ABSTRACTS
OF 
PART I: A GENERAL OVERVIEW 
This piece of text was written as an attempt to provide a popular summary about TGD. This is of course mission impossible since TGD is something at the top of centuries of evolution which has led from Newton to standard model. This means that there is a background of highly refined conceptual thinking about Universe so that even the best computer graphics and animations fail to help. One can still try to create some inspiring impressions at least. This chapter approaches the challenge by answering the most frequently asked questions. Why TGD? How TGD could help to solve the problems of recent day theoretical physics? What are the basic princples of TGD? What are the basic guidelines in the construction of TGD? These are examples of this kind of questions which I try to answer in using the only language that I can talk. This language is a dialect of the language used by elementary particle physicists, quantum field theorists, and other people applying modern physics. At the level of practice involves technically heavy mathematics but since it relies on very beautiful and simple basic concepts, one can do with a minimum of formulas, and reader can always to to Wikipedia if it seems that more details are needed. I hope that reader could catch the basic principles and concepts: technical details are not important. And I almost forgot: problems! TGD itself and almost every new idea in the development of TGD has been inspired by a problem. 
In this chapter a critical comparison of Mtheory and TGD as two competing theories is carried out. Dualities and black hole physics are regarded as basic victories of Mtheory. a) The counterpart of electric magnetic duality plays an important role also in TGD and it has become clear that it might change the sign of Kähler coupling strength rather than leaving it invariant. The different signs would be related to different time orientations of the spacetime sheets. This option is favored also by TGD inspired cosmology. b) The AdS/CFT duality of Maldacena involved with the quantum gravitational holography has a direct counterpart in TGD with 3dimensional causal determinants serving as holograms so that the construction of absolute minima of Kähler action reduces to a local problem. c) The attempts to develop further the nebulous idea about spacetime surfaces as quaternionic submanifolds of an octonionic imbedding space led to the realization of duality which could be called number theoretical spontaneous compactification. Spacetime can be regarded equivalently as a hyperquaternionic 4surface in M^{8} with hyperoctonionic structure or as a 4surface in M^{4}× CP_{2}. d) The duality of string models relating KaluzaKlein quantum numbers with YM quantum numbers could generalize to a duality between 7dimensional light like causal determinants of the imbedding space (analogs of "big bang") and 3dimensional light like causal determinants of spacetime surface (analogs of black hole horizons). e) The notion of cotangent bundle of configuration space of 3surfaces suggests the interpretation of the numbertheoretical compactification as a waveparticle duality in infinitedimensional context. Also the duality of hyperquaternionic and cohyperquaternionic 4surfaces could be understood analogously. These ideas generalize at the formal level also to the Mtheory assuming that stringy configuration space is introduced. The existence of Kähler metric very probably does not allow dynamical target space. In TGD framework black holes are possible but putting black holes and particles in the same basket seems to be mixing of apples with oranges. The role of black hole horizons is taken in TGD by 3D light like causal determinants, which are much more general objects. Black holeelementary particle correspondence and padic length scale hypothesis have already earlier led to a formula for the entropy associated with elementary particle horizon. The recent findings from RHIC have led to the realization that TGD predicts black hole like objects in all length scales. They are identifiable as highly tangled magnetic flux tubes in Hagedorn temperature and containing conformally confined matter with a large Planck constant and behaving like dark matter in a macroscopic quantum phase. The fact that string like structures in macroscopic quantum states are ideal for topological quantum computation modifies dramatically the traditional view about black holes as information destroyers. The discussion of the basic weaknesses of Mtheory is motivated by the fact that the few predictions of the theory are wrong which has led to the introduction of anthropic principle to save the theory. The mouse as a tailor history of Mtheory, the lack of a precise problem to which Mtheory would be a solution, the hard nosed reductionism, and the censorship in Los Alamos archives preventing the interaction with competing theories could be seen as the basic reasons for the recent blind alley in Mtheory. 
PART II:PHYSICS AS INFINITEDIMENSIONAL AND GENERALIZED NUMBER THEORY: TWO VISIONS 
In this chapter the classical field equations associated with the Kähler action are studied. The study of the extremals of the Kähler action has turned out to be extremely useful for the development of TGD. Towards the end of year 2003 quite dramatic progress occurred in the understanding of field equations and it seems that field equations might be in welldefined sense exactly solvable. Years later the understanding of quantum TGD at fundamental level deepened the understanding. 1. Preferred extremals and quantum criticality The identification of preferred extremals of Kähler action defining counterparts of Bohr orbits has been one of the basic challenges of quantum TGD. By quantum classical correspondence the nondeterministic spacetime dynamics should mimic the dissipative dynamics of the quantum jump sequence. It should also represent spacetime correlate for quantum criticality. The solution of the problem through the understanding of the implications number theoretical compactification and the realization of quantum TGD at fundamental level in terms of second quantization of induced spinor fields assigned to the modified Dirac action defined by Kähler action. Noether currents assignable to the modified Dirac equation are conserved only if the first variation of the modified Dirac operator D_{K} defined by Kähler action vanishes. This is equivalent with the vanishing of the second variation of Kähler action at least for the variations corresponding to dynamical symmetries having interpretation as dynamical degrees of freedom which are below measurement resolution and therefore effectively gauge symmetries. The vanishing of the second variation in interior of X^{4}(X^{3}_{l}) is what corresponds exactly to quantum criticality so that the basic vision about quantum dynamics of quantum TGD would lead directly to a precise identification of the preferred extremals. Something which I should have noticed for more than decade ago! The question whether these extremals correspond to absolute minima remains however open. The vanishing of second variations of preferred extremals suggests a generalization of catastrophe theory of Thom, where the rank of the matrix defined by the second derivatives of potential function defines a hierarchy of criticalities with the tip of bifurcation set of the catastrophe representing the complete vanishing of this matrix. In the recent case this theory would be generalized to infinitedimensional context. The spacetime representation for dissipation comes from the interpretation of regions of spacetime surface with Euclidian signature of induced metric as generalized Feynman diagrams (or equivalently the lightlike 3surfaces defining boundaries between Euclidian and Minkowskian regions). Dissipation would be represented in terms of Feynman graphs representing irreversible dynamics and expressed in the structure of zero energy state in which positive energy part corresponds to the initial state and negative energy part to the final state. Outside Euclidian regions classical dissipation should be absent and this indeed the case for the known extremals. 2. HamiltonJacobi structure Most known extremals share very general properties. One of them is HamiltonJacobi structure meaning the possibility to assign to the extremal so called HamiltonJacobi coordinates. This means dual slicings of M^{4} by string world sheets and partonic 2surfaces. Number theoretic compactification led years later to the same condition. This slicing allows a dimensional reduction of quantum TGD to Minkowksian and Euclidian variants of string model and allows to understand how Equivalence Principle is realized at spacetime level. Also holography in the sense that the dynamics of 3dimensional spacetime surfaces reduces to that for 2D partonic surfaces in a given measurement resolution follows. The construction of quantum TGD relies in essential manner to this property. CP_{2} type vacuum extremals do not possess HamiltonJaboci structure but this can be understood in the picture provided by number theoretical compactification. 3. Physical interpretation of extremals The vanishing of Lorentz 4force for the induced Kähler field means that the vacuum 4currents are in a mechanical equilibrium and dissipation is absent except in the sense that the superposition of generalized Feynman graphs representing the zero energy state represents dissipation. Lorentz 4force vanishes for all known solutions of field equations.
4. The dimension of CP_{2} projection as classifier for the fundamental phases of matter The dimension D_{CP2} of CP_{2} projection of the spacetime sheet encountered already in padic mass calculations classifies the fundamental phases of matter.
5. Specific extremals of Kähler action The study of extremals of Kähler action represents more than decade old layer in the development of TGD.

PART III: HYPERFINITE FACTORS OF TYPE II_{1} AND HIERARCHY OF PLANCK CONSTANTS 
Does TGD Predict Spectrum of Planck Constants? The quantization of Planck constant has been the basic them of TGD since 2005. The basic idea was stimulated by the finding of Nottale that planetary orbits could be seen as Bohr orbits with enormous value of Planck constant given by hbar_{gr}= GM_{1}M_{2}/v_{0}, where the velocity parameter v_{0} has the approximate value v_{0}≈ 2^{11} for the inner planets. This inspired the ideas that quantization is due to a condensation of ordinary matter around dark matter concentrated near Bohr orbits and that dark matter is in macroscopic quantum phase in astrophysical scales. The second crucial empirical input were the anomalies associated with living matter. The recent version of the chapter represents the evolution of ideas about quantization of Planck constants from a perspective given by seven years's work with the idea. A very concise summary about the situation is as follows. Basic physical ideas The basic phenomenological rules are simple and there is no need to modify them.
Spacetime correlates for the hierarchy of Planck constants The hierarchy of Planck constants was introduced to TGD originally as an additional postulate and formulated as the existence of a hierarchy of imbedding spaces defined as Cartesian products of singular coverings of M^{4} and CP_{2} with numbers of sheets given by integers n_{a} and n_{b} and hbar=nhbar_{0}. n=n_{a}n_{b}. With the advent of zero energy ontology, it became clear that the notion of singular covering space of the imbedding space could be only a convenient auxiliary notion. Singular means that the sheets fuse together at the boundary of multisheeted region. The effective covering space emerges naturally from the vacuum degeneracy of Kähler action meaning that all deformations of canonically imbedded M^{4} in M^{4}×CP_{2} have vanishing action up to fourth order in small perturbation. This is clear from the fact that the induced Kähler form is quadratic in the gradients of CP_{2} coordinates and Kähler action is essentially Maxwell action for the induced Kähler form. The vacuum degeneracy implies that the correspondence between canonical momentum currents ∂L_{K}/∂(∂_{α}h^{k}) defining the modified gamma matrices and gradients ∂_{α} h^{k} is not onetoone. Same canonical momentum current corresponds to several values of gradients of imbedding space coordinates. At the partonic 2surfaces at the lightlike boundaries of CD carrying the elementary particle quantum numbers this implies that the two normal derivatives of h^{k} are manyvalued functions of canonical momentum currents in normal directions. Multifurcation is in question and multifurcations are indeed generic in highly nonlinear systems and Kähler action is an extreme example about nonlinear system. What multifurcation means in quantum theory? The branches of multifurcation are obviously analogous to single particle states. In quantum theory second quantization means that one constructs not only single particle states but also the many particle states formed from them. At spacetime level single particle states would correspond to N branches b_{i} of multifurcation carrying fermion number. Twoparticle states would correspond to 2fold covering consisting of 2 branches b_{i} and b_{j} of multifurcation. Nparticle state would correspond to Nsheeted covering with all branches present and carrying elementary particle quantum numbers. The branches coincide at the partonic 2surface but since their normal space data are different they correspond to different tensor product factors of state space. Also now the factorization N= n_{a}n_{b} occurs but now n_{a} and n_{b} would relate to branching in the direction of spacelike 3surface and lightlike 3surface rather than M^{4} and CP_{2} as in the original hypothesis. Multifurcations relate closely to the quantum criticality of Kähler action. Feigenbaum bifurcations represent a toy example of a system which via successive bifurcations approaches chaos. Now more general multifurcations in which each branch of given multifurcation can multifurcate further, are possible unless on poses any additional conditions. This allows to identify additional aspect of the geometric arrow of time. Either the positive or negative energy part of the zero energy state is "prepared" meaning that single nsubfurcations of Nfurcation is selected. The most general state of this kind involves superposition of various nsubfurcations. 
PART IV: APPLICATIONS 
TGD predicts a lot of new physics and it is quite possible that this new physics becomes visible at LHC. Although the calculational formalism is still lacking, padic length scale hypothesis allows to make precise quantitative predictions for particle masses by using simple scaling arguments. The basic elements of quantum TGD responsible for new physics are following.
In this chapter the predicted new physics and possible indications for it are discussed.
