First Blog

One issue in teaching about big numbers is for students to understand just how big numbers can get.  But here we include not just students, but us all.  With modern computers and storage devices, we have become accustomed to some big numbers, notably megabytes, gigabytes, and even terabytes. In this brief article, we examine just how big numbers can get from innocent sounding problems.  This is combined with new ideas about fantasy problems and flying carpet solutions .   Fantasy problems are those arising in our minds from an array of possible disconnects with reality, and flying carpet solutions are those offered with disregard of possibility.  Some sound good; but fantasy may be the best descriptor. One particular example is given about tracking of all people, not dissimilar from information you may have about how your various devices can currently track you.  It is a good teaching exercise of how numbers can get huge, and completely unmanageable.  The tools are only simple fac

Here are my latest ruminations on this and that, what is and what is not. When creating a model that mimics a phenomenon perfectly, one is tempted to interpret the model as a full explanation of it.  This is errant causality.  It is the profound weakness of modeling. It is a never good idea to invite administrative jobs in the parlor door. They promise more than they deliver. They ask more than they give. It should be no other way.  The converse, to give more than they ask, renders as undesirable the newly appointed administrator. In the pursuit of truth, someone is always threatened. We are more likely to accept what we want to believe, or what fits within our precepts, or supports our goals - all regardless of the facts of the matter. Rejection of what we wish to be so is difficult. We live in a big data world but we still have small data brains. This is not to imply the brain has a small capacity, but it thinks in small data settings. It uses tools such as instinct, intuit

What was and still is Dateline, 1850 and Now...   We have arrived at the point where professionals have a large amount of knowledge about particularly narrowing topics. The narrowing has constricted now for a couple of centuries.   As in the past, investigators become saturated.   For ancient geometers, this occurred a couple of  centuries BCE. They can know little more, and little more was contributed.   Until...   a new idea emerges, it becomes the hammer to resolve all questions. Older outmoded techniques are diminished, deprecated, and eventually forgotten. This is the model of scientific investigations and other objective disciplines.   When the new is judged as more powerful and more predictive, the old is discarded. All this is according to Thomas Kuhn.   Advance of knowledge is not linear, it is not even monotone. What are new ideas and from where do they come?   A number of forms seem obvious. Technique Innovation Enhanced precision Increased dimension Disc