Monday, May 18, 2015

Sacred math, secular math

Started thinking about 'home ec' versus 'ec'. The name 'home ec' was an attempt by the humble Useful Trades to slide upward into colleges where the arrogant and imperial Useless Arts dominated. Industrial training for the farmer and the grocer and the housewife tried to wear the velvet cloaks of Holy Theory. It didn't hold up. The high priests of Sacred Uselessness eventually kicked out the Secular Useful Trades. Ideally the Secular Useful Trades shouldn't have humbly begged. Ideally they should have tortured and shot the Sacred Useless Arts and displayed their bloody heads on spikes.

This line of thought led to some questions.

= = = = =

**Question #1: Is there a basic difference between Secular and Sacred math?**

**Answer: Yes.**

High-theory math, cutting-edge math, is high-church math.*It always serves a religion.* A thousand years ago, high-church math served the needs of prayer and liturgy. Catholics developed astronomy and time-keeping to a high level to insure that Easter and other holy days were observed at exactly the right time. Muslims worked on geometry and trig to insure that prayers were pointing exactly at Mecca.

As the center of religion shifted, the center of scholarly math shifted as well, leading to a sudden reversal around 1800. Newton worked to serve a private mystical version of Christianity, and Laplace explicitly switched the focus to anti-theism, where it's been ever since.

Modern math scholars are always strongly religious in the modern sense. Their work specifically serves the evangelical advance of ferocious sadistic Dawkins/Darwin Gaia worship and murderous anti-theism. They are Dawkins jihadis.

Some pieces of scholarly math have escaped into non-priestly use, but they never make it all the way "down" into the secular masses. Calculus and algebra remain in the diaconate of engineers.

= = = = =

Secular math has not "advanced" into "new territory" because it doesn't feel the need. Secular math serves the merchant, the farmer, the carpenter, the cook, the housewife. Secular math includes the four basic functions and*proportions* and angles. (Not really trig as such; usually a written or internalized 'lookup table' for sin and cos.)

Our secular calculating devices, from written numerals to abacuses to computers, have always added and subtracted easily. Mult and div are tricky, and proportions simply don't work on these devices. We've developed other devices for proportions, often direct analog computers based on lever arms or gears. The slide rule is the ultimate proportioner, but it requires considerable skill and it doesn't SHOW the proportions nearly as well as an analog mechanism.

What's missing here? (If you've been reading this blog regularly, you know exactly what I'm going to say next.)

TANH! Everything we do in the real secular world, including everything our own bodies do with measurements, is loggish. Sometimes the result is Tanh, sometimes a two-ended Tanh with constraints at both ends. I call it a tuning curve because it's what you get from a bandpass filter.

The basic formula would be like

**y = tanh(x) * tanh(c-x)** where c defines the width of the hump.

Fussy but important: This shape looks like the bell curve or normal distribution, but the math for the bell doesn't conform to reality as well as the two-sided tanh. Real situations are more like a mesa than a peak, more like a mole than a zit. There's always a flat spot in the middle; sometimes the flat spot covers nearly all of the available range and sometimes the flat spot is zeroed out to provide a peak. The bell math always gives you a peak point.

Polistra tries to show the difference. First the bell curve:

Now the tuning curve:

I'm NOT saying that the bell should be replaced by tanh. I'm only showing the distinction dynamically because the tuning curve is unfamiliar. Bell works nicely for stat distributions; one-sided tanh works for most input-output situations (transfer functions) in life, and two-sided tanh it forms the life-patterns of critters and organizations.

The math for the tuning curve is complicated. Computers can handle it, but there should be a nicer way of calculating such a basic and necessary shape. Secular math ought to find a cleaner way of doing it and writing it, whether by an analog calculator or by a single button on a digital calculator.

Another piece of everyday secular math that is NOT handled by sacred math is 'bracketizing', a calculation that uses integers and continua in separate ways, boundaried by decisions, thresholds or containers. I discussed it in the grocery context here and here. Bracketizing also appears in tax forms. When Alleged Einstein called income tax the hardest math problem, he was speaking from a Sacred Math mindset. Calculations like this cannot be turned into a closed-form Sacred equation no matter how hard you try. If line 37 is greater than 3.2 times line 12a, multiply by 0.376; otherwise add 12 and divide by 5.021. A computer program can handle those mixes of decisions and operations, but ideally there should be a way to handle them in 'pure' Secular math.

= = = = =

**Question #2:** If everything in our life and senses runs logly, why did so much of secular math develop as pure linear addition and subtraction?

**Answer: Because one important sense is NOT loggish.**

Our senses of pressure and weight are linear. When I put one item, two items, three items, in your hand, the weight-measuring inputs to your brain are linear and even*countable.* A fast series of pulses from your muscle spindles.

What does that remind you of? Money. One shell, two shells, three shells. One coin, two coins, three coins. Money began as weight, and many monetary units still denote weights.

Because we weighed gold and silver, we became accustomed to treating money, and then transactions involving money, in linear form ... EVEN THOUGH the transactions and our judgments and feelings about the transactions are loggish.

Our sense of relative income is unquestionably log or percentage-based. Even economists have figured this out. As with decibels or lumens, our judgments are the log of the underlying quantity. "My neighbor is one step above me in income" = neighbor has 3 * my income. "If I could jump one step up in wealth I'd be satisfied" = If I had 3 * current wealth I'd be satisfied.

Actual prices of actual goods are also loggish. This is somewhat disguised by the piecewise linearity of a small part of any curve, but when you scale up you can see it. Two cans of soup = same price as one can + one can. Twenty cans of soup cost less than 20 * one can. A thousand cans cost MUCH less than 1000 * one can.

Because overhead is relatively constant, price is a loggish function of quantity.

= = = = =

**Question #3:** How would commerce and everyday life differ if we had a more loglike system of secular math?

**Unanswered for now.** As usual, I'm hoping to return to this. As usual, I probably won't.

Later partial answer or starting point.

= = = = =

**Bonus:**

I've supplied an attempted 'easy proportioner' or 'software slide rule' as mentioned above.

The proportioner is here. The ZIP contains a (hopefully) self-explanatory Python program. It has an Input side, a Ratio, and an Output side. When you fill in either the numerator or denominator on the Input side, the Ratio shows and the Output side changes appropriately. When you fill in numerator or denominator on the Output side, the Ratio doesn't change, but the other member on the Output side changes.

I've been wanting this little helper for a long time, especially to deal with Aspect Ratio in images. You may find other uses.

Started thinking about 'home ec' versus 'ec'. The name 'home ec' was an attempt by the humble Useful Trades to slide upward into colleges where the arrogant and imperial Useless Arts dominated. Industrial training for the farmer and the grocer and the housewife tried to wear the velvet cloaks of Holy Theory. It didn't hold up. The high priests of Sacred Uselessness eventually kicked out the Secular Useful Trades. Ideally the Secular Useful Trades shouldn't have humbly begged. Ideally they should have tortured and shot the Sacred Useless Arts and displayed their bloody heads on spikes.

This line of thought led to some questions.

= = = = =

High-theory math, cutting-edge math, is high-church math.

As the center of religion shifted, the center of scholarly math shifted as well, leading to a sudden reversal around 1800. Newton worked to serve a private mystical version of Christianity, and Laplace explicitly switched the focus to anti-theism, where it's been ever since.

Modern math scholars are always strongly religious in the modern sense. Their work specifically serves the evangelical advance of ferocious sadistic Dawkins/Darwin Gaia worship and murderous anti-theism. They are Dawkins jihadis.

Some pieces of scholarly math have escaped into non-priestly use, but they never make it all the way "down" into the secular masses. Calculus and algebra remain in the diaconate of engineers.

= = = = =

Secular math has not "advanced" into "new territory" because it doesn't feel the need. Secular math serves the merchant, the farmer, the carpenter, the cook, the housewife. Secular math includes the four basic functions and

Our secular calculating devices, from written numerals to abacuses to computers, have always added and subtracted easily. Mult and div are tricky, and proportions simply don't work on these devices. We've developed other devices for proportions, often direct analog computers based on lever arms or gears. The slide rule is the ultimate proportioner, but it requires considerable skill and it doesn't SHOW the proportions nearly as well as an analog mechanism.

What's missing here? (If you've been reading this blog regularly, you know exactly what I'm going to say next.)

TANH! Everything we do in the real secular world, including everything our own bodies do with measurements, is loggish. Sometimes the result is Tanh, sometimes a two-ended Tanh with constraints at both ends. I call it a tuning curve because it's what you get from a bandpass filter.

The basic formula would be like

Fussy but important: This shape looks like the bell curve or normal distribution, but the math for the bell doesn't conform to reality as well as the two-sided tanh. Real situations are more like a mesa than a peak, more like a mole than a zit. There's always a flat spot in the middle; sometimes the flat spot covers nearly all of the available range and sometimes the flat spot is zeroed out to provide a peak. The bell math always gives you a peak point.

Polistra tries to show the difference. First the bell curve:

Now the tuning curve:

I'm NOT saying that the bell should be replaced by tanh. I'm only showing the distinction dynamically because the tuning curve is unfamiliar. Bell works nicely for stat distributions; one-sided tanh works for most input-output situations (transfer functions) in life, and two-sided tanh it forms the life-patterns of critters and organizations.

The math for the tuning curve is complicated. Computers can handle it, but there should be a nicer way of calculating such a basic and necessary shape. Secular math ought to find a cleaner way of doing it and writing it, whether by an analog calculator or by a single button on a digital calculator.

Another piece of everyday secular math that is NOT handled by sacred math is 'bracketizing', a calculation that uses integers and continua in separate ways, boundaried by decisions, thresholds or containers. I discussed it in the grocery context here and here. Bracketizing also appears in tax forms. When Alleged Einstein called income tax the hardest math problem, he was speaking from a Sacred Math mindset. Calculations like this cannot be turned into a closed-form Sacred equation no matter how hard you try. If line 37 is greater than 3.2 times line 12a, multiply by 0.376; otherwise add 12 and divide by 5.021. A computer program can handle those mixes of decisions and operations, but ideally there should be a way to handle them in 'pure' Secular math.

= = = = =

Our senses of pressure and weight are linear. When I put one item, two items, three items, in your hand, the weight-measuring inputs to your brain are linear and even

What does that remind you of? Money. One shell, two shells, three shells. One coin, two coins, three coins. Money began as weight, and many monetary units still denote weights.

Because we weighed gold and silver, we became accustomed to treating money, and then transactions involving money, in linear form ... EVEN THOUGH the transactions and our judgments and feelings about the transactions are loggish.

Our sense of relative income is unquestionably log or percentage-based. Even economists have figured this out. As with decibels or lumens, our judgments are the log of the underlying quantity. "My neighbor is one step above me in income" = neighbor has 3 * my income. "If I could jump one step up in wealth I'd be satisfied" = If I had 3 * current wealth I'd be satisfied.

Actual prices of actual goods are also loggish. This is somewhat disguised by the piecewise linearity of a small part of any curve, but when you scale up you can see it. Two cans of soup = same price as one can + one can. Twenty cans of soup cost less than 20 * one can. A thousand cans cost MUCH less than 1000 * one can.

Because overhead is relatively constant, price is a loggish function of quantity.

= = = = =

Later partial answer or starting point.

= = = = =

I've supplied an attempted 'easy proportioner' or 'software slide rule' as mentioned above.

The proportioner is here. The ZIP contains a (hopefully) self-explanatory Python program. It has an Input side, a Ratio, and an Output side. When you fill in either the numerator or denominator on the Input side, the Ratio shows and the Output side changes appropriately. When you fill in numerator or denominator on the Output side, the Ratio doesn't change, but the other member on the Output side changes.

I've been wanting this little helper for a long time, especially to deal with Aspect Ratio in images. You may find other uses.

Labels: 20th century Dark Age, Experiential education, Real World Math

Free stuff at ShareCG

And some leftovers here.

ARCHIVES

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 /
April 2017 /
May 2017 /
June 2017 /
July 2017 /
August 2017 /
September 2017 /
October 2017 /
November 2017 /
December 2017 /
January 2018 /
February 2018 /
March 2018 /
April 2018 /
May 2018 /
June 2018 /
July 2018 /
August 2018 /
September 2018 /
October 2018 /
November 2018 /
December 2018 /
January 2019 /
February 2019 /
March 2019 /
April 2019 /
May 2019 /
June 2019 /
July 2019 /
August 2019 /
September 2019 /
October 2019 /
November 2019 /
December 2019 /
January 2020 /
February 2020 /
March 2020 /
April 2020 /
Carbon Cult

Carver

Constants and variables

Defensible spaces

Experiential education

From rights to duties

Grand Blueprint

Language updates

Metrology

Morsenet of Things

Natural law = Sharia law

Natural law = Soviet law

Shared Lie

Skill-estate

Switchover