Archive:New Draft of the Week

The New Draft of the Week is a chance to highlight a recently created Citizendium article that has just started down the road of becoming a Citizendium masterpiece.
It is chosen each week by vote in a manner similar to that of its sister project, the Article of the Week.

Add New Nominees Here

To add a new nominee or vote for an existing nominee, click edit for this section and follow the instructions

Table of Nominees

Nominated article	Vote Score	Supporters	Specialist supporters	Date created
William Harvey	3	Howard C. Berkowitz 15:22, 13 July 2009 (UTC)	Anthony.Sebastian	2009-06-18
Heat	5	Joe Quick; Peter Schmitt;Meg Ireland; Milton Beychok; Howard C. Berkowitz		2009-06-13
Air Quality Index	3	Paul Wormer; Milton Beychok; Meg Ireland		2009-06-18

If you want to see how these nominees will look on the CZ home page (if selected as a winner), scroll down a little bit.

Recently created pages are listed on Special:NewPages.

Transclusion of the above nominees (to be done by an Administrator)

• Transclude each of the nominees in the above "Table of Nominee" as per the instructions at Template:Featured Article Candidate.
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The next New Draft of the Week will be the article with the most votes at 1 AM UTC on Thursday, 16 July 2009. I did the honors this time. Milton Beychok 01:21, 9 July 2009 (UTC)

Text in this section is transcluded from the respective Citizendium entries and may change when these are edited.

Nominated article	Supporters	Specialist supporters	Dates	Score
Heat: A form of energy that flows spontaneously from hotter to colder bodies that are in thermal contact. [e] The metadata subpage is missing. You can start it via filling in this form or by following the instructions that come up after clicking on the [show] link to the right. Do you see this on PREVIEW? then SAVE! before following a link. To find out more about the use of metadata for the management of Citizendium pages, see CZ:Metadata. You may see this box for one of two reasons. Either: A - New page has been created, or subpages template was added to an existing page B - Cluster move is in progress Click either the A or B link for further instructions. [Feel free to recommend improvements to the text or links in this template] A - For a New Cluster use the following directions Subpages format requires a metadata page. Using the following instructions will complete the process of creating this article's subpages. Click the blue "metadata template" link below to create the page. On the edit page that appears paste in the article's title across from "pagename =". You might also fill out the checklist part of the form. Ignore the rest. For background, see Using the Subpages template Don't worry--you'll get the hang of it right away. Remember to hit Save! the "metadata template". However, you can create articles without subpages. Just delete the {{subpages}} template from the top of this page and this prompt will disappear. :) Don't feel obligated to use subpages, it's more important that you write sentences, which you can always do without writing fancy code. [Feel free to recommend improvements to the text or links in this template] B - For a Cluster Move use the following directions The metadata template should be moved to the new name as the first step. Please revert this move and start by using the Move Cluster link at the top left of the talk page. The name prior to this move can be found at the following link. [Feel free to recommend improvements to the text or links in this template] PD Image Energy of the hot gas flame flows into the kettle and the liquid water in it. Heat is a form of energy that is transferred between two bodies that are in thermal contact and have different temperatures. For instance, the bodies may be two compartments of a vessel separated by a heat-conducting wall and containing fluids of different temperatures on either side of the wall. Or one body may consist of hot radiating gas and the other may be a kettle with cold water, as shown in the picture. Heat flows spontaneously from the higher-temperature to the lower-temperature body. The effect of this transfer of energy usually, but not always, is an increase in the temperature of the colder body and a decrease in the temperature of the hotter body. Change of aggregation state A vessel containing a fluid may lose or gain energy without a change in temperature when the fluid changes from one aggregation state to another. For instance, a gas condensing to a liquid does this at a certain fixed temperature (the boiling point of the liquid) and releases condensation energy. When a vessel, containing a condensing gas, loses heat to a colder body, then, as long as there is still vapor left in it, its temperature remains constant at the boiling point of the liquid, even while it is losing heat to the colder body. In a similar way, when the colder body is a vessel containing a melting solid, its temperature will remain constant while it is receiving heat from a hotter body, as long as not all solid has been molten. Only after all of the solid has been molten and the heat transport continues, the temperature of the colder body (then containing only liquid) will rise. For example, the temperature of the tap water in the kettle shown in the figure will rise quickly to the boiling point of water (100 °C). Then, when the flame is not switched off, the temperature inside the kettle remains constant at 100 °C for quite some time, even though heat keeps on flowing from flame to kettle. When all liquid water has evaporated—when the kettle has boiled dry—the temperature of the kettle will quickly rise again until it obtains the temperature of the burning gas, then the heat flow will finally stop. (Most likely, though, the handle and maybe the metal of the kettle, too, will have melted before that). Units At present the unit for the amount of heat is the same as for any form of energy. Before the equivalence of mechanical work and heat was clearly recognized, two units were used. The calorie was the amount of heat necessary to raise the temperature of one gram of water from 14.5 to 15.5 °C and the unit of mechanical work was basically defined by force times path length (in the old cgs system of units this is erg). Now there is one unit for all forms of energy, including heat. In the International System of Units (SI) it is the joule, but the British Thermal Unit and calorie are still occasionally used. The unit for the rate of heat transfer is the watt (J/s). Equivalence of heat and work Although heat and work are forms of energy that both obey the law of conservation of energy, they are not completely equivalent. Work can be completely converted into heat, but the converse is not true. When converting heat into work, part of the heat is not—and cannot be—converted to work, but flows to the body of lower temperature that is out of necessity present to generate a heat flow. Heat and temperature The important distinction between heat and temperature (heat being a form of energy and temperature a measure of the amount of that energy present in a body) was clarified by Count Rumford, James Prescott Joule, Julius Robert Mayer, Rudolf Clausius, and others during the late 18th and 19th centuries. Also it became clear by the work of these men that heat is not an invisible and weightless fluid, named caloric, as was thought by many 18th century scientists, but a form of motion. The molecules of the hotter body are (on the average) in more rapid motion than those of the colder body. The first law of thermodynamics, discovered around the middle of the 19th century, states that the (flow of) heat is a transfer of part of the internal energy of the bodies. In the case of ideal gases, internal energy consists only of kinetic energy and it is indeed only this motional energy that is transferred when heat is exchanged between two containers with ideal gases. In the case of non-ideal gases, liquids and solids, internal energy also contains the averaged inter-particle potential energy (attraction and repulsion between molecules), which depends on temperature. So, for non-ideal gases, liquids and solids, also potential energy is transferred when heat transfer occurs. Forms of heat The actual transport of heat may proceed by electromagnetic radiation (as an example one may think of an electric heater where usually heat is transferred to its surroundings by infrared radiation, or of a microwave oven where heat is given off to food by microwaves), conduction (for instance through a metal wall; metals conduct heat by the aid of their almost free electrons), and convection (for instance by air flow or water circulation). Entropy If two systems, 1 (cold) and 2 (hot), are isolated from the rest of the universe (i.e., no other heat flows than from 2 to 1 and no work is performed on the two systems) then the entropy Stot = S1 + S2 of the total system 1 + 2 increases upon the spontaneous flow of heat. This is in accordance with the second law of thermodynamics that states that spontaneous thermodynamic processes are associated with entropy increase. In general, the entropy S of a system at absolute temperature T increases with $\Delta S={\frac {Q}{T}}$ when it receives an amount of heat Q > 0. Entropy is an additive (size-extensive) property. The hotter system 2 loses an amount of heat to the colder system 1. In absolute value the exchanged amounts of heat are the same by the law of conservation of energy (no energy escapes to the rest of the universe), hence $\Delta S_{\mathrm {tot} }=\Delta S_{1}+\Delta S_{2}=Q\left({\frac {1}{T_{1}}}-{\frac {1}{T_{2}}}\right)>0\quad {\hbox{because}}\quad T_{2}>T_{1}.$ Here it is assumed that the amount of heat Q is so small that the temperatures of the two systems are constant. One can achieve this by considering a small time interval of heat exchange and/or very large systems. Remark: the expression ΔS = Q/T is only strictly valid for a reversible (also known as quasistatic) flow of energy. It is possible to define: $\Delta S\equiv \Delta S_{\mathrm {ext} }+\Delta S_{\mathrm {int} }\quad {\hbox{with}}\quad \Delta S_{\mathrm {ext} }\equiv {\frac {Q}{T}}\quad {\hbox{and}}\quad \Delta S_{\mathrm {int} }\geq 0$ It is assumed that ΔSint is much smaller than ΔSext, so that it can be neglected. Semantic caveats It is strictly speaking not correct to say that a hot object "possesses much heat"—it is correct to say, however, that it possesses high internal energy. The word "heat" is reserved to describe the process of transfer of energy from a high temperature object to a lower temperature one (in short called "heating of the cold object"). The reason that the word "heat" is to be avoided for the internal energy of an object is that the latter can have been acquired either by heating or by work done on it (or by both). When we measure internal energy, there is no way of deciding how the object acquired it—by work or by heat. In the same way as one does not say that a hot object "possesses much work", one does not say that it "possesses much heat". Yet, terms as "heat reservoir" (a system of temperature higher than its environment that for all practical purposes is infinite) and "heat content" (a synonym for enthalpy) are commonly used and are incorrect by the same reasoning. The molecules of a hot body are in agitated motion and, as said, it cannot be measured how they became agitated, by work or by heat. Often, especially outside physics, the random molecular motion is referred to as "thermal energy". In classical (phenomenological) thermodynamics this is an intuitive, but undefined, concept. In statistical thermodynamics, thermal energy could be defined (but rarely ever is) as the average kinetic energy of the molecules constituting the body. Kinetic and potential energy of molecules are concepts that are foreign to classical thermodynamics, which predates the general acceptance of the existence of molecules. Quotation As a result Carathéodory was able to obtain the laws of thermodynamics without recourse to fictitious machines or objectionable concepts as the flow of heat. Reference  (Read more...)	Joe Quick; Peter Schmitt; User:Meg Ireland; Milton Beychok; Howard C. Berkowitz		5
Air Quality Index: A number used by government agencies to characterize the quality of the ambient air at a given location. [e] The metadata subpage is missing. You can start it via filling in this form or by following the instructions that come up after clicking on the [show] link to the right. Do you see this on PREVIEW? then SAVE! before following a link. To find out more about the use of metadata for the management of Citizendium pages, see CZ:Metadata. You may see this box for one of two reasons. Either: A - New page has been created, or subpages template was added to an existing page B - Cluster move is in progress Click either the A or B link for further instructions. [Feel free to recommend improvements to the text or links in this template] A - For a New Cluster use the following directions Subpages format requires a metadata page. Using the following instructions will complete the process of creating this article's subpages. Click the blue "metadata template" link below to create the page. On the edit page that appears paste in the article's title across from "pagename =". You might also fill out the checklist part of the form. Ignore the rest. For background, see Using the Subpages template Don't worry--you'll get the hang of it right away. Remember to hit Save! the "metadata template". However, you can create articles without subpages. Just delete the {{subpages}} template from the top of this page and this prompt will disappear. :) Don't feel obligated to use subpages, it's more important that you write sentences, which you can always do without writing fancy code. [Feel free to recommend improvements to the text or links in this template] B - For a Cluster Move use the following directions The metadata template should be moved to the new name as the first step. Please revert this move and start by using the Move Cluster link at the top left of the talk page. The name prior to this move can be found at the following link. [Feel free to recommend improvements to the text or links in this template] (CC) Photo: The Port of Los Angeles (California, USA) An air quality monitoring station. The Air Quality Index (AQI), also known as the Air Pollution Index (API), Pollutant Standard Index (PSI) or Air Quality Health Index (AQHI), is a number used by government agencies to characterize the quality of the ambient air at a given location. As the AQI increases, the severity of probable adverse health effects increases as does the percentage of the population expected to be affected by the adverse health effects. To compute the AQI requires an air pollutant concentration to be obtained from an air quality monitoring station. The method used to convert from air pollutant concentrations to AQIs varies for each air pollutant, and is different in different countries. In many countries, air quality index values are divided into ranges, and each range is assigned a descriptor (i.e., a very few words describing the air quality or the health effects of the range) and often a color code as well. A government agency might also encourage members of the public to avoid strenuous activities, use public transportation rather than personal automobiles and work from home when AQI levels are high. Many countries monitor ground-level ozone, particulate matter (PM10), sulfur dioxide (S02), carbon monoxide (CO) and nitrogen dioxide (NO2) and calculate air quality indices for these pollutants. Most other air contaminants do not have an associated AQI. Air Quality Indices by country Canada's AQHI Air Quality Health Index (AQHI) Health Risk Category Color Code 1 – 3 Low 4 – 6 Moderate  7 – 10 High 10+ Very High Canada Environment Canada, the national environmental protection agency of Canada, uses Air Quality Health Index (AQHI) categories ranging from 1 to 10+ and each category has an assigned color code (see adjacent table) that enables members of the general public to easily identify their health risks as indicated in published air quality forecasts. As shown in the adjacent table: The three AQHI levels of 1, 2 and 3 are all in the low risk category. The three AQHI levels of 4, 5 and 6 are all in the moderate risk category. The four AQHI levels of 7, 8, 9 and 10 are all in the high risk category. The AQHI level of 10+ is the very high risk category. As of 2009, many of the Canadian provinces, if not all, have adopted the AQHI categories implemented by Environment Canada. China China's National API Air Pollution Index (API) Air Quality Level Air Quality Category  0 – 50 I Excellent  51 – 100 II Good 101 – 200 III Slightly polluted 201 – 300 IV Moderately polluted 301+ V Heavily polluted Beijing's API  0 – 50   Good  51 – 100   Moderate 101 – 150   Unhealthy for sensitive groups 151 – 200   Unhealthy 201 – 250   Very unhealthy 251 – 500   Hazardous Hong Kong's API Air Pollution Index (API) Health Effect Category Color Code  0 – 25 Low   26 – 50 Medium    51 – 100 High   101 – 200 Very High   201 – 500 Severe   China's Ministry of Environmental Protection (MEP) is responsible for monitoring the level of air pollution in China. As of August 2008, MEP monitors daily pollution level in its major cities and develops an Air Pollution Index (API) level that is based on the ambient air concentrations sulfur dioxide, nitrogen dioxide, particulate matter (PM10), carbon monoxide, and ozone as measured at monitoring stations in each of those major cities. The adjacent table presents China's national API scale, which is not color coded and uses a scale 0 to more than 300, divided into five ranges of air quality categorized as excellent, good, slightly polluted, heavily polluted and hazardous. API Mechanics An individual score is assigned to the level of each pollutant and the final API is the highest of those 5 scores. The pollutant concentrations are obtained quite differently. Sulfur dioxide, nitrogen dioxide and PM10 concentrations are obtained as daily averages. Carbon monoxide and ozone are more harmful and are obtained as an hourly averages. The final API value is calculated as a daily average. The scale for each pollutant is non-linear, as is the final daily API value. Thus, an API value of 100 does not mean it is twice the pollution of API at 50, nor does it mean it is twice as harmful. Beijing's API China's capitol city, Beijing, has its own API scale, which was developed by the Beijing Municipal Environmental Protection Bureau. As can be seen in the adjacent table, the API scale used by Beijing differs quite significantly from China's national scale in that:     • The Beijing scale ranges from 0 to 500 (rather than 0 to 300 as in the national scale)     • The Beijing scale is divided into six ranges of air quality (rather than five ranges as in the national scale). Hong Kong The Hong Kong Environmental Protection Department (Hong Kong EPD) has developed a color coded Air Pollution Index (API) based upon the measured concentrations of ambient particulate matter (PM10), sulfur dioxide, carbon monoxide, ozone and nitrogen dioxide over a 24-hour period. Hong Kong's color coded Air Pollution Index (API) scale ranges from 0 to 500 corresponding to adverse health effects that range from low to severe as shown in the adjacent chart: An API at or below 100 means that the pollutant levels are in the satisfactory range over 24 hour period and pose no acute or immediate health effects. Persistent high API values (51 to 100) in a year may mean that the annual Hong Kong Air Quality Objectives for protecting long-term health effects could be violated. API values in excess of 100 (very high) mean that levels of one or more pollutant(s) is/are in the unhealthy range. The Hong Kong EPD provides advice to the public regarding precautionary actions to take for such levels. Although Hong Kong is now part of China, it can be seen that Hong Kong's API scale differs from both China's scale and Beijing's scale. Malaysia's API Air Pollution Index (API) Air Quality Category  0 – 50 Good  51 – 100 Moderate 101 – 200 Unhealthy 201 – 300 Very Unhealthy 301+ Hazardous Malaysia The air quality in Malaysia is described in terms of an Air Pollutant Index (API). The API is an indicator of air quality and was developed based on scientific assessment to indicate in an easily understood manner, the presence of pollutants and its impact on health. The API system of Malaysia closely follows the similar system developed by the U.S. Environmental Protection Agency (U.S. EPA). As shown in the adjacent table, Malaysia does not color code their air quality categories. Monitoring stations measure the concentration of five major pollutants in the ambient air: PM10, sulfur dioxide, nitrogen dioxide, carbon monoxide and ozone. These concentrations are measured continuously on an hourly basis. The hourly value is then averaged over a 24-hour period for PM110 and sulfur dioxide and an 8-hour period for carbon monoxide. The ozone and nitrogen dioxide are read hourly. An hourly index is then calculated for each pollutant. The highest hourly index value is then taken as the API for the hour. When the API exceeds 500, a state of emergency is declared in the reporting area. Usually, this means that non-essential government services are suspended, and all ports in the affected area closed. There may also be a prohibition on private sector commercial and industrial activities in the reporting area excluding the food sector. Mexico's IMECA Air Quality Index (IMECA) Air Quality Category Color Code  0 – 50 Good    51 – 100 Moderate   101 – 200 Unhealthy   201 – 300 Very Unhealthy   301+ Extremely Unhealthy   Mexico The air quality in Mexico is described and reported hourly in terms of a color coded Metropolitan Index of Air Quality (IMECA), developed by the Ministry of the Environment for the Government of the Federal District. The IMECA is calculated from the results of real-time monitoring of the ambient concentrations of ozone, sulfur dioxide, nitrogen dioxide, carbon monoxide and particulate matter (PM10). The IMECA was developed specifically for the Federal District of Mexico which only encompasses Mexico City and its surrounding suburbs and adjacent municipalities. The real-time monitoring of the ambient atmosphere is performed by the Sistema de Monitoreo Atmosférico de la Ciudad de México (SIMAT or System of Atmospheric Monitoring for Mexico City). SIMAT's real-time monitoring includes monitoring of the ultra-violet (UV) radiation from the sun and the results are also described and reported hourly as IUVs (Índice de Radiación Ultravioleta) in a manner that is similar to the reporting of the IMECAs. Singapore's PSI Pollution Standard Index (24-hour PSI) Air Quality Category  0 – 50 Good  51 – 100 Moderate 101 – 200 Unhealthy 201 – 300 Very Unhealthy 301+ Hazardous Singapore Singapore's National Environment Agency (NEA) in the Ministry of the Environment and Water Resources (MEWR) has the responsibility for the real-time monitoring of the concentrations of sulfur dioxide, nitrogen dioxide, carbon monoxide, ozone and PM10 in the ambient air of Singapore. The real-time monitoring of the ambient air quality is done by a telemetric network of air quality monitoring stations strategically located in different parts of Singapore. The NEA uses the real-time monitoring data to obtain and report 24-hour Pollution Standard Index (PSI) levels along with their corresponding air quality categories as shown in the adjacent table and which does not use color coding. The NEA states that the PSI scale developed for use in Singapore is very similar to the scale developed and used by the U.S. Environmental Protection Agency. The NEA also further states that the National Ambient Air Quality Standards (NAAQS) developed by the U.S. Environmental Protection Agency are used to assess Singapore's air quality. Although the adjacent table indicates that the NEA categorizes a 24-hour PSI level that is higher than 300 as being hazardous, the NEA also considers a 24-hour PSI level higher than 400 to be life-threatening to ill and elderly persons. United Kingdom's API Air Pollution Index (API) Health Effect Banding Color Code 1 – 3 Good   4 – 6 Moderate   7 – 9 High   10 Very High   United Kingdom AEA Technology, a British environmental consulting company, issues air quality forecasts for the United Kingdom (UK) on behalf of the Department for Environment, Food and Rural Affairs (Defra). The scale used in the United Kingdom is an Air Pollution Index (API) with levels ranging from 1 to 10 as shown in the attached table and it is color coded. The scale was thoroughly studied and approved by the United Kingdom's government advisory body, namely the "Committee on Medical Effects of Air Pollution Episodes" (COMEAP). The scale is based on continuous monitoring, in locations throughout the United Kingdom, of the ambient air for the concentrations of the major air pollutants, namely sulfur dioxide, nitrogen dioxide, ozone, carbon monoxide and PM10. The forecasts issued by AEA Technology are based on the prediction of air pollution index for the worst-case of the five pollutants. As shown in the adjacent table, the health effect of each API range is referred to as its banding rather than as its category. The health effect bandings for the API ranges are low, moderate, high and very high. United States' AQI Air Quality Index (AQI) Air Quality Category Color Code  0 – 50 Good    51 – 100 Moderate   101 – 150 Unhealthy for Sensitive Groups   151 – 200 Unhealthy   201 – 300 Very Unhealthy   301 – 500 Hazardous   United States The Air Quality Index (AQI) ranges used by the U.S. Environmental Protection Agency (U.S. EPA) and their corresponding health effect categories and color codes are provided in the adjacent table. The U.S. EPA's AQI is also known as the Pollution Standards Index (PSI). If multiple pollutants are measured at a monitoring site, then the largest or "dominant" AQI value is reported for the location. The U.S. EPA has developed conversion calculators, available online, for the conversion of AQI values to concentration values and for the reverse conversion of concentrations to AQI values. A national map of the United States of America containing daily AQI forecasts across the nation, developed jointly by the U.S. EPA and NOAA is also available online. The U.S. Clean Air Act requires the U.S. EPA to review its National Ambient Air Quality Standards every five years to reflect evolving health effects information. The Air Quality Index is adjusted periodically to reflect these changes. Air pollutant concentration measurement units In the United States, the concentrations of the air pollutants involved in the AQI are usually expressed as: Ozone and sulfur dioxides: ppbv = parts per billion (10 9) by volume = volume of pollutant gas per billion volumes of ambient air Carbon monoxide: ppmv = parts per million (10 6) by volume = volume of pollutant gas per million volumes of ambient air PM10, defined as particulate matter having an aerodynamic diameter of 10 μm (micrometer) or less: ug/m³ = micrograms of particulate matter per cubic metre of ambient air PM2.5, defined as particulate matter having an aerodynamic diameter of 2.5 μm (micrometer) or less: ug/m³ = micrograms of particulate matter per cubic metre of ambient air References  (Read more...)	Paul Wormer; Milton Beychok; Meg Ireland		3
William Harvey: (1579–1657) English physician who discovered the true nature of blood circulation and the function of the heart as a pump. [e] The metadata subpage is missing. You can start it via filling in this form or by following the instructions that come up after clicking on the [show] link to the right. Do you see this on PREVIEW? then SAVE! before following a link. To find out more about the use of metadata for the management of Citizendium pages, see CZ:Metadata. You may see this box for one of two reasons. Either: A - New page has been created, or subpages template was added to an existing page B - Cluster move is in progress Click either the A or B link for further instructions. [Feel free to recommend improvements to the text or links in this template] A - For a New Cluster use the following directions Subpages format requires a metadata page. Using the following instructions will complete the process of creating this article's subpages. Click the blue "metadata template" link below to create the page. On the edit page that appears paste in the article's title across from "pagename =". You might also fill out the checklist part of the form. Ignore the rest. For background, see Using the Subpages template Don't worry--you'll get the hang of it right away. Remember to hit Save! the "metadata template". However, you can create articles without subpages. Just delete the {{subpages}} template from the top of this page and this prompt will disappear. :) Don't feel obligated to use subpages, it's more important that you write sentences, which you can always do without writing fancy code. [Feel free to recommend improvements to the text or links in this template] B - For a Cluster Move use the following directions The metadata template should be moved to the new name as the first step. Please revert this move and start by using the Move Cluster link at the top left of the talk page. The name prior to this move can be found at the following link. [Feel free to recommend improvements to the text or links in this template] (PD) Image: From book: William Harvey, by D'Arcy Power, 1897 William Harvey. From book of that name by D'Arcy Power, 1897 (PD) Image: Levine & Associates, Inc. for U.S National Institutes of Health, National Institute on Aging at: http://bit.ly/MnJaE Anatomy of the Human Heart. For enlarged version of this image showing more detail, click here. A late 16th, early 17th century English anatomist, physiologist, and physician, William Harvey (1578-1657) bestowed on humanity one of the most important advances in the history of medical science — an explanation of the core physiology of the human cardiovascular system. In part by introducing quantitative methods into anatomical and physiological investigations, Harvey discovered that the left ventricle of the heart pumps blood through the body, doing so via a system of vessels such that the blood moves in a circular path, from the left side of the heart through the arteries and back to the right side of the heart through the veins, transiting from the right side of the heart to the left via blood vessels in the lung, the two sides of the heart separated by a blood-impermeable septum. He published those findings in his 1628 book, Exercitatio Anatomica de Motu Cordis et Sanguinis in Animalibus (Anatomical Exercises on the Motion of the Heart and Blood in Animals), usually referred to as De Motu Cordis. In his dissections of humans and animals, Harvey could not see vessels connecting the arteries to the veins, since, as it turns out, their minute size lies below the limits of visual acuity, even with the magnifying glass he used in his work. He had no access, and perhaps no knowledge, of the existence of microscopes, however primitive their state. Harvey could only infer that a connecting pathway existed. In 1661, a few years after Harvey died, the Italian biologist, Marcello Malpighi (1628-1694), using one of the early microscopes, discovered capillaries, tiny blood vessels not visible to the naked eye, connecting arteries to veins. In a seemingly fitting coincidence, Malpighi had entered the world the same year Harvey published De Motu Cordis. In works published little more than a century apart, 1543 to 1661, three men, Andreas Vesalius (1514-1564), William Harvey (1578-1657), and Marcello Malpighi (1628-1694), demonstrated central truths of human anatomy and physiology that had escaped Western medicine for more than a millennium following the erroneous teachings of the influential Greek physician, Galen of Pergamum (130-216 CE). It required three investigators to break the stranglehold of one. (CC) Image: Anthony Sebastian (adapted from data from Wolfram Alpha) Courtesy U.S. Cancer Institute. Cartoon showing capillaries, visible only with a microscope, connecting macroscopically visible arteries and veins. William Harvey’s Major Contributions Adapted from Sherwin B. Nuland (2008) He overturned the erroneous view of the roles of the heart, arteries and veins that Galen had taught — by delineating the cardinal features of the map depicting the transport path of blood through the body — that blood circulates continuously through the body from the heart and back to the heart; Harvey writes: And now returning to my immediate subject, I go on with what yet remains for demonstration, viz., that in the more perfect and warmer adult animals, and man, the blood passes from the right ventricle of the heart by the pulmonary artery, into the lungs, and thence by the pulmonary veins into the left auricle, and from there into the left ventricle of the heart. And, first, I shall show that this may be so, and then I shall prove that it is so in fact. De Motus Cordis, Chapter VI: Of The Course By Which the Blood Is Carried First of all, the auricle contracts, and in the course of its contraction forces the blood (which it contains in ample quantity as the head of the veins, the store-house and cistern of the blood) into the ventricle, which, being filled, the heart raises itself straightway, makes all its fibres tense, contracts the ventricles, and performs a beat, by which beat it immediately sends the blood supplied to it by the auricle into the arteries. The right ventricle sends its charge into the lungs by the vessel which is called vena arteriosa, but which in structure and function, and all other respects, is an artery. The left ventricle sends its charge into the aorta, and through this by the arteries to the body at large. De Motu Cordis, Chapter V: Of The Motion, Action And Office Of The Heart He reintroduced the concept and practice of experimentation in medical studies, earlier introduced by Galen but mostly ignored by medical researchers for nearly one and a half millennia; He introduced the use of quantitative methods in medical research — by estimating the volume of blood pumped by the heart each day and arguing the improbability that the body could generate that amount each day, even if it converted to blood everything ingested each day. Psychologist and science journalist, Robert E. Adler, gives a elegant description: The breakthrough came when Harvey started to think in terms of numbers—for the first time in the history of medicine. He knew that the left ventricle of the human heart expelled about two ounces of blood with each contraction. If the heart beat 72 times a minute, in one hour it would pump 540 pounds of blood—three times the weight of a grown man. With that simple calculation he ended two millennia of speculation. The liver could not possibly generate more than a person's entire weight in blood in an hour. And however it was generated or utilized, that much blood could not be on a one-way trip to the periphery of the body. So much blood could be moving through the body only if it was being recycled. "I began to think there was a sort of motion as in a circle," he wrote, in what now sounds like a thunderous understatement. Harvey introduced his quantitation method in De Motu Cordis with these words: Thus far I have spoken of the passage of the blood from the veins into the arteries, and of the manner in which it is transmitted and distributed by the action of the heart; points to which some, moved either by the authority of Galen or Columbus, or the reasonings of others, will give in their adhesion. But what remains to be said upon the quantity and source of the blood which thus passes is of a character so novel and unheard-of that I not only fear injury to myself from the envy of a few, but I tremble lest I have mankind at large for my enemies, so much doth wont and custom become a second nature. Doctrine once sown strikes deep its root, and respect for antiquity influences all men. Still the die is cast, and my trust is in my love of truth and the candour of cultivated minds. Chapter VIII: Of The Quantity Of Blood Passing Through The Heart Independently of his contemporary, Francis Bacon, he showed that reasoning by induction — generalizing from a collection of separate but related facts — could yield valid inferences about human physiology. Harvey writes: Since all things, both argument and ocular demonstration, show that the blood passes through the lungs, and heart by the force of the ventricles, and is sent for distribution to all parts of the body, where it makes its way into the veins and porosities of the flesh, and then flows by the veins from the circumference on every side to the centre, from the lesser to the greater veins, and is by them finally discharged into the vena cava and right auricle of the heart, and this in such a quantity or in such a flux and reflux thither by the arteries, hither by the veins, as cannot possibly be supplied by the ingesta, and is much greater than can be required for mere purposes of nutrition; it is absolutely necessary to conclude that the blood in the animal body is impelled in a circle, and is in a state of ceaseless motion; that this is the act or function which the heart performs by means of its pulse; and that it is the sole and only end of the motion and contraction of the heart. De Motu Cordis, Chapter XIV: Conclusion of the Demonstration of the Circulation Brief sketch of Williams Harvey’s life Born in 1578 (April 1, at Folkstone, on the east coast of Kent, England), of Thomas and Joan Harvey, as the eldest of seven brothers and two sisters (a "week of brothers" and a "brace of sisters"), William Harvey entered the world shortly after Andreas Vesalius (1514-1564) had died, though Vesalius's reputation had not died, owing to his remarkably detailed and elegantly drawn illustrations revolutionizing the understanding of human anatomy.    For his anatomical work, William Harvey had Vesalius's giant shoulders to stand on, and ultimately he saw further. Harvey received his early education in the classics, in Canterbury, at King's School (1588-1593), there "....admonished to speak Greek or Latin even on the playground." Harvey's father, a landowner and successful merchant, could afford to send Harvey to the University of Cambridge (specifically, Gonville and Caius College), which he entered at age 16 years (1593) and received his Bachelor of Arts (B.A.) degree at age 19 years (1597). Harvey developed an interest in medicine and decided to go to Italy, one of the major centers of intellectual activity in Europe at the time. He enrolled in the then renown University of Padua, studying medicine under Hieronymus Fabricius of Aquapendente, a noted anatomist in the Vesalian tradition, who had discovered the valves in the veins, a discovery which later contributed to Harvey's thinking that led to his discovery of the blood circulatory system. Harvey's earlier education in the classics helped ease his learning at Padua, as lecturers spoke in Latin. Harvey received his Doctor of Medicine degree in April, 1602, at age 24 years. After Padua, Harvey returned to England and developed a practice in medicine, married, and became a Fellow of the College of Physicians in London. He also secured a position as physician at St. Bartholomew’s Hospital, one of London’s great hospitals, and there and in his private practice distinguished himself as a physician. In 1615, at age 37 years, the College of Physicians elected him their Professor of Anatomy and Surgery, and gave him the honor of the Lumleian Lectureship, a lifetime remunerated position, in which he lectured on human anatomy, physiology and surgery, including performing demonstration dissections on human corpses, officially twice per week, from 1616 to 1656, the year before he died. The lecturership gave Harvey a great opportunity to organize his thinking and guide his research. His lecture notes survive as Lectures on the Whole of Anatomy as a manuscript in the British Library and in English translation. It is from the fabric of these short notes on the heart that De Motu Cordis was to be built. From 1616 until after the publication of De Motu Cordis there is no contemporary account of the impact of Harvey's lectures on his audience. However, in the Royal College of Physicians there is a manuscript of the anatomical lectures given by Baldwin Hamey (1600-1676), one of the great benefactors of the College, on January 22, 24, and 25, 1647/48. The manuscript, in Hamey's hand, gives us an excellent picture not only of the author's learning but also of the full content of lectures of this type. He had attended Harvey's lectures and obviously profited from them. When discussing the movement of the blood, Hamey gives a discussion on the theories put forward by the ancients and his predecessors and then says: From the left ventricle, it is, as I sayd, expel'd by the arteries into the whole body; and there, till of late yeares, it was thought to rest, nor was there any further heed taken, or account given of it, than this; that it served for nutrition and augmentation, for generation of spirits and of sperme in their due times. But now by the conduct of our renowned Professor and Colleague Dr. Harvey, there is a way found to bringe the greatest part back againe, and yet no part of the foresaid worke left undone. So that now we truely know what . . . is meant by Circularis Disciplina, for it may be shew'd us in every body that hath a Heart. In 1618 Harvey became physician extraordinary to the king (James I), and ministered to many eminent aristocrats, including Francis Bacon, for whom he had little regard as an intellectual. After Charles I succeeded the throne, in 1625, Harvey became Charles' physician, benefitting from the King’s patronage to pursue his medical investigations. When civil strife engulfed England, Harvey, now in his 60s retired to live with a brother, pursuing his experiments until he died in 1657, having lived nearly to the age of 80 years.  De Motu Cordis To read the full-text of De Motu Cordis in English translation, click on the "Works" tab in the banner at the beginning of this page. Equivalently, click De Motus Cordis, which brings you to same subpage of this article. A few revelatory quotes from the work: True philosophers, who are only eager for truth and knowledge, never regard themselves as already so thoroughly informed, but that they welcome further information from whomsoever and from wheresoever it may come; nor are they so narrow-minded as to imagine any of the arts or sciences transmitted to us by the ancients, in such a state of forwardness or completeness, that nothing is left for the ingenuity and industry of others. And no one denies the blood as such, even the portion of it which flows in the veins, is imbued with spirits. But if that portion of it which is contained in the arteries be richer in spirits, it is still to be believed that these spirits are inseparable from the blood, like those in the veins; that the blood and spirits constitute one body (like whey and butter in milk, or heat in hot water), with which the arteries are charged, and for the distribution of which from the heart they are provided. Of course, we now know that the richer 'spirit' in arterial blood is oxygen. Before the discovery of oxygen, the alchemists of the seventeenth century recognized that air contained an essential ingredient, an 'elixir of life' — a kind of 'spirit'. We also know today that venous blood, too, has its richer 'spirit', carbon dioxide (as bicarbonate). De Generatione Animalium Harvey received less repute for his other great work, De Generatione Animalium — On the Generation of Animals — a contribution to embryology.... References cited and notes  (Read more...)		Anthony Sebastian; Howard C. Berkowitz	3

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In mathematics, the continuum hypothesis is the statement that any arbitrary infinite set of real numbers has either as many elements as there are real numbers or only as many elements as there are natural numbers (i.e., there is no intermediate size). This is equivalent to the statement that there are as many real numbers as there are elements in the smallest set which is larger than the set of natural numbers.

Since the set of real numbers (or the real line) is also called the continuum this can be shortly expressed as:

Any set of real numbers is either countable or equivalent to the continuum.

This statement was first made by Georg Cantor (1877) when he studied subsets of the real line. Cantor (who introduced sets and cardinal numbers) believed this to be true, but tried in vain to prove it.

From then on it stayed, for a long time, a prominent open mathematical problem to resolve. In 1900, David Hilbert included the continuum hypothesis as the first problem, therefore also called "first Hilbert problem", in his famous lecture on 23 problems for the twentieth century.

The first step towards a solution was done in 1938 by Kurt Gödel who showed that – in set theory including the axiom of choice – the (generalized) continuum hypothesis cannot be proved to be false (and thus is consistent with it). Only much later, in 1963, Paul J. Cohen showed that it cannot be proved, either. Hence the continuum hypothesis is independent of the usual (ZFC) axioms of set theory. It therefore constitutes an important, not artificially constructed, example for Gödel's Second Incompleteness Theorem.

Consequently, either the continuum hypothesis or, alternatively, some contradicting assumption could be added to the axioms of set theory. But since – in contrast to the situation with the axiom of choice – there is no heuristically convincing reason to choose one of these possibilities, the "working" mathematician usually makes no use of the continuum hypotheses, and if a result depends on it, then it is explicitly mentioned.

Of course, in axiomatic set theory, and especially in the theory of cardinal and ordinal numbers, the situation is different and the consequences of the various choices concerning the continuum hypothesis are extensively studied.

The generalized continuum hypothesis is a much stronger statement involving the initial sequence of transfinite cardinal numbers, and is also independent of ZFC.

In terms of the arithmetic of cardinal numbers (as introduced by Cantor) the continuum hypothesis reads

$\aleph _{1}=2^{\aleph _{0}}$

while the generalized continuum hypothesis is

$\aleph _{n+1}=2^{\aleph _{n}}\ (\forall n\in \mathbb {N} )$

Georg Cantor 1877

The continuum hypothesis appears in a memoir of Cantor (dated Halle a.S., 11th July 1877, and published 1878) in which he investigates sets of real numbers. He concludes with the following remark:

Darnach würden die linearen Mannigfaltigkiten aus zwei Klassen bestehen von denen die erste alle Mannigfaltigkeiten in sich fasst, welche sich auf die Form: functio ips. ν (wo ν alle positiven ganzen Zahlen durchläuft) bringen lassen; während die zweite Klasse alle diejenigen Mannigfaltigkeiten in sich aufnimmt, welche auf die Form: functio ips. x (wo x alle reellen Werthe ≥0 und ≤1 annehmen kann) zurückführbar sind. Entsprechend diesen beiden Klassen würden daher bei unendlichen linearen Mannigfaltigkeiten nur zweierlei Mächtigkeiten vorkommen; die genaue Untersuchung dieser Frage verschieben wir auf eine spätere Gelegenheit.

Translated freely, this paragraph reads as follows:

Hence the linear manifolds would consist of two classes of which the first contains all manifolds that can be written in the form: function of ν (where ν takes all positive integers); while the second class contains all those manifolds that have the form: function of x (where x takes all values ≥0 and ≤1). Hence, corresponding to these two classes, there would be only two cardinalities of infinite linear manifolds; the detailed investigation of this problem will be postponed on a later opportunity.

David Hilbert 1900

In his lecture on Mathematical problems, delivered before the International Congress of Mathematicians at Paris in 1900, David Hilbert states the continuum hypothesis as follows:

1. Cantors Problem von der Mächtigkeit des Continuums.
Zwei Systeme, d. h. zwei Mengen von gewöhnlichen reellen Zahlen (oder Punkten) heißen nach Cantor aequivalent oder von gleicher Mächtigkeit, wenn sie zu einander in eine derartige Beziehung gebracht werden können, daß einer jeden Zahl der einen Menge eine und nur eine bestimmte Zahl der anderen Menge entspricht. Die Untersuchungen von Cantor über solche Punktmengen machen einen Satz sehr wahrscheinlich, dessen Beweis jedoch trotz eifrigster Bemühungen bisher noch Niemanden gelungen ist; dieser Satz lautet:
Jedes System von unendlich vielen reellen Zahlen d. h. jede unendliche Zahlen- (oder Punkt)menge ist entweder der Menge der ganzen natürlichen Zahlen 1, 2, 3, ... oder der Menge sämmtlicher reellen Zahlen und mithin dem Continuum, d. h. etwa den Punkten einer Strecke aequivalent; im Sinne der Aeqivalenz giebt es hiernach nur zwei Zahlenmengen, die abzählbare Menge und das Continuum.
Aus diesem Satz würde zugleich folgen, daß das Continuum die nächste Mächtigkeit über die Mächtigkeit der abzählbaren Mengen hinaus bildet; der Beweis dieses Satzes würde mithin eine neue Brücke schlagen zwischen der abzählbaren Menge und dem Continuum.

In the English translation which was published in 1902:

1. Cantor's problem of the cardinal number of the continuum
Two systems, i. e., two assemblages of ordinary real numbers or points, are said to be (according to Cantor) equivalent or of equal cardinal number, if they can be brought into a relation to one another such that to every number of the one assemblage corresponds one and only one definite number of the other. The investigations of Cantor on such assemblages of points suggest a very plausible theorem, which nevertheless, in spite of the most strenuous efforts, no one has succeeded in proving. This is the theorem:
Every system of infinitely many real numbers, i. e., every assemblage of numbers (or points), is either equivalent to the assemblage of natural integers, 1, 2, 3,... or to the assemblage of all real numbers and therefore to the continuum, that is, to the points of a line; as regards equivalence there are, therefore, only two assemblages of numbers, the countable assemblage and the continuum.
From this theorem it would follow at once that the continuum has the next cardinal number beyond that of the countable assemblage; the proof of this theorem would, therefore, form a new bridge between the countable assemblage and the continuum.

Hilbert continues this problem, now known as the "First Hilbert Problem" by describing another unproven claim of Cantor (which he thought to likely be related), namely the statement that there is a well-order of the real numbers. This property, however, turned out to be a consequence of the axiom of choice.

Kurt Gödel 1947

In an essay (published 1947, after his proof and before Cohen's result) Kurt Gödel argued that even if the continuum hypothesis would turn out to be independent (as he expected) this would not imply that it cannot be solved at all:

There might exist axioms so abundant in their verifiable consequences, shedding so much light upon a whole discipline, and furnishing such powerful methods for solving given problems (and even solving them, as far as that is possible, in a constructivistic way) that quite irrespective of their intrinsic necessity they would have to be assumed at least in the same sense as any well established physical theory.

He continues with a discussion of several arguments which support his position that the continuum hypothesis is likely to be wrong. (Read more...)

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