Gordon L. Shaw

Music training causes long-term enhancement of preschool children’s spatial–temporal reasoning

Predictions from a structured cortical model led us to test the hypothesis that music training enhances young childrens spatial-temporal reasoning. Seventy-eight preschool children participated in this study. Thirty-four children received private piano keyboard lessons, 20 children received private computer lessons, and 24 children provided other controls. Four standard, age-calibrated, spatial reasoning tests were given before and after training; one test assessed spatial-temporal reasoning and three tests assessed spatial recognition. Significant improvement on the spatial-temporal test was found for the keyboard group only. No group improved significantly on the spatial recognition tests. The magnitude of the spatial-temporal improvement from keyboard training was greater than one standard deviation of the standardized test and lasted at least one day, a duration traditionally classified as long term. This represents an increase in time by a factor of over 100 compared to a previous study in which listening to a Mozart piano sonata primed spatial-temporal reasoning in college students. This suggests that music training produces long-term modifications in underlying neural circuitry in regions not primarily concerned with music and might be investigated using EEG. We propose that an improvement of the magnitude reported may enhance the learning of standard curricula, such as mathematics and science, that draw heavily upon spatial-temporal reasoning.

Analytic study of the memory storage capacity of a neural network

Abstract Previously, we developed a model of short and long term memory which was based on an analogy to the Ising spin system in a neural network. We assumed that the modification of the synaptic strengths was dependent upon the correlation of pre- and post-synaptic neuronal firing. This assumption we denote as the Hebb hypothesis. In this paper, we solve exactly a linearized version of the model and explicitly show that the capacity of the memory is related to the number of synapses rather than the much smaller number of neurons. In addition, we show that in order to utilize this large capacity, the network must store the major part of the information in the capability to generate patterns which evolve with time. We are also led to a modified Hebb hypothesis.

ENHANCED LEARNING OF PROPORTIONAL MATH THROUGH MUSIC TRAINING AND SPATIAL-TEMPORAL TRAINING

It was predicted, based on a mathematical model of the cortex, that early music training would enhance spatial-temporal reasoning. We have demonstrated that preschool children given six months of piano keyboard lessons improved dramatically on spatial-temporal reasoning while children in appropriate control groups did not improve. It was then predicted that the enhanced spatial-temporal reasoning from piano keyboard training could lead to enhanced learning of specific math concepts, in particular proportional math, which is notoriously difficult to teach using the usual language-analytic methods. We report here the development of Spatial-Temporal Math Video Game software designed to teach fractions and proportional math, and its strikingly successful use in a study involving 237 second-grade children (age range six years eight months-eight years five months). Furthermore, as predicted, children given piano keyboard training along with the Math Video Game training scored significantly higher on proportional math and fractions than children given a control training along with the Math Video Game. These results were readily measured using the companion Math Video Game Evaluation Program. The training time necessary for children on the Math Video Game is very short, and they rapidly reach a high level of performance. This suggests that, as predicted, we are tapping into fundamental cortical processes of spatial-temporal reasoning. This spatial-temporal approach is easily generalized to teach other math and science concepts in a complementary manner to traditional language-analytic methods, and at a younger age. The neural mechanisms involved in thinking through fractions and proportional math during training with the Math Video Game might be investigated in EEG coherence studies along with priming by specific music.

Dendritic bundles: Survey of anatomical experiments and physiological theories

Dendritic bundles have been found throughout the mammalian brain. Unquestionably, these bundles must serve one or more important, fundamental roles in the brains functioning. However, no physiological experiments to determine their function have been performed on these well-established anatomical units. We survey the numerous anatomical reports of bundling. In addition, we discuss several physiological possibilities for the functional significance of bundles.

A statistical theory of short and long term memory.

We present a theory of short, intermediate and long term memory of a neural network incorporating the known statistical nature of chemical transmission at the synapses. Correlated pre- and post-synaptic facilitation (related to Hebbs Hypothesis) on three time scales are crucial to the model. Considerable facilitation is needed on a short time scale both for establishing short term memory (active persistent firing pattern for the order of a sec) and the recall of intermediate and long term memory (latent capability for a pattern to be re-excited). Longer lasting residual facilitation and plastic changes (of the same nature as the short term changes) provide the mechanism for imprinting of the intermediate and long term memory. We discuss several interesting features of our theory: nonlocal memory storage, large storage capacity, access of memory, single memory mechanism, robustness of the network and statistical reliability, and usefulness of statistical fluctuations.

Cooperativity in brain function: Assemblies of approximately 30 neurons

Abstract We propose that there is a mode of organization in the central nervous system characterized by small assemblies of as few as 30 cells acting as functional units. A major role of such assemblies is to provide cooperative effects such as the enhanced reliability of output response compared with that of the individual neuron. We review a number of separate arguments in support of this minimum number, and suggest that the assemblies may provide a response, based on spatial averaging, similar to what the investigator obtains through averaging experimental trials via the poststimulus histogram. Specific experiments to test these concepts are suggested.

Persistent states of neural networks and the random nature of synaptic transmission

Abstract Recently, Little demonstrated the existence of persistent states in a neural network when a certain transfer matrix has approximately degenerate maximum eigenvalues. He showed the direst analogy of the persistence of the neuronal firing patterns considered in discrete time steps, to the long range apatial order in an Ising spin crystal system. The ordered phase of the spin system occurs below the Curie point temparature. Hence in analogy, a factor representing the temparature of the neural network is assumed in Littles model for the transfer matrix. We derive his transfer matrix for a neural network and explicitly relate this temperature or “smearing” phenomenon to the experimentally observed fluctuations in the postsynaptic potentials.

Enhancement of spatial-temporal reasoning after a Mozart listening condition in Alzheimer’s disease: A case study

Several recent studies have investigated the effectiveness of various behavioral interventions on the cognitive performance of subjects with Alzheimers disease (AD). Simulations of Shaws structured model of the cortex led to the predictions that music might enhance spatial-temporal reasoning. A subsequent behavioral study in college students documented an improvement in scores on a spatial-temporal task after listening to a Mozart piano sonata. In this study, we investigated the enhancement of scores on a spatial-temporal task after a Mozart listening condition in a set of twins who are discordant for AD. After listening to an excerpt from a Mozart piano sonata, the AD twin showed considerable improvement on the spatial-temporal task when compared with pretest scores. Furthermore, no enhancement of scores was seen following either of the control conditions (i.e., silence or 1930s popular tunes). This finding suggests that music may be used as a tool to investigate functional plasticity in Alzheimers disease and to better understand the underlying pathophysiology.

Magnetic Moments of Composite Fermions

Abstract There have been a considerable number of papers proposing composite models for leptons and quarks. Recently, Gluck and Lipkin have stated that reproducing the observed magnetic moments of these fermions presents a serious difficulty for these composite models. We show for a renormalizable theory that, in contrast to Glucks and Lipkins nonrelativistic arguments, a deeply bound system (with heavy constituent particle masses mc) of (total) spin 1 2 , charge e and mass m has the magnetic moment (e/2m) [1 + “usual” (QED + QCD + weak) corrections +O (m/m c ) “new” bindng corrections] . Although there remains the considerable dynamical problem of obtaining “light” bound fermions from heavy constituents, there is no separate, additional magnetic moment difficulty.

Space-time correlations of neuronal firing related to memory storage capacity

Most viable theories of memory require some form of synaptic modification dependent on the correlation of pre- and postsynaptic neuronal firing (which we will denote as the Hebb hypothesis). We show here that a possible consequence of this hypothesis is that the storage capacity of a network of highly interconnected neurons is related to the number of synapses and that this implies that the network can be excited into many different time sequence of firing patterns of assemblies of neurons. The important role played by the assembly (as defined by E. R. John) is discussed in detail. A modified Hebb hypothesis is proposed. The crucial experiments to test the model involve the use of two (or more) extracellular microelectrodes to record, simultaneously, the firing activity of several neurons and thus determine the spatial and temporal cross correlations after presenting a mature animal with a variety of stimuli.