(" the truth-values of our mathematical assertions depend on facts involving platonic entities that reside in a realm outside of space-time ") Whilst our knowledge of concrete, physical objects is based on our ability to perceive them, and therefore to causally interact with them, there is no parallel account of how mathematicians come to have knowledge of abstract objects.

Whilst the magnification of both the field ion and atom probe microscopes is extremely high, the exact magnification is dependant upon conditions specific to the examined specimen, so unlike for conventional electron microscopes, there is often little direct control on magnification, and furthermore, obtained images may have strongly variable magnifications due to fluctuations in the shape of the electric field at the surface.

Whilst there, the Greek army surprised and outmaneuvered Artaphernes, marching to Sardis and burning the lower city.

Whilst there, the Queen met with Bernard of Clairvaux, demanding that he have the excommunication of Petronilla and Raoul lifted through his influence on the Pope, in exchange for which King Louis would make concessions in Champagne, and recognise Pierre de la Chatre as archbishop of Bourges.

Whilst human geography is interdisciplinary, there are a number of journals with a human geography focus.

Whilst there, he staged regular Merz recitals, including a performance of Silence, his first poem in English, but was apparently seen as a somewhat pathetic irrelevant figure by other artists at the camp.

Whilst prices have reduced and availability has increased considerably since the introduction of competition, there is little sign of TPSA's market share being seriously reduced.

Whilst Anglican priests who are members of religious orders must remain celibate ( although there are exceptions, such as priests in the Anglican Order of Cistercians ), the secular clergy – ( bishops, priests, and deacons who are not members of religious orders ) – are permitted to marry before or after ordination.

Whilst on the surface the new Potsdamer Platz appears so far to have lived up to its expectations as a futuristic centre of commerce at the heart of Europe's youngest capital city, there has been much debate as to just how successful it really is.

Whilst the action of rowing and equipment used remains fairly consistent throughout the world, there are many different types of competition.

Whilst there is little evidence to invalidate the letter as a whole, both the recipient ( s ) of the letter and whether such a letter actually nominates Barbastro as the first ' crusade ' are still a matter of dispute.

Bahā ' ad-Dīn writes, " Whilst we were there they brought two Franks to the Sultan ( Saladin ) who had been made prisoners by the advance guard.

Whilst the terms spirituality and religion both relate to a search for an Absolute or God, and thus have much overlap, there are also characteristic differences in their usage.

Also in S6: E5 Whilst the boys are watching the TV there are many cans of soda with the name " ZOOP " on them.

Whilst the styles were similar, there are some notable differences between both Rococo and Baroque architecture, one of them being symmetry, since Rococo emphasised the asymmetry of forms, whilst Baroque was the opposite.

(" the truth-values of our mathematical assertions depend on facts involving platonic entities that reside in a realm outside of space-time ") Whilst our knowledge of concrete, physical objects is based on our ability to perceive them, and therefore to causally interact with them, there is no parallel account of how mathematicians come to have knowledge of abstract objects.

Whilst there his task is a simple assignment to investigate the disappearance of Commander John Strangways, the head of MI6 Station J in Kingston, Jamaica, and his secretary.

Whilst anchored in Cumberland Bay, Robinson Crusoe Island, the Dresden was trapped and forced to scuttle after fighting a battle there with the British.

Whilst there, he met the American composers George Gershwin and Irving Berlin and brought Dédé to Broadway in 1922.

Whilst this elm has little innate resistance to Dutch elm disease, it is not favoured by the vector bark beetles and thus only becomes colonized and infected when there are no other choices, a rare situation in western Europe.

Whilst there, Telemachus is again treated as an honored guest as Menelaus and Helen tell complementary, yet contradictory stories of his father's exploits at Troy.

Whilst working at the Institute, Childe took up residence at Lawn Road Flats near to Hampstead, an apartment block perhaps recommended to him by the popular crime fiction author Agatha Christie ( the wife of his colleague Max Mallowan ), who had lived there during the Second World War.

Whilst there is no specific form of words provided for such proclamations, they must be made ' in the Queen's name '.

Whilst the idea that there is some objective sense in which time is flowing can be denied, the fact that conscious beings feel as though it is in some sense flowing cannot.

" Whilst there, Lumley was hailed ' Daughter of Nepal ' by the crowds of fans at the airport.

Whilst this had the advantage of being usable by untrained users via ' hunt and peck ' typing and requiring one less key switch than a conventional 12 button keypad, it had the disadvantage that some symbols required three times as much force to depress them as others which made it hard to achieve any speed with the device.

Whilst his early work was rooted in traditional late-19th century romantic Italian opera, he successfully developed his work in the ' realistic ' verismo style, of which he became one of the leading exponents.

Whilst greed is a recurring theme in the novel, with many of the episodes stemming from one or more of the characters ' simple desire for food ( be it trolls eating dwarves or dwarves eating Wood-elf fare ) or a desire for beautiful objects, such as gold and jewels, it is only by the Arkenstone's influence upon Thorin that greed, and its attendant vices " coveting " and " malignancy ", come fully to the fore in the story and provide the moral crux of the tale.

Whilst hierarchy is quickly established between individuals from a single group, this is not the case with organisms from different groups ; these are substantially more aggressive and very rarely climb one another or form aggregates.

Whilst Spangberg headed east to Okhotsk, Bering waited in Yakutsk, preparing two ships on the Lena ( one would be captained by Vasili Pronchishchev and the other first by Peter Lassenius and later by Dmitry Laptev ).

Whilst recovering from the fever, Rivers had formed a friendship with one of his father's speech therapy students, a young Army surgeon.

Whilst at one level conservative — harking back in foreign policy to the period of Phillip II, invoking traditional values at home — Philip's policies were also radical, rejecting the policy towards the rebellious Dutch that had held since 1609, entering into the Thirty Years ' War, and introducing a system of junta, or small committee, government across Spain in competition to the traditional system of royal councils.

Whilst historians such as Yitzhak Baer state, " the conversos and Jews were one people ", Kamen claims, " Yet if the conversos were hated by the Christians, the Jews liked them no better.

Whilst St Ann's Allotments in Nottingham, created in the 1830s, is regarded as one of the oldest allotments sites in England, as well as the largest site of Victorian gardens in the world, the accolade is actually reserved by Great Somerford Free Gardens in the Wiltshire village of Great Somerford.

Whilst not performing any kind of Mass per se, the Church of Scotland has a Watchnight ( similar to the one on Hogmanay ) service beginning just before midnight, wherein carols are sung.

Whilst undertaking the preliminary drawings for the book, Trog tried to make the fudge recipe included in the book and found it was not particularly good: the editors at Jonathan Cape spent a day making up batches from different recipes to find a better one to use.

Whilst Lady Windermere leaves the room to find one, the story is revealed: Mrs Erlynne left her husband for a lover shortly after Lady Windermere's birth.

Whilst in lay up at Clarence dry docks, she was offered for sale, with one prospective buyer hoping to use her to operate cruises around the Isle of Man.

Whilst not non-stop, as one must change trains at East Croydon in order to touch in or out of the Oyster card system, the frequency of trains between East Croydon and Gatwick Airport is such that changeover times are minimal ( as little as one minute ).

Whilst once two distinct villages, the Bookhams have long been interconnected with residential roads that give most newcomers the impression that it is in fact one large village.

Whilst the public image of science education may be one of simply learning facts by rote, science education in recent history also generally concentrates on the teaching of science concepts and addressing misconceptions that learners may hold regarding science concepts or other content.

Whilst one of these ( einsteinium ) is now available in macroscopic quantities, most are extremely rare, having only been prepared in microgram amounts or less.

Whilst one side favoured shock action and had faith in the effectiveness of the sword and lance, the opposite contended that the cavalry ’ s future lay in serving as mounted infantry.

Whilst Director, in 1950, he established the outdoor centre at Whitehall, near Buxton, one of the first of its kind in the UK.

" Whilst the character spent less time with his old friends, Denisof was " more or less isolated from the cast, barring one or two scenes of mild confrontation when they would come to visit me and we'd chew each other out.

Whilst the Theatre has a resident show, it is still able to have one off shows ; this is enabled by the scenery of the resident show being designed to be easily removed.

Whilst investigating possible sources for the word " Hobbit " Tolkien realised he had made a mistake in using hob -, which is traditionally used to mean a smaller entity, not a larger one.