Mathematics, nature and cryptography: Insights from philosophy of information

One influential image that is popular among scientists is the view that mathematics is the language of nature. The present article discusses another possible way to approach the relation between mathematics and nature, which is by using the idea of information and the conceptual vocabulary of cryptography. This approach allows us to understand the possibility that secrets of nature need not be written in mathematics and yet mathematics is necessary as a cryptographic key to unlock these secrets. Various advantages of such a view are described in this article.

Relook into the historical progress and philosophy of Indian space exploration

A study of the history and philosophy of the contribution of India towards the exploration of space since antiquity provides interesting insights. The contributions are described during the three periods namely: (1) the ten millenniums from 10,000 BC with a twilight period up to 900 AD; (2) the ten centuries from 900 AD to 1900 AD; and (3) the ten decades from 1900 AD to 2000 AD; called mythological, medieval, and modern respectively. Some important events during the above periods provide a reference view of the progress. The Vedas during the mythological period and the Siddhantas during the medieval periods, which are based on astronomical observations, indicate that the Indian contribution preceded other cultures. But most Western historians ignore this fact time and again in spite of many proofs provided to the contrary. This chapter also shows that Indians had the proper scientific attitude of developing any physical theory through the triplet of mind, model, and measurements. It is this same triplet that forms the basis of the present day well known Kalman filter technique. Up to about 1500 BC the Indian contribution was leading but during foreign invasion and occupation it lagged and has been improving only after independence.

A mean-reverting stochastic model for the political business cycle

In this article, we look at the political business cycle problem through the lens of uncertainty. The feedback control used by us is the famous NKPC with stochasticity and wage rigidities. We extend the New Keynesian Phillips Curve model to the continuous time stochastic set up with an Ornstein-Uhlenbeck process. We minimize relevant expected quadratic cost by solving the corresponding Hamilton-Jacobi-Bellman equation. The basic intuition of the classical model is qualitatively carried forward in our set up but uncertainty also plays an important role in determining the optimal trajectory of the voter support function. The internal variability of the system acts as a base shifter for the support function in the risk neutral case. The role of uncertainty is even more prominent in the risk averse case where all the shape parameters are directly dependent on variability. Thus, in this case variability controls both the rates of change as well as the base shift parameters. To gain more insight we have also studied the model when the coefficients are time invariant and studied numerical solutions. The close relationship between the unemployment rate and the support function for the incumbent party is highlighted. The role of uncertainty in creating sampling fluctuation in this set up, possibly towards apparently anomalous results, is also explored.