Genesis Anaximander Anaxagoras Democrit Pythagoras

01000 b.C. 2000

The Archimedes Mirror

Hans Grassmann, Isomorph srl, Univ. of Udine

La fisica communica con Medicina, Arte, Spiritualita'ICTP Trieste, Nov. 2014

...others Death of Archimedes

Aristotele

LutherKopernikus Brahe Kepler

Newton HuygensGalilei

Physics

One example of “physics disappeared”:

Mirror of Archimedes

According to Tzetzes, Galeno, Cassio Dione Cocceiano, Giovanni Zonara, the mirror of Archimedes did exist.

In modern times several “tests” were made to verify these accounts, One test on request of the American President, B. Obama.

Those “tests” failed to ignite wood, in the Obama test an array of hand held mirrors achieved only 100 °C.

it was concluded, that the burning mirror of Archimedes had not really existed.

Objection:the mirrors used in these tests correspond to the present state of the art of light concentration, but do not correspond to the historical record and they are not compatible with the laws of physics.

http://en.wikipedia.org/wiki/Burning_glasshttp://it.wikipedia.org/wiki/Specchio_ustorio

Physics objections

Parabolic mirrors have their focus between the mirror and the sun,If one reflects light sidewards, the focal point gets lost.

=> Parabolic mirrors cannot burn ships

Arrays of plane mirrors (as used in modern solar tower) need a computer for their control.

If one adjusts the mirrors by hand, one cannot see by eye where each individual mirror is reflecting the light (due to the strong illumination of the focal region).

=> arrays of hand held mirrors cannot burn ships

In order to make an array of mirrors dangerous for a ship (without computer control)

the mirrors must be connected mechanically, so that they can be adjusted concurrently.

In state of the art systems, this is not possible.

« Nam cum Archimedes lunae solis quinque errantium motus in sphaeram inligavit, effecit idem quod ille, qui in Timaeo mundum aedificavit, Platonis deus, ut tarditate et celeritate dissimillimos motus una regeret conversio. quod si in hoc mundo fieri sine deo non potest, ne in sphaera quidem eosdem motus Archimedes sine divino ingenio potuisset imitari. »

Cicerone, Tusculanae disputationes

« In realtà, quando Archimede racchiuse in una sfera i movimenti della luna, del sole e dei cinque pianeti, fece lo stesso che colui che nel Timeo edificò l'universo, il dio di Platone, e cioè che un' unica rivoluzione regolasse movimenti molto diversi per lentezza e velocità. E se questo non può avvenire nel nostro universo senza la divinità, neanche nella sfera Archimede avrebbe potuto imitare i medesimi movimenti senza un'intelligenza divina. »

The Antikythera Mechanism

The burning mirror of Archimedes is not his only achievement, which got lost. According to literature, Archimedes also built a very high quality astronomic clock,

again, modern scientists did not wish to believe the literary account:

scientists just refused to believe that it could be real and ignored it for 51 years,until the studies of de Solla Price.

Michael Edmunds, who led a 2006 study of the mechanism, described the device as "just extraordinary, the only thing of its kind", and said that its astronomy was "exactly right". He regarded the Antikythera mechanism as "more valuable than the Mona Lisa

http://en.wikipedia.org/wiki/Antikythera_mechanism

National Archaeological Museum of Athens

Mechanism of Antikythera

Even when in 1900 one of the astronomic clocks described by Cicero was found in a roman shipwreck near the island of Antikythera.

Antikythera Ephebe

For the following discussion note: the Antikythera Mechanismis linear,

while the planet movements seem to be complex

From a physics point of view a mirror system and an astronomical clock are similar :

When imagining in your mind the mirror system, do not use the mirror system as a reference,

rather observe the mirrors from the focal point: Watching the N mirrors from the focal point it seems, that there are N suns in the sky, and each mirror is following the position of one of them

This is identical to the task of an astronomic clock, which shows the position of several celestial bodies in the sky.

=> who could build the Antikythera Mechanism, could also build the burning mirrors

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John Tzteztes (twelfth century AD):

>> Archimedes … set similar small mirrors with four edges, moved by links and by a form of hinge <<

GREEK MATHEMATICAL WORKS, Tranlated by Ivor Thomas, Loeb Classical Library, Harvard Universiyt Press, Cambridge, 1941, Vol 2, page 19

A system with concurrently moving mirrors, corresponding to the description of John Tzetzes does exist,

The system was developed by Isomorph srl at Trieste at the beginning of the 21th century AD

9 kW thermal energy

With water: 100 °C (also in winter)

With oil: 180 °C (also in winter)

Can substitute 700 to 800 liters of oil per year

The system is called Linear Mirror II

Isomorph srl andIsomorph Production srl,www.isomorph-production.it

Ready industrial product withEuropean Solar Keymark certificate, eligible for state incentives:

Functioning of Linear Mirror II

For details see www.isomorph-production.it

In the present version of the Linear Mirror, the focal region is at a fixed position for convenience – the possibility to keep the focal region fixed is one important advantage of the system.

If instead one wants to follow the movement of a ship in direction and distance – for example – the focal region can be made adjustable as well.

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complete test report public on www.isomorph-production.it

Hotel “Al Cavliere”, Pordenone

Compared to conventional plants:SimplerCheaperless energy lossLess specific heatIntelligentcradle to cradle

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The Linear Mirror II can also perform solar pyrolysis: transform simple biomass (straw, hay, waste) to carbon and gas

Solar carbon and solar gas - CO2 neutral- compatible with existing infrastructure/technologies- store solar energy for long periods of time without loss

Solar carbon from straw:Heating value : 27.2 MJ/kg

Solar gas

art

The Evolution of art until Renaissance went together with an always improved resemblance of depiction :

In the following centuries art seems to have searched for what it really wanted to achieve: impressionism? expressionism? cubism?

However, the achieved capacity of resemblance was used to depict scenes, which do not exist, and therefore cannot have any resemblance whatsoever :

If humans would have taken paintings like these seriously

the horrors of the 20th century never could have happened

The crisis of European culture at the beginning of the 20th century shows the limits of traditional art

This leads to a new era of art, as for example explained in the works and words of Joseph Beuys - “erweiterter Kunstbegriff”.- extended concept of art and correspondingly to a new subject of art – social sculpture.

In 2012 the artist Elena Mazzi started her project “Reflecting Venice”.supported by the foundation Bevilacqua la Masa at Venice http://www.bevilacqualamasa.it/atelier-elena-mazzi

An artisan at Murano engraves these mirrors in the historical venetian technique with pictures of plants, which are in decline in the lagoon of Venice

Elena uses a Linear Mirror as an interface, connecting local reality,

history, and options for the future.

For Elena's project, the reflecting surfaces of a Linear Mirror II system are made from venetian class instead of aluminum.

A Linear Mirror, equipped with these engraved glass mirrors was to be installed at some commercial location at Venice, providing energy for the contemporary world, like for a hotel, or some company, or a restaurant. This location could furthermore have been a connection to the future, since the production of the Linear Mirror itself would be very well suited for Venice: the production of the Linear Mirror is a quiet industry, without much energy

consumption, noise, pollution or other hazards, it could operate well in Venice, as a new branch of the dying historical glass industry.

It turned out, that nobody at Venice wanted to have Elena's mirror, not even for free. Elena tried for more than one year to convince some company or hotel or restaurant or association to install a free mirror for producing 800 Euros of income each year. But nobody wanted that.

So the mirror did not only passively reflect on the decline of Venice, but interacting with its social environment it uncovered, made explicit and explained the reason for this decay.

now a strange thing happened: The Linear Mirror with its engravings and references was supposed to passively reflect the past and present, and also some future opportunities.

But maybe because it did this so well and so real, the passive process of reflection became an active one. The mirror began to reflect things, which it was not supposed to reflect, making these things happen on its own device, as if it were alive:

The Fittja Pavillion was voted to be one of the most interesting ones at the Biennale by the journal Domus.

Reflecting Venice was bought by Botkyrka Konsthall (Stockholm) and shown at the Biennale for Architecture at Venice as part of the Fittja Pavillion.

There are many other projects, which show how important the connection between art and physics is today, for example Fabiola Faidiga, Contemporary shower

Work in progress – we are looking for sponsors (could be you ?)

There is a not so small problem:

Many people are not able anymore to understand art. They wonder:

What is art?What does an artist do?

As history shows, the flourishing and perishing of art and physics are correlated. So physics should worry about this problem.

And in the same way – as physics should worry about art – society as a whole should worry about physics:

Had the Archimedes mirror not been lost 2.300 years ago, the “carbon era” could have been avoided, avoiding global heating, a number of wars and so called “cultural conflicts”.

The total absence of research on topics like this is frightening:How could it happen, that this important technology was lost?How could It remain in oblivion for 2.300 years?Why do we spent billions each year for solar energy, without any technical progress in the real world of solar energy?If somebody would re-invent the Archimedes mirror today, how would society react?

From this perspective, and since above questions go beyond the scope of this presentation, we do just a first little step towards these questions by asking what artists are doing, from a physics point of view?

Art & physics

What does art from a physics point of view?(Prolegomena)

Each painting can be represented by a 2 dimensional pixel array to any desired precision - there exist MN different arrays, forming a list of MN elements (“big list”)(N=number of pixels, M=number of colors and intensities)

most arrays show “white” noise.fraction of arrays showing a possible image of natural world is small beyond imagination <=> “reality is extremely unlikely” (unplug a TV set and wait for a movie to happen by chance)

Human beings are able to identify those rare images.Artists identify the subsample of “important” or “relevant” images,

they communicate those images to other human beings by pointing to the image - creating relevance.

These considerations can be extended to 3d works of art (statue), and temporal sequences (movies, performances)

Some elements of the big list can be found in nature or can be arranged.The artist can point to them by means of a photograph or a performance,without the need to produce a painting.

Some of the elements of the list of arrayscannot be found in the material world, a painting needs to be created, in order to perform the act of pointing.

Painting is a form of pointing.There is no preferred form of pointing, relevant is only the relevance found

Interesting physics questions arise with regards to art:

How many natural images are there?How many relevant images ?Can one explain or derive these numbers?

How much information is contained in the Universe?

How can the brain identify these subsamples, given the small number of

(mirror-) neurons? (« 1010 compared to O(1010.000.000.000 ) arrays)

Question to be asked in order to obtain a Linear Mirror system:How many motors are needed to make N mirrors follow the sun?(N mirror problem)

The key point of this presentation is the following observation:

the green (art) and the red (Linear Mirror) questions are very similarboth require an understanding of what one might call “physics of information”.

>> Merely by existing, all physical systems register information. And by evolving dynamically in time, they transform and process that information. The laws of physics determine the amount of information that a physical system can register (number of bits) and the number of elementary logic operations that a system can perform (number of ops). The universe is a physical system. This paper quantifies the amount of information that the universe can register and the number of elementary operations that it can have performed over its history. The universe can have performed no more than 10120 ops on 1090 bits. >>

Attempts to discuss questions of this kind in terms of physics do exist. For example:

:Phys.Rev.Lett.88:237901,2002:

Computational capacity of the universe, Seth Lloyd

But these attempts are usually based on Shannon's framework, where messages (and paintings) have no meaning, and where the amount of information is measured without defining what information is.

Neither art nor physics exist in that world, not even a Linear Mirror II.

From a physics point of view, the subject of information processing are “messages”, for example digital messages.

And from a mathematics point of view these (here digital) messages are vectors of the arithmetic vector space, F2

n.

Information processing can therefore be expressed in terms of a vector transformation T, transforming an input vector a to an output vector b

b = T(a)

Note, that the number of microstates of the Universe is final (Boltzmann) and that therefore finite message are sufficient for all physical messages.This is different from mathematics or information theory, where one of the central problems is the halting problem, associated to the possibility of infinte messages.

Considering b = T(a)“information” can be defined by its conservation:

If an information processing system T transforms a message a to a message b, b = T(a) and if there is a = T-1 (b)

then T conserves information, anda and b are identical messages – have the same meaning

Of course, identical messages must have the same “amount of information”,and since a and b will in general not have the same number of bits, the length of the message cannot be a measure for the information content.

Already here we are incompatible with Lloyd and Shannon

(In our new scenario the amount of information might be measured by the number of dimensions of the message space.)

In the following we consider only injective transformations, to shorten the discussion, while non-injective transformations are very interesting, too.

In the simplest case, T is linear. It is then true that

T maps Input vector space U on isomorphic output vector spave V

T is a matrix, consisting of vectors, which again form a vector space isomophic to U and V.

in everydays language: input and output messages may look different, but are not, and also the information processing system is not different from the messages. The information processing system must contain the same information as the input messages, before it can operate on them.

T

input output0001 00001

0010 00010

0100 00100

1000 01000

10000

Example: y=2·x

Digital numbers

No algorithm, no energy dissipation, no fundamental operations

000100

000010 000010

000001000001

100000000

001000

operation b=a2 on canonical numbers.

this is a RAM (random access memory)

If not tied to a digital space through a multiplexer,It can perform calculations concurrentlyIt therefore emulates a quantum computer – without disentanglement problem

Lookup table

For a non-linear T the situation is not much different:

we can always project the 2n vectors of U and V to 2n base vectors

so the operation T in the digital space can be substituted by a new operation D operating between two bases – D can therefore be written as a Matrix.

Another example:

images may be created by algorithms performed by computers,

like in a digital camera.

But pictures can also be taken by a pinhole camera, and as for example the work of the artist Luigi Tolotti shows, pinhole pictures are of high quality and relevance

Here, the algorithmic Turing machine is substituted by a hole.

And of course, also the DNA and the human brain are organized as lookup tables (for instance “mirror neurons”), they are not good at performing algorithms.

And just because of this, they are extremely powerful.

A wide field of research opens here!

Advantage: small lookup tablesPrice to pay: loss of concurrency

At the time of Turing, large lookup tables were not available, today they cost 3 €

a1 b1a2 b2

+

c2

1

+

+

c3

1

c1

1

+

Algorithms are of course allowed, and they are defined in our scenario:Algorithms and algorithmic machines are ordered systems of lookup tables.

Note. That also in a Turing machine the use of lookup table cannot be avoided, since the fundamental operations cannot be grounded in algorithms.

Complexity: number of lookup table elements of algorithm compared to number of full (concurrent) lookup table.

Algorithms are defined and allowed for in our scenario,

But they can as well be avoided

In the Shannon world, the position of each mirror of a N mirror system needs to be evaluated in two dimensions by an algorithm of its own, and therefore it must have 2 motors of its own correspondingly.

In our scenario this need for 2N algorithms does not exist anymore, one motor should be enough, it is needed for generating input number, it is a real time clock.

Some of the statements made refer to the vector space F2n and are true only

with respect to this.

Is it, for example, true, that also a T, which processes images (creating a correct description of the image) is an isomorphism?

For discussing pictures, Boolean Algebra is well suitedWe find:

1) m physics objects form a 2m – element Boolean algebra (that is, how Boolean algebra is taught at school: take objects like an apple, an orange, a car, and form ensembles with them: you can group them in 2m different ways)(In this context, objects at different positions are considered different objects.)

2) also the m images of the m objects from a 2m –element Boolean Algebra

It is then possible to associate to each image ai its correct description bi, bi = D(ai).

And it is by construction true that the image of a photograph of two objects will be the same as the logical-or of two images, each one showing one of these same objects:

D(ai V aj) = bi ∪ bj.

D is then an homomorphism, and since D is bijective, it is also an isomorphism.

Consequence:

in the list of all arrays describing all possible pictures

we do not need 2m elements in order to describe the 2m different images of m objects, but only m elements.

>> a total order, linear order, simple order, or (non-strict) ordering on a set X is any binary relation on X that is antisymmetric, transitive, and total. <<

>> an ideal of S is a subset J such that for all a, b in J we have(a V b) in J and for all x in S we have (a Λ x) in J. <<

From a practical point of view:

- Create the largest technically possible complete list of all images possible, for instance these may be images of 5x5 pixels.Use them as Boolean Atoms.

- Create total orders from these atoms (lines, curves etc)(This is done only by Boolean operations, no probability, do decision making.)

- continue this process in a linear way.

- occlusions and reconstruction problems are handled by Boolean Ideals.

>> an atom in a Boolean Algebra is a nonzero element a such that there is no element b with 0 < b < a Here a ≤ b precisely when a = a Λ b <<

For a more detailed discussion see Isomorph Letters: http://www.isomorph.it/letters/articles/on-the-mathematical-structure-of-messages-and-message-processing-systems

Sine in the context of this presentation a detailed discussion of Isomorph image identification is not possible, we show instead an example,written along the lines described in the previous slide:

.This program is executed on a Turing machine. Otherwise it would give a concurrent description of what it sees.

No probabilities, no decision trees, no fits

Linear structure – if we want to identify elephants, it is sufficient to add one subroutine.

We have shown that Grassmann Algebra can be used to discuss the particular case of “algorithmic information processing” and

Boolean Algebra for the particular case of understanding the meaning of pictures

Conjecture:

Physics of information should in more general be based on category theory

also the human brain should be an “isomorphy” (ideally) of the outside world, or a mirror of the world (“was der Fall ist”, Wittgenstein)

In full agreement with the findings of Rizzolatti, Kant et al.

But where does it come from? Where does the a priori come from?

While information processing always can be done without energy dissipation

It remains true (Boltzmann), that the creation of the information processing system (T) must dissipate energy.

At which point the second law of Thermodynamics applies:

The formation of brains becomes a spontaneous process,as a live form of its own with its own evolution (ordering “bits”)like organic live is a live form of its own (ordering molecules)

Note however, that information has now become “relative”, a brain cannot have an order by itself, it cannot create its own reality, it can only be a mirror of reality,Or an image, of what there is (Wittgenstein)

As a consequence, human consciousness can understood as the consciousness of the world, which indeed would not be conscious of its existence without the human.

It is often claimed, that science has “marginalized” the human being (Kopernikus, Darwin, Freud, genetics)

From what was said in this presentation it becomes clear, that this “marginalization” was based on a misunderstanding:

Up to now, science has discussed the human only as a form of organic live.With respect to organic live, the human being is indeed marginal.

With respect to intellectual live, the human being is moved back to the “center of the world” and is different from the animals.

Conclusion

Art is therefore (like physics) a live form of its own, a form of intellectual live

Its evolution is tantamount to improving our ability to see the world andto be the world, and as its living mirror to be the consciousness of the world.

Searching for relevance, art makes the human relevant.

Like all live forms, art (like physics) is spontaneous, but it is not a necessity – it can be extinguished

We should not do that, we should not extinguish it

Because we would cease to be images. We would drift away from the center of the worldand loose ourselves.

Maybe we should study category theory next?

Genesis Anaximander Anaxagoras Democrit Pythagoras

01000 b.C.

2000

Death of ArchimedesAristotele

LutherKopernikus Brahe Kepler

Newton HuygensGalilei