I think the WHO are global patriots who just wanted to save the global economy by knowingly taking measures that spread the virus too much. :roll:

@Joseph Ting (copy pasting your threads into the coronavirus thread)

(Thread 1)

The COVID 19 pandemic piqued my interrogation of the balance of staff safety and duty of care to imperilled communities. Front line clinicians fear for themselves and their families. Despite our valorization by communities, I as a frontline emergency specialist have noticed a surge in absenteeism among well nursing staff that claim “mental health days off” to avoid catching corona and spreading it their kids. Their defence of fraudulently claimed sick paid leave is not risking passing on the corona-contagion to young children when they return from school or day care (they remain open in Australia). One commented that as non-parent, I should take up additional burden of COVID19 health care presentations. This increases the number of my daily encounters with, and the cross-infection risk posed by, patients being screened or treated for corona. Without the nurse, I now take every throat swabs as the patient coughs or gags. There are no hospital contingency plan to make up for unplanned shortfalls in clinical staff. “No kids at home sacrificed” clinicians should not be subjected to the acute stresses, physical and psychological toll exacted by having to compensate for our well colleagues that refuse to turn up for work. How do you cope if an epidemic disrupted daily life, closing schools, packing hospitals, and putting social gatherings, sporting events and concerts, conferences, festivals and travel plans on indefinite hold? As a frontline doctor, staying healthily uninfected whilst we strive for containment remains a cause for celebration. Albert Camus’ The Plague is balm to the fear-riven tear in the fabric of global society. Just as the decimated inhabitants of Shakespeare’s London outlasted the plaque, without modern medicine and public health interventions, the burgeoning coro-demic is but one of Camus' "many plagues in history…yet plagues and wars (still) take people equally by surprise.“ Camus’ contagion will surely go “unaccountably” when it pleases, the sooner if communities adjust and adhere to “bewildering portents” with care and caution to the lives of others. Camus urges the social distancing and lock-downs that today will mitigate the coro-disruption’s festering tenacity, and encourages that the pandemic threat is not fated to last forever. As we face the rigours of self-isolation, the consumptive poet -doctor John Keats, exiled in the Bay of Naples as typhus raged, reminds the reader of life coming to a premature stop. The threat of cross-infection in my daily patient encounters incites Keat’s “mortality weigh(ing) heavily on me like unwilling sleep,” yet there is consolation in being “half in love with easeful death.” We should all salute the unsung scores of imperilled, some now dead, doctors and nurses that have risen to the occasion. Joseph Ting, MBBS MSc (Lond) BMedSc PGDipEpi DipLSTHM FACEM. Adjunct associate professor, School of Public Health and Social Work O Block, Room O-D610 Victoria Park Road Kelvin Grove, Brisbane QLD 4059 Queensland University of Technology, Brisbane Australia Mob 0404826650

(Thread 2)

Emergency services and police staff deserve our respect and admiration for risking life and limb in respnding to recent terrorist attacks at the Manchester Arena and in Central London. This is in addition to people throw themselves in the path of London Tube trains several times a week. Most are horrifically and mortally injured. The train driver is often traumatised. Medical workers face grave hazards trying to access the injured survivor, having to crawl underneath the train along potentially electrified tracks. Commuter journeys are lengthily disrupted. Apart from the ethical dilemma surrounding attempts to take one’s own life, is one obliged to not put others at risk of occupational hazards and inconvenience, more so now when rescue crews have to deal with frequent innocent mass casualties from barbaric acts?
Declaration: I was a prehospital doctor working in England until May 2013.

(Thread 3)

I was trying to insert a central venous catheter to help stabilise the condition of a critically ill man with suspected blood stream infection and dangerously low blood pressure on a busy shift in resuscitation. I had to work by myself as several doctors had called in sick, including my resident who recently told me she had cause to be aggrieved after being refused leave for the school holidays. There were many parent-doctors who had applied successfully ahead of her and leave was no longer available. I unfortunately punctured the patient’s carotid artery after being distracted with urgent information that several major trauma cases were due soon with no senior medical cover available from other hospital units.

Although the patient fared well and I completed the resuscitative procedure in time to attend to the incoming traumas, I believe that sick leave taken fraudulently by doctors (and nurses) lead to more stressful workloads and adverse risks for staff that turn up. Half of all sick leave taken in Australia is as a selfish entitlement to have rest and recreation. The expectation is that work presenters make up the shortfall as well as assuming responsibility for clinical and stress related errors and delays or deficiencies to care. I think this is grossly unfair-the average Australian takes most of their 10 days of sick leave each year.

(Thread 4)

Benefits intended to assist workers with an injury or illness is often abused. In 25 years of working as a hospital physician, I have taken three days off for acute injuries and for my mother’s funeral. My residents are predisposed to calling in sick on days that bookend their free weekend or a stretch of days rostered off work. The department’s secretary leaves early on a Friday or puts in a no-show. I regularly get a last minute phone call from residents who call in sick, which means that the doctors who are present are required to work an extra shift. Some get sent home from a day shift and are asked to return for night duty that cannot be filled in otherwise. It is common knowlege that a substantial proportion of sick leave in my clinical area is used for recreation. I have had to work marathon shifts for absent colleagues while fatigued and sleep-deprived. This has incurred errors in the care of the seriously ill. On one ocassion I have fallen asleep at the wheel on the way home and run through a red light. Dishonest sick leave takers are abusing an altruistic safety net and imposing risks to others who have to shoulder additional clinical work. Is it worth considering sick leave be paid at half to three quarters full pay, and the difference paid to a locum that can turn up for work at short notice, in the hope that patient care isn’t compromised?

Wow, Nos is really totally insane. Conspiracy theory nonsense, none of those links suggest anything like he thinks they do.

Oh dear. Silly me.

He isn't really trying to claim that. He's just putting the words out there so they can be found by search engines, and so other members will oblige to debate him on them so he and his posts get even more exposure. It's just trolling, and not the fun kind. — Echarmion

I usually don't correct the man for those reasons. I made an exception because of how obvious this was.

I never said nor implied that — NOS4A2

Ahh I see. You did the following things:

(1) Said that the WHO was spouting Chinese Communist Party propaganda based on a Tweet about a "preliminary report" from scientists in China on Jan 14.
(2) attempted to discredit the data they output for minor typographical errors and a change in their daily reporting time.

And you're trying to claim that many people will think the WHO has "blood on its hands", and won't escape THE HORRIFYING SCANDAL OF THE MINOR SPREADSHEET ERRORS AND AMBIGUOUSLY WORDED TWEET because you're completely supportive of the WHO and its track record for providing excellent advice on how to deal with a pandemic.

This post makes it sound like the WHO has no idea what they're talking about. It's really not true. If you check the link from Ourworld in Data, they're changing to the European Centre for Disease Prevention and Control's data because (1) the update time from the WHO changed:

Unfortunately, in the publication of WHO data on 18th March – Situation Report 58 – they shifted the reporting cutoff time from 0900 CET to 0000 CET. This means that comparability is compromised because there is an overlap between the last two WHO data publications

and (2) minor typographical errors that do things like change the global number of new cases in a day by 2.

The increase in case numbers for Guyana takes the global total to 153,523 confirmed cases (not 153,517 cases as detailed in the report). The increase in death numbers for Lebanon takes the global total to 5736 deaths (not 5735 deaths as detailed in the report)

They will probably "come out unscathed" because of course there are going to be typographical errors somewhere in a quickly updating global data set aggregated and recorded under incredibly stressful conditions.

What say...should we just cut off communication? — Frank Apisa

We could talk about belief I guess.

I think it's got a few meanings:

Belief in a statement: belief in a statement is holding it to be true. This is a largely cognitive act, requiring the higher brain functions that deal with language processing - I think that's justified because it specifically deals with a statement. "A belief" usually means "A belief which is a statement". People have beliefs. "I believe I have pasta in my home"

Belief as an attitude towards a statement; the disposition regarding a believed statement that applies when it is held to be true.

Belief as a disposition to act based off of a learned pattern or habit, characterised by an expectation that things will turn out in a specified way; a rat might believe that if it presses a button, it gets food. A rat however doesn't have the capacity to state "If I press the button I get food", nor does it have brain functions that deal with language processing like we do, so it is unlikely to be just the same as belief in a statement.

In any of these cases, we can believe things which are not true, or expect things which do not turn out to happen

People also "believe in other people"; a manner of having confidence in someone.

Depending upon the context, a belief may require evidence, justification or circumstances that otherwise facilitate understanding/explanation.

Evidence: "I believe the weight of a newborn baby is 10kg on average", "Really? Have you weighted them?", "No, I just believe it.".
Justification: "Pi is 4!" (assertion, indicating belief) "Why? That breaks everything" "Look at this proof..."
Otherwise case: "I'm sorry for being a jerk recently, I suppose I believed that everyone and everything's against me since I lost my job" (a belief as an explanation for an action)

Prediction: people in the US media will soon start framing the inflated death toll from shit poor US admin response to the coronavirus as inevitable. Whereas before, it was just that the data was poor and worst case scenarios were unjustified doom and gloom.

Simultaneously, framing the response to the virus in military terms will cast the elderly, sick and poor as soldiers patriotically giving their lives to keep liberty and democracy and all that bullshit going.

One fact is here taken for granted, and I wonder whether this is a necessary outcome in this setup, or whether this is an additional assumption: after some time the system ejects one body that flies off into the infinite distance, leaving behind a binary system. This is a dramatic transition in the system's dynamics, which helps understand the criterion of "irreversibility" that they use: — SophistiCat

:up: Good point.

The idea insofar as they concern rounding errors is similar in both cases.

For floating points, you have a given number of bits that represent significant digits. Then a given number of bits that shift the significant digits up and down (like powers of ten shift digits up and down their tens/hundreds etc columns). If you can only have 3 numbers to represent significant digits, and in reality you get the number 1199, you'll lose the last 9 if the rounding occurs by truncation, and it'll be 1190. If it occurs by some other method, you might get 1200.

Planck length would be through fixed rather floating? — bongo fury

I have no idea how they have implemented the Planck length. I guess that they represent it with a floating point number. If your intuition is that the Planck length is represented as fixed because it is a physical constant, I don't think that holds, because numbers like pi are often given floating point representations. I don't think the Planck length is known exactly anyway.

The internet told me floating was sig figs not dp? — bongo fury

It is. I changed to DP because it seemed easier to talk about rounding errors in that context.

Fixed not floating, then? (And fixed by Planck length, if I understand you.) — bongo fury

It was an example. I edited it with "for example". Thanks.

(I know you know what floating points are, but many readers will not)

They took a classical system; the three body problem but with black holes; evolved it forward in time from t = 0 to t = t. They then took the position of the objects in the system at t and perturbed them by the Plank length. They then ran the system backwards in time, using the same equations, from the perturbed position at t. They looked at how often the forward time trajectory wasn't just replicated, but backwards, and found it to be 5% of the time.

What this says is. quoting the article:

The movement of the three black holes can be so enormously chaotic that something as small as the Planck length will influence the movements," Boekholt said. "The disturbances the size of the Planck length have an exponential effect and break the time symmetry.

.

The original paper describes its methodology as:

The main idea of our experiment is the following. Each triple system has a certain escape time, which is the time it takes for the triple to break up into a permanent and unbound binary-single configuration. Given a numerical accuracy, , there is also a tracking time, which is the time that the numerical solution is still close to the physical trajectory that is connected to the initial condition. If the tracking time is shorter than the escape time, then the numerical solution has diverged from the physical solution, and as a consequence, it has become time irreversible. Only the systems with the smallest amplifications factors will pass the reversibility test. However, by systematically increasing the numerical accuracy (decreasing epsilon), we aim to increase the tracking time of each system. An increasing fraction of systems will obtain a tracking time exceeding its escape time, thus gradually decreasing the fraction of irreversible solutions

Key points:

(1) There's a numerical accuracy parameter; the numerical accuracy parameter arises because computers don't just store numbers like pi exactly like we can write down symbols for on paper, they store floating point approximations of them, and there's always some error. For example, if you can only represent 3 decimal places, the number 0.00099999 will be 0, despite it being close to 0.001. The computers only have so many bits to represent the number with.

(2) The numerical accuracy parameter can be varied with the simulation. The numerical accuracy parameter encodes how precisely all the variables in the system can be represented. If the numerical accuracy parameter for giving directions to your neighbour was 100km, you could give them "accurate" directions within that error-threshold by telling them that you live in the city you live in.

(3) A "solution" of these equations defining the three body system is a numerical solution; all the calculus and numbers are represented by computer approximations using these error prone floating points and functions taking floating points and spitting out floating points. (The scarequotes are not to say this is an illegitimate procedure, the scarequotes are to distinguish a numerical solution from an analytic - pen and paper - one, the analytic one is exact).

They highlight this distinction in the discussion:

In the limit of infinite accuracy (epsilon → 0) we retrieve the microscopic time-reversibility of Newton’s equations of motion. In the presence of perturbations of size epsilon, whether numerical or physical, a fraction of systems becomes irreversible...

Super take home message: the laws as you'd write them down on paper are time reversible.

(4) (1-3) are just maths, the next bit is physics. Something physically interesting would be if the accuracy of the numerical approximations broke down badly sometimes at a physical length scale; like say the diameter of an atom, or the Planck length.

(5) How to establish this? When they run the equations backwards from the end point - using the end point as a new start point - with perturbation of the order of 10^-74 for the system's motion relevant variables (position, velocity, acceleration at a time point it looks like); they receive a result which is statistically indistinguishable from the unperturbed one. But there are negligible differences, "micro differences" as the paper puts it, what this means is that for every forward run, there are a collection of backward runs which are negligibly different from it.

(5) What if we put in an error thresh-hold of the Planck length, run the system forward, then perturb its state by the plank length (approx 10^-32) and counted what proportion of times the system outputs a backward trajectory which is statistically distinguishable from the one we get from retracing the steps from the forward iterations exactly? Turns out this is 5%.

The paper does not discuss any QM effects, and whether there is anything physically meaningful about this result; the Planck-length result is merely suggestive of something significant without specifying what it is. As some speculation about what it is, the paper shows that even if you represent a very chaotic system's dynamics exactly, if there is some underlying "uncertainty" or "fluctuation" in the exact state variables, it will pull trajectories apart - it turns out that this is true 5% of the time for the three body system and the Planck length, which every material thing is presumably bigger than.

The paper's methodological take home message seems to be more about measuring how chaotic systems are numerically using this % of irreversible trajectories as a function of the error thresh-hold.

But fewer people would care about the paper if it didn't suggest (with plausible deniability in that typical academic way) that it has something to say about time irreversibility of physical/natural trajectories as opposed to time irreversibility of numerical algorithms representing them.

Edit: something this post didn't cover, and maybe suggests wrongly, is that the weird irreversibility can be blamed on the researchers' implementation/code; and that's wrong. The time irreversibility is framed as a feature of the system (under the numerical algorithms), not a bug. The whole graph representing "what proportion of simulations turn out to be time irreversible at this error threshold" is a system property, the system (or the equations defining it) imbues the numerical approximations with properties like that.

SEP is a gold mine. Free to access peer reviewed philosophy encyclopedia. The hyperlinked text in this post takes you to an article titled "Aristotle's Metaphysics".

A similar site IEP exists, and that link is to its article on Aristotle's metaphysics.

It seems you don't live in your own world.

What would you do? Avoid her? — NOS4A2

Ask from across the street before approaching, "Would you like help with your groceries?". If yes, "Are you sure? It seems you're in an at risk group for this bloody virus thing.", "Oh I know, have you been following the guidelines?" "I've been isolating, working from home, I washed my hands before coming out, and I've not been to see anyone non-necessary in person for about 10 days." "Ok then"

What is more likely to happen:

"No thank you"

I do not know what you are talking about... — Frank Apisa

In response to a post containing the following words (@Gregory):

So the system of theology in the Dark Ages (and latter) took Aristotle's idea that God is most actual, and that there is a hierarchy in "creation" where those higher up have more actuality than the lower. This literal deification of action has always puzzled me. First, maybe in thought the highest thing would be an infinite mind. That doesn't mean it must be that way in reality. I tend to believe that everything in creation has the same potency and actuality. How is this related to yin and yang however? Plotinus thought the highest Good to be pure potentiality. There is no clear argument from the Thomist camp to refute this (though they try so hard). Why is activity even better than passivity in any system

System. Theology. God. Actual. Hierarchy. Creation (with scarequotes around it), Actuality used as a comparative. Deification. Infinite. Infinite mind. Reality. Potency. A context in which this is all compared to Yin and Yang in an unspecified way. A reference to Aristotle, Plotinus and Thomism, and an unexplained link between all of this and activity and passivity... With all of that in the mix, all of these abstractions with brief mention of their context, you express the desire to clarify the meaning of the word belief?

...assume I meant that same thing... — Frank Apisa

When you're happy to allow some words the privilege of being ok to assume both people writing mean the same thing by them...

It beggars belief, that's all.

Okay, I was a bit abrupt there. Question like that seem to be a stalling or diverting tactic. — Frank Apisa

What do you mean by "I" and "was" and "question"?

...assume I meant that same thing... — Frank Apisa

If you can do this, then the OP unasks itself.

What do you mean by "what?" — Frank Apisa

What do you mean by "what", "do", "you", "mean", "by" and "what"?

What do you mean by "mean" in the OP question?

Something absent from the discussion so far is the idea of an ordering. Loosely an ordering is a way of defining when one object is bigger or smaller than another. Sets themselves, natural numbers and integers have an ordering on them.

Collections of sets have an ordering on them, the subset relationship. If we have the collection of sets:

{1,2,3}, {1,}, {2}, {3}, {1,2}, {1,3} , {2,3}

You can call one set X smaller than another Y if X is a subset of Y. So {1} would be less than {1,3}, since the first is a subset of the second. When there are orderings, there comes an associated idea of biggest and smallest with respect to the ordering. In the above list, {1,2,3} is the biggest element, since every element is a subset of it.

But the sets {2} and {3} are not comparable, since neither is a subset of the other.

Contrast natural numbers. Consider the set of natural numbers {1,2,3}. The number 3 is the biggest there; 3 is bigger than 2, 2 is bigger than 1. Every natural number is comparable to every other natural number with the usual idea of how to order them by size, but not every set is comparable to every other set when comparing them by the subset relationship.

Setting out the ordering on the natural numbers, you can call one natural number x greater than some natural number y if and only if (definitionally) x = S^n ( y ) for some n. IE, x is bigger than y if you can apply the successor function to y a few times and get x. This immediately ensures that all natural numbers are comparable; since every natural number is a successor of 0.

It's pretty clear that the way we compare fraction sizes resembles the way we compare natural numbers in some ways; for any two fractions, you can tell which is bigger or if they're the same. The way we compare fraction sizes does not resemble the way we compare sets by the subset relationship; there aren't pairs of fractions which are incomparable like {2} and {3} are.

But they have differences too, any pair of fractions has a fraction inbetween them, whereas natural numbers do not. Natural numbers come in lumps of 1, the smallest positive difference between two natural numbers. Fractions don't come in smallest differences at all.

It's also pretty clear that there's more than one way of ordering things; the kind of ordering sets have by the subset relation is not the kind of ordering natural numbers (or fractions) have by the usual way we compare them.

What this suggests is that it's important to make axioms for the different types of ordering relationships as suits our interest. One intuitive property the ordering on the natural numbers has but the subset one lacks is that the ordering on the natural numbers appears to represent something about magnitudinal quantities; the mathematical objects numbers /are/ are sizes, and those sizes can be compared.

Whereas, the subset relation breaks this intuition; it doesn't represent comparison of a magnitudinal property, it represents something like nesting or containedness. The UK contains Scotland and England and Northern Ireland, but Scotland doesn't contain England or Northern Ireland, and England doesn't contain Scotland or Northern Island, and Northern Island doesn't contain Scotland or England; Scotland, England and Northern Ireland can only be compared to the UK in that manner, and not to each other. Another example is that Eukaryotes contains Animals and Fungi, but Animals don't contain Fungi and Fungi don't contain animals.

What properties then characterise the ordering of naturals and fractions, and distinguish them from the ordering of province and country or the ordering of classifications of biological kinds?

I think it's more that if you want to predict the position of something based on whatever variables you have, and you perturb the position variables by the plank length, you can no longer tell which trajectory - what path the bodies trace over time - you're on.

They ran the system of planets for a while, until t say. Then they perturbed the planet positions at t by the plank length, then they tried to run the system back in time, and got a different end point (or more generally evaluated trajectory) 5% of the time.

The climate system is similar. People perturb the weather variables by 10^-64 or 10^-32 (either the plank length ^2 or 100 times the plank length), and they don't get the same results within days or weeks. Even if the underlying laws are time reversible, the system iterations might amplify any perturbation so much what trajectory you're on changes beyond an error thresh-hold.

When certain politicians are talking about the reaction being worse than letting CV run its course, they are most definitely comparing human lives to dollars. — Benkei

:point:

Could a healthcare system every be universal if they cannot care for their patrons universally? — NOS4A2

This is word games. Having the bandwidth and resources to give needed healthcare access to everyone would have made the collapse of our healthcare systems far less likely. Where are the private healthcare providers in all this? Absent. When it comes down to it, when socieities really need it, universal healthcare access is obviously a necessity.

Vaccination has the same logic.

The same shit that makes people angry at anti-vaccers killing their kids should make us angry at our countries' responses killing the elderly, the sick, the poor. If "killing" seems like an overstatement, call it "exacerbating the risk of severe long term health outcomes with substantial risk of mortality".

Prioritising healthcare allocation when it's so scarce is motivated by the same risk and efficiency principles that should have been guiding government responses in the US and the UK.

Say death is the outcome. You want to minimise the deaths of people in your care. If you give treatment to someone who is likely to die even with the treatment vs someone who is comparatively much less likely to die with the same treatment, you minimise the amount of deaths.

Say collapse of the healthcare system is the outcome. You want to minimise the risk of the collapse of the healthcare system. If you take measures to reduce the load on it, vs if you don't take measures to reduce the load on it, you minimise the risk of collapse.

Say getting measles, mumps or rubella is the outcome. You want to minimise the risk of people getting that, if you vaccinate vs not vaccinating, you reduce the amount of people that get measles, mumps and rubella.

Say global economic collapse due to a pandemic is the outcome. You want to take measures that minimise the risk. On the one hand, maybe you think that taking measures against the pandemic increases the risk of global economic collapse; and it might, instantaneously. But as we've seen, and as was predicted, if you don't do that, the risk is even greater.

Nurses, doctors and epidemiologists understand that better than politicians, apparently.

I don't blame you. Most people lose interest when arguments involve processing spreadsheets.

Schools just closed because it just got here — frank

US: confirmed 8 tested cases of coronavirus first of February. confirmed 11 3 days later.
Source: Kaggle's dataset, aggregated from global records.

It's not "just got there", other countries have responded far, far better within similar timeframes.

We actually had time to screw around and fuck up. We're an ocean away from you guys. — frank

Also this:



And this:

If you close businesses before the virus is there, you aren't slowing anything down. You're just hurting the economy. — frank

The US administration has known of the great risk of the virus spreading to its shores since at least mid February, received briefing on what the response should be to mitigate the pandemic, especially widespread testing for the disease, and waited a month to take minimal preventative measures. While administration members were happy to use the information for insider trading.

Most European countries have been taking preventative measures for about a month. Schools started to close in the last few days in the US. Responding to a pandemic; if you wait for the first confirmed case in an area to do literally anything, you're already way too late.

You're a healthcare worker right? Surely you know this.

What should his administration have done differently? — frank

If you just want to isolate the epidemiological failures from the broader economic ones like funding healthcare and universal healthcare access; the quicker responses like quarantine and non-essential for society's basic functioning business closures are adopted, and the quicker travel is restricted, the lower the ultimate effected number of the population is expected to peak, and the slower it is expected to spread. The USA administration has failed to act or acted too slowly on all of these measures.

It's not just Trump, the UK fucked up royally (hur hur) too.

Aren't the corner points just the dyadic rationals — fishfry

Ah yes! You can see them as the end points of the interval expressions here, should've seen that sooner.

"Almost none" of the limit points on the diagonal (let's just call it that for brevity) is a corner point, for the simple reason that there is only a countable number of them. Also, keep in mind that the diagonal (which we interpret as the limit point of the sequence of curves) is not itself part of the sequence and does not have the same properties. Every member of the sequence is piecewise-differentiable, while the diagonal is, of course, everywhere differential. — SophistiCat

Do you think it's the case that in the limit the corner points become dense in the straight line, despite remaining countable? Edit: it seems either that is true, or the notion of corner breaks down in the limit (and so the corner points are dense in the line by virtue of every line point being a corner point).

Your posts in this thread have been excellent!

For the uninitiated, the curse of dimensionality is a problem that occurs when fitting statistical models to data; it occurs (roughly) when there are more relevant factors to the model (model parameters) than there are observations (data) to train the model on.

Regarding the curse of dimensionality; If you look at the combinatorics of the learning, what would be required to store all the distinctions we need to store as binary strings, there's way more ways of manipulating muscles than there is input data for how to learn how to manipulate them in specified ways without strong prior constraints on the search space (configurations of muscle contractions, say). Neurons are in the same position, there's way more distinctions we recognise and act upon easily than could be embedded into the neurons in binary alone. Another way of saying this consequence is that there isn't (usually) a 'neuron which stores the likeness of your partner's face". What this suggests is that how we learn doesn't suffer from the curse of dimensionality in the way expected from machine learning algorithms as usually thought of.

There're a few ways that the curse of dimensionality gets curtailed. Two of which are:

Constraining the search space; which Vagabond covered by talking about central pattern generators (neurological blueprints for actions that can be amended while learning through rewarded improvisation).

Another way it can be curtailed is by reducing the amount of input information which is processed without losing the discriminatory/predictive power of your processed input information, this occurs through cleverly aggregating it into features. A feature is a salient/highly predictive characteristic derived from input data by aggregating it cleverly. A classical example of this are eigenfaces. which are images that are constructed to correspond to components of variation in images of human faces maximally; the pronounced bits in the picture in the link are the pronounced parts of the face which vary most over people. Analogically, features allow you to compress information without losing relevant information.

When people look at faces, they typically look at the most informative parts during an act of recognition - eyes, nose, hair, mouth. Another component of learning in a situation where the curse of dimensionality applies is feature learning; getting used to what parts of the environment are the most informative for what you're currently doing.

Once it manages to snatch something tasty (like a bug or grain), it can start to optimize the pecking motion to get more "reward" (a hard wired pleasure signal that plays an essential role in the emergence of intelligence and intention). — VagabondSpectre

Like with pecking, it's likely to be the case that features that distinguish good to peck targets (like seeds' shapes and sizes or bugs' motion and leg movements) from bad to peck targets become heavily impactful in the learning process, as once an agent has cottoned onto a task relevant feature, they can respond quicker, with less effort, and just as accurately, as features efficiently summarise task relevant environmental differences.

Edit: in some, extremely abstract, respect, feature learning and central pattern generators address the same problem; Imagine succeeding at a task as a long journey, central pattern generators direct an agent's behavioural development down fruitful paths from the very beginning, they give an initial direction of travel, feature learning lets an agent decide how to best get closer to their destination along the way; to walk the road rather than climb the mountain.

We're talking about linguistic analysis, a philosophical method associated with the ordinary language philosophy movement and Wittgenstein.

But I think that the history of philosophy is simply not possible without the kind of semantic blindness Wittgenstein puts his finger on. That is, if philosophers know this, they sure act like they don't — Snakes Alive

Some papers read like shuffling words about, the best ones don't. Something like intersectionality (in the heritage of Bell Hooks) turns on stuff out there happening; taking something as a topic and providing a lens to see it through.As such, I think good philosophy facilitates or enables and then provides good descriptions of how things are. Even if that thing is its own lens crafting.

Though I will ask for sources on this use of local exponential trend? Genuinely curious. I can see the appeal of having a model that splits the time trend like that.

However, insofar as the growth is best described as some percentage of the population, then we are still in the exponential growth regime (locally time). — boethius

I can't really be bothered continuing this.

Although this week has reduced the growth rate compared to the week previous which was consistently above 20%, this could represent a new growth rate that would be sustained until the critical 60-70% of the population is infected. — boethius

There was an uptick in growth today and yesterday in Italy, it doesn't swamp the downward trend in new case number acceleration when averaging. What I wrote is a summary of the past trend, not an attempt at extrapolation. What has happened: number of new cases per day's rate of increase has been trending toward 0. You simply don't get that behaviour from an exponential function applied to the entire case number trajectory.

This is still exponential, in a local region of time, just that the doubling time is getting steadily longer according to official diagnosis[/]. — boethius

"Exponential in a local region of time" is a lot different from "exponential". The initial burst of growth in new cases you get in epidemics is rightly thought of as exponential, even in an uncontrolled environment the rest of it is sub-exponential growth (due to behavioural changes or saturation effects).

If something is exponential, the doubling time doesn't change. (edit, well, if you have exponential growth and observe a population at time $t_1$, the population will be doubled at $(ln(2)/B)+t_1$ where B is the growth rate, there won't be any "local changes in doubling rate" between the two time points, editedit: well, there will be changes in the derivatives of the curve between the two time points, but no changes in growth parameter).

Putting more symbols on it.

Let $C$ be the set of continuous functions over $\mathbb{R}$, then define the function $d : C \times C \rightarrow \mathbb{R}^+$ by $d(f_1,f_2) = \sup_{x \in \mathbb{R}} |f_1 (x) - f_2 (x)|$. $d$ is a metric, so $(C,d)$ can be thought of as a topological space.

We want to consider functionals over $C$, which are mappings $C \rightarrow \mathbb{R}$. Consider some subset $M$ of $C$ and a function $f_0 \in M$. Call a functional $L$ continuous at a function $f_0 \in M$ when and only when for all $\epsilon \gt 0$ there exists an open $U \subset M$ with $f_0 \in U$ such that $| L(f) - L(f_0) | \lt \epsilon$.

(Edit: an open ball with radius R centred at a function f (the collection of which generates this topology) seem to be the collection of functions whose supnorm is less than R; so can be thought of as the set of continuous functions which converge uniformly to f with R as the "minimal" least upper bound which can be used in a uniform convergence proof to f for all the ball elements.)

Stipulate that continuous functions have an arc length, and let the approximating staircase with $2n$ steps be $S(n)$. If we consider $f_0$ as the straight line, $S(n)$ has arclength 2 for arbitrarily small $d$-balls around $f_0$, which contain an $S(n)$ by uniform convergence.

The arclength functional is probably nowhere continuous in that sense? There will always be a series of approximating curves you can construct that have any desired arclength that uniformly converge to the desired function.