Wednesday, November 27, 2013
  Want it gift-wrapped?

Noticed an interesting article on an unfathomable and completely pointless dispute among mathies. The 'foundational' types seem to be puzzled about the distinction between countable infinities and the continuum. This leads to some kind of irreconcilable thingamajig which must be resolved by either of two mutually exclusive and perfectly unfathomable thingamajigs.

The article mentions an alternate approach, first formulated by Aristotle, that makes sense. Just ignore infinity and continuity. Operate as if everything is countable. We don't actually handle infinity as an object or a number; real math works with limits and never tries to resolve the limits. We simply think of 'really really big numbers' and leave it there. Aristotle usually gets things right, while Plato usually leads to genocide.

Much as I hate to differ with Aristotle, I'm going to try. I'd say the simpler solution is the other way around. Set theory is useless. It's not the foundation of anything, though you can pretend it's a foundation. Counting is not the basis and springboard of useful math; counting is just a trick that intelligent animals have mastered.

Why did we animals need to count, and what were we counting before we improved the technique? We were counting Nature's wrapped-up packages. Fruits, trees, flowers, cows, wolves, our own eggs or larvae or babies. In short, present organisms or future organisms.

MUCH later we expanded counting to non-organism things like rocks or houses, and even later (within written history) to abstractions like hours of labor or acres of land. Some tribes still haven't made the first step of abstraction, still have distinct counting methods for living and non-living.

Counting is thus an important product of life and an important tool of life, but not crucial to survival. Counting is life recognizing life. Counting helps us to keep our own eggs or babies safe from predators, helps us to locate the best field to find nectar or the best field to plant alfalfa.

But counting doesn't get us anywhere close to the underlying substance for all living and non-living things. The substance is energy and waves, not particles.

These packages we see, whether fruits or bees or rocks, are made of waves gathered in even smaller packages that we call atoms. We can do useful stuff like chemistry and cooking by counting these packages, but even there we aren't really counting. We're using balances and ratios to measure quantities by mass or volume.

Life uses waves from the sun and gradients of gravitational or magnetic or static force to drive its infinitely complex processes. We have many built-in methods of measuring these waves and gradients: ears, eyes, electrostatic senses, gravity senses. From those we have created a wide variety of differential comparator tools for making refined external measurements, but these measurements are NOT counting. We can paste a list of numbers onto a stick to give us a speakable and writable record of a measurement, but we were able to handle these comparisons quite nicely before we pasted the numbers. Fold the rope in half, fold it again in thirds, ....

Well, what about this activity that I'm doing at the moment... or rather SHOULD be doing instead of maundering about numbers? I should be developing courseware using DIGITAL computers. Aha! Gotcha! DIGITAL means counting! And why SHOULD I be doing this? Because I have the probably false belief that my bankrupt publisher will send me money in return for my labor. Aha! Gotcha! MONEY means units and coins!

Really? The programming, which claims to be about basic countable numbers, is deeply about ratios, with some arbitrary packages involved in the measurement of ratios. I'm doing a lot of trig to manipulate lines and shapes on screen. Pure ratios. I'm using loops to determine when a file has been fully read. Ratios again, with an arbitrary linguistic marker (newline) as the list pasted on the stick. I'm figuring grades as percentages. Pure ratio, turned into linguistic markers for portability. And how does the computer turn ratios into linguistic markers? Balanced ratios of electrostatic charge in CMOS chips, arbitrarily grouped into 1's and 0's for portability.

And what about the MONEY that I may receive if JPMorgan doesn't decide to keep it all because JPMorgan's purpose on earth is to own everything? Coins are countable, aren't they? Yes, but they weren't countable to begin with. Coins arose as a measurable and balance-able weight of gold, serving as a portable carrier of labor. They went through a long phase as strictly countable arbitrary markers, but in the last few decades they've been reverting back into their natural continuity, into balanced ratios of electrostatic charge in CMOS chips, grouped into 1's and 0's for portability.

No matter where you look, you find that COUNTING is a wonderfully convenient trick, invented by life to help us remember and transfer ratios and gradients of energy, but the basic stuff, the universal stuff, is always ratios and gradients of energy. It's all continuum.

= = = = =

Sidenote: There's a parallel to randomness/entropy. In this case the Platonist mathies insist that Number was the primary ingredient of the universe; Number existed before humans came along and decided to use it. Nope, backwards. Number is strictly a product of life. In the randomness case, Platonic physicists insist that the distinction of order vs disorder is a natural part of the universe, existing before humans came along to use it. Nope, backwards. Order is strictly a product of life.

Labels: ,


<< Home

blogger hit counter
My Photo
Location: Spokane

Polistra was named after the original townsite of Manhattan (the one in Kansas). When I was growing up in Manhattan, I spent a lot of time exploring by foot, bike, and car. I discovered the ruins of an old mill along Wildcat Creek, and decided (inaccurately) that it was the remains of the original site of Polistra. Accurate or not, I've always liked the name, with its echoes of Poland (an under-appreciated friend of freedom) and stars. ==== The title icon is explained here. ==== Switchover: This 2007 entry marks a sharp change in worldview from neocon to pure populist. ===== The long illustrated story of Polistra's Dream is a time-travel fable, attempting to answer the dangerous revision of New Deal history propagated by Amity Shlaes. The Dream has 8 episodes, linked in a chain from the first. This entry explains the Shlaes connection.

My graphics products:

Free stuff at ShareCG

And some leftovers here.

March 2005 / April 2005 / May 2005 / June 2005 / July 2005 / August 2005 / September 2005 / October 2005 / November 2005 / December 2005 / January 2006 / February 2006 / March 2006 / April 2006 / May 2006 / June 2006 / July 2006 / August 2006 / September 2006 / October 2006 / November 2006 / December 2006 / January 2007 / February 2007 / March 2007 / April 2007 / May 2007 / June 2007 / July 2007 / August 2007 / September 2007 / October 2007 / November 2007 / December 2007 / January 2008 / February 2008 / March 2008 / April 2008 / May 2008 / June 2008 / July 2008 / August 2008 / September 2008 / October 2008 / November 2008 / December 2008 / January 2009 / February 2009 / March 2009 / April 2009 / May 2009 / June 2009 / July 2009 / August 2009 / September 2009 / October 2009 / November 2009 / December 2009 / January 2010 / February 2010 / March 2010 / April 2010 / May 2010 / June 2010 / July 2010 / August 2010 / September 2010 / October 2010 / November 2010 / December 2010 / January 2011 / February 2011 / March 2011 / April 2011 / May 2011 / June 2011 / July 2011 / August 2011 / September 2011 / October 2011 / November 2011 / December 2011 / January 2012 / February 2012 / March 2012 / April 2012 / May 2012 / June 2012 / July 2012 / August 2012 / September 2012 / October 2012 / November 2012 / December 2012 / January 2013 / February 2013 / March 2013 / April 2013 / May 2013 / June 2013 / July 2013 / August 2013 / September 2013 / October 2013 / November 2013 / December 2013 / January 2014 / February 2014 / March 2014 / April 2014 / May 2014 / June 2014 / July 2014 / August 2014 / September 2014 / October 2014 / November 2014 / December 2014 / January 2015 / February 2015 / March 2015 / April 2015 / May 2015 / June 2015 / July 2015 / August 2015 / September 2015 / October 2015 / November 2015 / December 2015 / January 2016 / February 2016 / March 2016 / April 2016 / May 2016 / June 2016 / July 2016 / August 2016 / September 2016 / October 2016 / November 2016 / December 2016 / January 2017 / February 2017 / March 2017 /

Major tags or subjects:

Carbon Cult
Defensible spaces
Experiential education
Grand Blueprint
Гром победы
Language updates
Natural law = Sharia law
New toys

Powered by Blogger