What is it like to be a bat?

You know what it is like to be a bat. To be a bat is to be a mammal like no other. You spend half the day dozing in caves, and then you all leave together. You flap about, in order to get anywhere. You find out where you are by seeing how the sounds you make come back to you. You are where all the others are. Each of you is there because everyone else is there. Everyone else is a bit batty. You know what it is like to be a bat.

Health and Safety

"Police officers are, quite rightly, furious at the government for failing to prioritise them in the vaccination schedule."

Click on that quote for more on that "quite rightly,"

Blaming the government is how our democracy works; but I was wondering, who failed to get the police vaccinated in the early days of this pandemic, when it would have done them (and therefore us) much more good?

Many months ago (here is a link to one timeline) the vaccines were safe enough to be given to thousands of volunteers, for phases II and III of the testing process (for a description of those phases see the quote below, which is cut-and-pasted from WHO). Could some of the vaccines not have been made available then, for key workers who volunteered (for the vaccines, not for participation in the trials, which were presumably randomized)? Tinkering with the timetable of the current roll-out of mass vaccinations would inevitably involve some risk to that roll-out. Why do people who failed to think this through earlier, when it would have done more good, now think that they know better than the government how to balance those risks?

Here is that WHO quote:

"An experimental vaccine is first tested in animals to evaluate its safety and potential to prevent disease. It is then tested in human clinical trials, in three phases:

In phase I, the vaccine is given to a small number of volunteers to assess its safety, confirm it generates an immune response, and determine the right dosage.

In phase II, the vaccine is usually given [to] hundreds of volunteers, who are closely monitored for any side effects, to further assess its ability to generate an immune response. In this phase, data are also collected whenever possible on disease outcomes, but usually not in large enough numbers to have a clear picture of the effect of the vaccine on disease. Participants in this phase have the same characteristics (such as age and sex) as the people for whom the vaccine is intended. In this phase, some volunteers receive the vaccine and others do not, which allows comparisons to be made and conclusions drawn about the vaccine.

In phase III, the vaccine is given to thousands of volunteers – some of whom receive the investigational vaccine, and some of whom do not, just like in phase II trials. Data from both groups is carefully compared to see if the vaccine is safe and effective against the disease it is designed to protect against."

Happy Valentines Day

Two Dragons

Flocks of susurrating starlings can look a bit like dragons.

And flocks, herds and tribes are deathless things.

Cultures endlessly accumulate knowledge.

They can be a bit robotic, though...

     Freedom has given us two parties, which compete for our votes. Individuals can choose to vote for one of them, or to waste their votes on other candidates, or not even vote at all. They can also apply to enter the parties. If they suit a party, they will do well within it if they dedicate themselves to performing well by its standards. Or they can leave the party, at will. And all of that freedom serves to maintain the culture of the party. The parties persist, each position filled by some appropriate person.

     And as they compete with each other, they evolve, in their own way, carrying us with them, as they evolve in an essentially mechanical way. They are a bit like a blue dragon and a red dragon, fighting over who gets to appoint our leader... or scapegoat? The parties compete for significant numbers of votes, but each vote is relatively insignificant. How can we feel responsible for what our representatives do? And yet, we are responsible for obeying the laws they make. And we are a democracy. Does the buck not stop with us?

     Could we make our parties more representative, if more of us joined them? Or would that tend to make our country even more divided? Perhaps we should get ourselves a more proportional system; then we could join (or at least vote for) a wider range of parties. If we do not, will the two parties move mechanically (in ways we barely understand) toward something even less representative? If so, then one way or another, we will be getting a different system. Should we think about voting for a transitional Liberal government and get a vote for PR (even though last time we got austerity and a vote for Brexit)?

     The people are collectively responsible for the form of their democracy, for voting within that system, for the outcome of that voting, and for what their leaders do. But most people in our democracies think that what is done in their name is not their fault. They scapegoat the politicians. And not without reason. Most of us did not vote for the people in charge. But everyone feels that their vote is relatively insignificant. And the outcome of an election really does have little or nothing to do with any particular vote, as though none of the voters are responsible.

Happy New Year (again ;-)

A limit of Empiricism

I set out to observe the world in a scientific way,
so I photograph the pond, and process the photo digitally,
and the sunlit willows being reflected in the shadows of other willows
show me that this part of the world at least is made of wave-mechanical string:

These Days

these days, those who are not "celebrities" for at least fifteen minutes are nobodies

Merry Xmas

Merry Custard (and a Happy New Year ;-)

(yesterday was the shortest day)

Looking back to what was once new, "Custard" :

Harold Budd (1936–2020)

The Village Duck-Pond, Winking

Living inside a rainbow!

 

Happy St Edmund's Day ;-)

20 November 869 AD was the day King Edmund of East Anglia was killed by Danish invaders. He became the patron saint of England.

St Edmund was replaced, as patron saint of England, by St George in the fourteenth century, mainly because Edward III wanted to be more involved with Europe (two centuries earlier, Richard I had been one of many Europeans uniting around St George as they defended Europe).

Ironically, English nationalists are fond of the flag of St George.

A true contradiction?

(a) the maths

Since adding zero to any amount does not change it, we can keep adding zeroes forever and it will make no difference: such additions always amount to adding zero.

We might write that as 0 = 0 + 0 + 0 + 0 + 0 + …, which can be spread out like this:

       0      =                             0                            +                             0                           +             . . .

Each 0 on the right-hand side can be replaced by 1 – 1, to give:

       0      =             (1            –             1)            +             (1            –             1)            +             . . .

In the next equation, the brackets have been removed.

       0      =             1              –             1              +             1              –             1            +             . . .

In the next equation, brackets have been put back in, in different places.

       0      =             1              +             (–1         +             1)            +             (–1         +             . . .

We now replace each (–1 + 1) with 0.

       0      =             1              +                             0                              +                         0              . . .

All those zeroes on the right-hand side add up to zero, of course. But that means that:

       0      =             1

Clearly 0 = 1 is false. So, where did we go wrong? Well, since the last equation was false, the equation above it must also have been false (the only difference between those two equations is the first equation, which was clearly true). And the next one, going upwards, 0 = 1 + (–1 + 1) + (–1 + 1) + ..., must have been false too, as each of those “(–1 + 1)” does equal zero.

Going the other way, from the first equation, 0 = 0 + 0 + ..., which was clearly true, the next equation, 0 = (1 – 1) + (1 – 1) + ..., is similarly true, because each of those “(1 – 1)” is zero.

In between those two equations, one false and one true, we have the infinite sum 1 – 1 + 1 – 1 + …, which was originally described by the Italian theologian and mathematician Guido Grandi (1671–1742).

Grandi was interested in the calculus (as described by Leibniz). And in the calculus, an infinite sum is equal to the limit of the initial finite sums as their length tends to infinity. Grandi’s infinite sum 1 – 1 + 1 – 1 + ... has initial sums that alternate between 1 and 0 = 1 – 1 endlessly (the next are 1 = 1 – 1 + 1 and 0 = 1 – 1 + 1 – 1). Since the initial sums tend to no limit, Grandi’s infinite sum is not given any value by the calculus.

By removing the brackets, we moved from an infinite sum of zeroes, which is equal to zero, to Grandi’s infinite sum, which has no value. Adding brackets differently then took us from Grandi’s infinite sum to a sum that is one plus an infinite number of zeroes, which is equal to one.

(b) the physics

You may be familiar with the idea of a particle/antiparticle pair appearing out of the vacuum. Such pairs give rise to Hawking radiation from a black hole, but all we need to know here is that such pairs can, in theory, appear from the background fields of the vacuum. Once formed, the particle and antiparticle are moving away from their point of origin, so we might picture them moving downwards, like this: /\ (near a black hole, one of them might be swallowed by the black hole, while the other flies away from the black hole, giving rise to Hawking radiation).

Space does not seem to be infinite, but an infinite space is a physical possibility. And in such a space, an endless line of such particles/antiparticle pairs is a possibility, for all that it is highly unlikely. We might picture them like this: /\/\/\/\/\... (the zig-zag continues to spatial infinity).

The top of that zig-zag pictures a line of particle/antiparticle pairs appearing, which might be modelled mathematically by modelling each particle as +1 and each antiparticle as –1. We then get this equation:

0 = (1 – 1) + (1 – 1) + (1 – 1) + (1 – 1) + (1 – 1) + ...

Each (1 – 1) represents a particle/antiparticle pair appearing.

They move downwards in such a way that each antiparticle collides with the particle from the pair to the right, so that they are both annihilated. The particle at the extreme left of the zig-zag is not annihilated. The bottom of the zig-zag therefore pictures events that are modelled rather well by this equation:

1 = 1 + (–1 + 1) + (–1 + 1) + (–1 + 1) + (–1 + 1) + (–1 + ...

Each (–1 + 1) corresponds to an antiparticle and a particle annihilating each other.

In between those two equations, there is no mathematical sum, neither 0 nor 1. That corresponds to infinitely many particles and antiparticles just being there, in between their creation and their almost total annihilation. The highly improbable, but physically possible, appearance of this particle from an infinite vacuum is therefore so well-modelled by 0 = 1 – 1 + 1 – 1 + ... = 1, that it is essentially an instance of it. It is in a very similar way that Jack and Jill being a couple is an instance of 1 + 1 = 2.

Such equations as 1 + 1 = 2 only exist because they are such good descriptions of any collection of two things. It is the physical instantiation that ultimately justifies the mathematical equation. And of course, to say of what is, that it is, is to say something that is true. Which raises the following question.

(c) the questions

Could 0 = 1 – 1 + 1 – 1 + ... = 1 be a true contradiction?

And in order to think about that question logically, should we use paraconsistent logic?

(d) my answers

Although a contradiction can be used as a description that is such a good description, it should count as a true description (as when we say that something is and isn’t a certain way, meaning that it is that way in one sense but not in another, or that it is that way about as much as it is not), that does not mean that the contradiction is true. Not too dissimilarly, there are two ways in which 1 + 1 = 2 is true. It is true as a description of Jack and Jill, and it is, in a different way, true by definition (of 2). And it is, in any case, not at all contradictory for there to be no particle and then, at a later time, one particle.

Why would anyone think that a mathematical model of reasoning that is not a very good model of logical reasoning (because if something is not the case, then it cannot also be the case: it not being the case means that it cannot) would help them to think logically?

Monochrome Monday

The same cat, who I used to meet

when out walking around the village

Sleepy Sunday

 Another photo from google+

SepiaCaturday

Have a Harrowing Halloween!!

Three years ago today,

a honeybee was contemplating the cosmos

Four years ago,

it was Trump and Mrs. Clinton, slugging it out. The general feeling over here was that Mrs. Clinton was a shoo-in. Indeed, her supporters called her "the only qualified candidate." But while she was certainly the most experienced candidate, I wondered at the time whether her experience would disqualify her, in the minds of a lot of the voters. Would they not feel that her two terms in the East Wing meant that her standing for president went against the spirit of the Constitution (amendment 22)?

Suppose that it had been Mr. Clinton in the East Wing for eight years, and that he had won against Trump (suppose that Mrs. Clinton only lost because she was a woman). If Mr. Clinton went on to win a second term, what would stop him divorcing Hilary at the end of his second term and marrying someone who became president for two terms? What would stop him continuing to remarry people who became president for two terms? The voters would: they would surely regard it as unconstitutional for him to stay indefinitely in the White House (as the traditional head of the presidential household).

As it is, of course, Trump won. "Will the same thing happen again this time?" the liberal elite wonder. I don't see how it could: neither Mr. nor Mrs. Biden have been president before. Nevertheless, if the liberal elite of America do not even know how America thinks about the unity of married couples, then how qualified could any of them be to embody America as its necessarily short-term president?

Five years ago today,

this Painted Lady butterfly was drinking from this butterfly bush: