High temporal resolution event-related brain potential and electroencephalographic coherence studies of the neural substrate of short-term storage in working memory indicate that the sustained coactivation of both prefrontal cortex and the posterior cortical systems that participate in the initial perception and comprehension of the retained information are involved in its storage. These studies further show that short-term storage mechanisms involve an increase in neural synchrony between prefrontal cortex and posterior cortex and the enhanced activation of long- (...) class='Hi'>term memory representations of material held in short-term memory. This activation begins during the encoding/comprehension phase and evidently is prolonged into the retention phase by attentional drive from prefrontal cortex control systems. A parsimonious interpretation of these findings is that the long-term memory systems associated with the posterior cortical processors provide the necessary representational basis for working memory, with the property of short-term memory decay being primarily due to the posterior system. In this view, there is no reason to posit specialized neural systems whose functions are limited to those of short-term storage buffers. Prefrontal cortex provides the attentional pointer system for maintaining activation in the appropriate posterior processing systems. Short-term memory capacity and phenomena such as displacement of information in short-term memory are determined by limitations on the number of pointers that can be sustained by the prefrontal control systems. Key Words: coherence; event-related potentials; imaging; long-term memory; memory; short-term memory; working memory. (shrink)

Whole genome sequencing is quickly becoming more affordable and accessible, with the prospect of personal genome sequencing for under $1,000 now widely said to be in sight. The ethical issues raised by the use of this technology in the research context have received some significant attention, but little has been written on its use in the clinical context, and most of this analysis has been futuristic forecasting. This is problematic, given the speed with which whole genome sequencing technology is likely (...) to be incorporated into clinical care. This paper explores one particular subset of these issues: the implications of adopting this technology in the prenatal context without a good understanding of when and how it is useful. Prenatal whole genome sequencing differs from current prenatal genetic testing practice in a number of ethically relevant ways. Most notably, whole genome sequencing would radically increase the volume and scope of available prenatal genetic data. The wealth of new data could enhance reproductive decision‐making, promoting parents' freedom to make well‐informed reproductive decisions. We argue, however, that there is potential for prenatal whole genome sequencing to alter clinical practice in undesirable ways, especially in the short term. We are concerned that the technology could (1) change the norms and expectations of pregnancy in ways that complicate parental autonomy and informed decision‐making, (2) exacerbate the deleterious role that genetic determinism plays in child rearing, and (3) undermine children's future autonomy by removing the option of not knowing their genetic information without appropriate justification. (shrink)

This paper is intended to give for a general mathematical audience a survey of intriguing connections between analytic combinatorics and logic. We define the ordinals below ε0 in non-logical terms and we survey a selection of recent results about the analytic combinatorics of these ordinals. Using a versatile and flexible compression technique we give applications to phase transitions for independence results, Hilbert’s basis theorem, local number theory, Ramsey theory, Hydra games, and Goodstein sequences. We discuss briefly universality and renormalization (...) issues in this context. Finally, we indicate how regularity properties of ordinal count functions can be used to prove logical limit laws. (shrink)

This study aimed to investigate whether the ordinal judgments of high math-anxious and low math-anxious individuals differ. Two groups of 20 participants with extreme scores on the Shortened Mathematics Anxiety Rating Scale had to decide whether a triplet of numbers was presented in ascending order. Triplets could contain one-digit or two-digit numbers and be formed by consecutive numbers, numbers with a constant distance of two or three or numbers with variable distances between them. All these triplets were also presented (...) unordered: sequence order in these trials could be broken at the second or third number. A reverse distance effect of equal size was found in both anxiety groups. However, HMA participants made more judgment errors than their LMA peers when they judged one-digit counting ordered triplets. This effect was related to worse performance of HMA individuals on a symmetry span test and might be related to group differences on working memory. Importantly, HMAs were less accurate than LMA participants at rejecting unordered D2 sequences. This result is interpreted in terms of worse cognitive flexibility in HMA individuals. (shrink)

Short-term or working memory provides temporary storage of information in the brain after an experience and is associated with conscious awareness. Neurons sensitive to the multiple stimulus attributes comprising an experience are distributed within many brain regions. Such distributed cell assemblies, activated by an event, are the most plausible system to represent the WM of that event. Studies with a variety of imaging technologies have implicated widespread brain regions in the mediation of WM for different categories of information. (...) Each kind of WM may thus be expected to involve many brain regions rather than a local, uniquely dedicated set of cells. Neurons in a distributed “cell assembly” may be self-selected by their temporally coherent activations. The process by which this fragmented representation of the recent past is reassembled to accomplish essentially automatic and reliable recognition of a recurrent event constitutes an important problem. One plausible mechanism to achieve the identification of past with previous events would require that the representational system mediating WM must coexist in spatial extent and somehow overlap in temporal activation with cell ensembles registering input from subsequent events. The detection of such a postulated mechanism required an experimental approach which would focus upon spatial patterns of coherent activation while information about different events was stored in WM and retrieved, rather than focusing upon the temporal sequences of activation in localized regions of interest. For this purpose, the familiar delayed matching from sample task was modified. A series of information-free flashes, or “noncontingent probes,” was presented before an initial series of visual information items, the Priming Sample, which were to be held in WM during a Delay Period. A second series of visual information items were then presented, the Matching Sample. The task required detection of any item in the second series which had beenabsentfrom the initial series. Thirty such trials with a particular category of visual information constituted a single task. Several DMS tasks with this standardized design, but with different categories of visual information, were presented within each test session. The information categories included letters of the alphabet, single digit numbers, or faces from a school yearbook. Event-related potentials , were computed from 21 standardized electrode placements, separately for information-free probes and for information items in each interval of the trials within a task. Because each electrode is particularly sensitive to coherent activation of neurons in the immediately underlying brain regions, topographic maps were constructed and interpolated across the surface of the scalp. The momentary fluctuations of the resulting voltage “landscapes” throughout the task were then subjected to quantitative analysis. Distinctive landscapes sometimes persisted for prolonged periods, implying sustained engagement of very large populations of neurons. “Difference landscapes” were constructed by subtraction of topographic maps evoked by noncontingent probes during the Delay Period from maps of probe ERPs before the presentation of the initial information in the Priming Sample. Such probe difference landscapes displayed recurrent high similarity to momentary landscapes elicited during subsequent presentation of the information items in the Matching Sample. It seemed as if the distributed cell assembly continuously engaged by mediation of WM of the diverse attributes of the initial stimuli was being dynamically compared to the ensembles engaged by registration of the subsequent stimuli. Spatial Principal Component Analysis was applied to the sequences of momentary voltage landscapes observed throughout trials of each task. This method sought a small number of spatial patterns with which these large sets of inhomogeneous spatial distributions of voltage could be reconstructed. This is the spatial analog of the reconstruction of local ERPs by temporal principal components, as often described previously. Five Spatial Principal Components were found which accounted for about 90% of the total variance of voltage across the surface of the scalp throughout every task. Theloadings,or distinguishing topographic features, of these SPCs, were highly similar during every cognitive task for every subject. However,factor scores,or relative average contribution to the overall voltage distributions, of the different SPCs varied substantially among subjects between the tasks and momentarily within successive intervals of each task. These five SPCs may reflect coherent activation of huge distributed ensembles of neurons which comprise independent but interacting functional brain subsystems. These subsystems may correspond to basic resources available to individuals for allocation to mediate conscious evaluation of information during cognitive activity, providing a filter to bind together fractionated representations of the past to evaluate the present. (shrink)

Miller (1956) summarized evidence that people can remember about seven chunks in short-term memory (STM) tasks. However, that number was meant more as a rough estimate and a rhetorical device than as a real capacity limit. Others have since suggested that there is a more precise capacity limit, but that it is only three to five chunks. The present target article brings together a wide variety of data on capacity limits suggesting that the smaller capacity limit is (...) real. Capacity limits will be useful in analyses of information processing only if the boundary conditions for observing them can be carefully described. Four basic conditions in which chunks can be identified and capacity limits can accordingly be observed are: (1) when information overload limits chunks to individual stimulus items, (2) when other steps are taken specifically to block the recoding of stimulus items into larger chunks, (3) in performance discontinuities caused by the capacity limit, and (4) in various indirect effects of the capacity limit. Under these conditions, rehearsal and long-term memory cannot be used to combine stimulus items into chunks of an unknown size; nor can storage mechanisms that are not capacity-limited, such as sensory memory, allow the capacity-limited storage mechanism to be refilled during recall. A single, central capacity limit averaging about four chunks is implicated along with other, noncapacity-limited sources. The pure STM capacity limit expressed in chunks is distinguished from compound STM limits obtained when the number of separately held chunks is unclear. Reasons why pure capacity estimates fall within a narrow range are discussed and a capacity limit for the focus of attention is proposed. Key Words: attention; enumeration; information chunks; memory capacity; processing capacity; processing channels; serial recall; short-term memory; storage capacity; verbal recall; working memory capacity. (shrink)

I argue here that a properly Platonic theory of the nature of number is still viable today. By properly Platonic, I mean one consistent with Plato's own theory, with appropriate extensions to take into account subsequent developments in mathematics. At Parmenides 143a-4a the existence of numbers is proven from our capacity to count, whereby I establish as Plato's the theory that numbers are originally ordinal, a sequence of forms differentiated by position. I defend and interpret Aristotle's report (...) of a Platonic distinction between form and mathematical numbers, arguing that mathematical numbers alone are cardinals, by reference to certain non-technical features of a set-theoretical approach and other considerations in philosophy of mathematics. Finally I respond to the objections that such a conception of number was unavailable in antiquity and that this theory is contradicted by Aristotle's report in Metaph . XIII that Platonic numbers are collections of units. I argue that Aristotle reveals his own misinterpretation of the terms in which Plato's theory was expressed. (shrink)

Having asked, “What, then, is time?” Augustine admitted, “I know well enough what it is, provided that nobody asks me; but if I am asked what it is and try to explain, I am baffled.” We all have a sense of time, but the description and explanation of it remain remarkably elusive. Through a series of detailed descriptions, Husserl attempted to clarify this sense of time. In my book, I trace the development of his account of our temporal self-awareness, starting (...) with his early 1905-1909 lectures on time consciousness and proceeding through the 1917-18 Bernau Manuscripts, the Analyses of Passive Syntheses of the 1920’s and ending with the C, B and E manuscripts on time and instincts of the 1930s. Although my book covers all the stages of Husserl’s account of temporality, it is nonetheless systematic in its approach. It is organized about a number of basic topics in the theory of time and presents and critically appraises Husserl’s positions on the issues pertaining to each. • THE ONTOLOGICAL STATUS OF TIME: Is time objective or subjective? Is it “out there,” a part of external reality or does it have a merely subjective existence, residing only in our memories and anticipations? Does Husserl’s “subjective” account presuppose ob-jective time? • THE “PRESENCE” OF THE PAST AS PAST: Memory, if it is to be distinguished from a direct, sensuous perception, must grasp the past as past. It must somehow “see” what no longer exists as no longer existing. The issue is: how do we do this? The same question arises with regard to our grasp through anticipation of the future as future. • THE TEMPORALITY OF OBJECTS: For Husserl, the apprehension of any sort of extended event, such as a melody, involves the synthesis of the “retentions” (the short term memories) of its notes and the anticipations these retentions awake in us. The question, here, is: what exactly is involved in this synthesis of retentions and anticipa-tions? How can these elements come together to present a single, individual object rather than presenting us with merely a collection of disparate presentations? In other words: How does temporal synthesis accomplish this presentation? • THE TEMPORALITY OF CONSCIOUSNESS: Husserl asserts that consciousness, in placing its object in time also places itself in time. How does it do this? What is the relation between the consciousness that places itself in time and the consciousness that is placed in time? How do we unify them? • THE ONTOLOGICAL STATUS OF TIME-CONSTITUTING PHENOMENA: Husserl claims that “time-constituting phenomena are evidently objectivities fundamentally different than those constituted in time. They are neither individual objects nor individual processes, and the predicates of such objects or processes cannot be meaningfully ascribed to them.” This assertion raises a number of questions about the ontological status of these time-constituting phenomena. If we cannot apply the predicates of individual objects to them, what is the nature of their being? Given that such phenomena com-pose the field of consciousness, what is the ontological status of consciousness? Furthermore, if our apprehension directs itself towards individual objects, how can our consciousness grasp the pre-individual, time-constituting phenomena that make it up? At issue here is the status of Husserl’s own descriptions of consciousness and the temporal process. Does his theory undermine the possibility of the evidence he presents for it? • THE RELATION OF CONSCIOUSNESS TO THE EGO: Our sense of self involves more than our consciousness, more than the memories, perceptions, and anticipations that give it its content. It involves our sense as the subjective referent of every act, as the person to whom the world appears, as the one who is affected by the world and who acts with regard to it. What is the relation of this sense of self to our time consciousness? How does the simultaneous constitution of consciousness and its object result in the presence of the I that is the subject of consciousness? (shrink)