence of macro-tunneling makes this 0.99 likely .

See “Non-locality” , http://andreswhy.blogspot.com/ , etc

Error-correction (Pinch)
Set “Usable=True” .

Then pinch your apparatus from a higher uncertainty to a lower uncertainty . This is a system like a transistor , or in general most non-linear amplifying devices .

Note that the entropy inside the device decreases , a general prerequisite for life .

Trial-and-error in a system designed to pinch Class2->Class1 Realities will give a fairly reliable quantum based system . (Like your computer , hifi,etc)

Ditto for Pinches of Class3->Class2->Class1 Realities , but the viability decreases drastically as YN increases . This is the definition of lifeforms like humans , advanced computers , etc .

Class4 pinches : highly dangerous . Not recommended unless you are a god .

See Prediction below .

Prediction and Postdiction .

Let YN>0 , like in the observable Universe .
This means that there are finite (0Define the paths as AB(1) , AB(2) , …,AB(n)
If any particular path AB(i) lies within the lightspeed cone from B , then any point on it can be accessed from A without violating relativistic (and thus causal) constraints . Note that the mechanism is probably tunneling .

There is some good news and some bad news .
The good news is that prediction is possible .
The bad news is that only a future AB(i) , not the future can be predicted .
The future is at B , where all the possibilities AB(i) are summed .

A further limitation is that only the futures entangled with A can be predicted . Influences outside AB path or outside the light cone cannot be predicted .

Algorithms for sampling AB(i) pathways can easily be constructed for Reality Class2 , and indeed are (quantum devices).

A corollary is that prophecies and mind-constructed scenarios are the same .
Seeing some futures are equated with intelligence and creativity . There is no functional way of differentiating them . Some think that the ability of the brain to pick up these small lengths on alternate futures is the human ability to foresee and create .

The problem here is that humans think that what they foresee is THE truth . Hence prophets like Cayce , hypnotic progression , etc do not realize that what they see are but one pathway , one possible future .

Creating algorithms for Reality class 3 systems is thus indistinguishable from intelligence and creativity enhancement .
This will involve powerful forces in the human sphere .

Just collating all the prophecies won’t hack it either . The prophet has to be entangled and free of Aristotelian prejudices . Nobody qualifies .

PostDiction

The past is even more unknowable than the future . Literally .

Since for paths AB(i) , we can also have DB(j) , postdiction from B has to involve both pathways . Even if there is a wave-function collapse , the AB and DB paths cannot be distinguished .

For Class 3 and better realities:
Ford was right . History is bunk .At best , it is an intellectual exercise .

Oh well .

Andre