Navigating the complex terrain of rail freight companies can be as challenging as plotting the route for an intercontinental delivery. The exercise involves understanding the who's and what's of the freight industry, the where and when of logistics, and the how and why of efficient shipping practices. The entire endeavor is an intricate melange of history, law, economics, mathematics, statistics, science, and social sciences.

Embarking on this journey, it's important to understand that rail freight companies function as key cogs in the global supply chain machine, transporting large volumes of goods over long distances. Freight trains are known for their efficiency and are often less expensive than their air and road counterparts, making them a preferred choice for businesses looking to tightly manage their operational costs. Yet, choosing the right rail freight company for your shipping needs requires more than just a cursory glance at cost efficiency.

Delving deeper, remember that transport law plays a crucial role in shaping the industry. It is a specialized field which, in addition to national and regional laws, incorporates various international treaties and conventions developed to streamline cross-border transactions. Thus, a prospective rail freight company should be proficient in navigating this legal labyrinth, ensuring timely and hassle-free shipments.

Your query to the freight company should also encompass the economic aspects of the shipment. Key economic theories like the economies of scale and scope are pertinent here. For instance, rail freight companies can handle large volumes of goods, providing economies of scale that can be translated into cost savings. Conversely, the economies of scope translate into the company's ability to provide diverse services such as warehousing, customs clearance, and door-to-door delivery, thereby offering a holistic logistics solution. Clearly, these economic aspects should figure prominently in your scrutinization of potential freight companies.

The mathematical and statistical aspects of freight shipping might seem more abstract, but they too have a significant role to play. The freight rates, for example, are determined by complex algorithms that factor in numerous variables like cargo type, distance, urgency, and other market conditions. Furthermore, the company's reliance on statistical models for risk management, predicting delivery times, and improving operational efficiency are vital indicators of its competence and reliability.

The freight industry, like any other, is influenced by advances in science and technology. The advent of digital platforms and advanced tracking systems has revolutionized the industry, enabling real-time tracking and improved coordination. Therefore, your inquiry should probe the company's technological savvy and its ability to leverage the latest innovations for efficient deliveries.

Social sciences too have appended their mark on the freight industry. With an increasing emphasis on sustainability and carbon footprint reduction, rail freight companies are being pushed to adopt greener operations. They are also expected to adhere to fair trade practices and uphold the rights of their employees. A company that aligns with these principles not only contributes to sustainable development but also shields you from potential reputation risks.

In conclusion, asking the right questions to a rail freight company is a multifaceted exercise that calls for a comprehensive understanding of various disciplines. As you embark on this quest, remember that your objective is not merely to find a company that transports goods but to identify a partner that complements your business ethos and supports your operational needs. Armed with these insights, you are now ready to probe, evaluate, and select the right rail freight company for your shipping needs.