# Until modern times, intuitive, rational thought was sufficient to describe the world ; mathematics remained an adjunct, simply helping to make our intuitive descriptions more precise.

This is because a microscopist with knowledge of the subject can accurately convert a three dimensional image into a precise two dimensional drawing.

The cause which had hitherto prevented the accurate determination of the power of a given medium to refract the rays of light and separate the different colors which they contain was chiefly the circumstance that the colors of the spectrum have no precise limits, and that the transition from one to another is gradual and not immediate ; hence, the angle of refraction could not be accurately measured.

By recording and analyzing these trends over time and applying to future scenarios, the US Military can accurately supply troops with the items necessary at the precise moment they are needed.

For example, a retailer is unable to accurately predict consumer demand for any particular hour more than a few days into the future and a producer is unable to predict the precise time that they will have plant outage or shortages of fuel.

The term rumba or rock-rumba is also used generically to refer to Congolese music, though both words have their own difficulties and neither is very precise nor accurately descriptive.

As well, large areas of Rupert's Land were not accurately mapped then to know the precise boundaries.

The internal resistance of the vaporiser is usually high, but because the supply pressure is constant the vaporiser can be accurately calibrated to deliver a precise concentration of volatile anaesthetic vapour over a wide range of fresh gas flows.

The fat-graft injection technique allows the plastic surgeon precise control in accurately contouring the breast — from the chest wall to the breast-skin envelope — with subcutaneous fat grafts to the superficial planes of the breast.

More complex motor controllers may be used to accurately control the speed and torque of the connected motor ( or motors ) and may be part of closed loop control systems for precise positioning of a driven machine.

By positioning the target object at a precise part of the field, the operator can use an accurately picked narrowband filter ( albeit over a very small part of the field ).

Bargello is considered particularly challenging, as it requires very precise counting of squares for the mathematical pattern connected with the various motifs to accurately execute designs.

The stars, whose positions were accurately determined, provided a framework on the photographic plate or film for a determination of precise directions from camera station to satellite.

GPS receivers are useful for programming the telescope with its precise location and time, which allows the telescope to point more accurately.

Axons often follow very precise paths in the nervous system, and how they manage to find their way so accurately is being researched.

Humans can perform very complicated and precise movements, such as controlling the tip of a fishing rod well enough to cast the bait accurately.

Here, the focus is not on finding precise solutions to the equations defining the dynamical system ( which is often hopeless ), but rather to answer questions like " Will the system settle down to a steady state in the long term, and if so, what are the possible attractors?

Focal length and diaphragm aperture affect the depth of field of a scene — that is, how much the background, mid-ground and foreground will be rendered in " acceptable focus " ( only one exact plane of the image is in precise focus ) on the film or video target.

Iyengar Yoga is characterized by great attention to detail and precise focus on body alignment.

The precise language of the Act's prohibitions confirms Congress ' interest in the communicative impact of flag destruction, since each of the specified terms -- with the possible exception of " burns " -- unmistakably connotes disrespectful treatment of the flag and suggests a focus on those acts likely to damage the flag's symbolic value.

The focus is on doing one precise and perfect movement, rather than many halfhearted ones.

These lenses make precise and repeatable focus pulls difficult, and use of a follow focus impractical.

For example, if an actor moves from 8 m away from the focal plane to 3 m away from the focal plane within a shot, the focus puller will change the distance setting on the lens during the take in precise correspondence to the changing position of the actor.

In some situations, such as on long lenses, wide apertures, very close distances, or any combination of the three, a subject moving even a few millimeters may require immediate and very precise focus correction.

Whip cracking competitions focus on the completion of complex multiple cracking routines and precise target work ; although other whips are also used in such competitions.

Some like dispensational premillennialism tend more toward an apocalyptic vision, while others like postmillennialism and amillennialism, while teaching that the end of the world could come at any moment, tend to focus on the present life and contend that one should not attempt to predict when the end should come, though there have been exceptions such as postmillennialist Jonathan Edwards, who attempted to calculate the precise timing of the end times.

Here, the focus is not on finding precise solutions to the equations defining the dynamical system ( which is often hopeless ), but rather to answer questions like " Will the system settle down to a steady state in the long term, and if so, what are the possible steady states?

The precise usages of focus in natural language are still uncertain.

Most early mirror devices attempted to confine plasma near the focus of a non-planar magnetic field, or to be more precise, two such mirrors located close to each other and oriented at right angles.

If you are good at estimating distances, or have a tape measure at hand, you can get precise, sharp focus with one of these cameras.

In order to distinguish esoteric currents based primarily on sources from late Antiquity and the European Middle Ages, from e. g. Islamic or Jewish currents with similar features, the more precise term " Western esotericism " is often employed.

Whatever the precise nature of Hecate's transition into folklore in late Antiquity, she is now firmly established as a figure in Neopaganism, which draws heavily on folkloric traditions associating Hecate with ' The Wild Hunt ', witches, hedges and ' hedge-riding ', and other themes that parallel, but are not explicitly attested in, Classical sources.

According to Margaret Bent ( 1997 ), " a piece of music in several parts with words " is as precise a definition of the motet as will serve from the 13th to the late 16th century and beyond.

It is best known in the form of late Romantic ballet or Ballet Blanc, which preoccupies itself with the female dancer to the exclusion of almost all else, focusing on pointe work, flowing, precise acrobatic movements, and often presenting the dancers in the conventional short white French tutu.

The precise division of Francia into a Neustrian, Austrasian, and Burgundian kingdom dates only from the late sixth century, so earlier kings who ruled from Soissons or Paris are here excluded.

While there is general disagreement about precise origin of the wave, most stories of the phenomenon's origin, suggest that the wave first started appearing at North American sporting events during the late 1970s and early 1980s.

Knowing these will enable the observer to be more precise when determining the cardinal directions from the sun's position, particularly in the early morning or late afternoon.

Though, as in the late 16th and 17th centuries, the 20th-century Royal Family were more or less supportive, British officialdom was far less so with English Heritage, who controlled the site of the real Globe nearby, refusing to allow the archaeology Wanamaker requested in order to ascertain its precise dimensions.

The precise circumstances of this transfer or encroachment have been lost to history, but the English authorities, themselves preparing to claim overlordship in Ulster and the rest of Ireland, still recognized the Bissetts as the lords of the Glynns as late as 1515.

Instead of calling it a " parody mass ", the term " Imitation mass " has been suggested as being both more precise and closer to the original usage, since the term " parody " is based on a misreading of a late 16th century text.

One of the most precise types of wet-dry bulb psychrometer was invented in the late 19th century by Adolph Richard Aßmann ( 1845 – 1918 ); in English-language references the device is usually spelled " Assmann psychrometer.

After no recordings under his name between late 1931 and late 1934, Russell recorded a session for ARC ( Melotone, Perfect, Oriole, Banner, Romeo ) in 1934 which yielded 6 very precise modern recordings ( three featured Sonny Woods ' novelty vocals, one featured the great, although obscure vocal group The Palmer Brothers.

The Anthropocene has no precise start date, but based on atmospheric evidence may be considered to start with the Industrial Revolution ( late eighteenth century ).

As the collector market for coins grew rapidly in the late 19th century and early 20th century, it became apparent that a more precise grading standard was needed.

His orders were sent out sometime between late June 1940, when planning for Operation Barbarossa first started, and May 1941 ; the surviving historical record does not permit firm conclusions to be drawn about the precise date.

As late as the early 20th century, manufacturing often involved filing parts to precise shape and size.

Trevor-Roper countered this criticism by arguing that Hitler expressed an intention to go to war sooner rather than later, and it was Hitler's intentions in foreign policy in late 1937 as opposed to his precise plans at this moment in history that really mattered.

Whatever the precise dates of Ramanuja's lifetime, it seems clear that all three of the great ācāryas lived under the relatively stable and ecumenical climate of the Chola empire, before its decline in the late 12th and 13th centuries.

The precise time of composition of the saga also remains unknown, but the late 13th century seems most likely.

In the late 1940s and early 1950s, she continued to paint precise figurative renderings of dream-like situations, working in New York City, Sedona, and Paris.

In an article entitled " Neither Denial nor Forgetfulness Will Free Us " first published in the Frankfurter Rundschau on December 1, 1986, Mommsen argued that Historikerstreit was a result of the failures of modern society Mommsen argued that in the prosperous 1950s-60s, most Germans were happy to forget about their recent past, and looked forward to a brighter future Starting with the oil shock of the early 1970s and the rise of fundamentalist Islam in the late 1970s, Mommsen argued that the idea of a progressively better future was discredited, leading to a pessimistic public mood, and the a renewed interest in history This had occurred in tandem in a period when German historians had started to make a more critical examination of their recent past As a result at the precise mood when public demanded a past that could make them feel good about being Germans, German historians came under attack for not writing the sort of history the public wanted Mommsen argued that the work of those like Ernst Nolte was intended to provide the sort of history that would allow Germans feel good about being Germans by engaging in “… an explanatory strategy that … will be seen as a justification of National Socialist crimes by all those who are still under the influence of the extreme anti-Soviet propaganda of National Socialism " Mommsen charged that Ernst Nolte was attempting to egregiously whitewash the German past.

The equinox can be as early as March 19 or as late as March 21, the precise time being about 5 hours 49 minutes later in a common year, and about 18 hours 11 minutes earlier in a leap year, than in the previous year.

They are thought to come from a range of dates covering the late 14th and the 15th centuries, and the decoration and precise shape of the body is different in each surviving example.