The Limitation of Size Conception

2020 ◽  
pp. 128-159
Keyword(s):  
Limitation Of Size

scholarly journals General principles of the design of all-purpose computing machines

1948 ◽  
Vol 195 (1042) ◽  
pp. 271-274 ◽  
Keyword(s):  
General Purpose ◽  
Algebraic Equations ◽  
Modern Times ◽  
Universal Machine ◽  
Linear Algebraic Equations ◽  
Definition Of ◽  
Clear Idea ◽  
Computing Machines ◽  
Limitation Of Size ◽  
Made In

Professor Hartree in his paper has recalled that all the essential ideas of the general-purpose calculating machines now being made are to be found in Babbage’s plans for his analytical engine. In modern times the idea of a universal calculating machine was independently introduced by Turing (1938) in connexion with a logical problem, which there is unfortunately no time to mention, and the construction of actual machines was begun independently in America, towards the end of the late war. A ‘universal’ machine is one which, when given suitable instructions, will carry out automatically any well-defined series of computations of certain specified kinds, say additions, subtractions, multiplications and divisions of integers or finite decimals. This is a rather doubtful definition, since it depends on what is meant by a ‘welldefined’ series of computations; and undoubtedly the best definition of this is ‘one that can be done by a machine ’. However, this description is not quite so circular as it may seem; for most people have a fairly clear idea of w hat processes can be done by machines specially constructed for each separate purpose. There are, for example, machines for solving sets of linear algebraic equations, for finding the prim e factors of large integers, for solving ordinary differential equations of certain types, and so on. A universal machine is a single machine which, when provided with suitable instructions, will perform any calculation that could be done by a specially constructed machine. No real machine can be truly universal because its size is limited—for example, no machine will work out π to lO 1000 places of decimals, because there is no room in the world for the working or the answer; but subject to this limitation of size, the machines now being made in America and in this country will be ‘ universal ’ —if they work a t all; that is, they will do every kind of job that can be done by special machines.

Cantorian set Theory and Limitation of Size.

1986 ◽  
Vol 36 (144) ◽  
pp. 429 ◽  
Author(s):  
John Mayberry ◽  
Michael Hallett
Keyword(s):  
Set Theory ◽  
Limitation Of Size

Set theory, different systems of

2018 ◽  
Author(s):  
Michael Potter
Keyword(s):  
Twentieth Century ◽  
Mathematical Logic ◽  
Set Theory ◽  
The Other ◽  
Von Neumann ◽  
Class Theory ◽  
Iterative Conception ◽  
The One ◽  
Limitation Of Size ◽  
As If

To begin with we shall use the word ‘collection’ quite broadly to mean anything the identity of which is solely a matter of what its members are (including ‘sets’ and ‘classes’). Which collections exist? Two extreme positions are initially appealing. The first is to say that all do. Unfortunately this is inconsistent because of Russell’s paradox: the collection of all collections which are not members of themselves does not exist. The second is to say that none do, but to talk as if they did whenever such talk can be shown to be eliminable and therefore harmless. This is consistent but far too weak to be of much use. We need an intermediate theory. Various theories of collections have been proposed since the start of the twentieth century. What they share is the axiom of ‘extensionality’, which asserts that any two sets which have exactly the same elements must be identical. This is just a matter of definition: objects which do not satisfy extensionality are not collections. Beyond extensionality, theories differ. The most popular among mathematicians is Zermelo–Fraenkel set theory (ZF). A common alternative is von Neumann–Bernays–Gödel class theory (NBG), which allows for the same sets but also has proper classes, that is, collections whose members are sets but which are not themselves sets (such as the class of all sets or the class of all ordinals). Two general principles have been used to motivate the axioms of ZF and its relatives. The first is the iterative conception, according to which sets occur cumulatively in layers, each containing all the members and subsets of all previous layers. The second is the doctrine of limitation of size, according to which the ‘paradoxical sets’ (that is, the proper classes of NBG) fail to be sets because they are in some sense too big. Neither principle is altogether satisfactory as a justification for the whole of ZF: for example, the replacement schema is motivated only by limitation of size; and ‘foundation’ is motivated only by the iterative conception. Among the other systems of set theory to have been proposed, the one that has received widespread attention is Quine’s NF (from the title of an article, ‘New Foundations for Mathematical Logic’), which seeks to avoid paradox by means of a syntactic restriction but which has not been provided with an intuitive justification on the basis of any conception of set. It is known that if NF is consistent then ZF is consistent, but the converse result has still not been proved.

Session 6: Vending Machines and Pillar Boxes: ‘G’ Type Stamp-Vending Machine

1969 ◽  
Vol 184 (8) ◽  
pp. 196-201
Author(s):  
R. J. Bath ◽  
M. Taylor
Keyword(s):  
Post Office ◽  
Additional Source ◽  
Design Specification ◽  
Vending Machines ◽  
Limitation Of Size

A new stamp-vending machine designed and developed for the British Post Office is described. A brief outline of stamp machine history is followed by a review of the reasons for the adoption of the particular design. A description of the mechanism shows how the design specification has been met, despite the limitation of size imposed by existing mountings. The stamps are issued from a roll by the user operating a lift flap after insertion of a valid coin, and no additional source of power is required. The machine may be readily set to issue any predetermined stamp combination.

Total Internal Reflection (TIR) Lens Design for Surface Mount Techonology (SMT) LED Application

2008 ◽  
Author(s):  
JaeYoung Joo ◽  
Do Kyun Woo ◽  
ChaBum Lee ◽  
SunKyu Lee
Keyword(s):  
Total Internal Reflection ◽  
Solid Angle ◽  
Diamond Turning ◽  
Internal Reflection ◽  
Lens Design ◽  
Surface Mount Technology ◽  
Surface Mount ◽  
Simulation Results ◽  
Limitation Of Size

In this paper, Total Internal Reflection (TIR) lens for a micro optical LED application is proposed. The aim of this paper is to design TIR lens in collimating light emitted from a surface mount technology (SMT) LED. To satisfy current technical needs, it was designed to have both thickness and diameter less than three millimeters with eleven facets where light refracts and reflects. Overall geometry of the TIR lens is numerically calculated and designed in Matlab and the central hyperboloid is designed through Code V. Manufacturability of TIR lens has been obstructing its realistic LED application because of its limitation of size. In this study, we have considered this issue and found the optimized each facet angles in which ultraprecision diamond turning is applicable. Typical blue SMT LED was modeled in LightTools to verify the decrease of solid angle. After designing, the solid angle of a LED was reduced from 120° to 20° while loosing source energy about 52%. The solid angle varies with respect to its distance from the source. The simulation results show collimation efficiency of the designed lens.

Cantorian Set Theory and Limitation of Size. Michael Hallett

1988 ◽  
Vol 55 (3) ◽  
pp. 461-478
Author(s):  
Robert Bunn
Keyword(s):  
Set Theory ◽  
Limitation Of Size
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