Saturday, September 14, 2019

How to Turn Matter into Antimatter

1) Turn matter into electricity, using a nuclear power station.

2) Turn that electricity into light of a particular frequency.

3) Those photons decay into particle/antiparticle pairs.

Thursday, September 05, 2019

Brexit, Boris and Statistics

In the 2016 Brexit referendum, only 38% of the electorate voted to leave the EU.

Over a third of the electorate voted to remain in the EU, while 28% did not bother to vote either way. The percentage voting to leave was higher than the percentage voting to remain, but this referendum was primarily a measure of the will of the people for a particular change, not a contest, despite the political rhetoric. And various factors made it a fairly poor measure, despite the high turnout. Some people, for example, treated it as an opportunity to deliver a protest vote, a vote for a more general change, by voting against both the Prime Minister and the status quo.

Did the 2016 results deliver a mandate for change? Should that Prime Minister have regarded Brexit as mandatory?

To see why not, you only have to consider the 28% who did not bother to vote, who were bothered neither by the status quo, nor by the thought of change. Did those people contribute to any such mandate? Hardly. To see why that matters, consider how big the vote had to be, for there to be a mandate. Had this been a matter that Parliament was indifferent about, then 38% (52% of the turnout) could have been good enough. Why not? But the people were asked, in that referendum, about a change that the majority of their democratically elected representatives did not want, and which the Prime Minister himself did not want. Had more than half of the electorate said that they did want that change, then perhaps their representatives should have taken that result to be mandatory, even if they did not think that Brexit was a good idea; why not? But, that was not what happened. What happened was that there was much talk of a mandate for Brexit, and a lot of other talk. What happened was politics.

All that politics was and is entirely appropriate, because it is up to our democratically elected representatives how to interpret such measures of the will of the people.

There were party manifesto commitments in the 2017 general election. But even those do not make Brexit mandatory, because people vote for a person, not a party, and the influence of a party manifesto on the average voter is arguably less than the influence of the showmanship of the leader of that party. Boris was not the leader of his party in 2017. He is now our Prime Minister, though; and he observes that there was nothing about a deal in the referendum question. As though that means that there was a mandate for Brexit whether deal or no-deal, or deal obtained by means of a threat of no-deal, or whatever. But there was never any such mandate, in the sense of something mandatory, for anything that Parliament did not want. Such a mandate does not trump the political rhetoric; talk of such a mandate is simply part of the political rhetoric. What should trump the rhetoric is logic and the facts, such as the fact that only 38% of the electorate expressed a desire for this rather democratically unpopular change.

Surely the people think that, when it comes to running the country, showmanship should be less important than the facts of the matter.

Wednesday, July 17, 2019

Saturday, March 23, 2019

My References

It is Vienna, 1894, and I am painting a goldfinch; but even in this fantasy I am painting very badly. Still, I am a prince and so everyone is pretending that I am not too bad at it. My painting is complimented, and hung up in a corridor.

Eventually the painting is found by the Nazis, who take it for a bad painting of a robin. Since it would make Hitler's paintings look good, they move it to Berlin. Everyone ignores it though. They are very busy. After the war it ends up in Boston, where someone says: "That bird was very well fed." And it was a rather plump goldfinch. But these people imagine that they are talking about a robin. Some of them assume that it was an imaginary robin, it was so badly painted. But in fact, all of them were talking about a goldfinch.

Or, do you think that they were talking about robins? How very modern! To see why they were not, suppose that we are  looking through a warped and dirty window, at a fat goldfinch in bad light. You might at first think that it is a robin. But you are looking at a goldfinch. If you point and say "that bird" then you are referring to a goldfinch.

Were you a mad man, used to seeing things that are not there, you might assume that it was your own personal hallucination of a robin that you were seeing. But even then, your "that bird" would refer to the bird that you were looking at. That is just the way reference works in our public language. And it is clearly the same if we are looking, instead, at a very bad photograph, of a very fat goldfinch.

Suppose the photograph is so bad that someone takes it for a bad picture of a robin. When she talks about the bird in the picture, she is referring to something that was photographed. And even if she thinks that the picture is a sketch of an imaginary robin, it is still actually a photograph of a goldfinch.

And we developed language on top of whatever else we already had, and so the same underlying principle would apply to the semantics of names; primarily to spoken names, and secondarily to written names like these: Mill knew that it did, whereas Russell appears not to have known.

Thursday, February 21, 2019

The Irony Age

It has always been ironic that Christians call upon saints to save them from acts of God. But nowadays you can get called "racist" for comparing Mohammed's "the Recitation" with Hitler's "my Struggle"; or for likening overdressed Muslim women to letterboxes (as Boris Johnson did), even though that is surely no worse than likening nuns to penguins, as in The Blues Brothers (hardly a racist movie). And what do we call criticizing the dresses of The Stepford Wives? Feminism? Ironically, Boris Johnson had been defending the British Muslim woman's right to dress conservatively in public, against a wave of European restrictions.

For such reasons I think of this as the Irony Age. For another example, hominids that were not human were presumably hunted by primitive tribes of humans. Many of them might have been hunted to extinction, as humans evolved; such is evolution. Neanderthals took their time becoming extinct, so they might have evolved an instinctive fear of the human form: those without some such fear may well have had a significant disadvantage. This is only a possibility. But since white people are the product of humans and neanderthals, it is conceivable that a fear of humans evolved in neanderthals and was then inherited by white people. That is, it is a reasonable scientific theory that racism was originally caused by black people (ironically). Maybe it is not a true theory, of course; but, do you find yourself wanting to say "probably not" instead of "maybe not"? Would that be for scientific, or for political reasons? Since most scientists would want to say "probably not" it would not only be politically correct, it would be scientifically correct to say that, because science is what scientists do (ironically).

So much for racism; what about sexism? Well, there is a slight difference in average height between women and men. Some of the causes of that fact may well have been sexist, but the fact itself is not. It is just a fact. Still, one of the consequences of it is that the tallest adults are predominantly male. That is mainly because of the bell curve: random variation produces values that lie on a curve shaped like a bell, most of them clustered around the middle. Put a bell curve close to another one and there is a lot of overlap in the middle, but on each extreme almost all the outliers are from just one of those curves. Again, that is not sexist, it is mathematics. Now, humans do tend, quite strongly, to look up to taller humans (pun intended); which is again probably not, in itself, sexist, but it does mean that when it comes to promotions to top positions, taller humans – who are mostly men – tend to do better. This results in part of the gender pay gap.

As a result of successful legislation against sexism, the gender pay gap is now mostly affecting older women, and those in the top jobs (who tend to be older). So the height factor might be a significant part of this gap. An irony is that trying to make things fairer by promoting women who apply for top jobs – probably taller women – over the least attractive men who apply – probably the smaller of the men – would worsen the actual unfairness of our looking up to taller humans. It is likely that seeking equality elsewhere could similarly worsen sexism (although describing too many particular cases would probably get me labelled as sexist). Another irony is that you might, in general, want to pay women more than fairness would demand, in order to get more role models, to help to combat centuries of sexism.

There is lots of irony when it comes to abortion. Those who are against it because it is, they believe, murder, are usually for the death penalty; this is called "ironic", ironically, by people who are usually called "clever". It is not ironic, because the death penalty is for guilty people, not babies. No, abortion is ironic because those who are for it usually say that they are defending women's right to control their own bodies. They are defending no such thing (as follows), and it is ironic that they are regarded as the scientific ones, the ones saying it how it is, the clever ones. People who are for abortion do not want women to have the right to try to abort their own baby, they want doctors to have the right to do it for them. So consider a woman who wants to kill herself (or just hurt herself). If it was about a woman's right to control her own body, then there should be a demand that doctors be allowed to help the woman to kill herself (or hurt herself, etc.) just because she wants it. To say that it is OK if she is terminally ill, but not OK if she is mentally ill, is like saying that abortion is OK if the baby or the mother was going to die anyway and the abortion is to save the life of the other (the mother or the baby respectively).

Plenty of people who wanted to kill themselves end up glad that they did not; and similarly, plenty of people who wanted an abortion end up glad that they did not have one. Less closely analogous: what about a woman's right to control her own home? Can she kill anyone who is in her home? Would the difference be that unborn babies are not people? That, I think, is the difference. If so, then it is not really about the right of women to control their own bodies, it is about whether and when an unborn baby is a person. The day before birth? A month before? A month and a day? A month and two days? There is no good scientific answer, and so the proponents of abortion on demand talk about something else, something that sounds good; which makes this a sort of populism. Ironically, the left have turned "populism" into a word that means something else, by way of their predominance in academia and the intelligent media. Actually, that is not just ironic.

Wednesday, September 05, 2018

What Do Philosophers Do?

For myself, I just notice such facts as:

(A) The overwhelming majority of professional mathematicians are not going to be wrong about what numbers are.

(B) The overwhelming majority of mathematicians assume, in their professional work, that numbers are axiomatic sets.

(C) Numbers are not axiomatic sets.

The conjunction of (A), (B) and (C) would be a contradiction, were the mathematicians of (B) not just assuming that numbers are axiomatic sets for the purposes of proving theorems from axioms, as I suspect they do. But many analytic philosophers deny (C), because of that apparent contradiction. Such philosophers also ask questions like: “Do numbers (or sets) exist? If they do, where are they? If they don’t, then what does ‘2’ refer to?”

The implication is that since numbers (or sets) are abstract objects, hence if they do exist then they exist in some Platonic realm of abstract objects, raising the question: “How is it that we can access that realm, in order to know such properties of numbers as arithmetic?” To see how stupid such questions are, one only has to ask such questions as: “Does value exist; and if so, where is it?” Clearly some things have value, but it makes no sense to ask where it is (or what colour it is); such questions hardly further the analytical task of describing accurately what value is.

A question similar to the one about numbers might be: “Do shapes exist?” Shapes are instantiated in, and abstracted from, shaped things, clearly; and similarly, whole numbers are instantiated in, and abstracted from, numbers of things. That is basically what John Stuart Mill said (in passing); it is only common sense, although his observation was jumped on by a founder of analytic philosopher, Gottlob Frege (incorrectly).

Sunday, September 02, 2018


F is six

The ancient Greeks used alpha, when doing arithmetic, instead of our one, 1, and had beta for 2, gamma for 3 and so forth. The symbol for gamma was like a reflected L, and so our letter F began life as digamma (an anagram of mad magi), which they used for 6.

Since the New Testament was originally written in ancient Greek, the Number of the Beast was basically FEX, which is indeed the name of a man.

Or, is Mark Zuckerberg the Antichrist? Revelation 13:17 is:
no man might buy or sell, save he that had the mark, or the name of the beast, or the number of his name
And even this very Blogger have facebook at the top of these pages (under “More”). Even the BBC, who are not supposed to advertise (they famously say “sticky-backed plastic” instead of sellotape) show us the Facebook symbol, the ancient Greek number of his name.

Or, is the Beast Money?

This post is about physics (ancient Greek for “nature”) though; and in particular, an urban myth:

Urban Myth

The myth concerns a small machine with a clock-face of light bulbs, one of which is on at any given time when the machine is on. Which bulb it is that is on is determined by which one was previously on and how a small radioactive sample has decayed in the unit of time of the machine: the light will have moved one place clockwise if the sample emitted a detected particle in that time, one place anticlockwise if no such particle was detected. The unit of time is such that there is a 50% chance of a particle being detected in that time.

The machine (which is clearly from The Fury, which was about magical Jews, who were also exactly the sort of people who wrote the Bible, according to the Bible itself) is placed in front of a human subject, who has to try to make the light move clockwise by really wanting it to. The myth is that some physicists built such a machine and got the light to move clockwise more often than would be expected from random motion. Other physicists tried to repeat the experiment and, according to the myth, they got no positive results. The original results were explained as being random after all (quite likely because things that are truly random tend to look more structured), or as being due to methodological errors (they were physicists, not parapsychologists).

However, the original results could hardly have been undermined by similar results not being obtained with other people, who might not have had the same abilities. Further research, of an appropriate kind, would have had to have been carried out, because of the enormous implications for physics: Modern physics is based on particle physics, which is based on observations of what is essentially a scaled-up and much more complicated version of the small machine. If physicists could affect the events inside particle accelerators, via their expectations and desires, then that would throw a whole new light on particle physics, and hence the whole of physics.

Had there been something to find, then they would have found it, and physics would have changed accordingly. Now, we would have noticed, because there would hardly be this urban myth floating about had they wanted to keep it secret (the possibility of secrets arises because of the money in innovation, the world wars, the cold war and so forth). So, it must be a myth because conversely, had there not been anything to find, then that would have put micro-psychokinesis to sleep forever. Since the physicists would have wanted to be quite sure, hence they would have been quite exhaustive in their investigations. Whereas, parapsychologists still investigate micro-psychokinesis.

Evidence that there is micro-psychokinesis could therefore include, given the above, the very success of relativistic physics. The equations of relativistic space-time were developed at the end of the nineteenth century, even before the quantum-mechanical nature of moving particles had been noticed. It was an amazing discovery, and it is even more amazing that it has not fundamentally altered because it is inconsistent with quantum mechanics. But, particle physicists keep finding patterns that verify it. (Particle physicists are very proud of their understanding of the sophisticated mathematical language of relativistic physics, of course.)

The main evidence is the operation of the human brain (how else is the mind going to influence the working of the brain?) and a few paranormal phenomena; but how odd that the equations of relativity arrived out of nowhere when wars were still being fought on horseback. We are asked to imagine how the world would look were we going at the speed of light, because physics should always look just the same. Then we find such equations. But what if bats did physics? Would Bert the bat assume that nothing goes faster than the speed of sound? What if his equations ended up being very complicated? What would that mean? That he was a batty bat?!

There was an experiment to test the speed of light in various directions. It was small enough to fit inside a plane. So imagine how sensitive it was. Then it was taken up in a plane!! (There just are not enough exclamation marks there, but I do not wish to come across as mad!) (?)

Saturday, September 01, 2018

Curry's Paradox

Last year’s new SEP entry on Currys paradox followed in Haskell Curry’s footsteps by saying nothing about where our reasoning goes wrong in such informal versions of the paradox as the examples in the introductory section of that entry, the first of which was as follows:
Suppose that your friend tells you: “If what I’m saying using this very sentence is true, then time is infinite”. It turns out that there is a short and seemingly compelling argument for the following conclusion:

(P) The mere existence of your friend’s assertion entails (or has as a consequence) that time is infinite.

Many hold that (P) is beyond belief (and, in that sense, paradoxical), even if time is indeed infinite.


Here is the argument for (P). Let k be the self-referential sentence your friend uttered, simplified somewhat so that it reads “If k is true then time is infinite”. In view of what k says, we know this much:

(1) Under the supposition that k is true, it is the case that if k is true then time is infinite.

But, of course, we also have

(2) Under the supposition that k is true, it is the case that k is true.

Under the supposition that k is true, we have thus derived a conditional together with its antecedent. Using modus ponens within the scope of the supposition, we now derive the conditional’s consequent under that same supposition:

(3) Under the supposition that k is true, it is the case that time is infinite.

The rule of conditional proof now entitles us to affirm a conditional with our supposition as antecedent:

(4) If k is true then time is infinite.

But, since (4) just is k itself, we thus have

(5) k is true.

Finally, putting (4) and (5) together by modus ponens, we get

(6) Time is infinite.

We seem to have established that time is infinite using no assumptions beyond the existence of the self-referential sentence k, along with the seemingly obvious principles about truth that took us to (1) and also from (4) to (5).
That may look rather formal to you, but formal logic is not even logic (it is mathematics); the above is just very well laid out. Note the two uses of modus ponens, the two sets of three steps, with the first three steps, (1), (2) and (3), all beginning “Under the supposition that”. You should note that because we cannot always use modus ponens within the scope of a supposition, e.g.:

(a) Under the supposition that modus ponens is invalid under a self-referential supposition, (A) implies (C).

(b) Under the supposition that modus ponens is invalid under a self-referential supposition, (A).

With (a) and (b) we have, under the supposition that modus ponens is invalid under a self-referential supposition, a conditional and its antecedent, but it would of course be absurd to use modus ponens within the scope of that supposition, to obtain

(c) Under the supposition that modus ponens is invalid under a self-referential supposition, (C).

There was, then, at least one step in the above argument for (P) that stood in need of some justification, i.e. the step to (3). Were no other step deficient in justification we could conclude, from the absurdity of (P), that the step to (3) was invalid.

Of course, it would be more satisfying to see where precisely that step lacked justification, so presumably we need an analysis of what would in general count as justification for such a step. For now, note that in order to get to (3) we used modus ponens under the supposition that k is true, which was no less self-referential than the supposition that modus ponens is invalid under a self-referential supposition. In the step to (3) we had k being true instead of (A) implying (C), and “k is true” instead of (A).

To progress, we need to step back, I think, because I suspect that the reason why we find (P) to be beyond belief is that the above argument for (P) has exactly the same logical structure as a clearly invalid argument for the obviously false (Q):
Let your friend say instead: “If what I’m saying using this very sentence is true, then all numbers are prime”. Now, mutatis mutandis, the same short and seemingly compelling argument yields (Q):

(Q) The mere existence of your friend’s assertion entails (or has as a consequence) that all numbers are prime.
My suspicion is based on the fact that one could conceivably have a valid argument for

(S) The mere existence of “happy summer days” entails (or has as a consequence) that time is infinite.

For a start, the mere existence of some words can entail the actual existence of something important, as when Descartes proved that he existed: I think, therefore I am. But furthermore, there is a surprisingly valid argument from the existence of “happy summer days” to the probable existence of a transcendent Creator of all things ex nihilo (this links to that), and it might only take some tidying up to get to (S), because such a Creator is an omnipotent being endlessly generating a temporal dimension. (Such a Creator could possibly have a logical existence proof, because of its unique ontological status.) And of course, were there a valid argument for (S), then there would be an identical, equally valid argument for (P).

Anyway, a six-step argument for (Q) that is identical to the Curry-paradoxical argument for (P) would have, in place of k, some such l as “If is true, then all numbers are prime”. And is likely to be about as true as not, because (i) it is about as true as not that a contradiction follows from a statement that is about as true as not, since such a statement is about as false as not, and also because (ii) one informal meaning of is the obvious meaning of the liar sentence “is not true”, which is, if meaningful, about as true as not, according to my The Liar Proof. And of course, our logic is naturally suited to that part of our language where propositions are either true or else not true, exclusively and exhaustively. For a proposition that is otherwise, we have natural clarification procedures that enable us to construct new propositions that are more suited to logical reasoning. So, it seems likely that propositions that might be about as true as not should be ruled out from the use of modus ponens within the scope of a too-self-referential supposition (to say the least).

Curry’s paradox entered into the analytic philosophy of the Forties, where the logical paradoxes were in general thought to be reasons for replacing our informal logical reasoning with formal logical reasoning (via the mathematical philosophy of formal languages), on such grounds as that (i) one would not expect primates, even highly evolved primates, to be able to reason perfectly, and (ii) the physical sciences use mathematics to get to the underlying physical laws. However, why would such primates not take themselves to be reasoning perfectly adequately; and why should I be doing mathematics when I am really doing philosophy?