Thinking About Probability #2

I left off my previous post with Hume’s problem of induction and a way forward coming from Uwe Saint-Mont.

For this post, I was originally planning to do a deep dive on the structure of logic and epistemic uncertainty to help frame future discussions. Fortunately Sean McLure has already done a better job than I could ever do in a recent series on his podcast, NonTrivial.

I highly recommend the listen as a primer for logical analysis to help understand where logic can be useful and where risk management becomes a better proxy, particularly in complex situations.

He spends a lot of time talking about inductive logic and Popperian falsification, which I think will become foundational as this probability series progresses.

Here is the link to the first part of the Facts and Logic Series on NonTrivial: https://overcast.fm/+ctunQ1iqg

Here is a link to Sean’s comprehensive list of logical fallacies: https://www.notes2tree.com/published_tree/?publish_tree=h7aGQYBbDd

Next post I’ll get back to probability starting with the Uwe Saint-Mont paper.

Thinking About Probability #1

This is my first attempt at adding some of the Notability maths into the blog – we’ll see how it goes.

As I mentioned in my previous post I am starting to chronicle my re-learnings in probability and statistics starting with the textbook “Probability, Random Variables and Stochastic Processes” by Papoulis and Pillai. The writing is pretty engaging for a math book and I’m hope to make it at least a chapter before getting distracted. Joe Norman incorporated parts of the book in his Applied Complexity Science course I took recently and I grabbed it off Amazon where I was pleasantly surprised to find a positive review from Taleb.

On to the learning. It’s late here so I’ll start from the beginning and maybe get through some thoughts on a few ideas/equations.

We start with an intro to probability and I think one of the key takeaways is that probability is dealing specifically with mass phenomena. How many events? Well, it depends. More on this later I suppose.

A physical interpretation of probability is provided by the following equation (Notability works great btw):

Where P means probability, A stands for an event, n(A) is the number of times the event occurred and n is the number of experiments run.

In a classic example of flipping a coin, if you flip the coin 10 times and you get heads 4 times out of the 10, then your probability P(A) of getting head (funny undergrad story on this I might tell later) is 4/10 or 0.4.

Easy enough… but is it?

This equation is an approximation of the probability and has a couple key assumptions baked in (assumptions to me are like kernels or rules of an automaton, perhaps more on this later). The first assumption is that the relative frequency of the occurrence of A is close to P(A) provided that n is sufficiently large. Obvious question: how large is large enough? The second assumption is that provided you have meet the first demand then only with a “high degree of certainty” is the equation valid.

Any use of this equation for prediction in the real word takes us down the path of induction. You’ll never be able to run an experiment an infinite amount of times and so to estimate the probability of an event occurring on the n+1 experiment it is going to have to be based on a priori knowledge. Say you flip a coin 100 times and see heads half of the time, then you would induce that the next 100 flips would yield heads half of the time.

David Hume had a problem with inductive logic. Gauche had the following summary of his argument:

“(i)Any verdict on the legitimacy of induction must result from deductive or inductive arguments, because those are the only kinds of reasoning.

(ii)A verdict on induction cannot be reached deductively. No inference from the observed to the unobserved is deductive, specifically because nothing in deductive logic can ensure that the course of nature will not change.

(iii)A verdict cannot be reached inductively. Any appeal to the past successes of inductive logic, such as that bread has continued to be nutritious and that the sun has continued to rise day after day, is but worthless circular reasoning when applied to induction’s future fortunes.

Therefore, because deduction and induction are the only options, and because neither can reach a verdict on induction, the conclusion follows that there is no rational justification for induction.”

Whoops. Now what?

It’s fucking late now and I’m just one page into Papoulis. I’m having fun though so I’ll keep doing this (daily?) and hopefully have time to go back and properly reference things.

Next post, I want to pick this up with a way-out of the inductive reasoning trap which I found in a recent paper by Uwe Saint-Mont. Then maybe I’ll move on to deductive (math-fun) reasoning.

Han Zero

To be accompanied with the music video “Han Zero (lofi)” https://youtu.be/xm2hvD-NF7Q

“Han!” she yelled.

“What?” He replied in a tired tone.

“We’re moving.” She said, pointing out the window.

Han sat up rubbing his eyes. He got out of the bed and moved over to where Agatha was standing. Peering out the window he could see the telltale signs of motion as the station they had been docked at slowly became smaller and smaller.

Sure enough, they were on a trajectory, but when had he put in the coordinates? He drifted off into his mind trying to piece together events in the last few hours. As he re-entered that mental space between sleep and wakefulness he remembered that he was startled earlier by that easily forgotten clattering of the Bernoulli Drive.

Snapping to attention he reached down to grab his pants and got up to walk over to the Bernoulli Drive. It was a surprisingly simple machine that liked to play games – always leaving the pilot guessing as to whether it would work or not. They had gotten enough thrust from the previous burn that they were still moving, but without a proper kick their orbit around the station would decay and they would collide back on the Rebel station.

He smacked the drive with his hand and it sputtered and wheezed a breathy mechanical note. They waited. There was nothing, no lights not even a hum or a hiss. It had been doing this more often recently. 

“Shit.” He said. 

The Bernoulli Drive’s function was always discontinuous, bursting between fantastic possibilities of one moment and eery silence in another.  He much preferred the predictability of the Ensemble drives. While they were impossible to understand – complex beyond interpretability – at least they produced something! Han knew that was a cop-out though. Ensemble drives were prone to overfitting and you could easily run off the Graph if you didn’t have a team of technicians constantly tuning the device and retroactively explaining deviations.

Ensemble drive aside he still would have liked to retool the Bernoulli Drive at the last docking. The unpredictability was really starting to get on his nerves! Unfortunately his handler for this trip, an unpleasant fellow by the name of Darth was eager to get his cargo to the Axis. They would have to put up with the finicky drive and hope the input parameters didn’t drift any further than they already had.

He slapped the drive again, this time with a noise so loud Agatha’s attenuators whizzed to life. 

“Easy!” Agatha demanded, putting her hands on her ears with a languishing scoff as she adjusted her settings.

The Bernoulli Drive was silent. He tried to think of nothing. Let the drive give him clues. Dealing with pure randomness was like trying to peer into an additional dimension beyond your senses. He caught the Moment and renormalized. With a pinch he started the drive and it sputtered into life in discrete bursts. Chop! Chop chop! Then, with an instantaneous jolt and a loud Wham! they were actively accelerating. He felt satisfied with himself even though he intimately knew that controlling randomness was a rouse.

“I fucking hate that thing,” Han said, exasperated “it’s never predictable when you need it to be.” He leaned back into his pilot seat giving a cursory glance at the Graph monitor. The trajectory was set, there was no changing that now. All they could do was wait.

He adjusted the seat setting to lift his feet up and relaxed. With the last output from the Bernoulli Drive they had all the momentum they needed to make it to their destination.

“Han?” Agatha said after several minutes.

He snapped back to attention and looked over at her. As he acknowledged her with a dumb smile, he gazed past her trying to remember where he had found her again. Was it on the Edge during one of his cargo missions? Or was it the inner worlds of the Axis on the last delivery? Trips down the Graph always left the short-term memory a little hazy. It didn’t matter any more. 

There was one thing that was clear: Agatha was an AI babe he couldn’t live without.

Han had first met Agatha in the Machine Learning Academy where she had been studying irreducible systems, one of the last subjects that AI’s had not completely overturned since the Awakening. He had completed his pilot apprenticeship a few years before and had been back at the Academy’s cantina for a reunion. Agatha had spotted him in one of the smoky corners of the establishment. Han wasn’t your usual smuggler shooting holes cargo containers like the Talebian fixers busting holes through shaky logic. No, Han understood the real world and had learned his trade through experiences that only a proper apprenticeship could provide. It was the deviation from her training that attracted Agatha to Han. He just wasn’t like other things she had seen before. It was galactic romance at first sight.

Han recalled giving up a gig to spend an extra month with her on the Academy world before finally getting back on the graph with a cargo bounty he couldn’t refuse. That was the last time he saw her until he picked her up at the Foundry on one the Edge worlds – that’s where he had found her!

“What happens when we get there?” She asked.

His thought interrupted,, Han reflected on that question. How many times had he been to the Axis since he had gotten his ship? Nine? Ten? Every trip was the same. Grab some illicit cargo in one of the Edge worlds and travel down the Graph to make a delivery to one of the stations or dock worlds near the Axis. Nobody had ever actually been to the Axis before, that was just a saying. People living near the Axis were comfortable living at the limit, never daring to crossover to the Indeterminate. Once the cargo was delivered he would head towards the Axis getting flung out to the Edge again by the Torus-like geometry of space there.

“I guess we do it again.” Han said. He cracked open a beer and sat down reflecting on the unknown lying in wait for him at the Axis…

Coronavirus Guidelines for Cleaning and Disinfecting to Prevent COVID-19 Transmission

Aaron Green, Chen Shen and Yaneer Bar-Yam, Coronavirus guidelines for cleaning and disinfecting to prevent COVID-19 transmission, New England Complex Systems Institute (April 9, 2020). link to NECSI website

COVID-19 is mainly transmitted via aerosols and droplets and can exist on fomites—surfaces, equipment, utensils, fabric, hair, dust and other particles—for days. The disease may be spread when people touch contaminated surfaces and then touch their face. Regular cleaning and disinfecting of surfaces that are frequent touch-points helps to prevent disease spread.

Cleaning removes germs, dust, dirt and impurities from surfaces. Some forms of cleaning also kill germs. Even when cleaning doesn’t kill germs, removing them from the immediate environment where people are located reduces the risk of spreading infection.

Killing germs by disinfection should be performed after cleaning to further reduce the risk of spreading infection. The coronavirus causing COVID-19 can be killed by soap, alcohol and chlorine bleach.

More specifically: SARS-CoV-2 can be neutralized by lipid solvents including ether (75%), ethanol, chlorine-containing disinfectant, peroxyacetic acid and chloroform except for chlorhexidine. A list of disinfectants for SARS-CoV-2 can be found on the EPA’s website.

Time also kills viral particles. Current information indicates that over a period of hours, low density viral particles on cardboard become inactive, and over a period of a few days, they become inactive on hard plastic and metal surfaces. However, systematic inactivation on a variety of fomites and conditions is not yet well understood. This includes its dependence on the quantity of viral deposits, temperature, humidity, and other ambient conditions. For high density or large areas, the reliability of inactivation decreases and chemical disinfection is highly recommended. Washing and the use of disinfectants also should allow time for the effects to occur. Applying disinfectant and leaving on surfaces before rinsing is important.

In general there are two types of surfaces that need to be cleaned and they require different protocols. Soft, porous materials include carpeting, rugs, towels, clothing, sofas, chairs, bedding, soft fabric toys (i.e., stuffed animals), etc. Hard non-porous surfaces include stainless steel, floors, kitchen surfaces, countertops, tables and chairs, sinks, toilets, railings, light switch plates, doorknobs, metal/plastic toys, computer keyboards, remote controls, recreation equipment.

Supplies

  • Waterproof gloves such as latex, nitrile or dishwashing
  • Soap/detergent, warm water, clean towels, leak-proof plastic trash bags
  • Disposable gowns for extensive cleaning related tasks including taking out industrial trash
  • Face mask
  • Goggles (optional to prevent reactions to cleaning and disinfecting solvents)
  • Disinfectants

General Guidelines for Cleaning

  • Discard rather than clean or disinfect highly contaminated items.
  • Immediately throw away all disposable cleaning items
  • Wash hands frequently, including after emptying waste baskets and touching tissues and similar waste.
  • Wash your hands thoroughly with soap and water for at least 20 seconds or use an alcohol-based hand sanitizer that contains at least 60% alcohol

Clothing and Other Soft, Porous Materials That Can Be Laundered

  • Place materials in a sealed plastic bag until laundering
  • Launder using hot water and a detergent, preferably containing color-safe bleach
  • Dry on high heat

Soft, Porous Materials That Can Not Be Laundered (Carpets, Couches, Other Porous Surfaces)

  • Vacuum to keep dust from spreading into the air
  • Spot-clean spills of bodily fluid promptly following safe procedures
  • Deep clean carpets while avoiding splashing as much as possible
  • Use steam cleaners to clean carpets and other porous surfaces as needed

Hard, Non-Porous Surfaces

  • Follow labeled instructions on all containers
  • Clean surface with soap and water to remove all visible debris and stains
  • Rinse surface with clean water and wipe with clean towel
  • Apply the disinfectant. To effectively kill the virus, make sure the surface stays wet with the disinfectant for at least 10 minutes before wiping with a clean towel. If an EPA registered disinfectant is not available a 2% chlorine bleach solution can be used. Take care with alcohol based disinfectants as they tend to evaporate quickly and may not fully disinfect if instructions are not followed
  • Rinse with water and allow surface to air dry. Rinsing following use of a disinfectant is especially important in a food preparation area
  • Mop heads should be cleaned with soap and hot water and sanitized with an EPA-registered disinfectant or bleach solution and allowed to dry. Consider using single-use, disposable mop heads or cloths as an alternative
  • Remove gloves and place in a trash bag and discard
  • Wash hands after removing gloves and handling any contaminated material, trash or waste