- Facts are generally produced by measurement or observation. These are things such as the sky being blue in the daytime in North America, or that it is easier to crush a clay pot than an iron one. Generally speaking, the facts themselves are considered pretty objective, in that everyone can see the outcome when a test is performed or a measurement is conducted. The caveat is that facts are usually interpreted within a specific framework. We will return to this later.
- Laws are statements that describe a phenomenon or event that occurs every time a measurement or observation is made. Generally speaking, if you hold some object at shoulder height and then open your hand and let it go, it will fall towards the ground. Laws don’t describe why the object falls toward the ground - just that it happens, over and over again. The more carefully we study dropping objects, the more detailed the law can be - we may even be able to describe how quickly it will fall, how much time it will take to reach the ground, and whether or not it will speed up as it falls. These details still don’t answer the question of why. Laws are called such because they can be reliably reproduced under a given set of circumstances. Now, if those circumstances change, eventually we can set up a situation in which these laws break down.
- A hypothesis is an untested idea or hunch about something that has been observed. Many times, these ideas arise from studying laws and making predictions about what would happen under various changes in the circumstances. A good hypothesis will be testable and falsifiable - that is, you can set up some type of experiment or search that will test the hypothesis, and they hypothesis is set up in such a way that it can be proven wrong. Often, hypotheses begin to try to answer some of the why questions surrounding laws and facts. Successful hypotheses (confirmed by experiment) can help bolster confidence that your understanding of some of the why questions is on the right track, because you were able to successfully predict what should happen in a specific case. It doesn’t necessarily prove, however, that every part of it is correct.
- A theory is a framework in which you try to make a consistent, coherent interpretation of facts and laws. It can include or inform hypotheses, but theories are not the same as hypotheses. Theory will make predictions that can be turned into hypotheses based on previous observations, facts, and laws. If tests of those hypotheses turn out to be successful, the theory gains credibility. Well-established theories have been tested over and over again, ideally by making predictions that have been shown to be correct. This does not mean that the theory is completely true, or that it will never need to be modified as new information comes to light. It can, however, show that the theory is a good framework from which a basic understanding of the underlying laws can be gained, and that it makes sense to consider the theory a reasonable interpretation of the facts.
- An interpretation of facts, in the way that I use it here, is the set of things that we assume the facts tell us, based on the coherent picture or framework or theory that we use to explain the facts. In other words, once we have collected the facts and built a reasonable theory about why they should be so, we begin to look at new facts through the lens of what they would mean in our theory.
Saturday, February 13, 2016
Shall we begin? Facts, theories, and laws (1)
Sunday, January 10, 2016
Computing Sidebar: TeX stuff
I recently upgraded my setup to Mac OS 10.11, which broke a few things, one of which was my TeX installation. TeXshop is an open source distribution avaialble for Mac OS X that is installed with TeX Live when you download MacTex from the home page of the TeX Users Group (www.tug.org). TeX is frequently used (including by me) for publications and dissertations (yay!)
Reinstalling MacTeX is relatively painless and well described by the instructions on the MacTeX download page (http://www.tug.org/mactex/mactex-download.html), so I will not repeat them here. However, I did find that upon attempting to run the Tex Live Utility, I was unable to use the utility to update packages, and repeatedly encoutering the error “Listing Failed” under the update section
My problem was that the utility was unable to access the server for the repository that it was attempting to use for the software updates. After searching blogs on some slightly different bugs and problems (e.g. http://mirror.ctan.org/systems/texlive/tlnet), I finally resolved the issue by switching to a new repository. The steps:
- Select the menu “Configure" —> “Manage repositories”
- Choose another repository by double-clicking or whatever you do for your computer to follow a link selection
Finally, after the repository change and upgrading the utility, I am able to use the utility to update my TeX packages by selecting “Update All Packages” from the “Actions” menu (updating selected packages is also possible).
This fix was performed for Tex Live Utility v1.23 on Mac OSX 10.11.2 (El Capitan).
Voila! Happy TeXing!