in the past decade , there has been a rising practical significance for ad - hoc wireless networks . starting with the emergence of sensor networks and the increased importance and distribution of local wireless networks like wifi networks , and now with the new paradigm of heterogeneous networks, there is an interest to understand ad - hoc networks even for the design of cellular networks .further , the expected future popularity of device networks under the umbrella of the internet of things ( iot ) is drawing attention to research in the area of ad - hoc wireless networks .  at the core of the wireless communication task , lies the problem of interference management , as the interference limitation stands as a bottleneck towards increasing the reliable rate of communication . while there has been tremendous effort over the past two decades to tackle the interference management problem from both theoretical and practical aspects , most of the results obtained can not apply directly to recent ad - hoc networks .traditional results on the interference management problem are either tailored for fixed infrastructural cellular networks or rely on distributed approaches where cell association and transmission schedule decisions are based on local knowledge of the network .most interference management solutions for ad - hoc networks rely on local knowledge to make distributed decisions. many advances in distributed transmission schemes have accompanied the rise of sensor networks in the past decade .the reason is that prior to the new technology of cloud computing , the common wisdom was that centralized solutions or relying on global network knowledge would not be feasible for networks that are not supported by fixed planned infrastructure .further , the nature of cellular networks prior to the novel paradigm of heterogeneous networks did not include any form of ad - hoc networks .now , with these two new advances : cloud computing and heterogeneous networks , a centralized approach for managing wireless transmission in ad - hoc networks is both more feasible and enjoys significant practical relevance ( see e.g. , - ) .we attempt to tackle the problem of managing interference in ad - hoc networks in this work through studying the information - theoretic model of a linear interference network ( introduced by wyner in  ) with no channel state information available at the transmitters ( no csit ) .transmitters are only aware of the network topology in our model .further , to capture the benefit of the cloud we make two assumptions .first , global information about the network topology is available .second , each receiver is interested in one message that can be available at transmitters .the constraints on the number of transmitters that can be aware of each message relects a limited backhaul capacity constraint .assigning messages to transmitters in this model mirrors taking cell association decisions in a cellular heterogeneous network .further , the flexibility of being able to assign any message to any subset of transmitters reflects a cloud - based centralized controller that takes message assignment ( cell association ) as well as transmission schedule decisions .system models that share similarities with the considered model have been studied thoroughly in the literature . in particular , with the availability of channel state information at the transmitters , the problem of finding message assignments to transmitters that maximize the asymptotic per user degrees of freedom ( dof ) has been solved for linear interference networks in  .it was shown in this work that combining centralized decisions for message assignment with cooperative transmission can achieve significant dof gains through a simple delay - free zero - forcing transmit beamforming scheme .the question we answer in this work with regard to this previous work is whether the same insight hold even with no csit .the problem of interference management with no csit , known as the topological interference management problem , has been studied with no cooperative transmission in  and . in  and  , this problem was considered for both constant channel and time - varying channel models , respectively . while the constant channel model assumes that the channel coefficients remain the same during a whole block of communication time slots , the time - varying channel model assumes a coherence time of unity , meaning that the channel changes from each time slot to the next .the results in these works show that dof conclusions as well as the design of optimal interference management schemes differ dramatically between these two channel models . in this work ,we show that enabling centralized decisions for assigning messages to transmitters allows us to reach the same conclusion for both time - varying and constant channel models , as long as the coherence time is the same for all communication links .recently , the problem of interference management through cooperative transmission has been studied with weak and no csit in - . in , it was shown that assigning each message to all the transmitters connected to the desired receiver is beneficial compared to assigning each message only to the transmitter having the same index as the desired receiver .however , the proposed coding scheme in  relies solely on interference avoidance and no cooperative transmission is exploited . in our problem , we try to understand the effect of cooperative transmission by allowing for a flexible assignment of messages to transmitters even when each message can be available at exactly one transmitter .the main conclusion of this work is that cooperative transmission does not increase the per user degrees of freedom in large linear interference networks .we reach this conclusion by proving an information theoretic converse for the case when each message can be available at more than one transmitter , i.e. , .we prove that the asymptotic per user dof for any is the same as the one for the case when , which is achieved by interference avoidance .the remainder of this paper is organized as follows . in section [ sec : problem ] , we introduce the problem formulation . the main result is stated in section [ sec : result ] .we present the interference avoidance scheme for the case when in section [ sec : example ] .we then prove the information theoretic upper bound for the case when in section [ sec : converse ] . before concluding , we discuss an extension of our problem to arbitrary network topologies in section [ sec : discussion ] .we finally provide concluding remarks in section [ sec : conclusion ] .we use the standard model for the interference channel with a single antenna at each node .,\ ] ] where is the time index , is the transmitted signal of transmitter , is the received signal of receiver , is the zero mean unit variance gaussian noise at receiver , is the channel coefficient from transmitter to receiver over the time slot , and  ] , we define the complement set , i\notin { \cal a}\} ] , let be the message intended for receiver , we use the abbreviations and to denote the sets and , respectively .each transmitter is connected to its corresponding receiver as well as one following receiver , and the last transmitter is connected only to its corresponding receiver .more precisely ,  .\ ] ]  the channel connectivity model is illustrated for in figure [ fig : wynermodel ] .  .in the figure , a solid line connects a transmitter - receiver pair if and only if the channel coefficient between them is not identically zero . ]  each non - zero channel coefficient is drawn independently from the same continuous distribution . unless stated otherwise , all results in the paper are valid regardless of the coherence time of the channel ( whether the channel remains constant across time slots or changes ) .while all receivers are assumed to be aware of the channel state information , the knowledge available for the design of the transmission scheme is that of the network topology . in other words ,no channel state information is available at transmitters ( no csit ) .for each  ] be the transmit set of message .the transmitters in cooperatively transmit the message to the receiver .the messages are assumed to be independent of each other .the _ cooperation constraint _ is defined as the maximum size of a transmit set :    in this work , we restrict our attention to linear precoding schemes , where the transmit signal at each transmitter is given by a linear combination of signals ; each depending only on one message .more precisely , ,\ ] ] where depends only on message .each message is represented by a vector of complex symbols that are desired to be delivered to the receiver .this message is encoded to one or both of the transmit vectors and , where and denote the linear beamforming _ precoding _matrices used by transmitters and to transmit .the rank of ( ) is ( ) , where and .under such a scheme , the received signal of receiver over the time slots in ( [ eq : signal ] ) can be rewritten as , l \in \{j-1,j\ } \cap { \cal t}_i } ( h_{j , l}^n v_{l , i}^n ) \mathbf{w}_i+\mathbf{z}_j^n,\end{aligned}\ ] ] where for every , is an diagonal matrix with the diagonal element being equal to the value of the channel coefficient between transmitter and receiver in time slot .each precoding matrix is an matrix that can only depend on the knowledge of topology , and has rank .the total power constraint across all the users is .the rates are achievable if the error probabilities of all messages can be simultaneously made arbitrarily small for a large enough block length .the capacity region is the set of all achievable rate tuples .the dof ( ) is defined as , where is the sum capacity .since depends on the specific choice of transmit sets , we define as the best achievable over all choices of transmit sets satisfying the cooperation order constraint in for a channel satisfying .we define the per user dof to measure how the sum degrees of freedom scales with the number of users for a fixed cooperation order .   it is worth noting here that modifying the channel model such that the channel coefficient between the last transmitter and first receiver ( ) is non - zero ( cyclic model ) does not change the value of .the main result in this work is a characterization of the asymptotic per user dof for all values of the cooperation constraint in wyner s linear interference networks .[ thm : main ] under the restriction to linear cooperation schemes , transmitter cooperation with no csit does not increase the asymptotic per user dof in linear interference networks .more precisely , the following message assignment for the case where .the problem in this case is a link scheduling problem whose solution is given as follows .  further , the messages are not transmitted .recall that the objective here is to maximize the sum degrees of freedom , so deactivating some transmitters or not transmitting some messages can make sense .now , we can see that message can be delivered without interference through to .also , message can be delivered without interference through to .for every three messages , two are delivered to their intended receivers without interference and one is not transmitted .hence , degrees of freedom are achieved for each group of successive messages .in order to prove the converse , we prove a statement about general network topologies . first , we make that statement and show how it implies our desired upper bound , and then we prove it .we define the following condition to refer to a class of network topologies of interest . for any network topology ,let be the set of indices of transmitters connected to at least one receiver with an index in .in other words , are the neighbors of receivers in .we say that a network topology satisfies condition if there exists a set  ] has full column rank of almost surely , then , )\nonumber\\&&\overset{a.s.}{\geq } \mathsf{rank}\left([h_{i , i}^n v_{i , i}^n + h_{i , i-1}^n v_{i-1,i}^n]\right)\overset{a.s.}{\geq } m_i,\end{aligned}\ ] ] where and represent the interference caused by message at receivers and , respectively , over time slot .more precisely ,  ] .we provide the main concepts behind the proof .note that , &=&[h_{i-1,i-1}^n v_{i-1,i}^n \quad h_{i+1,i}^n v_{i , i}^n]\nonumber\\&+&[h_{i-1,i-2}^n v_{i-2,i}^n \quad h_{i+1,i+1}^n v_{i+1,i}^n].\end{aligned}\ ] ] further , )\nonumber\\&\geq & \mathsf{rank}([h_{i-1,i-1}^n v_{i-1,i}^n+h_{i+1,i}^n v_{i , i}^n ] ) \overset{a.s.}{\geq } m_i . \end{aligned}\] ] finally , we prove by induction on the parameter that the addition of  ] , a function , and a function whose definition does not depend on the transmit power constraint , and , then the sum dof .  in the above lemma , we used as the set of indices of transmitters that exclusively carry the messages for the receivers in , and the complement set is the set of indices of transmitters that carry messages for receivers outside .more precisely , \backslash\cup_{i \notin { \cal b } } { \cal t}_i ] .the set of transmit signals is the set .note that we can reconstruct if we can reconstruct the symbols .assume w.l.o.g .that .we now apply lemma [ lem : dofouterbound ] by designing the functions and such that we remove the contribution of the signals and from , to obtain the matrices that are used in lemma [ lem : noiccanc ] . from these matrices, we can reconstruct the desired symbols almost surely , and hence , the statement of lemma [ lem : dofouterbound ] holds .the general version of this argument would use the fact that neighboring sets of receivers in do not overlap , , and then we obtain equations in at most variables . from condition , we know that each variable appears in at least one unique equation ( for almost all channel realizations ) , and hence the system of linear equations can be solved to obtain the signals is a feature of linear interference networks that enables the proof of theorem [ thm : main ] .when we look at the set that is used to prove that linear interference networks satisfy condition , we note that the size of the complement set .in fact , for condition to be satisfied , a necessary condition would be that .now , let s consider an extreme example where this necessary condition is violated for all choices of the receiver set . consider a network where the following holds , : |{\cal a}| \geq 1 , |\bar{\cal a}| < |{\cal n}({\cal a})|.\ ] ] the network satisfying  is the fully connected network . hence , using the same technique for proving a converse as in section [ sec : converse ] would not yield a low upper bound on the dof for fully connected networks .however , one can use a different argument for this network : all receivers in a fully connected network observe a linear combination of all transmit signals , but the coefficients of these linear combinations vary because of the different channel coefficients .however , since we are assuming that the channel coefficients are not known at transmitters and each is drawn independently from the same distribution , the following holds .if receiver can decode message for almost all channel realizations , then any other receiver will also be able to decode for almost all channel realizations , regardless of the choice of message assignment and coding scheme .further , the same conclusion holds for any other message .it follows that the sum dof is bounded by the sum dof of a network that has transmitters and only one receiver , which is unity .hence , transmitter cooperation can not increase the dof in fully connected networks as well , even if we are not restricted to linear cooperation schemes .we can generalize the above argument for fully connected networks to any general topology .that is , whenever there are two or more receivers connected to the same set of transmitters , the sum dof for messages intended at these receivers is unity .we havent used this fact in section [ sec : converse ] because for linear interference networks , each receiver is connected to a unique set of transmitters .another way to look at our result for linear interference networks is that it is not useful to assign any message to a transmitter that is not connected to receiver .we do not know whether this conclusion holds for general network topologies .in particular , consider a network topology as the one depicted in figure [ fig : case1fig ] , where subnetworks and represent arbitrary sets of transmitters .message is delivered in the first time slot to receiver through . now, suppose that in the second time slot , we want to repeat the transmission of to cancel its interference at , without causing interference at because another transmitter in subnetwork is delivering a message to receiver in the second time slot . the only way to do this is to transmit from in the second time slot . however , we do not know whether this scenario can appear in an optimal coding scheme .we just provide this example to stimulate thinking about solving the problem for general network topologies .[ sec : identical ] while we have not made an assumption on the coherence time of the channel in section [ sec : model ] , we have assumed that all channel coefficients are drawn from the same distribution .this assumption was essential to our converse proof in section [ sec : converse ] as well as the argument we made in section [ sec : identicalneighbors ] .in this section , we consider an example where assuming that channel coherence time varies across channels that are observed at different receivers , leads to a different conclusion .consider the example -user network in figure [ fig : case2fig ] , and assume that is only available at transmitter .i.e. , .if all channel coefficients are drawn from the same distribution , then the sum dof is unity .the converse follows from the following argument . assuming a reliable communication scheme ,if receiver can decode , then it can remove the contribution of from , and consequently , obtain a statistically equivalent signal to .hence , if receiver can decode , then so will receiver .receiver can then remove the contribution of from , and finally obtain a statistically equivalent signal to .it follows that all messages can be decoded at receiver , and hence , the sum dof is at most unity .if we consider the scenario where the channels and ( dashed green in figure [ fig : case2fig ] ) have coherence time of unity but and ( solid red in figure [ fig : case2fig ] ) have coherence time of two , then dof is achievable .the achievability scheme is based on achieving dof in time slots . in the first time slot ,all three transmit signals are active , and in the second time slot , transmitters and repeat their transmissions .receiver then obtains two equations in and , and these two equations are linearly independent almost surely .hence , receiver can decode both and .since and remain constant over the two time slots , receiver can use its received signal in the second time slot , to cancel the interference received in the first time slot .it follows that all receivers can decode their desired messages over two time slots , and hence , dof is achieved .  ]we characterized the asymptotic per user dof for linear interference networks with no csit .we considered the possibility of transmitter cooperation by allowing for assigning each message to transmitters . under the restriction to linear cooperation schemes, we proved that transmitter cooperation is not useful in the considered setting . to prove the result, we showed that the per user dof for any value of can be achieved by assigning each message to a single transmitter and using an interference avoidance scheme .we then discussed in section [ sec : discussion ] the extension of our result to general network topologies .we argued that the fully connected network admits the same conclusion about the utility of transmitter cooperation , even without the restriction to linear cooperation schemes .we then shed light on the difficulty of making the same claim to any network topology through an exemplary scenario .finally , we showed through an example why changing the assumption of identical coherence time for all channel coefficients may lead to different conclusions and insights.  we do not know whether transmitter cooperation can be useful , from a dof point of view , in any network topology where no channel state information is available at any transmitter .we are interested in attempting to answer this question in future work .a. checko , h. l. christiansen , y. yan , l. scolari , g. kardaras , m. s. berger and l. dittmann , cloud ran for mobile networks - a technology overview , " _ ieee communication surveys tutorials _ , vol .17 , no . 1 ,pp . 405 - 426 , first quart .2015 .o. simeone , a. maeder , m. peng , o. sahin and w. yu .( 2015 , dec . ) .cloud radio access network : virtualizing wireless access for dense heterogeneous systems .[ online ] .available : http://arxiv.org/abs/1512.07743 .    , v. s. annapureddy , and v. v. veeravalli , interference channels with coordinated multi - point transmission : degrees of freedom , message assignment , and fractional reuse " , _ ieee trans .theory_. vol .60 , no . 6 ,3483 - 3498 , mar .2014 .n. naderi , a. el gamal and s. avestimehr , topological interference management with retransmission : what are the best topologies ? , " _ ieee international conference on communications ( icc ) _ , london , jun. 2015 .s. a. jafar and a. j goldsmith , isotropic fading vector broadcast channels : the scalar upper bound and loss in degrees of freedom , " _ ieee transactions on information theory _ , vol .51 , no .3 , pp . 848 - 857 , mar .2005 .a. g. davoodi and s. a. jafar .( 2014 . ) .aligned image sets under channel uncertainty : setting a conjecture by lapidoth , shamai and wigger on the collapse of degrees of freedom under finite precision csit .[ online ] .available : http://arxiv.org/abs/1403.1541 .

Abstract: we study the problem of managing interference in linear networks , with backhaul constraints that admit centralized allocation of messages to transmitters through the cloud . our setting is that of a generic channel , where no channel state information is available at the transmitters . knowing only the network topology , we characterize the optimal decisions for assigning messages to transmitters , given that each receiver is interested in one message that can be available at transmitters . we show that using linear cooperation schemes , the per user degrees of freedom does not increase as we increase beyond unity . hence , we conclude for the considered problem that cooperative transmission does not increase the degrees of freedom .   tim , coordinated multi - point , c - ran , blind interference management , cloud - based wireless


it is a quite common view among people , that are not aware of the developments in modern physics , that it is part of human nature to substitute religious faith in places where there is no knowledge .therefore , an increase in knowledge would lead to a decrease in the necessity of faith .a classical example is the medieval belief that the sun , moon , and stars were moved in their orbits by souls ( ` anima ' ) , who had to carry on this work until the last day .this belief was made obsolete by kepler s laws of planetary motion .further , it is argued that , ideally speaking , a full knowledge of the laws of nature would make obsolete any sort of religious faith and would ultimately allow a complete control of nature by man .  since referring to nature, such views must be founded in the natural sciences of which physics is the most fundamental .therefore , the question whether such views are compatible with the current state of natural sciences is ultimately decided in physics .indeed , it is likely that the above simplistic views have their origin in the classical world view generated by the successes of newtonian physics from the middle of the century until the beginning of the century which viewed the physical world as a type of mechanical clock in which the motion of the gears affect each other in a precise and predictable way .it was assumed that with some more effort all the connections between those gears would soon be found .it is generally accepted that most physicists in the century believed that all the fundamental laws of nature were already known . in this world viewthere is no space for a christian god or religious faith .the paper points out that the above views are no longer supported by current physics and that abstracted world views can not be considered as part of natural sciences , but only as belief systems .for this , it sketches the medieval world view as the starting point of the development of physics in the century , describes and analyzes that development and states cornerstones of newtonian physics which have been assumed evident , but nevertheless have been destroyed by the theory of special relativity , the theory of general relativity , quantum mechanics , quantum electrodynamics and the standard model of particle physics .at the beginning of the development of modern physics in the century by johannes kepler , galileo galilei and issac newton , the medieval world picture derived from the ptolemaic universe prevailed in europe .it consisted of a series of concentric transparent spheres or ` heavens ' with the earth at their center .fixed to the first innermost spheres were the ` planets ' , i.e. , the moon , mercury , venus , the sun , mars , jupiter and saturn .fixed to the sphere were the stars .the sphere was called the ` first movable ' that carries no luminous body and therefore is invisible . finally , the sphere is ` the very heaven ' and full of the god , whose is considered immaterial and unaffected by time .hence god is unmovable , but the love for him puts the the ` first movable ' into rotation from east to west and transfers its to the other spheres . the lower spheres are rotating more slowly from west to east and are forced back by the daily impulse of the ` first movable ' .all spheres are inhabited by ` intelligences ' .the terrestrial domain of the universe inside the first innermost sphere contains bodies made out of the elements fire , air , water and earth .the heavenly bodies above the moon are made of a more perfect fifth element , the ` quintessence ' or ` aether ' .in the following , we have a brief look at some of the scientific achievements of kepler , galilei , newton and their influences on the philosophic and religious views in the last half of the century ._ kepler _ was a devout christian .one of kepler s favorite biblical passages is  * john 1:14 ( kjv ) + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ `` and the word was made flesh , and dwelt among us , ( and we beheld his glory , the glory as of the only begotten of the father , ) full of grace and truth . '' _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  for him , this indicates that the divine archetypes were made visible as geometric forms in nature .in particular , a sphere was a reflection of christian trinity with god the father as its center , christ the son as periphery and the intervening space as holy spirit .he tried to explain the distances among the six copernican planets by circumscribing and inscribing each orbit with one of the five regular polyhedrons . in a letter from , he views the universe no longer as a divinely animated being , but as a clockwork   _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ `` scopus meus hic est , ut caelestem machinam dicam non esse instar divinj animalis , sed instar horologij ( qui horologium credit esse animatum , is gloriam artificis tribuit operj ) , . ''_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  one of kepler s main scientific achievements are his three laws of planetary motion .they are as follows :  1 .all planets move around the sun in _ elliptical _ orbits , with the sun in one of the foci .2 .  a radius vector joining a planet withthe sun sweeps out equal areas in equal lengths of time .the square of the time required by a planet to complete one orbit is directly proportional to the cube of its mean distance from the sun ._ galilei _ can be considered as the father of experimental sciences by performing precise measurements on mechanical systems with a subsequent mathematical analysis of the results . in particular , he studied balls rolling on inclined planes .from the results , he concluded that bodies do not need a proximate cause to stay in motion which contradicts the aristotelian view that any motion presupposes a mover .this result led , after generalization by rene descartes to motion on a straight line , to newton s law of inertia . timing the rate of the descent of balls, he deduced that freely falling bodies would be uniformly accelerated at a rate independent of their mass .moreover , he understood that the motion of any projectile was the result of simultaneous and independent motion in the horizontal direction and falling motion in the vertical direction . in , galilei wrote ,  _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ `` it has been observed that missiles and projectiles describe a curved path of some sort ; however no one has pointed out the fact that this path is a parabola . butthis and other facts , not few in number or less worth knowing , i have succeeded in proving ; ... '' _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  finally , in the ` assayer ' from , galilei insisted that ` the book of the universe ' is written in the language of mathematics   _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ `` philosophy is written in this grand book , the universe , which stands continually open to our gaze .but the book can not be understood unless one first learns to comprehend the language and read the letters in which it is composed .it is written in the language of mathematics , and its characters are triangles , circles and other geometric figures without which it is humanly impossible to understand a single word of it ; without these , one wanders about in a dark labyrinth . ''_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  influenced by the results of kepler , galilei and later newton , the dominant philosophy of the last half of the century was that of rene descartes .mechanics is the basis of his physiology and medicine . _descartes _ believed that all material bodies , including the human body , are machines that operate by mechanical principles .it is known that newton studied the works of descartes and other _ mechanical philosophers _ , who _ viewed physical reality as composed entirely of particles of matter in motion and _ who _ held that all the phenomena of nature result from their mechanical interaction_.  in , _ newton _ published his famous three laws of motion which provide the basis of mechanics to this day . together with his and independently gottfried wilhelm leibniz s discovery of differential and integral calculus , these laws transformed the field of mechanics into an exact science . in ,newton formulated his law of gravitation that have kepler s laws of planetary motion and the results of galilei s experiments on motion on inclined planes as particular consequences .hence the laws of mechanics also unified the knowledge on mechanical systems at that time .after the groundbreaking work of newton , the motion of the planets and comets of the solar system was predictable to high accuracy and understood on the basis of natural laws .the announcement by le verrier in , that there was an unexplained advance in the perihelion of mercury , was not regarded as a failure of newtonian mechanics , but due to unknown gravitational sources .an explanation for this advance was given by einstein s theory of general relativity in  . a first indication for the breakdown of classical physics appeared at the end of century in form of the failure of the rayleigh - jeans law to describe the observed behaviour of black body radiation . in ,max planck derived his radiation law that gave a correct description , but a the cost of assuming that the oscillators comprising the blackbody could absorb energy only in discrete amounts , in quanta of energy .this led to the development of quantum mechanics .    _ because of its highly accurate descriptions , mechanics became regarded as the ultimate explanatory science .phenomena of any kind , it was believed , could and should be explained in terms of mechanical concepts .newtonian physics was used to support the deistic view , in particular represented by voltaire , that god had created the world as a perfect machine that then required no further interference from him , the newtonian world machine or clockwork universe . _the confidence in the validity of these ideas is best described by the following statement of laplace in :      _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ `` we ought then to regard the present state of the universe as the effect of its anterior state and as the cause of the one which is to follow . given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it an intelligence sufficiently vast to submit these data to analysis it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom ; for it , nothing would be uncertain and the future , as the past , would be present to its eyes . ''_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  in the aftermath , the method of newtonian mechanics was applied successfully to a growing number of areas of nature .the marvelous development of mechanics in the century , thermal engineering and thermodynamics in the beginning of the century give evidence of the power of that approach .   in the following , from a modern perspective, we analyze the important changes in the approach to nature that have occurred in century .first , the method of natural sciences had been established .this method tries to separate nature into systems that are to a good approximation ` isolated ' , in the sense that the inclusion of their interaction with the remaining part of nature would introduce only small changes below the intended accuracy of description .note that such separation is non - trivial and involves an _ assumption _ that itself can not be verified .such supposedly isolated systems are studied by precise experiments or observations .the corresponding measurements are subjected to a mathematical analysis with the goal of abstraction of a natural law or ` theory ' .predictions of the theory are tested by additional experiments or observations .if the results are consistent with those predictions within the accuracy of the measurements , the theory is maintained . otherwise , the theory is revised . in the last case ,the process is continued until consistency with known experiments and observations is reached .  note that even if the initial assumption of isolation of the system is false , this process can still lead to an accurate description by the theory if , for some reason , it successfully ` captures ' the influence of the surrounding . the simplest way to achievethis is to include a larger number of constants into the theory that can be adapted to measurements . to avoid the last, it is generally demanded that a theory should be in some sense ` simple ' or ` aesthetic ' .experiments and observations provide the basis of the method of natural sciences in that their outcome decides on the ` truth ' of a theory .if predicted qualitatively and quantitatively correctly by a theory , a natural phenomenon is considered to be ` understood ' or ` explained ' _ in terms of the theory_.  note that in the case of a false assumption of isolation of the system , a ` true ' theory is still ` false ' in the sense that it can not be expected that it describes correctly the ` nature ' of the system .note also that _ there are no proofs in natural sciences _ , although galilei uses this notion in the above cited passage from . differently to mathematics , those are based on experiment , not on logic . ultimately , in natural sciences even logic is subject to experimental verification .the focus on mechanical phenomena allowed the development of a highly successful theory , i.e. , newtonian mechanics , that was believed to be consistent with experiments and observations of increasing accuracy until the beginning of the century .that there was an unexplained advance in the perihelion of mercury was not regarded as a failure of newtonian mechanics , but due to unknown gravitational sources . ] under the impression of the successes of this theory , there was abstracted a philosophical world view , the clockwork universe where god is regarded as a creator of natural laws governing its evolution and the agent that set the clock initially into motion .after that , the evolution of the world is thought to be completely deterministic .it is believed that a miracle , in the sense of a divine intervention into nature which does contradict natural laws , does not occur .that abstraction of a philosophical world view , although tempting , provides a classic example of the quite common _ mistake _ of the layman _ to identify a theory with the part of nature it only describes_. the method of natural sciences _ defines _ the ` truth ' of a theory as its consistency with known experiments and observations within the accuracy of measurements .there is no generally accepted method available to decide whether the theory is true in some absolute sense . on the contrary, the history of physics showed that ultimately every theory turned out to be ` false ' , in the sense that its predictions were inconsistent with more precise experiments or observations which made its revision necessary .such revisions led to new theories which explained the phenomena of the older theories qualitatively and quantitatively and at the same a large number of additional natural phenomena those older theories could not account for . _ but , as will be pointed out later on , in every step in this sequence , concepts that were fundamental in the formulation of the older theory were negated by its successor . from this point of view , it can very well be said that fundamental aspects of the older theories were false ._ there is no reason to believe that this will be different for future theories . here, it should also be taken into account that by the rules of logic , a false statement can imply a true statement .for instance , a compound statement falsely claiming a true statement and a false statement at the same time leads to a true statement by omitting that false part of the statement .the statement  _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ` tigers are mammals and mice are reptiles ' _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  is false , but it implies the true statement  _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ` tigers are mammals'_. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  hence , a false theory can very well lead to results consistent with experiments or observations . for these reasons ,the abstraction of philosophical a world view from such theories is inherently flawed ._ therefore , the abstraction of philosophical world views from natural sciences leads to a belief system , only .in particular , differently from these sciences , such views can not claim exactness ._  in addition , from a christian point of view , it appears that the creation of a philosophic world view , _ by abstraction from natural sciences or by theological reasoning from statements in the bible _ , violates commandments in the bible :  * exodus 20 ( kjv ) + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ `` 4 thou shalt not make unto thee any graven image , or any likeness of any thing that is in heaven above , or that is in the earth beneath , or that is in the water under the earth .5 thou shalt not bow down thyself to them , nor serve them : ... '' _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ * or in deuteronomy 5 ( kjv ) + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ `` 8 thou shalt not make thee any graven image , or any likeness of any thing that is in heaven above , or that is in the earth beneath , or that is in the waters beneath the earth : 9 thou shalt not bow down thyself unto them , nor serve them : ... '' _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _   since i am no biologist , i will make only some very general remarks on the relation between physics and the natural sciences of biology and chemistry .these start from definitions of these fields given in the encyclopedia britannica :  _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ `` biology is the study of living things and their vital processes . ''_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  a large part of those processes have been recognized as chemical processes which led to the creation and growing importance of the subfields of biochemistry and molecular biology .judging from the successes of those , it does not seem to be too far fetched to say that biology will ultimately turn out to be ( at least in principle ) a subdivision of chemistry ._ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ [ chemistry is ] `` the science that deals with the properties , composition , and structure of substances ( elements and compounds ) , the reactions and transformations they undergo , and the energy released or absorbed during those processes . ''_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  the laws that govern those properties of substances have been recognized as the laws of quantum mechanics .hence , it can be said that chemistry is ( at least in principle ) a subdivision of physics .  as a consequence ,physics increasingly emerges as the root of the natural sciences .therefore , there is reason to view darwin s and other theories of evolution from a physicist s point of view .presently , because of their ad hoc nature and lack of quantitative statements , from this point of view , those theories seem to be more working hypotheses than theories .also for this reason , they seem to be unsuitable for the abstraction of a world view .in the following , we state the established physical theories subsequent to newtonian mechanics in chronological order and give a short description of fundamental changes they introduced .that descent of the mechanical theory of nature started with the analysis of electrical and magnetic phenomena in the century , in particular with the discovery of radio waves propagating at the speed of light in vacuum .meters per second ] such waves were predicted by the electromagnetic theory of james clerk maxwell from  . they were produced and measured in the laboratory by heinrich hertz in .it is worth noting that in attempting to illustrate faraday s law of induction , maxwell constructed a mechanical model .also , it was assumed that those waves had some sort of a material carrier , the so called ` ether ' , similar to sound waves that are compression waves in matter . in and ,this theory was shattered by the michelson - morley experiments , which were designed specifically to detect the motion of the earth through the ether and which indicated that there was no such effect ._ as a consequence , the existence of non - mechanical entities in addition to matter was realized , i.e. , force fields that are propagating through empty space . _maxwell s electromagnetic equations require waves to move at the speed of light in vacuum in every inertial system , that is in every reference frame where free matter moves with constant speeds and on a straight lines .two such reference frames move relative to each other at a constant speed .therefore , the propagation of electromagnetic waves contradicts common experience that suggests that the wave speed should appear to be different as measured from different inertial systems .    in , albert einstein made the constancy of the speed of light and the requirement that the laws of physics should assume the same form in every inertial system _ postulates _ of his special theory of relativity .this led to radical changes of newtonian mechanics .the concept of absolute time or rather of absolute simultaneity of events lost its meaning and became dependent on the reference frame instead .as a consequence , also the concept of rigid bodies had to be abandoned ._ all these notions are central in newtonian mechanics_.   newton s law of gravitation is incompatible with the theory of special relativity and therefore needed a revision after the arrival of this theory .this was achieved in by albert einstein s theory of general relativity that absorbs the gravitational field into the geometry of space - time . in this, the theory generalizes the special theory of relativity and again radically alters newtonian mechanics on a fundamental level .in particular , it removes the gravitational field from any energy momentum balance of a physical system under the influence of such a ` field ' . as a consequence ,in general there is no conserved total energy or momentum associated to such a system .the theory of quantum mechanics or more general quantum theory was developed by werner heisenberg , max born and pascual jordan in because of the clear failure of newtonian mechanics to describe the physical phenomena in the range of atomic distances , i.e , meter nanometer and below .this theory shook the foundations of physics like no other before or after because of its probabilistic character . that character allows statements on individual systems only in the exceptional cases of the occurrence of probabilities of value ._ it denies the possibility of a deterministic description simultaneously of the positions and the momenta of the members of a mechanical system .it gives a deterministic description only for the probability distribution of those quantities ._  in this , it departs radically from the previous theories which were from then on referred to as ` classical ' .the statistical nature of the theory was a major shock for physicists and is the reason why a few physicists still consider it to be an incomplete theory .notably , albert einstein was among them .the desperation of physicists , caused by the inapplicability of the ideas from classical physics to atomic systems , is very well depicted in a letter from of wolfgang pauli , later a nobel prize winner in physics , to his assistant ralph kronig :  _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ` currently , physics is again very muddled . for me at least ,it is to complicated and i wished i would be a comic artist of the screen or similar and would never have heard anything from physics .but still i hope that bohr will save us with a new idea . ' _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _     quantum electrodynamics is the result of the attempt to develop a quantum mechanics which is compatible with the theory of special relativity .it describes the interaction of charged matter . in this theory , matter and the electrodynamic fieldare treated on the same footing , namely as objects that can act as particles or fields . _ in classical physics both properties are incompatible_. in addition , it leads on the existence of antimatter that in collision with the corresponding matter annihilates to light .also the opposite process is possible . as a consequence , matter and lightcan be considered as two manifestations of one field .some of the most precise tests of quantum electrodynamics have been experiments dealing with the properties of subatomic particles known as muons .the magnetic moment of this type of particle has been shown to agree with the theory to nine significant digits .agreement of such high accuracy makes quantum electrodynamics one of the most successful physical theories so far devised .the standard model of particle physics is a generalization of quantum electrodynamics which also includes weak and strong nuclear forces that are in particular responsible for radioactive decay and the stability of atomic nuclei .it does not take into account the gravitational field . until recently , it has proved highly successful in the description of experimental observations .however , experiments in , ( k2k - i ) ( k2k - ii ) and ( minos ) indicate that neutrinos have mass which is not taken into account in the standard model .  also , one of the basic assumptions of particle physics in general is the ancient idea ( democritus , ca . ) of the existence of ` atoms , ' i.e. , of particles that are ` fundamental ' in the sense of not being composites of others .the history of particle physics does not seem to support this idea .i hope , it has been made clear that natural sciences pose _ no threat to faith because of the inherent limitations of their approach_. abstracted world views pose a potential threat , but leave the firm ground of natural sciences and therefore constitute belief systems that can not claim exactness .that such abstractions are inherently flawed can also be read off from the development of the root of natural sciences , i.e. , physics .its development led to a sequence of theories which give the impression of insights into nature of increasing deepness and comprehensiveness .still , each new theory negated fundamental aspects of its predecessor .it is not to be expected that this will change in future .this indicates that every physical theory contains some fundamentally false aspects which would be inherited by an abstracted world view ._ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ kepler , galilei , newton , descartes , laplace , leibniz , maxwell , planck , heisenberg and jordan _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  were christians that did not see any contradiction between their work and their faith .finally , i see no better way to conclude this paper with the final words of max planck in his speech `` religion und naturwissenschaft '' ( religion and natural sciences ) from 1937 :

Abstract: it is a quite common view among people , that are not aware of the developments in modern physics , that it is part of human nature to substitute religious faith in places where there is no knowledge . therefore , an increase in knowledge would lead to a decrease in the necessity of faith . further , it is argued that , ideally speaking , a full knowledge of the laws of nature would make obsolete any sort of religious faith and would ultimately allow a complete control of nature by man . since referring to nature , such views must be founded in the natural sciences of which physics is the most fundamental . therefore , the question whether such views are compatible with the current state of natural sciences is ultimately decided in physics . indeed , it is likely that these simplistic views have their origin in the world view generated by the successes of newtonian physics from the middle of the century until the beginning of the century which viewed the physical world as a type of mechanical clock in which the motion of the gears affect each other in a precise and predictable way . in particular , the paper points out that the above views are no longer supported by current physics and that abstracted world views can not be considered as part of natural sciences , but only as belief systems .


zero - shot learning ( zsl ) aims at solving the problem when the new test image categories are not seen in the training samples .different from the open set recognition and novelty detection which only distinguish abnormalities in the testing data , zsl seeks to classify the unseen testing classes .this is a practical problem setting in image classification , as there are thousands of categories of objects we intend to recognize , but only a few of them may have been appropriately annotated .consequently , it is more challenging than the conventional image classification problems .the key ideas of zsl are to choose better side information ( also known as modalities ) and to develop an effective common semantic space .the side information provides a bridge to transfer knowledge from the seen classes for which we have training data to the unseen classes for which we do not , and the common space offers a fusion feasibility for the visual features and the side information .two types of commonly used side information in zsl are attributes and word vectors , .particularly , attributes act as intermediate representations shared across multiple classes , indicating the presence or absence of several predefined properties .direct attribute prediction ( dap ) is one of the first efforts to exploit the attributes to zsl .it learns attribute - specific classifiers with the seen data and infers the unseen class with the learned estimators. however , attribute - based approaches suffer from a poor scalability as the attributes ontology for each class is generally manually defined .word - vector - based approaches avoid this limitation since word vectors are extracted from a linguistic corpus with neural language models such as golve and word2vec .therefore , word vectors have become another popular side information in zsl .for instance , socher _ et al . _ construct a two layer neural network to project images into the word vector space . in ,frome _ et al ._ present a deep visual - semantic embedding model with a hinge loss function , which trains a linear mapping to link the image visual space to the word vector space .besides attributes and word vectors , some other side information , such as wordnet , visual prototypical concepts , class co - occurrence statistics , is also applied in zsl .further , since different types of side information captures different aspects of the structure of the semantic space , several studies have been made to combine them to achieve higher classification performance ,, .for example , in , akata _ et al . _ first learn the joint embedding weight matrices corresponding to different types of side information , then perform a grid search over the coefficients on a validation set to get the joint compatibility model . in ,semantic projections are trained for attributes and word vectors independently , followed by a transductive multi - view semantic embedding space to alleviate the projection domain shift problem .these efforts demonstrate that different types of side information complement each other and construct a better embedding space for knowledge transfer .however , although multiple types of side information are utilized , they still exploit each type of side information in its own semantic space independently , and then just combine the predicted scores together , .this can not make full use of the complementary knowledge of different types of side information .a more efficient and robust solution is to investigate multiple types of side information in a unified space .unfortunately , to the best of our knowledge , there has been little previous work exploiting this idea . to this end , we present a novel approach called mbfa - zsl to employ multiple types of side information in a unified space , as shown in fig .[ fig1 ] .it is worth highlighting several aspects of the proposed mbfa - zsl approach .( 1 ) it develops an advanced multi - view embedding algorithm named multi - battery factor analysis ( mbfa ) , which extends tucker s inter - battery factor analysis ( ibfa ) .( 2 ) as far as we know , it represents one of the first attempts that embeds both the image visual features and multiple types of side information into one unified semantic space , which fully utilizes the interrelations among different types of information .( 3 ) the close - form solution makes it simple to implement and efficient to run on large datasets . ( 4 ) extensive experiments on popular datasets demonstrate its significant superiority over the existing state - of - the - art approaches .the reminder of this paper is structured as follows .section 2 introduces the proposed multi - battery factor analysis ( mbfa ) algorithm , and section 3 describes the proposed mbfa - zsl approach in detail .experimental results are presented in section 4 , and conclusions are drawn in the final section .multi - battery factor analysis ( mbfa ) is developed to provide a unified semantic space for both the visual features and multiple types of side information .it originates from tucker s inter - battery factor analysis ( ibfa ) , which transforms two modalities into a shared space where they are not only well explained but also as much correlated as possible with each other .thus , we first briefly introduce the ibfa algorithm , and then extend it to a multi - view version , i.e. , mbfa .  given a set of instances from two modalities , \in{\mathbb{r}^{p_1\times{n}}} ] , where and are their dimensionalities , respectively . with , centered , ibfa finds two projection matrices , and , by the following constrained maximization : where is an identity matrix .ibfa maximizes the total covariance between the two modalities , which can be seen plainly by rewriting as . with the lagrange multiplier method , ( [ eq : ibfa ] ) can be solved analytically through the eigenvalue decomposition .compared with canonical correlation analysis ( cca ) , ( [ eq : ibfa ] ) can be rewritten as : where denotes the pearson correlation , and is the variance. it can be seen from ( [ eq : ibfav2 ] ) that ibfa attempts to capture both the correlation and variation of and .this is different from cca that only aims at maximizing their correlation . in particular , the maximized correlation and variance in ( [ eq : ibfav2 ] ) depict the relationship between and and strengthen their own discriminant capabilities , respectively .to broaden ibfa to a multi - view scenario , we develop the mbfa algorithm on the basis of ibfa .given a set of instances from modalities , \in{\mathbb{r}^{p_i\times{n } } } , i=1,\dots , c$ ] , where denotes the dimensionality , with centered , the objective function of mbfa is expressed as : similar to ibfa , mbfa tries to find a set of projection matrices that maximize the total covariance in the common space .equation ( [ eq : mbfa ] ) can be rewritten as : where and are as follows : ^t.\ ] ] , \mathbf{m}_{ij } = \left\ { \begin{array}{ll }   0 , & i = j \\\mathbf{x}_i\mathbf{x}_j^t , & i \neq j. \end{array } \right.\ ] ] equation ( [ eq : mbfav2 ] ) can be solved via the eigenvalue decomposition ; thus each projection matrix can be obtained .it is obvious that ibfa can be considered as a special case of mbfa when is 2 .in addition , the main difference between mbfa and multi - view canonical correlation analysis ( mcca ) , is worth highlighting .both of them find a set of linear transformations to project multiple modalities into one common space .however , mcca seeks to maximize the total correlation in the common space , whereas mbfa maximizes the total covariance , which is equivalent to maximize the total correlation and variance simultaneously . to the best of our knowledge, there is no previous work using mcca on zsl . in this paper, we also implement mcca on zsl as a comparative approach ( we call this approach as mcca - zsl ) .in a zsl setting , we are given labeled training instances and unlabeled testing instances . and are the -dimensional visual feature vectors of training and testing instances respectively . and are the seen and unseen class label vectors , and .we have different types of side information , and denote the -th type of -dimensional side information for training and testing datasets respectively .note that for the testing dataset , is missing as testing instances are unlabeled .the task of zsl is to predict the class labels .the proposed mbfa - zsl algorithm mainly contains the following two steps :  _ step 1 : build a mbfa space with the seen data . _the mbfa algorithm provides an unified semantic space for different types of side information as well as the visual features . with the seen images together with the side information , we can train the mbfa model to obtain a set of projection matrices  , where is the sum of all the types of side information and the visual features , such that . for example , if we use both attributes and word vectors as the side information , then is 3 .  _step 2 : unseen category inference . _ with the projection matrix learned from the seen data , the unseen image features can be embedded into the common space by .typically , the unseen category of can be inferred by searching for the nearest output embedding vector that corresponds to one of the unseen classes , if there is only single side information available in .since there are multiple types of side information used in the mbfa - zsl approach , we introduce a multi - modality fusion method to predict the unseen category of the with : ,l=1,2,\dots , n , \end{aligned}\ ] ] where is a weight associated with each type of side information , which can be determined by a grid search on the validation set .each type of side information that corresponds to the -th unseen class is denoted as , and it can be embedded into the common space by .the similarity between two vectors can be represented as the common distance measurements , such as dot product similarity and euclidean distance . in this paper ,the cosine distance is utilized , i.e. ,   moreover , mbfa - zsl has an explicit , close - form solution , which makes it simple to implement and efficient to run on large datasets .* algorithm 1 * outlines the procedures of the proposed mbfa - zsl approach .  .construct the covariance matrix with the labeled visual features and the corresponding side information .solve the eigenvalue decomposition problem in ( [ eq : mbfav2 ] ) , and the eigenvectors corresponding to the largest eigenvalues form the projection matrices .learn the weight parameters of the category inference function ( [ eq : inference ] ) in the validation set .project the unseen visual feature and the side information of the unseen classes into the unified space with projection matrices .predict the labels of with ( [ eq : inference ] ) .we evaluate the proposed mbfa - zsl approach on three publicly popular datasets : animals with attributes ( awa ) , caltech - ucsd - birds-200 - 2011 ( cub ) , and sun attribute . specifically , awa is a collection of 30,475 images on 50 classes of animals , with 85 associated class - level attributes .we use the standard training / test ( seen / unseen ) split as that in , which chooses 40 classes for training and validation and 10 classes for testing .cub provides 200 classes of birds ( 11,788 images ) , and each class is annotated with 312 attributes . particularly , cub is a much more challenging dataset in that it is designed for fine - grained image classification and contains more classes but fewer images .similar to , we use 150 classes as training and validation set , leaving 50 disjoint classes as test set .sun attribute dataset consists of 14,340 images from 717 scene categories , and each category is annotated with a taxonomy of 102 discriminate attributes .we adopt the popular training / test ( seen / unseen ) split as that in , which selects 707 classes for training and validation , and takes the remaining 10 classes as testing set .we cross - validate the parameters in ( [ eq : inference ] ) .the example images in these datasets are shown in fig .[ fig2 ] .  on the awa dataset, we use the vgg ( very deep 19-layer cnn ) features provided in as visual features . on the cub and sun dataset, we use a pre - trained vgg model to extract visual features . for each image ,the 4,096 dimensional top - layer hidden unit activations ( fc7 ) of vgg are taken as visual features .we use both the word vectors ( t ) and attributes ( a ) as the side information in mbfa - zsl . specifically , we train the word2vec model on a corpus of wikipedia documents to form 1000-d word vectors for the three datasets. meanwhile , we use the attribute information provided by the datasets . the average per - class top-1 accuracy on the test sets is reported .we compare the proposed mbfa - zsl with 7 state - of - the - art approaches as well as mcca - zsl , which utilize a range of side information . among them , dap , , eszsl , and sse - relu only use attributes ; latem can make use of either word vectors or attributes ; sje , amp , tmv - hlp and mcca - zsl employ more than one type of side information .different cnn visual features are applied in these approaches , such as googlenet , overfeat , and vggnet-19 .additionally , we also implement mbfa - zsl and mcca - zsl in the situation where only attributes ( a ) or word vectors ( t ) are available .the performance of mbfa - zsl are taken via ten times of cross validation .it should be noticed that when only t or a is avaliable , the single parameter in ( [ eq : inference ] ) does not need to be tuned , thus there is no standard deviation for the corresponding results .furthermore , the standard deviations of some comparative results are absent as they are not avaliable in the original papers .the comparative results are summarized in table [ performance ] , from which we can observe that mbfa - zsl achieves the amazingly best performance in all cases for all the three datasets . besides , we also have the following observations :  max width=  c|c|ccccccccc & & & & + & & t & a & t+a & t & a & t+a & t & a & t+a + & sje & 51.2 & 66.7 & 73.5 * & 28.4 & 50.1 & 51.0 * & - & - & - + & latem & 61.1 & 71.9 & - & 31.8 & 45.5 & - & - & - & - + & amp & - & - & 66.0 & - & - & - & - & - & - + & tmv - hlp & - & - & 73.5 & - & - & 47.9 & - & - & - + & dap & - & 60.8 & - & - & - & - & - & 72.0 & - + & sse - relu & - & 76.3.8 & - & - & 30.4.2 & - & - & 82.5.3 & - + & eszsl * * & - & 74.6.7 & - & - & 50.8.4 & - & - & 84.5.4 & - + & mcca - zsl * * & 65.8.7 & 74.9.3 & 75.3.8 & 32.1.3 & 45.8.2 & 46.4.7 & 59.5.7 & 82.8.5 & 85.1.5 + & mbfa - zsl * * & * 72.5 * & * 77.8 * & * 79.9.7 * & * 32.4 * & * 51.7 * & * 52.2.4 * & * 61.5 * & * 85.0 * & * 87.4.2* +  +  +  \(1 ) for awa dataset , the second - best approaches are mcca - zsl , sse - relu , and mcca - zsl in the cases of t , a , and t+a , respectively .mbfa - zsl outperforms them in 6.7% , 1.5% , and 4.6% , respectively . for cub dataset, mbfa - zsl outperforms the second - best approaches , mcca - zsl in 0.3% , eszsl in 0.9% , and sje in 1.2% in the three cases , respectively . for sun dataset , in the three cases , mbfa - zsl outperforms the second - best approaches , mcca - zsl in 2.0% , eszsl in 0.5% , and mcca - zsl in 2.3% , respectively .these are very promising results .\(2 ) for mbfa - zsl , the performance on awa in t+a is better than those in t and a in 7.4% and 2.1% , respectively .on cub , the performance in t+a is better than those in t and a in 19.8% and 0.5% , respectively . on sun ,the promotions are 25.9% and 2.4% , respectively .similar observation can also be found in mcca - zsl .the excellent performance in t+a of mbfa - zsl and mcca - zsl demonstrates that it is effective to embed multiple types of side information into a unified space .it also confirms that different types of side information complement each other in transferring knowledge .\(3 ) in the situation of `` t+a '' , it can be found that mbfa - zsl outperforms the others significantly .take the awa for example , the performance improvements of mbfa - zsl over sje , amp and tmv - hlp are 6.4% , 13.9% , and 6.4% , respectively .this demonstrates that embedding the visual features and multiple types of side information in a unified space is more promising than the conventional methods that projecting the visual features to each type of side information space independently at first , and then combining them together .\(4 ) when only single type of side information is available , attributes often help achieve a higher accuracy than word vectors .this is due to that attributes are manually defined for a specific dataset , so they are able to describe category relationship of the dataset more effectively ; nevertheless , word vectors are extracted from the corpus in an unsupervised manner , whose capacity is constrained by the size or specific domain of the corpus , as well as the polysemy issue .\(5 ) interestingly , the performance on cub is inferior to that on awa and sun .the reason may lie in the fine - grained characteristic of cub .both the visual appearance and the class names in it are similar to each other , which make it hard to recognize .  to clearly evaluate the performance of mbfa - zsl on each class , we present the confusion matrix of awa with t+a , as illustrated in fig . [ confusionmat ] .the diagonal elements denotes the correct prediction accuracy of each class , from which we can see that the proposed mbfa - zsl can achieve relatively high performance on every class .[ confusionmat ]   there are two types of parameters in mbfa - zsl : the weights in ( [ eq : inference ] ) and the dimensionality of the unified space that multiple modalities are projected into .the weights are decided by the cross validation .the impact of dimensionalities is shown in fig .[ parameter ] .the optimal dimensionalities for awa , cub , and sun are 40 , 50 , and 120 , respectively .it can be observed that a higher dimensionality has no performance improvement .   finally ,as shown in table [ speed ] , we report the running times of the training and testing stages for awa , cub , and sun , respectively .our implementation is based on an unoptimized matlab code . on our computer with i5 4590 cpu and 12 g memory , the training times for the three datasets are 18.8s , 22.2s , and 17.4s , respectively .the test times on each image for the three datasets are 0.006ms , 0.010ms , and 0.019ms , respectively .therefore , mbfa - zsl is extremely efficient .max width=  [ cols="^,^,^,^",options="header " , ]in this paper , we have proposed the mbfa - zsl approach to projecting both the visual features and multiple types of side information into one unified semantic space to perform zsl .it can also be applied to the situation where only a single type of side information is available .the results on the three popular datasets show its superior performance over the state - of - the - art approaches on the cases of utilizing a ( attributes ) , t ( word vectors ) , and a+t ( attributes + word vectors ) as an effective and efficient method .moreover , it has a close - form solution .+  + * acknowledgements *  this work was supported by the national basic research program of china ( 973 program ) under grant 2014cb340400 , the national natural science foundation of china under grant 61271325 , grant 61472273 , the elite scholar program of tianjin university under grant 2015xrg-0014 , and the research program of application foundation and advanced technology of tianjin under grant 15jcybjc17100 .0 m. palatucci , d. pomerleau , g. e. hinton , and t. m. mitchell , `` zero - 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Abstract: zero - shot learning ( zsl ) extends the conventional image classification technique to a more challenging situation where the test image categories are not seen in the training samples . most studies on zsl utilize side information such as attributes or word vectors to bridge the relations between the seen classes and the unseen classes . however , existing approaches on zsl typically exploit a shared space for each type of side information independently , which can not make full use of the complementary knowledge of different types of side information . to this end , this paper presents an mbfa - zsl approach to embed different types of side information as well as the visual feature into one shared space . specifically , we first develop an algorithm named multi - battery factor analysis ( mbfa ) to build a unified semantic space , and then employ multiple types of side information in it to achieve the zsl . the close - form solution makes mbfa - zsl simple to implement and efficient to run on large datasets . extensive experiments on the popular awa , cub , and sun datasets show its significant superiority over the state - of - the - art approaches .   zero - shot learning , multi - battery factor analysis , image classification , attribute , word vector .