Category Archives: Uncategorized

Calorie claims of exercise classes and Strava

This machine burns more calories per minute than any other– up to 800 calories in a 45-minute session” (SWEAT by BXR | VersaClimbing)

Strava shows: Morning Elliptical 1h36m 1,115Cal 136bpm.

If the ad and Strava mean calories (small calories), not kilocalories (large calories), then the unit Cal must be a typo for cal – see “Calories” vs “calories” – History of Science and Mathematics Stack Exchange.

Both “up to 800 calories in a 45-minuteand 1,115 cal in 1h36m are less than the basal metabolic rate of 1200kcal/day =50kcal/h =50,000cal/h. (Examining Variations of Resting Metabolic Rate of Adults: A Public Health Perspective – PMC (nih.gov)) Thus false. The marketing claims probably intend to say kilocalories.

The sustained (an hour or more) power output of elite cyclists is about 400W. (Lance Armstrong: Cycling Power | CIO , Tour de France 2009: Power estimates (sportsscientists.com) )

1W =1J/s =3600J/h, so 400W =1440kJ/h =344 kcal/h because a calorie is 4.184 Joules.

Less-than-elite athletes likely burn significantly fewer calories than 344kcal in an hour, especially when not competing. Any exercise class, app or sports watch claiming over 200 kcal/h is suspect.

Activities to do in London

Notation: + means I tried and liked it. – means either does not look interesting or I tried it and didn’t like it. No symbol means either I have not tried or feel neutral.

Classpass was useful for trying different classes for free over two weeks.

 

Roller derby.

Juggling.

-Aerial yoga https://www.thelodge.space/class-description.

-Surfskating in Decathlon.

+Unicycle hockey in Queensbridge Sports Centre Thursdays 20-22, free for beginners.

-Water aerobics Group Classes | Locations – Aqua Fit Pro Barbican, Elephant.

+Pole dancing https://www.kelechnekoff.com/Beginner Pole Classes | Akila Pole Studio

-Horse polo – requires years of practice, riding is expensive and far.

BMX track Burgess park. Lee Valley VeloPark BMX skills. £12 plus bike hire £13 (requires id and proof of address <3 months old.).

-Haggerston Park pump track.

Mountain bike. MTB skills Lee Valley VeloPark £12 plus bike hire £13 (hire requires personal identification and proof of address (utility, bank statement <3 months) ).

-rent electric bike, carbon bike, mountain bike Fat Llama | Rent (almost) anything

Aerial hoop, silks, etc gymnastics.

+Parkour Generation.

Footyaddicts. sportas.co.uk. Rabble.

+https://playculture.com/events.php

-Longsword fighting in Decathlon: choreographed moves, not real fighting.

-Clays Bar virtual clay pigeon shooting.

+Hyperreality Whitechapel VR zombie shooting.

Other.world_VR, otherVR experiences.

Immersive Gamebox not VR but motion tracking and surrounding screens.

Archeryfit Greenwich £30 Hatfield House, Merryweather Place, London, SE10 8EW. Club gate is next to the Premier Inn Hotel and 100 yards down Greenwich High Road from Pure Gym. Please dial 888-call on the gate buzzer to get in. Our entrance is across the yard to the right from the gate. 2020 Archery Druid St. Geronigo Sutton-at-Hone, Kent.

+Mile End Climbing Wall (mileendwall.org.uk) £30 intro bouldering

-Climb O2

-Climb Tottenham Hotspur Stadium

Things to do in Battersea Park | London Zip Wire | Go Ape

Lee Valley White Water Centre Activities (visitleevalley.org.uk) from April to Oct. Activity 1h. +Whitewater kayaking and courses all year.

+THCC kayak club in Shadwell basin. Beginner courses all year.

Regent’s canoe club in Islington. Castle Canoe Club

Kayak practice, including rolling, in the pool: have to do beginner exercises for 40 min, then can practice rolling for 15 min.

Night Kayak Across London | Secret Adventures Exploring Central London by kayak, paddling on the River Thames (londonkayakcompany.com) £65

King George V Reservoir sailing club, including windsurfing, wing foiling in the summer. West Reservoir Centre sailing.

+Choirs. Free Taster (londoncityvoices.co.uk). London International Choir has audition.

Salsa: Hyde Park bandstand outdoors, Temple, -Salsateca, -Adulis, -Bar Salsa Soho: crowded dark noisy basement.

+Bachata: Primrose St behind Liverpool St station outdoors, large crowd.

Other dances: -Swing. -Rocknroll and jive. -Brazilian Forro. Zouk: well taught but slow and simple. -Kizomba: very slow and simple. Society for International Folk Dancing (sifd.org) Islington seems to be the folk dance area. Irish dancing in Decathlon. Swing dance Bishopsgate.

+FREE Outdoor Trips From London | Meetup. +Hikes by London Wellness Group | Meetup led by Tharaphy. Ramblers hikes – mostly old Brits. Metropolitan Walkers is a Ramblers group.

Running clubs: +Runner Beans, +Runners Connect.

 

Team activities

Combat archery. Group 10-16. Cost 24-32. E.g., Walworth (Lambeth): St George’s Rd SE1 6ER.

HiddenCity | How It Works (inthehiddencity.com) scavenger treasure hunt for a team.

Crystal maze for a team

London Hen and Stag Parties | It’s a Knockout® (itsaknockout.net) for a team.

-Ice climbing – closed permanently.

Zorb & Bubble Football Shoreditch and Waterloo £320 for up to 20 people. Bubble Football : Excel Activity Group.

Paintball in London (ultimaterecreation.co.uk) 3 Herringham Road 46min by public transit or bike. Need to book early. Adult Paintballing Packages | Great Day Out | Delta Force Paintball (paintballgames.co.uk) East London Upminster 75min by public transit, 15 miles.

 

Outside London

+Windsurf Minster: train to Sheerness

Kitesurf and +wingfoil Shoeburyness East beach, £100 for 3-4h, 1h by c2c train from Stratford.

Wakeup Docklands wakeboarding from April to Sept. Thorpe Lakes Watersports Resort I LEARN TO WAKE/SKI Outside London.

MTB in Epping forest.

Ridge scrambling in the Peak District (Edale easiest to get to) or the Lake District. Scotland takes 8-10h to get to, like the Alps.

-Delft U Tech unusual bicycles – no mention of being able to try these.

12 Incredible Extreme Outdoor Activity Breaks in the UK (timeout.com)

Caving in the Yorkshire Dales.

Indoor ski/snowboard. Chill Factore Lesson Prices | Snow Activity Prices £56 per day. Manchester.

Fly a Spitfire Biggin Hill and Cotswold Airport or fly a Mustang. £2250-7450.

Sword fighting full contact in armour. Geronigo Keynsham near Bristol and Bath £41.

Quirky Quarter Chinese Arch in Liverpool City Centre. £15-96. 3h from Euston station by Avanti.

Tank Paintball Battle – Armourgeddon. Leicestershire. Seems no availability in winter. 3-person crew.

Grey Seal Snorkel Safari | The Fifth Point Diving Centre Northumberland. No availability in winter. £65.

Bungee Jump in Experiences in the UK, Gift Vouchers, Bungee Days Out, Bungee Stunts, Bungee Events – UKBungee

Paragliding Training – Green Dragons Airsports BHPA „fun day” 250.

Coasteering Gower peninsula near Swansea (4-5h travel), Bournemouth

+surf Croyde (all Devon locations transit via Barnstaple, 5-6h travel)

SUP surfing

Beginner Surf Lessons – The Wave Bristol

Adventure weekends: The 11 best you can have in 2019 (redbull.com) North Wales Activities (adventure-northwales.com)

Indoor Skydiving – Book Now (skydivinglondon.com) Basingstoke, Milton Keynes or Manchester

-LOTNA-LARP Star Trek themed laser tag in the woods in an airsoft arena.

 

Museums, tours

+Imperial War Museum

Visit HMS Belfast – Plan Your Visit | Imperial War Museums (iwm.org.uk) £22,7.

Cutty Sark Rig Climb | Experience the London Adventure (rmg.co.uk) £41.

Kew Gardens Tickets and prices | Kew £16.5.

+Museum of London

Join as a Historic Royal Palaces member | Historic Royal Palaces (hrp.org.uk)

https://www.biketouroflondon.com/

https://alternativeldn.co.uk/

 

Volunteering and networking

+Friends of Brookmill Park: river cleanup in waders.

+GoodGym runs and volunteering.

+Lambeth repair cafe 336 Brixton. Nunhead repair cafe in The Green.

+Eco Around London litter pick. +WaSh Wombles litter pick.

The Conservation Volunteers (tcv.org.uk)

Volunteer With Us | Bikeworks CIC Sat Victoria Park

Make New Friends | Meet New People | Drinking Partners

Meet New People & Make Friends in London | Find friends with We3 (we3app.com)

Networking | Young Professional Socials | London (mikfit.co.uk)

Find Events & Groups | Meetup

 

Robustness is a form of efficiency

Efficiency means using the best way to achieve a goal. Mathematically, selecting the maximizer of an objective function. The goal may be anything. For example, the objective function may be a weighted average of performance across various situations.

Robustness means performing well in a wide variety of circumstances. Mathematically, performing well may mean maximizing the weighted average performance across situations, where the weights are the probabilities of the situations. Performing well may also mean maximizing the probability of meeting a minimum standard – this probability sums the probabilities of situations in which the (situation-specific) minimum standard is reached. In any case, some objective function is being maximized for robustness. The best way to achieve a goal is being found. The goal is either a weighted average performance, the probability of exceeding a minimum standard or some similar objective. Thus robustness is efficiency for a particular objective.

The robustness-efficiency tradeoff is just a tradeoff between different objective functions. One objective function in this case is a weighted average that puts positive weight on the other objective function.

Whatever the goal, working towards it efficiently is by definition the best thing to do. The goal usually changes over time, but most of this change is a slow drift. Reevaluating the probabilities of situations usually changes the goal, in particular if the goal is a weighted average or a sum of probabilities that includes some of these situations. A rare event occurring causes a reevaluation of the probability of this event, thus necessarily the probability of at least one other event. If the probabilities of rare events are revised up, then the goal tends to shift away from single-situation efficiency, or performance in a small number of situations, towards robustness (efficiency for a combination of a large number of situations).

To be better prepared for emergencies and crises, the society should prepare efficiently. The most efficient method may be difficult to determine in the short term. If the expected time until the next crisis is long, then the best way includes gathering resources and storing these in a large number of distributed depots. These resources include human capital – the skills of solving emergencies. Such skills are produced using training, stored in people’s brains, kept fresh with training. Both the physical and mental resources are part of the economic production in the country. Economic growth is helpful for creating emergency supplies, raising the medical capacity, freeing up time in which to train preparedness. Unfortunately, economic growth is often wasted on frivolous consumption of goods and services, often to impress others. Resources wasted in this way may reduce preparedness by causing people to go soft physically and mentally.

Solving a crisis requires cooperation. Consumption of social media may polarize a society, reducing collaboration and thus preparedness.

Bayesian updating of higher-order joint probabilities

Bayes’ rule uses a signal and the assumed joint probability distribution of signals and events to estimate the probability of an event of interest. Call this event a first-order event and the signal a first-order signal. Which joint probability distribution is the correct one is a second-order event, so second-order events are first-order probability distributions over first-order events and signals. The second-order signal consists of a first-order event and a first-order signal.

If the particular first-order joint probability distribution puts higher probability on the co-occurrence of this first-order event and signal than other first-order probability distributions, then observing this event and signal increases the likelihood of this particular probability distribution. The increase is by applying Bayes’ rule to update second-order events using second-order signals, which requires assuming a joint probability distribution of second-order signals and events. This second-order distribution is over first-order joint distributions and first-order signal-event pairs.

The third-order distribution is over second-order distributions and signal-event pairs. A second-order signal-event pair is a third-order signal. A second-order distribution is a third-order event.

A joint distribution of any order n may be decomposed into a marginal distribution over events and a conditional distribution of signals given events, where both the signals and the events are of the same order n. The conditional distribution of any order n>=2 is known by definition, because the n-order event is the joint probability distribution of (n-1)-order signals and events, thus the joint probability of a (n-1)-order signal-event pair (i.e., the n-order signal) given the n-order event (i.e., the (n-1)-order distribution) is the one listed in the (n-1)-order distribution.

The marginal distribution over events is an assumption above, but may be formulated as a new event of interest to be learned. The new signal in this case is the occurrence of the original event (not the marginal distribution). The empirical frequencies of the original events are a sufficient statistic for a sequence of new signals. To apply Bayes’ rule, a joint distribution over signals and the distributions of events needs to be assumed. The joint distribution itself may be learned from among many, over which there is a second-order joint distribution. Extending the Bayesian updating to higher orders proceeds as above. The joint distribution may again be decomposed into a conditional over signals and a marginal over events. The conditional is known by definition for all orders, now including the first, because the probability of a signal is the probability of occurrence of an original event, which is given by the marginal distribution (the new event) over the original events.

Returning to the discussion of learning the joint distributions, only the first-order events affect decisions, so only the marginal distribution over first-order events matters directly. The joint distributions of higher orders and the first-order conditional distribution only matter through their influence on updating the first-order marginal distribution.

The marginal of order n is the distribution over the (n-1)-order joint distributions. After reducing compound lotteries, the marginal of order n is the average of the (n-1)-order joint distributions. This average is itself a (n-1)-order joint distribution, which may be split into an (n-1)-order marginal and conditional, where if n-1>=2, the conditional is known. If the conditional is known, then the marginal may be again reduced as a compound lottery. Thus the hierarchy of marginal distributions of all orders collapses to the first-order joint distribution. This takes us back to the start – learning the joint distribution. The discussion above about learning a (second-order) marginal distribution (the first-order joint distribution) also applies. The empirical frequencies of signal-event pairs are the signals. Applying Bayes’ rule with some prior over joint distributions constitutes regularisation of the empirical frequencies to prevent overfitting to limited data.

Regularisation is itself learned from previous learning tasks, specifically the risk of overfitting in similar learning tasks, i.e. how non-representative a limited data set generally is. Learning regularisation in turn requires a prior belief over the joint distributions of samples and population averages. Applying regularisation learned from past tasks to the current one uses a prior belief over how similar different learning tasks are.

How to learn whether an information source is accurate

Two sources may be used to check each other over time. One of these sources may be your own senses, which show whether the event that the other source predicted occurred or not. The observation of an event is really another signal about the event. It is a noisy signal because your own eyes may lie (optical illusions, deepfakes).

First, one source sends a signal about the event, then the second source sends. You will never know whether the event actually occurred, but the second source is the aggregate of all the future information you receive about the event, so may be very accurate. The second source may send many signals in sequence about the event, yielding more info about the first source over time. Then the process repeats about a second event, a third, etc. This is how belief about the trustworthiness of a source is built.

You cannot learn the true accuracy of a source, because the truth is unavailable to your senses, so you cannot compare a source’s signals to the truth. You can only learn the consistency of different sources of sensory information. Knowing the correlation between various sensory sources is both necessary and sufficient for decision making, because your objective function (utility or payoff) is your perception of successfully achieving your goals. If your senses are deceived so you believe you have achieved what you sought, but actually have not, then you get the feeling of success, but if your senses are deceived to tell you you have failed, then you do not feel success even if you actually succeeded. The problem with deception arises purely from the positive correlation between the deceit and the perception of deceit. If deceit increases the probability that you later perceive you have been deceived and are unhappy about that perception, then deceit may reduce your overall utility despite initially increasing it temporarily. If you never suspect the deception, then your happiness is as if the deception was the truth.

Your senses send signals to your brain. We can interpret these signals as information about which hypothetical state of the world has occurred – we posit that there exists a world which may be in different states with various probabilities and that there is a correlation between the signals and these states. Based on the information, you update the probabilities of the states and choose a course of action. Actions result in probability distributions over different future sensations, which may be modelled as a different sensation in each state of the world, which have probabilities attached. (Later we may remove the states of the world from the model and talk about a function from past perceptions and actions into future perceptions. The past is only accessible through memory. Memory is a current perception, so we may also remove time from the model.)

You prefer some future sensations to others. These need not be sensory pleasures. These could be perceptions of having improved the world through great toil. You would prefer to choose an action that results in preferable sensations in the future. Which action this is depends on the state of the world.

To estimate the best action (the one yielding the most preferred sensations), you use past sensory signals. The interpretation of these signals depends on the assumed or learned correlation between the signals and the state. The assumption may be instinctive from birth. The learning is really about how sensations at a point in time are correlated with the combination of sensations and actions before that point. An assumption that the correlation is stable over time enables you to use past correlation to predict future correlation. This assumption in turn may be instinctive or learned.

The events most are interested in distinguishing are of the form “action A results in the most preferred sensations”, “action B causes the most preferred sensations”, “action A yields the least preferred sensations”. Any event that is useful to know is of a similar form by Blackwell’s theorem: information is useful if and only if it changes decisions.

The usefulness of a signal source depends on how consistent the signals it gives about the action-sensation links (events) are with your future perceptions. These future perceptions are the signals from the second source – your senses – against which the first source is checked. The signals of the second source have the form “memory of action A and a preferred sensation at present”. Optimal learning about the usefulness of the first source uses Bayes’ rule and a prior probability distribution on the correlations between the first source and the second. The events of interest in this case are the levels of correlation. A signal about these levels is whether the first source gave a signal that coincided with later sensory information.

If the first source recommended a “best action” that later yielded a preferred sensation, then this increases the probability of high positive correlation between the first source and the second on average. If the recommended action was followed by a negative sensation, then this raises the probability of a negative correlation between the sources. Any known correlation is useful information, because it helps predict the utility consequences of actions.

Counterfactuals should be mentioned as a side note. Even if an action A resulted in a preferred sensation, a different action B might have led to an even better sensation in the counterfactual universe where B was chosen instead. Of course, B might equally well have led to a worse sensation. Counterfactuals require a model to evaluate – what the output would have been after a different input depends on the assumed causal chain from inputs to outputs.

Whether two sources are separate or copies is also a learnable event.

Exaggerating vs hiding emotions

In some cultures, it was a matter of honour not to show emotions. Native American warriors famously had stony visages. Victorian aristocracy prided themselves in a stiff upper lip and unflappable manner. Winston Churchill describes in his memoirs how the boarding school culture, enforced by physical violence, was to show no fear. In other cultures, emotions are exaggerated. Teenagers in North America from 1990 to the present are usually portrayed as drama queens, as are arts people. Everything is either fabulous or horrible to them, no so-so experiences. I have witnessed the correctness of this portrayal in the case of teenagers. Jane Austen’s “Northanger Abbey” depicts Victorian teenagers as exaggerating their emotions similarly to their modern-day counterparts.

In the attention economy, exaggerating emotions is profitable to get and keep viewers. Traditional and social media portray situations as more extreme than these really are in order to attract eyeballs and clicks. Teenagers may have a similar motivation – to get noticed by their peers. Providing drama is an effective way. The notice of others may help attract sex partners or a circle of followers. People notice the strong emotions of others for evolutionary reasons, because radical action has a higher probability of following than after neutral communication. Radical action by others requires a quick accurate response to keep one’s health and wealth or take advantage of the radical actor.

A child with an injury or illness may pretend to suffer more than actually to get more care and resources from parents, especially compared to siblings. This is similar to the begging competition among bird chicks.

Exaggerating both praise and emotional punishment motivates others to do one’s bidding. Incentives are created by the difference in the consequences of different actions, so exaggerating this difference strengthens incentives, unless others see through the pretending. Teenagers may exaggerate their outward happiness and anger at what the parents do, in order to force the parents to comply with the teenager’s wishes.

On the other hand, in a zero-sum game, providing information to the other player cannot increase one’s own payoff and usually reduces it. Emotions are information about the preferences and plans of the one who shows these. In an antagonistic situation, such as negotiations or war between competing tribes, a poker face is an information security measure.

In short, creating drama is an emotional blackmail method targeting those with aligned interests. An emotionless front hides both weaknesses and strengths from those with opposed interests, so they cannot target the weakness or prepare for the precise strength.

Whether teenagers display or hide emotion is thus informative about whether they believe the surrounding people to be friends or enemies. A testable prediction is that bullied children suppress emotion and pretend not to care about anything, especially compared to a brain scan showing they actually care and especially when they are primed to recall the bullies. Another testable prediction is that popular or spoiled children exaggerate their emotions, especially around familiar people and when they believe a reward or punishment is imminent.

Signalling the precision of one’s information with emphatic claims

Chats both online and in person seem to consist of confident claims which are either extreme absolute statements (“vaccines don’t work at all”, “you will never catch a cold if you take this supplement”, “artificial sweeteners cause cancer”) or profess no knowledge (“damned if I know”, “we will never know the truth”), sometimes blaming the lack of knowledge on external forces (“of course they don’t tell us the real reason”, “the security services are keeping those studies secret, of course”, “big business is hiding the truth”). Moderate statements that something may or may not be true, especially off the center of all-possibilities-equal, and expressions of personal uncertainty (“I have not studied this enough to form an opinion”, “I have not thought this through”) are almost absent. Other than in research and official reports, I seldom encounter statements of the form “these are the arguments in this direction and those are the arguments in that direction. This direction is somewhat stronger.” or “the balance of the evidence suggests x” or “x seems more likely than not-x”. In opinion pieces in various forms of media, the author may give arguments for both sides, but in that case, concludes something like “we cannot rule out this and we cannot rule out that”, “prediction is difficult, especially now in a rapidly changing world”, “anything may happen”. The conclusion of the opinion piece does not recommend a moderate course of action supported by the balance of moderate-quality evidence.

The same person confidently claims knowledge of an extreme statement on one topic and professes certainty of no knowledge at all on another. What could be the goal of making both extreme and no-knowledge statements confidently? If the person wanted to pretend to be well-informed, then confidence helps with that, but claiming no knowledge would be counterproductive. Blaming the lack of knowledge on external forces and claiming that the truth is unknowable or will never be discovered helps excuse one’s lack of knowledge. The person can then pretend to be informed to the best extent possible (a constrained maximum of knowledge) or at least know more than others (a relative maximum).

Extreme statements suggest to an approximately Bayesian audience that the claimer has received many precise signals in the direction of the extreme statement and as a result has updated the belief far from the average prior belief in society. Confident statements also suggest many precise signals to Bayesians. The audience does not need to be Bayesian to form these interpretations – updating in some way towards the signal is sufficient, as is behavioural believing that confidence or extreme claims demonstrate the quality of the claimer’s information. A precisely estimated zero, such as confidently saying both x and not-x are equally likely, also signals good information. Similarly, being confident that the truth is unknowable.

Being perceived as having precise information helps influence others. If people believe that the claimer is well-informed and has interests more aligned than opposed to theirs, then it is rational to follow the claimer’s recommendation. Having influence is generally profitable. This explains the lack of moderate-confidence statements and claims of personal but not collective uncertainty.

A question that remains is why confident moderate statements are almost absent. Why not claim with certainty that 60% of the time, the drug works and 40% of the time, it doesn’t? Or confidently state that a third of the wage gap/racial bias/country development is explained by discrimination, a third by statistical discrimination or measurement error and a third by unknown factors that need further research? Confidence should still suggest precise information no matter what the statement is about.

Of course, if fools are confident and researchers honestly state their uncertainty, then the certainty of a statement shows the foolishness of the speaker. If confidence makes the audience believe the speaker is well-informed, then either the audience is irrational in a particular way or believes that the speaker’s confidence is correlated with the precision of the information in the particular dimension being talked about. If the audience has a long history of communication with the speaker, then they may have experience that the speaker is generally truthful, acts similarly across situations and expresses the correct level of confidence on unemotional topics. The audience may fail to notice when the speaker becomes a spreader of conspiracies or becomes emotionally involved in a topic and therefore is trying to persuade, not inform. If the audience is still relatively confident in the speaker’s honesty, then the speaker sways them more by confidence and extreme positions than by admitting uncertainty or a moderate viewpoint.

The communication described above may be modelled as the claimer conveying three-dimensional information with two two-dimensional signals. One dimension of the information is the extent to which the statement is true. For example, how beneficial is a drug or how harmful an additive. A second dimension is how uncertain the truth value of the statement is – whether the drug helps exactly 55% of patients or may help anywhere between 20 and 90%, between which all percentages are equally likely. A third dimension is the minimal attainable level of uncertainty – how much the truth is knowable in this question. This is related to whether some agency is actively hiding the truth or researchers have determined it and are trying to educate the population about it. The second and third dimensions are correlated. The lower is the lowest possible uncertainty, the more certain the truth value of the statement can be. It cannot be more certain than the laws of physics allow.

The two dimensions of one signal (the message of the claimer) are the extent to which the statement is true and how certain the claimer is of the truth value. Confidence emphasises that the claimer is certain about the truth value, regardless of whether this value is true or false. The claim itself is the first dimension of the signal. The reason the third dimension of the information is not part of the first signal is that the claim that the truth is unknowable is itself a second claim about the world, i.e. a second two-dimensional signal saying how much some agency is hiding or publicising the truth and how certain the speaker is of the direction and extent of the agency’s activity.

Opinion expressers in (social) media usually choose an extreme value for both dimensions of both signals. They claim some statement about the world is either the ultimate truth or completely false or unknowable and exactly in the middle, not a moderate distance to one side. In the second dimension of both signals, the opinionated people express complete certainty. If the first signal says the statement is true or false, then the second signal is not sent and is not needed, because if there is complete certainty of the truth value of the statement, then the statement must be perfectly knowable. If the first signal says the statement is fifty-fifty (the speaker does not know whether true or false), then in the second signal, the speaker claims that the truth is absolutely not knowable. This excuses the speaker’s claimed lack of knowledge as due to an objective impossibility, instead of the speaker’s limited data and understanding.

A “chicken paper” example

The Nobel prize winner Ed Prescott introduced the term “chicken paper” to describe a certain kind of economics research article to the audience at ANU in a public lecture. For background, a macroeconomics paper commonly models the economy as a game (in the game theory sense) between households, sometimes adding the government, firms or banks as additional players. A chicken paper relies on three assumptions: 1) households like chicken, 2) households cannot produce chicken, 3) the government can provide chicken. Prescott’s point was to criticize papers that prove that the intervention of the government in the economy improves welfare. For some papers, such criticism on the grounds of “assuming the result” is justified, for some, not. This applies more broadly than just in macroeconomics.

One example that I think fits Prescott’s description is Woodford (2021, forthcoming in the American Economic Review), pages 10-11:We suppose that units are unable to credibly promise to repay, except to the extent that the government allows them to issue debt up to a certain limit, the repayment of which is guaranteed by the government. (We assume also that the government is able to force borrowers to repay these guaranteed debts, rather than bearing any losses itself.)” The “units” that Woodford refers to are households, which are also the only producers of goods in the model. Such combined producer-consumers are called yeoman farmers and are a reasonable simplification for modelling purposes.

The inefficiency that the government solves in Woodford (2021) is the one discussed in Hirshleifer (1971) section V (page 568) that public information destroys mutually beneficial trading and insurance opportunities. In Woodford (2021), a negative shock to exactly one industry out of N in the economy occurs and becomes public at time 0 before trade opens. Thus the industries cannot trade contingent claims to insure against this shock. They are informed of the shock before trade. However, the government can make a transfer at time 0 to the shock-affected industry and tax it back later from all industries.

If the government also has to start its subsidizing and taxing after trade opens, it can still provide “retrospective insurance” as Woodford calls it by taxes and subsidies. Market-based “insurance” would also work: the affected industry borrows against the collateral of the government subsidy that is anticipated to arrive in the same period.

P-value cannot be less than 1/1024 in ten binary choices

Baez-Mendoza et al (2021) claim that for rhesus macaques choosing which of two others to reward in each trial, „the difference in the other’s reputation based on past interactions (i.e., how likely they were to reciprocate over the past 20 trials) had a significant effect on the animal’s choices [odds ratio (OR) = 1.54, t = 9.2, P = 3.5 × 10^-20; fig. S2C]”.

In 20 trials, there are ten chances to reciprocate if I understand the meaning of reciprocation in the study (monkey x gives a reward to the monkey who gave x a reward in the last trial). Depending on interpretation, there are 6-10 chances to react to reciprocation. Six if three trials are required for each reaction: the trial in which a monkey acts, the trial in which another monkey reciprocates and the trial in which a monkey reacts to the reciprocation. Ten if the reaction can coincide with the initial act of the next action-reciprocation pair.

Under the null hypothesis that the monkey allocates rewards randomly, the probability of giving the reward to the monkey who previously reciprocated the most 10 times out of 10 is 1/1024. The p-value is the probability that the observed effect is due to chance, given the null hypothesis. So the p-value cannot be smaller than about 0.001 for a 20-trial session, which offers at most 10 chances to react to reciprocation. The p-value cannot be 3.5*10^-20 as Baez-Mendoza et al (2021) claim. Their supplementary material does not offer an explanation of how this p-value was calculated.

Interpreting reciprocation or trials differently so that 20 trials offer 20 chances to reciprocate, the minimal p-value is 1/1048576, approximately 10^-6, again far from 3.5*10^-20.

A possible explanation is the sentence “The group performed an average of 105 ± 8.7 (mean ± SEM) trials per session for a total of 22 sessions.” If the monkey has a chance to react to past reciprocation in a third of the 105*22 sessions, then the p-value can indeed be of the order 10^-20. It would be interesting to know how the authors divide the trials into the reputation-building and reaction blocks.

Symmetry of matter seems impossible

I am not a physicist, so the following may be my misunderstanding. Symmetry seems theoretically impossible, except at one instant. If there was a perfectly symmetric piece of matter (after rotating or reflecting it around some axis, the set of locations of its atoms would be the same as before, just a possibly different atom in each location), then in the next instant of time, its atoms would move to unpredictable locations by the Heisenberg uncertainty principle (the location and momentum of a particle cannot be simultaneously determined). This is because the locations of the atoms would be known by symmetry in the first instant, thus their momenta unknown.

Symmetry may not provide complete information about the locations of the atoms, but constrains their possible locations. Such an upper bound on the uncertainty about locations puts a lower bound on the uncertainty about momenta. Momentum uncertainty creates location uncertainty in the next instant.

Symmetry is probably an approximation: rotating or reflecting a piece of matter, its atoms are in locations close to the previous locations of its atoms. Again, an upper bound on the location uncertainty about the atoms should put a lower bound on the momentum uncertainty. If the atoms move in uncertain directions, then the approximate location symmetry would be lost at some point in time, both in the future and the past.