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The Chinese government bureaucracy under the Tang (618-906 CE) and Song (960-1279 CE) dynasties had several similarities and differences in terms of organization, functions, and methods of recruitment. Both dynasties adopted the imperial examination system, established a hierarchical bureaucracy, and utilized local administration. However, there were significant differences in terms of the scope of government functions, the extent of Confucianism influence, and changes in the examination system.
Similarities:

1. Imperial examination system: Both Tang and Song dynasties used an examination system to recruit civil service officials. The system was rooted in Confucian ideas and aimed to create a bureaucracy based on meritocracy.

2. Hierarchy: The bureaucracies of both dynasties were organized into hierarchical structures with the emperor at the top, followed by central government ministries and departments, and with provincial and local administration at the lower levels.

3. Local administration: Both Tang and Song governments believed in strong local administration. During both periods, local governments administered regions and were responsible for tax collection, public order maintenance, and the implementation of central government policies.

Differences:

1. Scope of government functions: The Tang bureaucracy had a broader scope of functions that extended to many facets of society, including agriculture, military, economy, and transportation. The Song government mainly focused on administration, education, and the civil examination system, with a lesser emphasis on direct control over various facets of society.

2. Influence of Confucianism: The Song dynasty, especially under Emperor Taizu, placed a stronger emphasis on Confucian values and principles in its bureaucracy compared to the Tang dynasty, which incorporated more Legalist and cosmopolitan ideas. The Song government institutionalized Neo-Confucianism and expanded Confucian education, influencing the attitudes and practices of the bureaucracy.

3. Changes in the examination system: The Song dynasty made significant changes to the imperial examination system. The Tang dynasty's system had multiple levels of exams, which gradually evolved into local, provincial, and metropolitan examinations during the Song dynasty. The Song government introduced multiple examination routes, which allowed candidates with different levels of education to have access to the imperial examinations. Moreover, the Song period witnessed a greater emphasis on the writings of Confucian classics for testing intellectual knowledge and the development of the "eight-legged essay."

4. Increasing bureaucratization: While both dynasties had elaborate bureaucracies, the Song government was more bureaucratic than the Tang government. The Song civil service system had a larger number of officials, and the bureaucracy was more centralized, with greater emphasis on record-keeping and organization.

In conclusion, the bureaucracies of the Tang and Song dynasties both followed Confucian principles, utilized the imperial examination system, and emphasized local administration. However, the Song dynasty not only expanded the influence of Confucianism in its bureaucracy but also made changes to the examination system and enhanced bureaucratization, thus strengthening and transforming the Chinese government system in the process.

The Chinese government bureaucracies under the Tang and Song dynasties had similarities in their use of the imperial examination system, hierarchical organization, and emphasis on local administration. However, they differed in the scope of government functions, the influence of Confucianism, changes in the examination system, and level of bureaucratization. The Song dynasty, in particular, placed a stronger emphasis on Confucian values, made significant changes to the examination system, and had a more bureaucratic government compared to the Tang dynasty.