Archive for the 'math' Category

Taking something back, or sharing?

March 19, 2014

There’s this spiritual story about an adolescent who really feels strongly that a grown man has stolen from her her jewels.  He feels equally convinced she has robbed him of something equally valuable, namely, something required to maintain his stature and status in the community.

So how to restore equilibrium?

There’s an attempt, which doesn’t succeed, in which he returns something and she returns something, but they both accuse the other of returning a false approximation of what was stolen.

There are attempts at partial returns, there are empty promises, there are claims nothing was stolen — lots of adversarial attempts to restore without actually completely participating.

In the meantime, they are each using some “ill-gotten gain” from the other to try to maintain themselves.  They each end up in situations in which they are ill-equipped in some way, and this does not serve the greater good, either.

A lot of the trouble reconciling was probably a trust issue — “If I give to you, will you really give to me or will it just be throwing good money after bad, as they say?”

So here’s how it got resolved:  they both were agreeable with sharing with a disinterested third party, and through something like the mathematical transitive principle or something like a concept of mixing cooking ingredients, eventually they both ended up with a portion of what they felt they were missing.  What they shared with the intermediary included the “stolen good,” and through sharing with the intermediary, they had access again to what they considered the good stolen by the other.

Footnote:  disinterested third party did not have an easy time of it, as they were often treated as if they were actually the other person in the dispute.

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Cost basis methods

November 7, 2013

I was trying to understand the current rules for assessing gain or loss on the sale of part of an account’s holdings in a particular mutual fund.  And while I won’t go into the nitty-gritty, I thought it was worth remarking that people who think they know what the rules are, offer assessments which conflict with one another’s.  I’m talking about people who work for brokerage firms and people who write explanations online on reputable websites, purporting to explain the rules.  They can’t all be right simultaneously.

Some seemed not to distinguish between what is the IRS’s default method and what is a particular firm’s internal choice of default method.  Or so it seemed to me.  When must a selection or a change in selection of method be made in writing by an investor?  How does a method used for one sale affect the choice of methods for future sales from the same fund in the same account?  How does it impact the valuation of remaining shares?  The sources I looked at varied on these issues or confused them, and it wasn’t just because the rules changed for shares bought after a certain date.

My sense is that we develop systems that are too complicated for many of the people who are involved with their use and implementation to understand adequately.  Plenty of small-fry people own shares of mutual funds, people who may not use accountants or financial managers or tax advisers.  The complexity of the rules may give them more choices and ways to reduce their taxes, but confuse them.  If the people who work in the field professionally have trouble explaining how the rules play out in practice, then, I think all the more that something is amiss.

Statistical likelihood

March 23, 2013

I did some errands on foot this afternoon.  One was at a store at which I paid $24.41.  I paid in cash and with exact change (I had a lot of singles and loose change I wanted to use up).

I continued home, through a park.  I sat for a bit in the park on a bench and then went up the steps on its other side to the street.  I turned up the hill without crossing the street first, because there was a snowbank in the way, and that’s when I saw some coins on the sidewalk.  $.41, exactly.  What is the statistical likelihood of that happening, I wondered.  Willy would have been able to give me an approximation.

(Both times it was a quarter, a dime, a nickel, and a penny.)

Make friends with your subconscious

November 18, 2012

I should be outside pruning rose bushes, but I just wanted to write something brief using a different type of approach to, not so much the subjects of my previous two posts, but to a comment I wrote in response to one of those NYTimes sort of philosophical pieces in “The Stone” subset of their Opinionator section.

My point is about how there are multiple strands to our “selves.”  Most of us using the internet dwell (and overly so, in my opinion) in only some of these strands and may not be aware there are others.

So that’s why I called this post “Make friends with your subconscious.”  People not adverse to theism or spiritual development tend to do this through prayer and meditation, but I think other people may do it through the arts (especially music), sports, nature, communicating with pets.  I think some people may do through higher math, but I think it’s trickier to lose the intellectualizing self enough through doing that as a way to be in the strand of the self that slides around without the constraints the intellectualizing strand has.  Of course, some people do this (whether intentionally or not) in ways that cause them and others distress, and it can become extreme enough that we label it an illness (as in, mental illness) — I certainly don’t advocate doing that.

But just as we talk about parents spending quality time with their children, I think we need to spend quality time with our subconscious.

Piercing the veil

October 2, 2012

I just wrote something as a comment to a column on the mathematical puzzle of matching birthdays that I’m not sure I got right, so I thought I’d try to improve on it here.

I suspect I set up a false dichotomy between what mathematicians do and what mystics do — I suspect they probably both use their subconscious.  Maybe they just take that leap in different ways or at different points in the mental process.

To backtrack:  What I said in my comment took off from the end of the piece.  The piece explained why the number of people in a sample is what it is for having enough people to make it more likely than not that two of them will have the same birthday (I hope I got that right — please read the column itself to be sure.)  At the end it mentioned the fact that Adams and Jefferson both died on July 4, 1826 and commented, “Math can’t explain everything.”  (Steven Strogatz, “It’s My Birthday, Too, Yeah,” NYTimes, Oct. 1, 2012)  I wrote about the wisdom to know when to use a mathematical approach and when to look for other sorts of patterns.  I was trying to say that using the subconscious — access to which I identified with engaging in this other sort of pattern recognition — gets you to deeper understandings of the universe faster.

But higher math and pattern recognition (that mystics use, for example) probably both use the subconscious —  I’m just wondering now whether it’s more accurate to say that math requires a longer runway for the launch than do mystical ways of thinking (which would kind of be like the helicopter in my metaphor).

After all, they’re probably both just different languages human beings have developed through which to communicate on our little sphere of Babel we call earth.

Similes and metaphors

February 2, 2012

I sometimes wonder whether we have taken too literally what was meant as an analogy in our monotheism: the idea of loving God as if he were a parent.  I think God, the universe, forces we can’t see, need our positive regard as much as we want theirs.  I don’t think God is grudging and I do think our attitude towards God matters.  So, I’m inclined to believe that the notion of God that portrays him as a parent could be a development out of an attempt to get people to love God with more effective focus.  As I see it, a problem arises, in terms of making spiritual progress, if we get stuck in the analogy and can’t move on to faith in and a relationship with a more impersonal “God.”  Just as we need to get our own egos out of the way, we need to stop insisting that God have one, too, at a certain point in our spiritual development.  In this regard, I think physicists and mathematicians have a leg up, with their ease with abstract thinking.  I suspect that relating to the universe involves both an earthy component of loving from the heart (as we would a parent, spouse, or child) and a more diffuse component of perceiving without our usual limits of material consensus reality (a sort of abstract mental process).  To me, combining the two in one person, integrating the two components in ourselves, is the great mystery.

 

Einstein, math, and Gilson brothers

January 4, 2012

Well, this is fun.  Having posted a few weeks ago a picture of me in Einstein’s lap, or at his knee, or whatever, that sat on Willy’s windowsill in his office at Lincoln Lab, and then, more recently having posted about how my brother-in-law and I were in the same number theory class years before his brother and I met and married, I received today from Michael for my birthday the book Einstein: His Life and Universe, by Walter Isaacson.  And it’s not as if Michael and his family usually give me science biographies for my birthday — last year I got some beautiful bookends, other years tea paraphernalia or soaps or note cards.

Renconciling with science

December 21, 2011

I think a lot about how to resolve what many people experience as a divide between viewing the world through science and viewing it through a spiritual lens.  I’ve had people in my life terrified I would succumb to the family pressure to become a scientist, and others who campaigned to dissuade me from the liberal arts, or at least from my teachers there who clearly wanted my participation in their magisterium, if not their lives.

So, it amused me to remember this picture, which Willy kept in his office:

I was visiting my sister, who was working in Washington, D.C. at the time, and my cousin Gail was visiting at the same time, as I recall.  I’m pretty sure Gail took the picture.  I’m not entirely sure what the picture meant to Willy, who hadn’t come with me on that trip.  I think he seemed to get a kick out of it as something I had done when I had gone off “on a frolic and a detour” without him.

The way I would like to interpret the picture is as illustrating part of the on-going “ping-pong match,” or mirroring back and forth, between spiritual partners:  I am reading someone else’s understanding of the universe, in their own, scientific language, and I will sing back that understanding as accurately as possible in my own language.  How I have been able to understand what I am “reading” in that language I suspect has something to do with Willy as some sort of interpreter, whose understanding I could absorb through some other means; he certainly had the physics and math for the scientific understanding, and I suspect, in retrospect, he had other kinds of understandings in other languages, as well.