Rebirth of Reason

Post to this threadMark all messages in this thread as readMark all messages in this thread as unread

Post 0

Thursday, June 25, 2015 - 5:24amSanction this postReply

Thank you for another informative and challenging essay.  Like you, I write to see where an idea goes.  As with fiction, sometimes these things just write themselves.  Once you start with a premise, the characters (ideas) seem to have a life of their own. 


Your thesis is that achievements are not singular, isolated events.  I agree that the biographies of great people often demonstrate lifelong commitment to their chosen work.  On the other hand, we have interesting people such as Pancho Barnes who never stuck with anything very long, and who left a long arc of singular, isolated events.  I think that Sir Isaac Newton was like that, also.  He continued to apply his fantastic intellect to new problems much different from the motion of bodies.  But I agree that for many great people, it is as Pasteur said: fortune favors the prepared mind.  And he had a lifetime of successes within a single (albeit broad) field.


Also like you, I continue to play at high school mathematics.  I recently read The Man Who Loved Only Numbers by Paul Hoffman, a biography of Paul Erdős. (Danika McKellar and Natalee Portman have "Erdős numbers" for co-authoring articles with mathematicians who co-authored articles...  Reviewed on my blog here.)  With credit to Paul Hoffman who got other mathematicians to explain much to him, the fact remains that many of these esoteric theorems in number theory can be explained to a child just using integers and simple fractions.  (Your example from Euler was like that, also.)  Two aspects of that are troubling.


First, in your closing paragraphs, you seem to implicitly accept the notion that fun and hard work are different from each other.  I know that consicously you believe just the opposite. (You are an Objectivist, of course.) My point is only that this is deeply engrained in our culture, and we have a hard time getting past it.  I judge science fairs and engage in similar social activities, and teachers and parents are always wringing their hands over "how to make science fun" and "how to make mathematics fun."  You can not make it fun.  It is or it is not.  No one tries to make baseball fun, and baseball is hard work. Speaking to a computer user group about technical writing, I cited The Fountainhead. Near the end, when Keating and Roark are dealing with Courtland, Roark understands Keating's best intentions, and Roark says that in order to do things for other people you have to be the kind of man who can get things done, but to get things done, you have to love the doing.  


The other is the impact on K-12 education, especially K-6.  Long before Common Core, those of us interested in individualism knew about "The Tyranny of Testing."  Standardized tests may have a position in the game, but we have given them center court.  When teachers follow "standard" curricula designed by others, no room is left for creative exploration.  Again,  number theory offers truly an infinite set of possible discoveries that a child can understand.  But they are not allowed to take the time to see where a problem goes.  That applies not just in mathematics and science, but in any study: history, music, the full range of human endeavors.  But in school, you have to stop painting before the bell rings.  You do not get the time to take it further...

Sanction: 6, No Sanction: 0
Sanction: 6, No Sanction: 0
Post 1

Thursday, June 25, 2015 - 2:39pmSanction this postReply

My understanding of human nature is that our mode of thinking follows a pattern where we imagine something that is different from what we have known or understood before, however minor this new thing might be.  This is as a response to some kind of mental stimuli - maybe something connected to a desire or to a goal, or something experienced as a problem or negative emotion.  We create imaginary alternatives in our mind.  Then we mentally compare the alternatives, perhaps choose one, and begin to act on it.  The actual process involves some variables including the choice to think about it or not, the choice to exercise reason versus being swayed between alternatives by emotional responses and the intensity of thought we might apply*.


The example of this that I usually give is of a person is commuting to work in their car - say a 30 minute trip - and they reach a place where traffic almost always slows down.  Perhaps this is few blocks before an intersection of two majors streets.  This slowdown feels a bit irritating - just sitting in traffic.  That can be seen as the seed of the stimuli.  The mind converts it to a question like, "There must be a better way to get to work."   Now the mind is open to looking to alternatives to this route they have been taking for months.  One alternative that pops up is to make a right turn a few blocks before the intersection, travel for a number of blocks, then take a left turn and possibly bypass the slowdown area.  The mind can reason critically on that alternative: "It will be longer, but maybe it will take less time?"  There may be yet other possible routes created in the imagination and then examined as well.  If any of the alternatives pass the critical examination, the one that seems the best may be tried.  This is the most obvious point at which choice is seen.  And the choice can lead to action.


Another path the mind can follow when it begins to look at alternatives is to shift the context, or the level of fundamentality, or the purpose.  For example, the thoughts might go to taking a bus and reading on the way to work, or it might go to listening to a book on a cd or tape so that time would be spent enjoyably even when moving slower.


The next part of what I want to say is something I got from Ray Kurzweil in his book "The Singularity is Near" - he was talking about how technology expands exponentially, not linearly.  One of the reasons he pointed out for this was that each new technical invention creates new 'points' of possible improvement for future technical growth.  E.g., at the beginning of man's use of imagining alternatives, reasoning on them, and choosing, we can envision how a stick became a club and evolved into a thinner stick with a rock lashed to the end.  We can imagine another early man seeing a stick used as a club and imagining it becoming a spear.  And each new item of invention has a new set of 'points' to focus on for new developments.  Spears becoming arrows, etc. These 'points' are and have always increased exponentially.


Now back to Joe's fine article.  Joe mentions a scientist who sees a pattern that can be followed across a number of instances (conservation of matter in a chemical element as it changes state) and the result of applying that pattern in different places turns out to be very productive.  Joe sees a lesson in this about following up on ones ideas and thoughts.


As I read that I began to see it as an application of the basic process I mentioned above (stimuli, focus on a 'point', imagine alternatives, reasoning about the alternatives, etc.)  Now if we hold in mind this process, and then add to it the insight of Kurzweil on the exponential growth of 'points' of possible improvements on objects of technology, we can see that knowledge itself can be viewed an object (or collection of objects) that are rich in 'points'.  The more knowledge we have the more points (in an individual of course, but also as the level of knowledge available in our historical place as a society) - and from that we see that exponential growth of knowledge is possible**.  But the important take-away is in the study-appoaches that lead to a person expanding their knowledge. 


What Joe talks about are techniques or practices that greatly empower this process of taking what we know and then finding new ideas and to do this in ways that our expansion of knowledge grows, and then grows again. 

  • Follow up on ideas (work them, chew on them).
  • Be open to where they take you (getting critical later and not prematurely).
  • Write about the idea - this is a process that seems to feed that part of the mind that is actively seeking alternatives to examine.
  • When writing, examine down to deeper levels - to the details - that might float to the surface tricky cases and they are good for finding better understanding of the principles that divide or make up the essence of what is being looked at.
  • Look for the meta level of the idea under consideration and from there you might become aware of patterns that apply beyond your current idea.
  • Actively asking questions of how something works, and what are the more fundamental ideas that are the 'genetic' antecedents to the idea can create an understanding of how something works, i.e., the principles at work (and then you 'own' that idea in much more substantial way).



For me, this reply has been an example of practicing what Joe preached - writing about how I see a connection between what he wrote, what Kurzweil wrote, and my theory of a core element of human nature.  Writing (and thinking about it) brought out what comes of joining these thoughts.  It took me deeper in my understaning of some specific areas in which it would pay us to study the way we study - procedures we might employ to tease out a concept's metadata or its dimensions (e.g., context, purpose, foundational concepts, sister concepts) and other ways to do as Joe suggested: Follow up on ideas.



* Note: Choice is actually exercised as a precondition to nearly every mental operation, if only to decide to continue, or stop, to think more deeply, or less so, to follow a rising emotion, or to set that aside, to open the mind to new things more, or to focus more tightly towards an specific purpose.  


(One useful way to look at choices is to put them in categories such as:  

  1. Those that are just part of the inner and lowest level of mental processses as such - kind of 'do more of this, or do less of this',

  2. Those that are significant to which outcome a mental operation will have - like the choice to blank out or not,

  3. Those choices that change a belief or establish an idea or belief as ours, and finally,

  4. Those choices that are the shift from mental operations to physical actions in the outside world).



**I used the word 'possible' because with a material object evolving in technology its test, its functionality, its continued use is a more powerful force in the retaining or discarding of an new object.  It works or it doesn't.  But with ideas it is less about it 'works' and more about the understanding of its truth - and through that door walks different theories of truth - some of which are very backwards. The 'points' still get expanded on, and multiply, but some of the new ideas are objectively not 'working' while some are.  Real knowledge is connected to reality, pseudo-knowledge can lead to a dark age.


Post 2

Monday, June 29, 2015 - 4:33pmSanction this postReply

Interesting points, Steve, very reflective.  Thanks.

Post to this thread

User ID Password or create a free account.