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Exact Sciences

Exact sciences

Exact science refers to systematized knowledge. So that predictions, and their verification, are possible, by measurement, experiment, observation, and rigorous logical argument. Or at least, more realistically, so that predictions undergo this kind of testing, and may eventually get rejected, if it becomes agreed that they do not satisfy the tests. Mathematics, the natural sciences, and the applied sciences are considered exact. It is essential that their results and hypotheses be public, so that repeated testing and development is a universal endeavor. For this reason, it can be said that exact science, at least in the strict sense, did not arise until the invention of the publicly available scientific journal, say around 1640, or at least with the availability of printed books, say around 1540, in Europe. This does not necessarily imply that results before that time were invalid. But many are seen that way today, in the light of the intense scrutiny that characterizes today's exact sciences. This relentless testing, and the ensuing error-correction, so to speak, translates into the very high degree of reliability of the established results in these sciences. Exact sciences are distinguished from the social sciences on the one hand, and from the humanities, theology, the arts on the other. Nevertheless, some fields of study, such as for example economics, may share some of the features characteristic of the exact sciences. The primary distinction lies in whether experimentation is feasible (or indeed advisable), and whether experiments can be designed so that they provide reproducible evidence. As distinct from so-called anecdotal evidence, obtained from a single observation only. In this respect, astronomy is hard put to qualify as an exact science, precisely for the lack of experimentation. However, there are huge numbers of stars to be observed, in (almost) all relevant stages of the stellar life cycle, and this provides almost as reproducible data as experiments otherwise do.

Predictions

Prediction

Measurement

In classical physics and engineering, measurement is the process of estimating or determining the ratio of a magnitude of a quantitative property or relation to a unit of the same type of quantitative property or relation. A process of measurement involves the comparison of physical quantities of objects or phenomena, or the comparison of relations between objects (e.g. angles). A particular measurement is the result of such a process, normally expressed as the multiple of a real number and a unit, where the real number is the ratio obtained from the measurement process. For example, the measurement of the length of an object might be 5 m, which is an estimate of the object's length, a magnitude, relative to a unit of length, the meter. Measurement is not limited to physical quantities and relations but can in principle extend to the quantification of a magnitude of any type, through application of a measurement model such as the Rasch model, and subjecting empirical data derived from comparisons to appropriate testing in order to ascertain whether specific criteria for measurement have been satisfied. In addition, the term measurement is often used in a somewhat looser fashion than defined above, to refer to any process in which numbers are assigned to entities such that the numbers are intended to represent increasing amount, in some sense, without a process that involves the estimation of ratios of magnitudes to a unit. Such examples of measurement range from degrees of uncertainty to consumer confidence to the rate of increase in the fall in the price of a good or service. It is generally proposed that there are four different levels of measurement, and that different levels are applicable to different contexts and types of measurement process. In scientific research, measurement is essential. It includes the process of collecting data which can be used to make claims about learning. Measurement is also used to evaluate the effectiveness of a program or product (known as an evaluand). :: A measurement is a comparison to a standard. -- William Shockley :: By number we understand not so much a multitude of Unities, as the abstracted Ratio of any Quantity to another Quantity of the same kind, which we take for Unity -- Sir Isaac Newton

Units and systems of measurement

:Main articles: Units of measurement and Systems of measurement Because measurement involves the estimation of magnitudes of quantities relative to particular quantities, called units, the specification of units is of fundamental importance to measurement. The definition or specification of precise standards of measurement involves two key features, which are evident in the Système International d'Unités (SI). Specifically, in this system the definition of each of the base units makes reference to specific empirical conditions and, with the exception of the kilogram, also to other quantitative attributes. Each derived SI unit is defined purely in terms of a relationship involving itself and other units; for example, the unit of velocity is 1 m/s. Due to the fact that derived units make reference to base units, the specification of empirical conditions is an implied component of the definition of all units. The measurement of a specific entity or relation results in at least two numbers for the relationship between the entity or relation under study and the referenced unit of measurement, where at least one number estimates the statistical uncertainty in the measurement, also referred to as measurement error. Measuring instruments are used to estimate ratios of magnitudes to units. Prior comparisons underlie the calibration, in terms of standard units, of commonly used instruments constructed to measure physical quantities.

Metrology

Metrology is the study of measurement. In general, a metric is a scale of measurement defined in terms of a standard: i.e. in terms of well-defined unit. The quantification of phenomena through the process of measurement relies on the existence of an explicit or implicit metric, which is the standard to which measurements are referenced. If I say I am 5, I am indicating a measurement without supplying an applicable standard. I may mean I am 5 years old or I am 5 feet high, however the implicit metric is that.

History

:Main article: History of measurement Laws to regulate measurement were originally developed to prevent fraud. However, units of measurement are now generally defined on a scientific basis, and are established by international treaties. In the United States, commercial measurements are regulated by the National Institute of Standards and Technology NIST, a division of the United States Department of Commerce. The history of measurements is a topic within the history of science and technology. The metre (us: meter) was standardized as the unit for length after the French revolution, and has since been adopted throughout most of the world. The United States and the UK are in the process of converting to the SI system. This process is known as metrication.

Difficulties in measurement

Measurement of many quantities is very difficult and prone to large error. Part of the difficulty is due to uncertainty, and part of it is due to the limited time available in which to make the measurement. Examples of things that are very difficult to measure in some respects and for some purposes include social related items such as:
- A person's knowledge (as in testing, see also assessment)
- A person's feelings, emotions, or beliefs.
- A person's senses (qualia). Even for physical quantities gaining accurate measurement can be difficult. It is not possible to be exact, instead, repeated measurements will vary due to various factors affecting the quantity such as temperature, time, electromagnetic fields, and especially measurement method. As an example in the measurement of the speed of light, the quantity is now known to a high degree of precision due to modern methods, but even with those methods there is some variability in the measurement. Statistical techniques are applied to the measurement samples to estimate the speed. In earlier sets of measurements, the variability was greater, and comparing the results shows that the variability and bias in the measurement methods was not properly taken into account. Proof of this is that when various group's measurements are plotted with the estimated speed and error bars showing the expected variability of the estimated speed from the actual number, the error bars from each of the experiments did not all overlap. This means a number of groups incorrectly accounted for the true sources of error and overestimated the accuracy of their methods.

Miscellaneous

Measuring the ratios between physical quantities is an important sub-field of physics. Some important physical quantities include:
- Speed of light
- Planck's constant
- Gravitational constant
- Elementary charge (electric charge of electrons, protons, etc.)
- Fine-structure constant

References

Newton, I. (1728/1967). Universal Arithmetic: Or, a Treatise of Arithmetical Composition and Resolution. In D.T. Whiteside (Ed.), The mathematical Works of Isaac Newton, Vol. 2 (pp. 3-134). New York: Johnson Reprint Corp.

External links

- [http://www.unc.edu/~rowlett/units/index.html A Dictionary of Units of Measurement]
- [http://www.geocities.com/qubestrader/conversion.html Conversion Calculator]
- [http://www.euromet.org/docs/pubs/docs/Metrology_in_short_2nd_edition_may_2004.pdf 'Metrology In Short', 2nd Edition] ja:測定 simple:Measurement

Experiment

In the scientific method, an experiment is a set of actions and observations, performed to support or falsify a hypothesis or research concerning phenomena. The experiment is a cornerstone in the empirical approach to knowledge. See the list of famous experiments for historically important scientific experiments. The word is derived from the Latin ex- + -periri, "from trying".

An experiment in baking

As a simple example, consider that many bakers have noticed that the amount of "fluffiness" in a loaf of bread seems to be related to how much humidity there is in the air when the dough is being made. This can be formalized as the hypothesis: "all other things being considered equal, the greater the humidity, the fluffier the bread". Whilst this hypothesis might arise naturally from baking many loaves over time, an experiment to determine whether this is really true would be to carefully prepare bread dough, as identically as possible, on two types of days: days when the humidity is high, and days when the humidity is low. If the hypothesis is true, then the bread prepared on the high humidity days should be fluffier. Several features of this experiment hold in general for all experiments:
- We must try to make all other conditions of the process as similar as possible between the trials. For example, the amounts of flour and water added, the temperature of the butter, and the amount of kneading all may have an effect on the fluffiness; so the experiment should explicitly attempt to control the other variables which could have an effect on the outcome. This gives us some confidence in the statement "all other things being equal,...".
- Although "fluffiness" may seem to be an easily understood idea, one baker's idea of "fluffy bread" may be different than another baker's. The experiment must be based on objective quantities - for example "fluffiness is measured as the total volume of the loaf of bread from one pound of flour". This idea, coupled with the exactness of the description of how the experiment is to be performed, is sometimes called the operational aspect of the experiment; the idea that all actions, quantities, and observations can be agreed upon by reasonable people.
- Noting that once, on a humid day, one baked a fluffy loaf is not enough. The experiment should be repeatable; given that one performs the experiment exactly as described, one should expect to see the same results, no matter who performs the experiment or how many times it is performed. :Repeatability of an experiment helps to eliminate various types of experimental errors - one may think that one has accurately described all of the relevant techniques and measurements in an experiment, but certain other effects (such as the brand of the flour, trace impurities in the water used in the dough, etc.) may actually be contributing to the observed effects. In the scientific method, someone may claim that they have performed an experiment with a particular result, and thereby supported a particular hypothesis. However, until other scientists have performed the same experiment in the same way and gotten the same results, the experiment is usually not considered as a "proven" result (see cold fusion for a recent example).
- Finally, even though one has baked bread a hundred times, occasionally a loaf will completely fail "because the kitchen gods are unhappy". It is important to realize that some hypotheses cannot be tested experimentally - since we cannot make a measurement which will tell us whether or not the "kitchen gods" are "happy", we cannot perform an experiment which either proves or disproves the hypothesis "the best bread happens when the kitchen gods are happy".

Design of experiments

Design of experiments attempts to balance the requirements and limitations of the field of science in which one works so that the experiment can provide the best conclusion about the hypothesis being tested. In some sciences, such as physics and chemistry, it is relatively easy to meet the requirements that all measurements be made objectively, and that all conditions can be kept controlled across experimental trials. On the other hand, in other cases such as biology, and medicine, it is often hard to ensure that the conditions of an experiment are performed consistently; and in the social sciences, it may even be difficult to determine a method for measuring the outcomes of an experiment in an objective manner. For this reason, sciences such as physics are often referred to as "hard sciences", while others such as sociology are referred to as "soft sciences"; in an attempt to capture the idea that objective measurements are often far easier in the former, and far more difficult in the latter. In addition, in the soft sciences, the requirement for a "controlled situation" may actually work against the utility of the hypothesis in a more general situation. When the desire is to test a hypothesis that works "in general", an experiment may have a great deal of internal validity, in the sense that it is valid in a highly controlled situation, while at the same time lack external validity when the results of the experiment are applied to a real world situation. One of the reasons why this may happen is because of the Hawthorne effect. As a result of these considerations, experimental design in the "hard" sciences tends to focus on the elimination of extraneous effects (type of flour, impurities in the water); while experimental design in the "soft" sciences focuses more on the problems of external validity, often through the use of statistical methods. Occasionally events occur naturally from which scientific evidence can be drawn, which is the basis for natural experiments. In such cases the problem of the scientist is to evaluate the natural "design".

Controlled experiments

:Main article: Control experiment Many hypotheses in sciences such as physics can establish causality by noting that, until some phenomenon occurs, nothing happens; then when the phenomenon occurs, a second phenomenon is observed. But often in science, this situation is difficult to obtain. For example, in the old joke, someone claims that they are snapping their fingers "to keep the tigers away"; and justifies this behavior by saying "see - its working!" While this "experiment" does not falsify the hypothesis "snapping fingers keeps the tigers away", it does not really support the hypothesis - not snapping your fingers keeps the tigers away as well. To demonstrate a cause and effect hypothesis, an experiment must often show that, for example, a phenomenon occurs after a certain treatment is given to a subject, and that the phenomenon does not occur in the absence of the treatment. (See Baconian method.) Baconian method A controlled experiment generally compares the results obtained from an experimental sample against a control sample, which is practically identical to the experimental sample except for the one aspect whose effect is being tested. In many laboratory experiments it is good practice to have several replicate samples for the test being performed and have both a positive control and a negative control. The results from replicate samples can often be averaged, or if one of the replicates is obviously inconsistent with the results from the other samples, it can be discarded as being the result of an experimental error (some step of the test procedure may have been mistakenly omitted for that sample). Most often, tests are done in duplicate or triplicate. A positive control is a procedure that is very similar to the actual experimental test but which is known from previous experience to give a positive result. A negative control is known to give a negative result. The positive control confirms that the basic conditions of the experiment were able to produce a positive result, even if none of the actual experimental samples produce a positive result. The negative control demonstrates the base-line result obtained when a test does not produce a measurable positive result; often the value of the negative control is treated as a "background" value to be subtracted from the test sample results. Sometimes the positive control takes the form of a standard curve. An example that is often used in teaching laboratories is a controlled protein assay. Students might be given a fluid sample containing an unknown (to the student) amount of protein. It is their job to correctly perform a controlled experiment in which they determine the concentration of protein in fluid sample (usually called the "unknown sample"). The teaching lab would be equipped with a protein standard solution with a known protein concentration. Students could make several positive control samples containing various dilutions of the protein standard. Negative control samples would contain all of the reagents for the protein assay but no protein. In this example, all samples are performed in duplicate. The assay is a colorimetric assay in which a spectrophotometer can measure the amount of protein in samples by detecting a colored complex formed by the interaction of protein molecules and molecules of an added dye. In the illustration, the results for the diluted test samples can be compared to the results of the standard curve (the blue line in the illustration) in order to determine an estimate of the amount of protein in the unknown sample. Controlled experiments can be performed when it is difficult to exactly control all the conditions in an experiment. In this case, the experiment begins by creating two or more sample groups that are probabilistically equivalent, which means that measurements of traits should be similar among the groups and that the groups should respond in the same manner if given the same treatment. This equivalency is determined by statistical methods that take into account the amount of variation between individuals and the number of individuals in each group. In fields such as microbiology and chemistry, where there is very little variation between individuals and the group size is easily in the millions, these statistical methods are often bypassed and simply splitting a solution into equal parts is assumed to produce identical sample groups. Once equivalent groups have been formed, the experimenter tries to treat them identically except for the one variable that he or she wishes to isolate. Human experimentation requires special safeguards against outside variables such as the placebo effect. Such experiments are generally double blind, meaning that neither the volunteer nor the researcher knows which individuals are in the control group or the experimental group until after all of the data has been collected. This ensures that any effects on the volunteer are due to the treatment itself and are not a response to the knowledge that he is being treated. In human experiments, a subject (person) may be given a stimulus to which he or she should respond. The goal of the experiment is to measure the response to a given stimulus. (Example???)

Natural experiments

Sometimes controlled experiments are prohibitively difficult, so researchers resort to natural experiments. Natural experiments take advantage of predictable natural changes in simple systems to measure the effect of that change on some phenomenon. Much of astronomy relies on experiments of this type. It is clearly impractical, when trying to prove the hypothesis "suns are collapsed clouds of hydrogen", to start out with a giant cloud of hydrogen, and then perform the experiment of waiting a few billion years for it to form a sun. However, by observing various clouds of hydrogen in various states of collapse, and other implications of the hypothesis (for example, the presence of various spectral emissions from the light of stars), we can collect the experimental data we require to support the hypothesis. An early example of this type of experiment was the first verification in the 1600s that light does not travel from place to place instantaneously, but instead has a measurable speed. Observation of the appearance of the moons of Jupiter were slightly delayed when Jupiter was farther from Earth, as opposed to when Jupiter was closer to Earth; and this phenomenon was used to demonstrate that the difference in the time of appearance of the moons was consistent with a measurable speed of light.

Quasi-experiments

Quasi-experiments are very much like controlled experiments except that they lack probabilistic equivalency between groups. These types of experiments often arise in the area of medicine where, for ethical reasons, it is not possible to create a truly controlled group. For example, one would not want to deny all forms of treatment for a life-threatening disease from one group of patients to evaluate the effectiveness of another treatment on a different group of patients. Researchers compensate for this with complicated statistical methods. See also quasi-empirical methods.

Examples

- MTT assay
- Colony Formation Assay
- Ames Test
- western blot

Quotes

: "We have to learn again that science without contact with experiments is an enterprise which is likely to go completely astray into imaginary conjecture." — Hannes Alfven : "Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality." — Nikola Tesla

External links

- [http://trochim.human.cornell.edu/kb/index.htm] Trochim, William M. The Research Methods Knowledge Base, 2nd Edition. (version current as of January 15, 2005).
- [http://www.verrueckte-experimente.de/index_e.html Description of weird experiments (with film clips)]

Literature

The Character of Physical Law, by Richard P. Feynman Category:Research
- ja:実験 simple:Experiment

Observation

:For the railroad use of the term observation, see observation car. ---- Observation in its most basic version means watching something and taking note of anything it does - although vision is the most often used, all the senses can be used to observe. For instance, you might observe a bird flying by watching it closely with binoculars. Direct observations form the foundations of all natural sciences. Some disciplines, such as biology and astronomy, have their historical basis in observations by amateurs - the participation of hobbyists is explained by the fact that there is pleasure in observation.

The role of Observation in the Scientific Method

The scientific method includes the following steps: # 'observe' a phenomenon, #'Hypothesize' an explanation for the phenomenon, #'predict' a logical consequence of the guess, #'test' the prediction, and #'review' for any mistakes. Observation plays a role in the first and fourth steps in the above list. Reliance is placed upon the five physical senses: visual perception, hearing (sense), taste, feeling, and olfaction, and upon measurement techniques. It is therefore understood that there are always certain limitations in making observations.

Example - The Big Bang

In cosmology, the original observation was that we seem to live in a firmament. The sun seemed to rise and set, travelling on a huge transparent bowl which was set around our world. Various paradigms which explained our world, came and went, but the universe seemed static. Even Einstein believed this.

Observation: Hubble's redshift

In the 1920s Edwin Hubble of Mount Wilson observatory [http://www.mtwilson.edu/his/art/g1a4.htm], observed that the galaxies, on the whole, were moving away from each other. Thus we live in an 'expanding universe'. The speed of expansion was apparently constant (Hubble's 'constant'), as evidenced by light from the galaxies, which was doppler-shifted in color toward the red side of the spectrum. Einstein correspondingly modified his field equation. See Cosmological constant

Hypothesis about the abundance of the elements

If the universe is expanding, then it must have been much smaller and therefore hotter and denser in the past. George Gamow hypothesized that the abundance of the elements in the Periodic Table of the Elements, might be accounted for by nuclear reactions in a hot dense universe. He was disputed by Fred Hoyle, who invented the term 'Big Bang' to disparage it. Fermi and others noted that this process would have stopped after only the light elements were created, and thus did not account for the abundance of heavier elements. Gamow's prediction: One consequence of this hypothesis was a 5–10 kelvin black body radiation temperature for the universe, after it cooled during the expansion.

Observation: the microwave background

In 1965, Arno A. Penzias and Robert W. Wilson announced that microwave radiation was surrounding us in all directions, at a level which was of the order of magnitude predicted by Gamow. Penzias and Wilson got the Nobel Prize for this discovery.

Big Bang Hypothesis now corroborated

After this piece of evidence, Gamow's hypothesis was now more likely. The age of the universe is currently estimated to be 13.7 billion years after the Big Bang.

Current observations

More refined measurements, such as those from the COBE satellite, are best fit by radiation from a pure 2.7 kelvin black body.

Future observations

It is, of course, entirely possible that observations made in the future may enable a different understanding. People of the future, looking back on the Big Bang theory may, perhaps, regard it with as much derision as the people of today regard the apparent geocentric universe of previous observations. All that is possible is to keep looking at the evidence as it comes in. Reference: J.A. Peacock, A.F. Heavens, A.T. Davies (eds.), 1989. Physics of the Early Universe. Proceedings of the 36th Scottish Universities Summer School in Physics (SUSSP). ISBN 0905945190.

The role of Observation in Philosophy

"Observe always that everything is the result of a change, and get used to thinking that there is nothing Nature loves so well as to change existing forms and to make new ones like them." Meditations. iv. 36. -Marcus Aurelius Observation in philosophical terms is the process of filtering sensory information through the thought process. Input is received via hearing, sight, smell, taste, or touch and then analyzed through either rational or irrational thought. You see a man beat his wife; you observe that such an action is either good or bad. Deductions about what behaviors are good or bad may be based on preferences about building relationships, or study of the consequences resulting from the observed behavior. With the passage of time, impressions stored in the consciousness about many related observations, together with the resulting relationships and consequences, permit the individual to build a construct about the moral implications of behavior. The defining characteristic of observation is that it involves drawing conclusions, as well as building personal views about how to handle similar situations in the future, rather than simply registering that something has happened. Observing is part of the process of developing a morality.

Hobbies that involve observation

Hobbies that involve observation depend for their interest on items being observed. A knowledge of these items and their habitats will develop over time in the observer, who may draw upon the experiences of others as conveyed in books or websites or by word of mouth. Most such hobbies involve classification of the items seen, with the precision and reliability of such classifications generally increasing over time. Depending on the geographic dispersal of the creatures or things being observed, pursuit of the hobby might well require or entice travel. When spotting natural creatures, an understanding of their migration patterns may be essential. Specific creatures may only be visible in particular places at certain times of the year. The creatures that can be observed include humans, e.g. from a sidewalk café. This may be especially interesting in an exotic country, or at a place where exotic people pass. Also one may like to look at sexually attractive people. There are parallels in those hobbies relating to man-made items. International political events may sometimes generate a gathering of VIP aircraft, and an international football match may cause a sudden influx of charter airliners to the region where the match is played. There is likely to be a social aspect to such hobbies, since fellow enthusiasts will normally alert a hobbyist to forthcoming (or even current) opportunities to witness unusual items within the scope of the shared pastime. New technologies such as mobile telephones and the Internet have clearly increased the opportunities for passing such information between fellow enthusiasts when it is timely.

Logical argument

An argument is an attempt to demonstrate the truth of an assertion called a conclusion, based on the truth of a set of assertions called premises. The process of demonstration of deductive (see also deduction) and inductive reasoning shapes the argument, and presumes some kind of communication, which could be part of a written text, a speech or a conversation. In ordinary, philosophical and scientific argumentation abductive arguments and arguments by analogy are also commonly used. Arguments can be valid or invalid, although how arguments are determined to be in either of these two categories can often itself be an object of much discussion. Informally one should expect that a valid argument should be compelling in the sense that it is capable of convincing someone about the truth of the conclusion. However, such a criterion for validity is inadequate or even misleading since it depends more on the skill of the person constructing the argument to manipulate the person who is being convinced and less on the argument itself. Less subjective criteria for validity of arguments are often clearly desirable, and in some cases we should even expect an argument to be rigorous, that is, to adhere to precise rules of validity. This is the case for arguments used in mathematical proofs. Note that a rigorous proof does not have to be a formal proof. In ordinary language, people refer to the logic of an argument or use terminology that suggests that an argument is based on inference rules of formal logic. Though arguments do use inferences that are indisputably purely logical (such as syllogisms), other kinds of inferences are almost always used in practical arguments. For example, arguments commonly deal with causality, probability and statistics or even specialized areas such as economics. In these cases, logic refers to the structure of the argument rather than to principles of pure logic that might be used in it.

Argument validity

In evaluating an argument, we consider separately the truth of the premises and the validity of the logical relationships between the premises, any intermediate assertions and the conclusion. The main logical property of an argument that is of concern to us here is whether it is truth preserving, that is if the premises are true, then so is the conclusion. We will usually abbreviate this property by saying simply that argument is valid. If the argument is valid, the premises together entail or imply the conclusion. The ways in which arguments go wrong tend to fall into certain patterns, called logical fallacies. Validity is a semantic characteristic of arguments; independently of this property, and more controversially, arguments should also be scrutinizable, in the sense that the argument be open to public examination and systematic in the sense that the structural components of the argument have public legitimacy.

The mathematical paradigm

In mathematics, an argument can be formalized using symbolic logic. In that case, an argument is seen as an ordered list of statements, each one of which is either one of the premises or derivable from the combination of some subset of the preceding statements and one or more axioms using rules of inference. The last statement in the list is the conclusion. Most arguments used in mathematical proof are rigorous, but not formal. In fact, strictly formal proofs of all but the most trivial assertions are extremely hard to construct and hard to understand without some assistance from a computer. One of the goals of automated theorem proving is to design computer programs to produce and check formal proofs. A study of formal systems of mathematics together with semantic questions such as completeness and validity is often called metamathematics. Of particular note in this direction are the Gödel's incompleteness theorems for first order theories of arithmetic. The prevalent belief among mathematical authors is that valid arguments in mathematics are those that can be recognized as being in principle formalizable in the encompassing formal theory. It follows that the theory of valid arguments in mathematics is reducible to the theory of valid inferences in formal mathematical theories. A theory of validity of formal mathematical theories posits two distinct elements: syntax which gives the rules for when a formula is correctly constructed and semantics which is essentially a function from formulas to truth values. An expression is said to be valid if the semantic function assigns the value true to it. A rule of inference is valid if and only if it is validity-preserving. An argument is valid if and only if it utilizes valid rules of inference. Note that in the case of mathematical semantics, both the syntax and semantics are mathematical objects. In general usage, however, arguments are rarely formal or even have the rigor of mathematical proofs.

Theories of arguments

Theories of arguments are closely related to theories of informal logic. Ideally, a theory of argument should provide some mechanism for explaining validity of arguments. One natural approach would follow the mathematical paradigm and attempt to define validity in terms of semantics of the assertions in the argument. Though such an approach is appealing in its simplicity, the obstacles to proceeding this way are very difficult for anything other than purely logical arguments. Among other problems, we need to interpret not only entire sentences, but also components of sentences, for example noun phrases such as The present value of government revenue for the next twelve years. One major difficulty of pursuing this approach is that determining an appropriate semantic domain is not an easy task, raising numerous thorny ontological issues. It also raises the discouraging prospect of having to work out acceptable semantic theories before being able to say anything useful about understanding and evaluating arguments. For this reason the purely semantic approach is usually replaced with other approaches that are more easily applicable to practical discourse. For arguments regarding topics such as probability, economics or physics, some of the semantic problems can be conveniently shoved under the rug if we can avail ourselves of an model of the phenomenon under discussion. In this case, we can establish a limited semantic interpretation using the terms of the model and the validity of the argument is reduced to that of the abstract model. This kind of reduction is used in the natural sciences generally, and would be particularly helpful in arguing about social issues if the parties can agree on a model. Unfortunately, this prior reduction seldom occurs, with the result that arguments about social policy rarely have a satisfactory resolution. Another approach is to develop a theory of argument pragmatics, at least in certain cases where argument and social interaction are closely related. This is most useful when the goal of logical argument is to establish a mutually satisfactory resolution of a difference of opinion between individuals.

Argumentative dialogue

Arguments as discussed in the preceding paragraphs are static, such as one might find in a textbook or research article. They serve as a published record of justification for an assertion. Arguments can also be interactive, in which the proposer and the interlocutor have a more symmetrical relationship. The premises are discussed, as well the validity of the intermediate inferences. For example, consider the following exchange, illustrated by the No true Scotsman fallacy: : Argument: "No Scotsman puts sugar on his porridge." : Reply: "But my friend Angus likes sugar with his porridge." : Rebuttal: "Ah yes, but no true Scotsman puts sugar on his porridge." In this dialogue, the proposer first offers a premise, the premise is challenged by the interlocutor, and finally the proposer offers a modification of the premise. This exchange could be part of a larger discussion, for example a murder trial, in which the defendant is a Scotsman, and it had been established earlier that the murderer was eating sugared porridge when he or she committed the murder. In argumentative dialogue, the rules of interaction may be negotiated by the parties to the dialogue, although in many cases the rules are already determined by social mores. In the most symmetrical case, argumentative dialogue can be regarded as a process of discovery more than one of justification of a conclusion. Ideally, the goal of argumentative dialogue is for participants to arrive jointly at a conclusion by mutually accepted inferences. In some cases however, the validity of the conclusion is secondary. For example; emotional outlet, scoring points with an audience, wearing down an opponent or lowering the sale price of an item may instead be the actual goals of the dialogue. Walton distinguishes several types of argumentative dialogue which illustrate these various goals:
- Personal quarrel.
- Forensic debate.
- Persuasion dialogue.
- Bargaining dialogue.
- Action seeking dialogue.
- Educational dialogue. Van Eemeren and Grootendorst identify various stages of argumentative dialogue. These stages can be regarded as an argument protocol. In a somewhat loose interpretation, the stages are as follows:
- Confrontation: Presentation of the problem, such as a debate question or a political disagreement
- Opening: Agreement on rules, such as for example, how evidence is to be presented, which sources of facts are to be used, how to handle divergent interpretations, determination of closing conditions.
- Argumentation: Application of logical principles according to the agreed-upon rules
- Closing: This occurs when the termination conditions are met. Among these could be for example, a time limitation or the determination of an arbiter. Van Eemeren and Grootendorst provide a detailed list of rules that must be applied at each stage of the protocol. Moreover, in the account of argumentation given by these authors, there are specified roles of protagonist and antagonist in the protocol which are determined by the conditions which set up the need for argument. Many cases of argument are highly unsymmetrical, although in some sense they are dialogues. A particularly important case of this is political argument. Much of the recent work on argument theory has considered argumentation as an integral part of language and perhaps the most important function of language (Grice, Searle, Austin, Popper). This tendency has removed argumentation theory away from the realm of pure formal logic. One of the original contributors to this trend is the philosopher Chaim Perelman, who together with Lucie Olbrechts-Tyteca, introduced the French term La nouvelle rhetorique in 1958 to describe an approach to argument which is not reduced to application of formal rules of inference. Perelman's view of argumentation is much closer to a juridical one, in which rules for presenting evidence and rebuttals play an important role. Though this would apparently invalidate semantic concepts of truth, this approach seems useful in situations in which the possibility of reasoning within some commonly accepted model does not exist or this possibility has broken down because of ideological conflict. Retaining the notion enunciated in the introduction to this article that logic usually refers to the structure of argument, we can regard the logic of rhetoric as a set of protocols for argumentation.

Other theories

In recent decades one of the more influential discussions of philosophical arguments is that by Nicholas Rescher in his book The Strife of Systems. Rescher models philosophical problems on what he calls aporia or an aporetic cluster: a set of statements, each of which has initial plausibility but which are jointly inconsistent. The only way to solve the problem, then, is to reject one of the statements. If this is correct, it constrains how philosophical arguments are formulated.

References

- Rober Audi, Epistemology, Routledge, 1998. Particularly relevant is Chapter 6, which explores the relationship between knowledge, inference and argument.
- J. L. Austin How to Do things with Words, Oxford University Press, 1976.
- H. P. Grice, Logic and Conversation in The Logic of Grammar, Dickenson, 1975.
- R. A. DeMillo, R. J. Lipton and A. J. Perlis, Social Processes and Proofs of Theorems and Programs, Communications of the ACM, Vol. 22, No. 5, 1979. A classic article on the social process of acceptance of proofs in mathematics.
- Yu Manin, A Course in Mathematical Logic, Springer Verlag, 1977. A mathematical view of logic. This book is different from most books on mathematical logic in that it emphasizes the mathematics of logic, as opposed to the formal structure of logic.
- Ch. Perelman and L Olbrechts-Tyteca, The New Rhetoric, Notre Dame, 1970. This classic was originally published in French in 1958.
- Henri Poincaré, Science and Hypothesis, Dover Publications, 1952
- Frans van Eemeren and Rob Grootendorst, Speech Acts in Argumentative Discussions, Foris Publications, 1984.
- K. R. Popper Objective Knowledge; An Evolutionary Approach, Oxford: Clarendon Press, 1972.
- L. Stebbing, A Modern Introdcution to Logic, Methuen and Co., 1948. An account of logic that covers the classic topics of logic and argument while carefully considering modern developments in logic.
- Douglas Walton, Informal Logic: A Handbook for Critical Argumentation, Cambridge, 1998
- Carlos Chesñevar, Ana Maguitman and Ronald Loui, Logical Models of Argument, ACM Computing Surveys, vol. 32, num. 4, pp.337-383, 2000.

Mathematics

Mathematics is often defined as the study of topics such as quantity, structure, space, and change. Another view, held by many mathematicians, is that mathematics is the body of knowledge justified by deductive reasoning, starting from axioms and definitions. Practical mathematics, in nearly every society, is used for such purposes as accounting, measuring land, or predicting astronomical events. Mathematical discovery or research often involves discovering and cataloging patterns, without regard for application. The remarkable fact that the "purest" mathematics often turns out to have practical applications is what Eugene Wigner has called "the unreasonable effectiveness of mathematics." Today, the natural sciences, engineering, economics, and medicine depend heavily on new mathematical discoveries. The word "mathematics" comes from the Greek μάθημα (máthema) meaning "science, knowledge, or learning" and μαθηματικός (mathematikós) meaning "fond of learning". It is often abbreviated maths in Commonwealth English and math in North American English.

History

:Main article: History of mathematics The evolution of mathematics might be seen to be an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction was probably that of numbers. The realization that two apples and two oranges do have something in common, namely that they fill the hands of exactly one person, was a breakthrough in human thought. In addition to recognizing how to count concrete objects, prehistoric peoples also recognized how to count abstract quantities, like time -- days, seasons, years. Arithmetic (e.g. addition, subtraction, multiplication and division), naturally followed. Monolithic monuments testify to a knowledge of geometry. Further steps need writing or some other system for recording numbers such as tallies or the knotted strings called khipu used by the Inca empire to store numerical data. Numeral systems have been many and diverse. Historically, the major disciplines within mathematics arose, from the start of recorded history, out of the need to do calculations on taxation and commerce, to understand the relationships among numbers, to measure land, and to predict astronomical events. These needs can be roughly related to the broad subdivision of mathematics, into the studies of quantity, structure, space, and change. Mathematics since has been much extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries have been made throughout history and continue to be made today.

Inspiration, pure and applied mathematics, and aesthetics

Mathematics arises wherever there are difficult problems that involve quantity, structure, space, or change. At first these were found in commerce, land measurement and later astronomy; nowadays, all sciences suggest problems studied by mathematicians, and many problems arise within mathematics itself. Newton invented infinitesimal calculus and Feynman his Feynman path integral using a combination of reasoning and physical insight, and today's string theory also inspires new mathematics. Some mathematics is only relevant in the area that inspired it, and is applied to solve further problems in that area. But often mathematics inspired by one area proves useful in many areas, and joins the general stock of mathematical concepts. As in most areas of study, the explosion of knowledge in the scientific age has led to specialization in mathematics. One major distinction is between pure mathematics and applied mathematics. Within applied mathematics, two major areas have split off and become disciplines in their own right, statistics and computer science. Many mathematicians talk about the elegance of mathematics, its intrinsic aesthetics and inner beauty. Simplicity and generality are valued. There is beauty also in a clever proof, such as Euclid's proof that there are infinitely many prime numbers, and in a numerical method that speeds calculation, such as the fast Fourier transform. G. H. Hardy in "A Mathematicians Apology" expressed the belief that these esthetic considerations are, in themselves, sufficient to justify the study of pure mathematics. Main article: Mathematical beauty.

Notation, language, and rigor

Mathematical writing is not easily accessible to the layperson. A Brief History of Time, Stephen Hawking's 1988 bestseller, contained a single mathematical equation. This was the author's compromise with the publisher's advice, that each equation would halve the sales. The reasons for the inaccessibility even of carefully-expressed mathematics can be partially explained. Contemporary mathematicians strive to be as clear as possible in the things they say and especially in the things they write (this they have in common with lawyers). They refer to rigor. To accomplish rigor, mathematicians have extended natural language. There is precisely-defined vocabulary for referring to mathematical objects, and stating certain common relations. There is an accompanying mathematical notation which, like musical notation, has a definite content and also has a strict grammar (under the influence of computer science, more often now called syntax). Some of the terms used in mathematics are also common outside mathematics, such as ring, group and category; but are not such that one can infer the meanings. Some are specific to mathematics, such as homotopy and Hilbert space. It was said that Henri Poincaré was only elected to the Académie Française so that he could tell them how to define automorphe in their dictionary. Rigor is fundamentally a matter of mathematical proof. Mathematicians want their theorems to follow mechanically from axioms by means of formal axiomatic reasoning. This is to avoid mistaken 'theorems', based on fallible intuitions; of which plenty of examples have occurred in the history of the subject (for example, in mathematical analysis). Axioms in traditional thought were 'self-evident truths', but that conception turns out not to be workable in pushing the mathematical boundaries. At a formal level, an axiom is just a string of symbols, which has an intrinsic meaning only in the context of all derivable formulas of an axiomatic system. It was the goal of Hilbert's program to put all of mathematics on a firm axiomatic basis, but according to Gödel's incompleteness theorem every (strong enough) axiom system has undecidable formulas; and so a final axiomatization of mathematics is unavailable. Nonetheless mathematics is often imagined to be (as far as its formal content) nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory.

Is mathematics a science?

Carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. The mathematician-physicist Leon M. Lederman has quipped: "The physicists defer only to mathematicians, and the mathematicians defer only to God (though you may be hard pressed to find a mathematician that modest)." If one considers science to be strictly about the physical world, then mathematics, or at least pure mathematics, is not a science. An alternative view is that certain scientific fields (such as theoretical physics) are mathematics with axioms that are intended to correspond to reality. In fact, the theoretical physicist, J. M. Ziman, proposed that science is public knowledge and thus includes mathematics. [http://info.med.yale.edu/therarad/summers/ziman.htm] In any case, mathematics shares much in common with many fields in the physical sciences, notably the exploration of the logical consequences of assumptions. Intuition and experimentation also play a role in the formulation of conjectures in both mathematics and the (other) sciences.

Overview of fields of mathematics

As noted above, the major disciplines within mathematics first arose out of the need to do calculations in commerce, to understand the relationships between numbers, to measure land, and to predict astronomical events. These four needs can be roughly related to the broad subdivision of mathematics into the study of quantity, structure, space, and change (i.e. arithmetic, algebra, geometry and analysis). In addition to these main concerns, there are also subdivisions dedicated to exploring links from the heart of mathematics to other fields: to logic, to set theory (foundations) and to the empirical mathematics of the various sciences (applied mathematics). The study of quantity starts with numbers, first the familiar natural numbers and integers and their arithmetical operations, which are characterized in arithmetic. The deeper properties of whole numbers are studied in number theory. The study of structure began with investigations of Pythagorean triples. Neolithic monuments on the British Isles are constructed using Pythagorean triples. Eventually, this led to the invention of more abstract numbers, such as the square root of two. The deeper structural properties of numbers are studied in abstract algebra and the investigation of groups, rings, fields and other abstract number systems. Included is the important concept of vectors, generalized to vector spaces and studied in linear algebra. The study of vectors combines three of the fundamental areas of mathematics, quantity, structure, and space. The study of space originates with geometry, beginning with Euclidean geometry. Trigonometry combines space and number. The modern study of space generalizes these ideas to include higher-dimensional geometry, non-Euclidean geometries (which play a central role in general relativity) and topology. Quantity and space both play a role in analytic geometry, differential geometry, and algebraic geometry. Within differential geometry are the concepts of fiber bundles, calculus on manifolds. Within algebraic geometry is the description of geometric objects as solution sets of polynomal equations, combining the concepts of quantity and space, and also the study of topological groups, which combine structure and space. Lie groups are used to study space, structure, and change. Topology in all its many ramifications may be the greatest growth area in 20th century mathematics. Understanding and describing change is a common theme in the natural sciences, and calculus was developed as a most useful tool. The central concept used to describe a changing quantity is that of a function. Many problems lead quite naturally to relations between a quantity and its rate of change, and the methods of differential equations. The numbers used to represent continuous quantities are the real numbers, and the detailed study of their properties and the properties of real-valued functions is known as real analysis. These have been generalized, with the inclusion of the square root of negative one, to the complex numbers, which are studied in complex analysis. Functional analysis focuses attention on (typically infinite-dimensional) spaces of functions. One of many applications of functional analysis is quantum mechanics. Many phenomena in nature can be described by dynamical systems; chaos theory makes precise the ways in which many of these systems exhibit unpredictable yet still deterministic behavior. Beyond quantity, structure, space, and change are areas of pure mathematics that can be approached only by deductive reasoning. In order to clarify the foundations of mathematics, the fields of mathematical logic and set theory were developed. Mathematical logic, which divides into recursion theory, model theory, and proof theory, is now closely linked to computer science. When electronic computers were first conceived, several essential theoretical concepts in computer science were shaped by mathematicians, leading to the fields of computability theory, computational complexity theory, and information theory. Many of those topics are now investigated in theoretical computer science. Discrete mathematics is the common name for the fields of mathematics most generally useful in computer science. An important field in applied mathematics is statistics, which uses probability theory as a tool and allows the description, analysis, and prediction of phenomena where chance plays a part. It is used in all the sciences. Numerical analysis investigates methods for using computers to efficiently solve a broad range of mathematical problems that are typically beyond human capacity, and taking rounding errors or other sources of error into account to obtain credible answers.

Major themes in mathematics

An alphabetical and subclassified list of mathematical topics is available. The following list of themes and links gives just one possible view. For a fuller treatment, see Areas of mathematics or the list of lists of mathematical topics.

Change

:Ways to express and handle change in mathematical functions, and changes between numbers. : :Arithmetic – Calculus – Vector calculus – Analysis – Differential equations – Dynamical systems – Chaos theory – List of functions

Foundations and methods

:Approaches to understanding the nature of mathematics. :philosophy of mathematics – mathematical intuitionism – mathematical constructivism – foundations of mathematics – set theory – symbolic logic – model theory – category theory – Logic – reverse mathematics – table of mathematical symbols

Discrete mathematics

:Discrete mathematics involves techniques that apply to objects that can only take on specific, separated values. : :Combinatorics – Naive set theory – Theory of computation– Cryptography – Graph theory

Applied mathematics

:Applied mathematics uses the full knowledge of mathematics to solve real-world problems. :Mathematical physics – Mechanics – Fluid mechanics – Numerical analysis – Optimization – Probability – Statistics – Mathematical economics – Financial mathematics – Game theory – Mathematical biology – Cryptography – Information theory

Important theorems

:These theorems have interested mathematicians and non-mathematicians alike. :See list of theorems for more :Pythagorean theorem – Fermat's last theorem – Gödel's incompleteness theorems – Fundamental theorem of arithmetic – Fundamental theorem of algebra – Fundamental theorem of calculus – Cantor's diagonal argument – Four color theorem – Zorn's lemma – Euler's identity – classification theorems of surfaces – Gauss-Bonnet theorem – Quadratic reciprocity – Riemann-Roch theorem.

Important conjectures

See list of conjectures for more :These are some of the major unsolved problems in mathematics. :Goldbach's conjecture – Twin Prime Conjecture – Riemann hypothesis – Poincaré conjecture – Collatz conjecture – P=NP? – open Hilbert problems.

History and the world of mathematicians

Mathematics and other fields

:Mathematics and architecture – Mathematics and education – Mathematics of musical scales

Common misconceptions

Mathematics is not a closed intellectual system, in which everything has already been worked out. There is no shortage of open problems. Pseudomathematics is a form of mathematics-like activity undertaken outside academia, and occasionally by mathematicians themselves. It often consists of determined attacks on famous questions, consisting of proof-attempts made in an isolated way (that is, long papers not supported by previously published theory). The relationship to generally-accepted mathematics is similar to that between pseudoscience and real science. The misconceptions involved are normally based on:
- misunderstanding of the implications of mathematical rigour;
- attempts to circumvent the usual criteria for publication of mathematical papers in a learned journal after peer review, with assumptions of bias;
- lack of familiarity with, and therefore underestimation of, the existing literature. The case of Kurt Heegner's work shows that the mathematical establishment is neither infallible, nor unwilling to admit error in assessing 'amateur' work. And like astronomy, mathematics owes much to amateur contributors such as Fermat and Mersenne. Mathematics is not accountancy. Although arithmetic computation is crucial to accountants, their main concern is to verify that computations are correct through a system of doublechecks. Advances in abstract mathematics are mostly irrelevant to the efficiency of concrete bookkeeping, but the use of computers clearly does matter. Mathematics is not numerology. Numerology uses modular arithmetic to reduce names and dates down to numbers, but assigns emotions or traits to these numbers intuitively or on the basis of traditions. Mathematical concepts and theorems need not correspond to anything in the physical world. In the case of geometry, for example, it is not relevant to mathematics to know whether points and lines exist in any physical sense, as geometry starts from axioms and postulates about abstract entities called "points" and "lines" that we feed into the system. While these axioms are derived from our perceptions and experience, they are not dependent on them. And yet, mathematics is extremely useful for solving real-world problems. It is this fact that led Eugene Wigner to write an essay on The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Mathematics is not about unrestricted theorem proving, any more than literature is about the construction of grammatically correct sentences. However, theorems are elements of formal theories, and in some cases computers can generate proofs of these theorems more or less automatically, by means of automated theorem provers. These techniques have proven useful in formal verification of programs and hardware designs. However, they are unlikely to generate (in the near term, at least) mathematics with any widely recognized aesthetic value.

Bibliography

- Benson, Donald C., The Moment Of Proof: Mathematical Epiphanies (1999).
- Courant, R. and H. Robbins, What Is Mathematics? (1941);
- Davis, Philip J. and Hersh, Reuben, The Mathematical Experience. Birkhäuser, Boston, Mass., 1980. A gentle introduction to the world of mathematics.
- Boyer, Carl B., History of Mathematics, Wiley, 2nd edition 1998 available, 1st edition 1968 . A concise history of mathematics from the Concept of Number to contemporary Mathematics.
- Gullberg, Jan, Mathematics--From the Birth of Numbers. W.W. Norton, 1996. An encyclopedic overview of mathematics presented in clear, simple language.
- Hazewinkel, Michiel (ed.), Encyclopaedia of Mathematics. Kluwer Academic Publishers 2000. A translated and expanded version of a Soviet math encyclopedia, in ten (expensive) volumes, the most complete and authoritative work available. Also in paperback and on CD-ROM.
- Kline, M., Mathematical Thought from Ancient to Modern Times (1973).
- Pappas, Theoni, The Joy Of Mathematics (1989).

External links

- [http://www.cut-the-knot.org/ Interactive Mathematics Miscellany and Puzzles] — A collection of articles on various math topics, with interactive Java illustrations at cut-the-knot
- Rusin, Dave: [http://www.math-atlas.org/ The Mathematical Atlas]. A guided tour through the various branches of modern mathematics.
- Stefanov, Alexandre: [http://us.geocities.com/alex_stef/mylist.html Textbooks in Mathematics]. A list of free online textbooks and lecture notes in mathematics.
- Weisstein, Eric et al.: [http://www.mathworld.com/ MathWorld: World of Mathematics]. An online encyclopedia of mathematics.
- Polyanin, Andrei: [http://eqworld.ipmnet.ru/ EqWorld: The World of Mathematical Equations]. An online resource focusing on algebraic, ordinary differential, partial differential (mathematical physics), integral, and other mathematical equations.
- A mathematical thesaurus maintained by the [http://nrich.maths.org/ NRICH] project at the University of Cambridge (UK), [http://thesaurus.maths.org/ Connecting Mathematics]
- [http://planetmath.org/ Planet Math]. An online math encyclopedia under construction, focusing on modern mathematics. Uses the GFDL, allowing article exchange with Wikipedia. Uses TeX markup.
- [http://www.mathforge.net/ Mathforge]. A news-blog with topics ranging from popular mathematics to popular physics to computer science and education.
- [http://www.youngmath.net/concerns Young Mathematicians Network (YMN)]. A math-blog "Serving the Community of Young Mathematicians". Topics include: Math News, Grad and Undergrad Life, Job Search, Career, Work & Family, Teaching, Research, Misc...
- [http://metamath.org/ Metamath]. A site and a language, that formalize math from its foundations.
- [http://world.std.com/~reinhold/dir/mathmovies.html Math in the Movies]. A guide to major motion pictures with scenes of real mathematics
- [http://math.cofc.edu/faculty/kasman/MATHFICT/default.html Mathematics in fiction]. Links to works of fiction that refer to mathematics or mathematicians.
- [http://www.mathhelpforum.com/math-help Math Help Forum]. A forum, for math help, math discussion and debate.
- [http://www.sosmath.com/CBB S.O.S. Mathematics Cyberboard] a math help forum which incorporates a LaTeX extension, making it easier for members to write and display math formulae.
- [http://www-history.mcs.st-and.ac.uk/~history/ Mathematician Bibliography]. Extensive history and quotes from all famous mathematicians.
- [http://www.physicsmathforums.com/ Physics Math Forums]
- Category:School subjects fiu-vro:Matõmaatiga zh-min-nan:Sò·-ha̍k ko:수학 ms:Matematik ja:数学 simple:Mathematics th:คณิตศาสตร์

Natural science

] Natural science is the study of the physical, nonhuman aspects of the Earth and the universe around us. Natural sciences generally attempt to explain the workings of the world via natural processes rather than divine processes. The term natural science is also used to identify science as a discipline following the scientific method, in contrast to natural philosophy, or in contrast with social sciences, which use the same scientific method applied to different subjects. Natural sciences form the basis for the applied sciences. Together, the natural and applied sciences are distinguished from the social sciences on the one hand, and from the humanities, theology and the arts on the other. Mathematics is not itself a natural science, but provides many tools and frameworks used within the natural sciences. Alongside this traditional usage, more recently the words "natural sciences" are sometimes used in a way more closely matching their everyday meaning, stemming from natural history. In this sense "natural sciences" can be an alternative phrase for biological sciences, involved in biological processes, or perhaps also the earth sciences, as might distinguished from the physical sciences (more directly involved in the study of physical and chemical laws underlying the universe). See :Category:Science for articles about the individual Natural sciences

Natural sciences

- Astronomy, the study of the stars, the cosmos, etc.
- Biology, the study of life.
- Ecology, the study of the interrelationships of life.
- Chemistry, the study of chemical reactions.
- Earth science, the study of earth and specialties including:
- Geology
- Science-based or Physical Geography
- Soil science
- Physics, the study of physical laws.

External links

- [http://www.cam.ac.uk/cambuniv/natscitripos/ Natural Sciences at Cambridge University]
- [http://hrst.mit.edu/ The History of Recent Science and Technology]
- [http://www.scibooks.org/ Reviews of Books About Natural Science] This site contains over 50 previously published reviews of books about natural science, plus selected essays on timely topics in natural science. Category:Science Category:Nature ko:자연과학 ja:自然科学 th:วิทยาศาสตร์ธรรมชาติ

Applied science

Applied science is the exact science of applying knowledge from one or more natural scientific fields to practical problems. It is closely related or identical to engineering. Applied science can be used to develop technology.

Reference

- [http://www.cogsci.princeton.edu/cgi-bin/webwn?stage=1&word=applied+science applied science]; WordNet entry. Category:Applied sciences ko:응용 과학 ja:応用科学 th:วิทยาศาสตร์ประยุกต์

Scientific journal

In academic publishing, a scientific journal is a periodical publication intended to further the progress of science, usually by reporting new research. Most journals are highly specialized, although some of the oldest journals such as Nature publish articles and scientific papers across a wide range of scientific fields. Scientific journals contain articles that have been peer-reviewed, in an attempt to ensure that articles meet the journal's standards of quality, and scientific validity. Although scientific journals are superficially similar to magazines, they are actually quite different. Issues of a scientific journal are rarely read casually, as one would read a magazine. The articles are written as part of the scientific method; they generally must supply enough details of an experiment, so that an independent research could potentially repeat the experiment to verify the results. Such journal articles are considered part of the permanent scientific record. The standards that a journal uses to determine publication can vary widely. Some journals, such as Nature, Science, or Physical Review, will not publish an article unless they believe that it marks a fundamental breakthrough in its field, and hence will reject papers which contain good work that does not meet this criterion. In many fields, an informal hierarchy of scientific journals exists; the most prestigious journal in a field tends to be the most selective in terms of the articles it will select for publication. It is also common for journals to have a regional focus, specializing in publishing papers from a particular geographic region. Articles tend to be highly technical, representing the latest theoretical research and experimental results in the field of science covered by the journal. They are often incomprehensible to anyone except for researchers in the field. Scientific journals are a crucial part of the scientific literature.
Types of articles
There are several types of journal articles; the exact terminology and definitions vary by field and specific journal, but often include:
- Letters (not to be confused with letters to the editor) are short descriptions of important current research findings which are usually fast-tracked for immediate publication because they are considered urgent.
- Articles are usually between five and twenty pages and are a complete descriptions of current original research finding, but there are considerable variations between scientific fields and journals: 80-page articles are not rare in mathematics or theoretical computer science.
- Supplemental articles contain a large volume of tabular data that is the result of current research and may be dozens or hundreds of pages with mostly numerical data. Some journals now only publish this data electronically on the internet.
- Review articles do not cover original research but rather synthesize the results of many different articles on a particular topic into a coherent narrative about the state of the art in that field. Examples of reviews include the 'Nature Reviews' series of journals and the 'Trends in' series, which invite experts to write on their specialisation and then have the article peer-reviewed before accepting the article for publication. Other journals, such as the Current Opinion series, are less rigorous in peer-reviewing each article and instead rely on the author to present an accurate and unbiased view.
- Research notes are short descriptions of current research findings which are considered less urgent or important than Letters The formats of journal articles vary, but almost always follow the following general scheme. They begin with an abstract, which is a two-to-four-paragraph summary of the paper. The introduction describes the background for the research including a discussion of similar research. The materials and methods section provides specific details of how the research was conducted. The results and discussion section describes the outcome and implications of the research, and the conclusion section places the research in context and describes avenues for further exploration. In addition to the above, some scientific journals such as Science will include a news section where scientific developments (often involving political issues) are described. These articles are often written by science journalists and not by scientists. In addition some journals will include an editorial section and a section for letters to the editor. Interestingly, while these are articles published within a journal, they are not generally regarded as scientific journal articles because they have not been peer-reviewed.
Issues
It has been argued that peer-reviewed paper journals are in the process of being replaced by electronic publishing. There is usually a delay of several months after an article is written before it is published in a journal and this makes journals not an ideal format for disseminating the latest research. In some fields such as astronomy, the role of the journal at disseminating the latest research has largely been replaced by preprint databases such as arXiv.org. However, scientific journals still provide an important role in quality control, archiving papers, and establishing scientific credit. In general, the electronic materials uploaded to preprint databases are still intended for eventual publication in a peer-reviewed journal. Another controversy is the cost of scientific journals. Many scientists and librarians have protested against the cost of journals, especially as they see these fees going to large for-profit publishing houses. Also the fact that copyright is assigned to the journal publisher, and not the authors, causes much discussion. There is an article titled "Online or Invisible?" (see below) which uses statistical arguments to claim that electronic publishing provides wider dissemination. A number of journals have, while retaining their peer-review process, established electronic versions or even moved entirely to electronic publication.
See also

- Academic conference
- Citation index
- Citeseer
- Open access
- Public Library of Science
Related lists

- List of scientific journals
External links

- [http://citeseer.ist.psu.edu/online-nature01/ Online Or Invisible?] by Steve Lawrence of the NEC Research Institute
- [http://www.dlib.org/dlib/december99/12harnad.html 'Free at Last: The Future of Peer-Reviewed Journals'] by Stevan Harnad

Humanities

The humanities (sometimes called Human Studies) are a group of academic subjects united by a commitment to studying aspects of the human condition and a qualitative approach that generally prevents a single paradigm from coming to define any discipline. In academia, the humanities are generally considered to be, along with the social sciences and the natural sciences, one of three major components of the liberal arts and sciences. While the precise definition of the humanities can be contentious, the following disciplines are generally recognized to form their core:
- Literature, literary criticism, and comparative literature
- Philosophy
- The Classics:
- Ancient Greek
- Latin
- The study of religion
- Law and Jurisprudence
- Art, art history, art criticism, and theory
- Music and Musicology
- Cultural and Area studies
- Regional interdisciplinary fields such as East Asian studies, American studies, and African-American studies (Interdisciplinarity) History, while also considered at times a social science, is one of the most prominent humanities in the United States as measured by foundation contributions, National Endowment for the Humanities projects, and National Humanities Centers fellowships. Some expand the definition to include other studies of human life using qualitative description and analysis, including at large parts of the following fields:
- Cultural anthropology
- Sociology
- Political science
- Archaeology
- Some branches of economics The 1980 United States Rockefeller Commission on the Humanities described the humanities in its report, The Humanities in American Life: : Through the humanities we reflect on the fundamental question: What does it mean to be human? The humanities offer clues but never a complete answer. They reveal how people have tried to make moral, spiritual, and intellectual sense of a world in which irrationality, despair, loneliness, and death are as conspicuous as birth, friendshi

Exact sciences

See also

Predictions

Measurement

Units and systems of measurement

Metrology

History

Difficulties in measurement

See also

Miscellaneous

References

External links

Experiment

An experiment in baking

Design of experiments

Controlled experiments

Natural experiments

Quasi-experiments

Examples

Quotes

See also

External links

Literature

Observation

The role of Observation in the Scientific Method

Example - The Big Bang

Observation: Hubble's redshift

Hypothesis about the abundance of the elements

Observation: the microwave background

Big Bang Hypothesis now corroborated

Current observations

Future observations

The role of Observation in Philosophy

Hobbies that involve observation

See also

Logical argument

Argument validity

The mathematical paradigm

Theories of arguments

Argumentative dialogue

Other theories

References

See also

Mathematics

History

Inspiration, pure and applied mathematics, and aesthetics

Notation, language, and rigor

Is mathematics a science?

Overview of fields of mathematics

Major themes in mathematics

Quantity

Structure

Space

Change

Foundations and methods

Discrete mathematics

Applied mathematics

Important theorems

Important conjectures

History and the world of mathematicians

Mathematics and other fields

Common misconceptions

See also

Bibliography

External links

Natural science

Natural sciences

See also

External links

Applied science

Reference

Scientific journal

Types of articles

Issues

See also

Related lists

External links

Humanities