We generalize two of our previous results on abelian definable groups in p-adically closed fields [12, 13] to the non-abelian case. First, we show that if G is a definable group that is not definably compact, then G has a one-dimensional definable subgroup which is not definably compact. This is a p-adic analogue of the Peterzil–Steinhorn theorem for o-minimal theories [16]. Second, we show that if G is a group definable over the standard model $\mathbb {Q}_p$, then $G^0 = G^{00}$. (...) As an application, definably amenable groups over $\mathbb {Q}_p$ are open subgroups of algebraic groups, up to finite factors. We also prove that $G^0 = G^{00}$ when G is a definable subgroup of a linear algebraic group, over any model. (shrink)

Historically, deserts have served to distinguish the essential from the superfluous. Therefore, a desert experience has been an excellent lens with which to focus on what really matters and to learn what may be impossible to learn in more stable environments. The desert experience of the ancient Hebrews, as they journeyed from Egypt, land of slavery, to Canaan, land of promise, embodied a number of timeless spiritual truths in the context of an environmental framework where priorities became crystal clear. Three (...) elements of this framework will be presented here as we examine the Jewish people, liberated in a land "that was not sown." First, the desert environment revealed the reality of God. While the portrait of God painted on the sandy canvas of the Sinai Peninsula was incomplete, it served well to reacquaint this wayward people with their Lord. Second, the way in which the Israelites were sustained pictures a specific attribute of God, that of provider. He actively met the needs of His chosen people as a loving father meets the needs of his children. God provided everything from food and water for physical survival to discipline and guidance for healthy spiritual and emotional growth. Finally, their desert experience illustrated that disobeying God caused environmental disaster. The desert they crossed sustained life when the Israelites trusted God but failed to do so when they disobeyed Him. Through the physical experience of wandering in the wilderness, the Hebrews learned a spiritual lesson of faith and saw how their corporate faith affected the quality of the natural environment for the entire nation. This timeless lesson, if applied today would result in significant environmental improvement worldwide. Moreover, brethren, I would not that ye should be ignorant, how that all our fathers were under the cloud, and all passed through the sea; And were all baptized unto Moses in the cloud and in the sea; And did all eat the same spiritual meat; And did all drink the same spiritual drink: for they drank of that spiritual Rock that followed them: and that Rock was Christ. But with many of them God was not well pleased: for they were overthrown in the wilderness. Now all these things happened unto them for ensamples: and they are written for our admonition, upon whom the ends of the world are come. Wherefore let him that thinketh he standeth take heed lest he fall. There hath no temptation taken you but such as is common to man: but God is faithful, who will not suffer you to be tempted above that ye are able; but will with the temptation also make a way to escape, that ye may be able to bear it. I Corinthians 10:1-5,11-13. (shrink)

This article's thesis is that religion and science are ultimately about the same thing, that they affect one another, and that people in the two fields therefore need to communicate. The authors begin by discussing the importance of ethical transformations to a life of love and character, arguing that the development of a technological society does not free us from ethical demands. They then move to advocating dialogue about the shared truths of science and religion. Wanting both, and positing that (...) the former is a foundation for the latter, the authors state that Einstein's famous logian cannot be ignored: "The situation may be expressed by an image: Science without religion is lame, religion without science is blind". (shrink)

It may come as a surprise to some, but the Bible has a great deal to say about the environment and its conservation some 20 centuries since it was written. Perhaps among the most surprised will be Bible-toting church goers who may have never heard a sermon related to the "environmental crisis" which has become such a concern to so many around the world. This lack of attention by Christians is especially perplexing since many of our environmental problems are rooted (...) in the Christian faith, according to some scholars. However, by examining the doctrine of Christianity, the basic text of the faith, the Bible, we find an entirely different message. The purpose of this discussion is to present the entire portion of Scripture which relates to environmental principles whereby we may develop a Bible-based, 21st Century prescription of environmental conservation. Some 2,463 verses have been topically organized into nine sections. Four appendices present the full-text of this collection in addition to selected hymns, which have been instrumental in teaching the truths of Scripture over the years. This compilation of verses constitutes approximately eight percent of the Bible. The Authorized Version, also known as the King James Version, was used in the preparation of this collection due its widespread distribution and influence since 1611. Based on the Bible, Christianity’s positive contribution to environmental conservation is consistent with its positive contributions to other fields such as literature, art, music, education, health, and science. (shrink)