#error term

[isomorphismes]

Learn more about viruses than 99% of the population in under 20 hours

Fun coursera on virology.

Viruses are so numerous (10³⁰) and filling up everywhere. It gives this Boltzmann flavour of 'enough stuff" to really do statistics on.

Viruses are just a bundle of {proteins, lipids, nucleic acids} with a shell. It's totally value-free, no social Darwinism or "survival of the fittest" being imbued with a moral colour. Just a thing that happened that can replicate.

Maybe this is just because I was reading about nuclear spaces (⊂ topological vector space) and white-noise processes that I think of this. Viruses have a qualitatively different error structure than Gaussian. Instead of white-noise it's about if they can get past certain barriers, like:

survive out in the air/water/cyanide

bind to a DNA

spread across a population

adapt to the host's defences

... it seems like a mathematician or probabilist could use the viral world of errors to set out different assumptions for a mathematical object that would capture the broad features of this world that's full of really tiny things but very different to gas particles.

Did I mention that I love how viral evolution is totally value-neutral and logic-based?

Did I mention how I love that these things are everywhere all the time, filling up the great microspace my knowledge had left empty between man > animals > plants > ... > bacteria > ... > minerals?

[tymkrs]

What is a servo + clarifying examples

So in the IRC yesterday, I mentioned that Whisker and I were thinking of eventually motorizing our screen and I suggested servos.  You know, cuz I think of servos as these mechanical things that spin around and around:

But apparently servos aren't just rotating "things", they are actual systems.  Per @JohnS_AZ, a servo is a system and it may or may not include an electric motor.  There are also hydraulic servos, pneumatic servos, electrical servos, and completely mechanical servos. 

Some examples from John:

Home thermostat = servo

Gas kitchen stove = not a servo

Kitchen oven = servo

Cruise control = servo

Autopilot in airplane = servo

I expressed some doubt at a kitchen oven being a servo because you know, ovens don't have rotating parts in them.  And I was corrected:

A servo is a system that adjusts some action, position, speed, or process based on a "error term" which it gets by measuring some parameter.

A kitchen oven has a temperature sensor, and a temperature set point.  The error term is (set point) - (actual).  If the term is greater than 0, turn on the heat.  The stove has no measurement, no feedback (as it's just a valve).

Example 1. Blood Pressure Cuff

So an automatic blood pressure cuff would be a servo.  It senses when the blood flow has stopped after inflating, pumps maybe 10% more, then starts to deflate.  They also have an upper limit so that the inflation doesn't pop the arm cuff if no arm is in it.  While deflating, it stops venting when a pulse is detected.  Systolic is read, then valve is reopened until pulse disappears whereupon the diastolic number is read.

Example 2. Motorized Projector Screen

Whisker and I were also discussing motorizing our projector screen and I wondered if the motors would be considered a servo system if we set it up so that if I clicked a button, it came down, and when it sensed something, it stopped.  And if the button was clicked again, the screen would go up, sense something, and stop. 

John said that in that example, it wouldn't be a servo, it'd just be a screen controlled by limit switches. 

But if there were a sensor that detected how far up or down it was, and you gave it a specific position to go to, and it went there - THEN it would be a servo.

Example 3. Parallax Servo

In the servo picture I show of a Parallax servo above, John says that inside the box is an electric motor which rotates the arm that sticks out the top.  There is ALSO a small potentiometer that measures exactly where the arm is so when you hook it up, it can give that information to the MCU.

When you send a PWM signal to it, that signal represents where you want the arm to point.  So a little circuit inside the servo compares your PWM signal to the measurement from the internal pot, and ends up with an error term.  It then drives the motor one direction or the other to make the internal pot match your PWM signal.

Example 4. Computer Fan

So I wanted to know whether or not the temperature system on a computer fan was a servo.  Essentially, if the sensor is used to turn the fan on and off, then yes, it is a servo. 

This is where I realized that servos don't have to be mechanical.  They can be electrical and John mentioned that there are high end audiophile audio amps that are servo systems.

So a servo has nothing to do with the motor.  It's a system where something is automatically controlled by measuring some form of feedback.

Huh. This changes what I think about servos completely! And for more discussion, join us on our forums: http://www.tymkrs.com/forum/viewtopic.php?id=148

@atdiy/@tymkrs

[isomorphismes]

Leonardo da Vinci's ability to embrace uncertainty, ambiguity, and paradox was a critical characteristic of his genius. --J Michael Gelb

Say you want to use a mathematical metaphor, but you don't want to be really precise. Here are some ways to do that:

Tack a +ε onto the end of an equation.

Use bounds ("I expect to make less than a trillion dollars over my lifetime and more than $0.")

Speak about a general class without specifying which member of the class you're talking about. (The members all share some property like, being feminists, without necessarily having other properties like, being women or being angry.)

Use fuzzy logic (the ∈ membership relation gets a percent attached to it: "I 30%-belong-to the class of feminists | vegetarians | successful people.").

Use a specific probability distribution like Gaussian, Cauchy, Weibull.

Use a tempered distribution a.k.a. a Schwartz function.

Tempered distributions are my current favourite way of thinking mathematically imprecisely, thanks to this book: Theory of Distributions, a non-technical introduction.

Tempered distributions have exact upper and lower bounds but an inexact mean and variance. T.D.'s also shoot down very fast (like exp −x², the gaussian) which makes them tractable.

For example I can talk about the temperature in the room (there is not just one temperature since there are several moles of air molecules in the room), the position of a quantum particle, my fuzzy inclusion in the set of vegetarians, my confidence level in a business forecast, ..... with a definite, imprecise meaning.

Classroom mathematics usually involves precise formulas but the level of generality achieved by 20th century mathematicians allows us to talk about a cobordism between two things without knowing precisely everything about them.

It's funny, the more "advanced" and general the mathematics, the more casual it can become. Even post calc 1, I can speak about "a concave function" without saying whether it's log, sqrt, or some non-famous power series.

Our knowledge of the world is not only piecemeal, but also vague and imprecise. To link mathematics to our conceptions of the real world, therefore, requires imprecision.

I want the option of thinking about my life, commerce, the natural world, art, social networks, and ideas using manifolds, metrics, groups, functors, topological connections, lattices, orthogonality, linear spans, categories, geometry, and any other metaphor, if I wish.