Monday, December 25, 2006
The International System of Units
The International System of Units is the modern form of the metric system. It is the world's most widely used system of units, both in everyday commerce and in science.
The older metric system included several groupings of units. The SI was developed in 1960 from the metre-kilogram-second system, rather than the centimetre-gram-second system which, in turn, had many variants.
The SI introduced several newly named units. The SI is not static; it is a living set of standards where units are created and definitions are modified with international agreement as measurement technology progresses.
With few exceptions, the system is used in every country in the world, and many countries do not maintain official definitions of other units. In the United States, industrial use of SI is increasing, but popular use is still limited. In the United Kingdom, conversion to metric units is official policy but not yet complete. Those countries that still recognize non-SI units have redefined their traditional non-SI units in terms of SI units.
The older metric system included several groupings of units. The SI was developed in 1960 from the metre-kilogram-second system, rather than the centimetre-gram-second system which, in turn, had many variants.
The SI introduced several newly named units. The SI is not static; it is a living set of standards where units are created and definitions are modified with international agreement as measurement technology progresses.
With few exceptions, the system is used in every country in the world, and many countries do not maintain official definitions of other units. In the United States, industrial use of SI is increasing, but popular use is still limited. In the United Kingdom, conversion to metric units is official policy but not yet complete. Those countries that still recognize non-SI units have redefined their traditional non-SI units in terms of SI units.
Sunday, December 17, 2006
In Mathematics
Space is a set, with some particular properties and usually some additional structure. It is not a formally defined concept as such, but a generic name for a number of similar concepts, most of which generalize some abstract properties of the physical concept of space.
In particular, a vector space and specifically a Euclidean space can be seen as generalizations of the concept of a Euclidean coordinate system. Important varieties of vector spaces with more imposed structure include Banach space and Hilbert space. Distance measurement is abstracted as the concept of metric space and volume measurement leads to the concept of measure space.
As far as the concept of dimension is defined, although three-dimensional space is the most commonly thought of dimensional space, the number of dimensions for a space to exist need not be three: it can also be zero, one, two, more than three, finite or infinite, and with some definitions, a non-integer value. Mathematicians often study general structures that hold regardless of the number of dimensions
In particular, a vector space and specifically a Euclidean space can be seen as generalizations of the concept of a Euclidean coordinate system. Important varieties of vector spaces with more imposed structure include Banach space and Hilbert space. Distance measurement is abstracted as the concept of metric space and volume measurement leads to the concept of measure space.
As far as the concept of dimension is defined, although three-dimensional space is the most commonly thought of dimensional space, the number of dimensions for a space to exist need not be three: it can also be zero, one, two, more than three, finite or infinite, and with some definitions, a non-integer value. Mathematicians often study general structures that hold regardless of the number of dimensions
Monday, December 11, 2006
The Canadian Pacific Railway
The Canadian Pacific Railway known as CP Rail between 1968 and 1996, is a Canadian Class I railway operated by Canadian Pacific Railway Limited. Its rail network stretches from Vancouver to Montreal, and also serves major cities in the United States such as Minneapolis, Chicago, and New York City. Its headquarters are in Calgary, Alberta.
The railway was originally built between eastern Canada and British Columbia between 1881 and fulfilling a promise extended to British Columbia when it entered Confederation in 1871. It was Canada's first transcontinental railway. Now primarily a freight railway, the CPR was for two decades the only practical means of long distance passenger transport in most regions of Canada, and was instrumental in the settlement and development of Western Canada. Its primary passenger services were eliminated in 1986 after being assumed by VIA Rail Canada in 1978. A beaver was chosen as the railway's logo because it is one of the national symbols of Canada and represents the hardworking character of the company. The object of both praise and damnation for over 120 years, the CPR remains an indisputable icon of Canadian nationalism.
Tunisia officially the Tunisian Republic is a country situated on the Mediterranean coast of North Africa. It is the northernmost African country and the smallest of the nations situated along the Atlas mountain range, bordering Algeria, to the west, and Libya to the south east. Around forty percent of the country is composed of the Sahara desert, with much of the remainder consisting of particularly fertile soil, and a 1300-km coastline. Both played a prominent role in ancient times, first with the famous Phoenician city of Carthage, and later, as the Africa Province, which became known as the bread basket of the Roman Empire.
It is thought that the name Tunis originated from Berber, meaning either a geographical promontory, or, "to spend the night."
The railway was originally built between eastern Canada and British Columbia between 1881 and fulfilling a promise extended to British Columbia when it entered Confederation in 1871. It was Canada's first transcontinental railway. Now primarily a freight railway, the CPR was for two decades the only practical means of long distance passenger transport in most regions of Canada, and was instrumental in the settlement and development of Western Canada. Its primary passenger services were eliminated in 1986 after being assumed by VIA Rail Canada in 1978. A beaver was chosen as the railway's logo because it is one of the national symbols of Canada and represents the hardworking character of the company. The object of both praise and damnation for over 120 years, the CPR remains an indisputable icon of Canadian nationalism.
Tunisia officially the Tunisian Republic is a country situated on the Mediterranean coast of North Africa. It is the northernmost African country and the smallest of the nations situated along the Atlas mountain range, bordering Algeria, to the west, and Libya to the south east. Around forty percent of the country is composed of the Sahara desert, with much of the remainder consisting of particularly fertile soil, and a 1300-km coastline. Both played a prominent role in ancient times, first with the famous Phoenician city of Carthage, and later, as the Africa Province, which became known as the bread basket of the Roman Empire.
It is thought that the name Tunis originated from Berber, meaning either a geographical promontory, or, "to spend the night."
Tuesday, December 05, 2006
Philosophy of space and time
Space has a range of definitions:
One view of space is that it is part of the fundamental structure of the universe, a set of dimensions in which objects are separated and located, have size and shape, and through which they can move. A contrasting view is that space is part of a fundamental abstract mathematical conceptual framework within which we compare and quantify the distance between objects, their sizes, their shapes, and their speeds. In this view space does not refer to any kind of entity that is a "container" that objects "move through". These opposing views are relevant also to definitions of time. Space is typically described as having three dimensions, and that three numbers are needed to specify the size of any object and/or its location with respect to another location. Modern physics does not treat space and time as independent dimensions, but treats both as features of space-time – a conception that challenges intuitive notions of distance and time.
An issue of philosophical debate is whether space is an ontological entity itself, or simply a conceptual framework we need to think about the world. Another way to frame this is to ask, "Can space itself be measured, or is space part of the measurement system?" The same debate applies also to time, and an important formulation in both areas was given by Immanuel Kant.
In his Critique of Pure Reason, Kant described space as an a priori intuition that allows us to comprehend sense experience. With Kant, neither space nor time are conceived as substances, but rather both are elements of a systematic framework we use to structure our experience. Spatial measurements are used to quantify how far apart objects are, and temporal measurements are used to quantify how far apart events occur.
Schopenhauer, in the preface to his On the Will in Nature, stated that "space is the condition of the possibility of juxtaposition." This is in accordance with Kant's understanding of space as a form in the mind of an observing subject.
Similar philosophical questions concerning space include: Is space absolute or purely relational? Does space have one correct geometry, or is the geometry of space just a convention? Historical positions in these debates have been taken by Isaac Newton, Gottfried Leibniz, and Henri Poincare. Two important thought-experiments connected with these questions are: Newton's bucket argument and Poincare's sphere-world.
One view of space is that it is part of the fundamental structure of the universe, a set of dimensions in which objects are separated and located, have size and shape, and through which they can move. A contrasting view is that space is part of a fundamental abstract mathematical conceptual framework within which we compare and quantify the distance between objects, their sizes, their shapes, and their speeds. In this view space does not refer to any kind of entity that is a "container" that objects "move through". These opposing views are relevant also to definitions of time. Space is typically described as having three dimensions, and that three numbers are needed to specify the size of any object and/or its location with respect to another location. Modern physics does not treat space and time as independent dimensions, but treats both as features of space-time – a conception that challenges intuitive notions of distance and time.
An issue of philosophical debate is whether space is an ontological entity itself, or simply a conceptual framework we need to think about the world. Another way to frame this is to ask, "Can space itself be measured, or is space part of the measurement system?" The same debate applies also to time, and an important formulation in both areas was given by Immanuel Kant.
In his Critique of Pure Reason, Kant described space as an a priori intuition that allows us to comprehend sense experience. With Kant, neither space nor time are conceived as substances, but rather both are elements of a systematic framework we use to structure our experience. Spatial measurements are used to quantify how far apart objects are, and temporal measurements are used to quantify how far apart events occur.
Schopenhauer, in the preface to his On the Will in Nature, stated that "space is the condition of the possibility of juxtaposition." This is in accordance with Kant's understanding of space as a form in the mind of an observing subject.
Similar philosophical questions concerning space include: Is space absolute or purely relational? Does space have one correct geometry, or is the geometry of space just a convention? Historical positions in these debates have been taken by Isaac Newton, Gottfried Leibniz, and Henri Poincare. Two important thought-experiments connected with these questions are: Newton's bucket argument and Poincare's sphere-world.