Wolfgang Pauli, Nobel Laureate, was a stunningly good physicist by any metric. He discovered (invented – we can debate this ’till the cows come home) the “exclusion principle”. Now this is true. Full on true. Basically it means Fermions can’t occupy the same energy levels but Baryons can. For this he won the Nobel*. So did Barack Obama. It really is a fucking laughing academy. Anyway, Pauli made the Universe (or discovered it) and that matters. Apart from getting pissed and having sex that was kinda what I did at College. I once had to do this. If that sounds dull, it was.

I also wrote a thesis on Kurt Gödel, He had some interesting views on GR (I’m a bit of a spesh on GR). Seriously! And time travel and formal logic – I am very dull. Well, I’m a Whovian so… I mean what is the effing point of having degrees in physics and astrophysics if you can’t build a time machine? None! I did this to understand the Universe and not be carted round as a spacka. That is a terrible thing to say but I said it. I also have a shed and no time machine. Possibly because it’s impossible. It is BTW.

Tonight I’m off to the Royal Exchange Theatre to see *Orlando* starring the TARDIS. Yes, that is me. She is also known as Suranne Jones. But she is still the TARDIS. And bow-ties *are* cool.

Always the TARDIS for me. Well, I don’t watch Corrie do I? So should be fun seeing Idris and the Royal Exchange is a lovely theatre. It really is but then I guess you expect that in what to all extents and porpoises is our second city – Glasgow is Jockulent and Brum is well, Brum. I live in abouts Manc for a reason. I mean we have a proper China Town and stuff. We have a Gay Village and not just a street as Newcastle has. Having said that Newcastle does have the best named gay bar ever – “Camp David” – always cracks me up. That is the work of Genius. My bro pointed it out to me and I was Laughing and Grief for like 20 minutes. A few years back the council tried to pursue the “pink pound” to risible results. Nobody – gay, straight or whatever goes on holiday to Newcastle. They just don’t. I mean I might be tempted to go see Stephenson’s Cottage and his first railway but that is walking distance from my Mum’s house and that is not exactly a holiday is it? I’ve walked there with my wife – actually every girl I have dated. I am a hot date! I’ll also use it as an opportunity to get onto the theory of thermodynamics – upon which I can bore for the Commonwealth. It is quite amazing I happen to have spent the best part of the last twenty years in relationships with girls.

H/T to Samizdata for getting me thinking on Pauli. Now, the Pauli quote is “ganz falsch”. Literally “quite wrong” with the meaning in German of, “Not even wrong”. Or in Geordie, “best bollocks”.

* Dear Joe Stalin objected. He believed Pauli was trying to prove Fermions refused to collectivise. Seriously. Of course. They have half integer spin! This has nowt to do with politricks. This is truth. This is just the way things are. No quantity of Marxist-Leninism changes reality.

Pauli wasn’t just a great physicist (though he was – money quote comes from Richard Feynman – he get’s doorstepped at the Nobel “do” and asked by a press fella to explain in five minutes what he did to win the Nobel, “Right, pal, if I could explain in five minutes it wouldn’t have been worth a Nobel would it?” I guess not). He was a great critic of physics. You utilise sloppy thinking in a seminar and Pauli is there and mutters “ganz falsch” you have met a stranger in the Alps.

Discovered not invented. Fichte was wrong (even Kant attacked him). The universe exists independently of our minds – it really is “out there” (objectively) waiting to be discovered.

That does not mean that the mind can not create thins – for example the TARDIS.

Unless somewhere out there……..

Well, yes and no Paul. Reality might be real (though how would we know?) though I tend towards Dr Johnson’s rock-kicking but our knowledge of it is not necessarily utterly true. Oh, some of it is at least in principle and the fundamentals. But the invented/discovered thing still has cojones. It still matters. We do have theoretical structures (superconductors spring to mind) and no bloody idea how they work. The theory works fine (as such) but there is no real understanding there. Huge areas of maths are a complete mystery and possibly such in principle. I leave you with the Berry Paradox…

“The number of syllables in the English names of finite integers tend to increase as the integers grow larger, and must gradually increase indefinitely, since only a finite number of names can be made with a given finite number of syllables. Hence the names of some integers must consist of at least nineteen syllables, and among them there must be a least. Hence “the least integer not nameable in fewer than nineteen syllables” must denote a definite integer; in fact, it denotes 111,777. But “the least integer not nameable in fewer than nineteen syllables” is itself a name consisting of eighteen syllables; hence the least integer not nameable in fewer than nineteen syllables can be named in eighteen syllables.”

- Russell & Whitehead, p. 61, Principia Mathematica. They take roughly 400 pages to prove 2+2=4.

That’s logic for ya!

Now here’s a mentalist bugger for you. How do you prove there are no uninteresting numbers…

My wife says that has a big white beard… So, if one accepts the Copenhagen Interpretation of QM when precisely does the wave collapse and become “stuff”? Buggered if I know.

There is a most interesting word in the abstract to which Nick linked, to wit: “maghemite … is usually of pedogenic origin.”

Now it should be clear to any fool that the “ped” root in “Wikipedia” is from the Latin

pes, pedis,* “foot.” Hence my frequent reference to “The Foot of All Knowledge.”Whereas in the phrase cited, the “ped” (or “pedo”) root is equally clearly built on the Greek stem

pedo,* meaning “boy” or “child.” From this, one may clearly deduce that maghemite is created by children. Or, in particular, by boys.*Sigh… being verbal is SO inconvenient. Almost as bad a time-consumer as being connected to the Internet. … Just for the sake of intellectual honesty, I did look those up to verify what I thought I knew, and discovered that while I wasn’t exactly wrong, the real roots lay farther back than I thought.

. . .

Seriously, having gone that far I got curious to see what the meaning of “pedogenic” really is. Online, the Oxford Dictionaries say, “Relating to or denoting processes occurring in soil or leading to the formation of soil.”

To me that’s somewhat of a stretch, but geeks of all persuasions use maladopted [sic] terms all the time, so …. However, the O.D. also give “meaning 2″ for the root “pedo,” as being

pedon,“ground.”Which is interesting because it takes us back to my wordplay on “Wikipedia” as the “foot,” or “ground,” of all knowledge….

‘How do you prove there are no uninteresting numbers…’

Two fallacies, proving a negative, and assuming that the characteristic of being ‘interesting’ (or not) is objective.

Nick and Paul,

“Pauli made the Universe (or discovered it)” doesn’t specify the possibility that seems correct to me, although I think Nick put it that way for stylistic effect rather than meaning literally that Pauli

madethe Universe.(Of course, I can’t read Nick’s mind, so I Could Be Wrong. But if he really thinks it possible that, literally, Pauli, “made the Universe,” then he, Nick, should be referring to Pauli as “He,” not merely “he.” And if my understanding that Nick is more or less an atheist in some sense or other, I don’t see how he, Nick, could believe that he, Pauli, is (was??) God. *g*)

I would say that Pauli invented a theory that (as far as we can tell at this point) explains (or describes) a phenomenon for which we have no other or better theory or explanation.

And actually, I take “Pauli made the Universe” as a poetical, metaphorical way of saying that Pauli came up with a theory that’s apparently correct and that explains something

fundamentalabout the physical world as it appears to us. My own metaphor for human understanding generally is that as we go along we develop mental maps of the world (i.e. of Reality); thus Pauli contributed a large and important filling-in of a part of the map where it was formerly written, “Here there be dragons.”Abstractions, concepts, theories are invented by humans (and 100′ round blobs that are philosophers from other galaxies, as Paul once pointed out) to explain to ourselves in terms we can understand the world in which we find ourselves. And to the extent that those explanations or theories really do reflect what goes on in that world — how it works, in human terminology — we can, must, and do use them to make our way about that world.

Nick has found the Creator, and Julie is concerned about capitalisation, nice to see that standards are maintained.

Mr. Ed,

“Proving a negative” isn’t a logical fallacy. “Proving a negative” is a process whereby one produces an argument, which may or may not be fallacious. The fallacy (if there is one) is a step, or minor conclusion, within the argument that purports to be logical but is not.

There was a discussion awhile back (end of December I think) on whether it’s true that “you can’t prove a negative.” Well, of COURSE you can — we all do it all the time.

(1) “There is no real, adult, full-sized elephant riding in the basket of this bicycle right now.” This is clearly a negative (i.e. negative proposition), no? All I have to do to prove my statement to any particular other person is to show that person this bicycle, the one in question, which doesn’t even have a basket — as the other person will see just by looking at it — let alone an elephant as described, riding in the non-existent basket.

(2) Or, an example I gave back then, more true-to-life: I’m in the grocery store. Gee, I’d love to buy a lobster tail for dinner. But I can’t [first negative proposition: I cannot here and now buy a lobster tail], because [proof:] I haven’t got enough money with me [second negative proposition]. [Proof:] Look, here’s my purse. Count my money. If you want, you can do a strip-search and even a cavity search, but you will still find only a dollar available for me to spend, whereas the cheapest lobster tail here is priced at $ 24.99.

Thus, a 2-fer: Two negative propositions about the real world of objects, proven.

(3) An abstract one: There is no integer x such that x-1 = x+1.

Proof: Suppose the contrary. Then we have (x-1) – x = (x+1) – x ; or, -1 = +1

—–which is a contradiction (or, “which is absurd”). Therefore the assumption that such x exists is false, which is the same as saying that no such x exists, which is what we were to prove.

Surely everyone here has heard of the “argument by contradiction” or the

reductio ad absurdum,to give it its Latin name.. . .

As for Nick’s second point, about whether some number is “uninteresting” — Mr. Ed is using the word in the common, everyday sense of interesting. “That’s an interesting piece of rock.” “No it’s not — it’s one of the most boring, repetitive, cacophonous, unsophisticated and uninteresting example of sheer unmitigated RACKET I’ve ever heard in my life.”

But within mathematics, at least, “interesting” can have a much narrower meaning. A number is “interesting” if it is one of some particular set of numbers that mathematicians finding interesting for its (the set’s) mathematical properties, or for the interesting mathematical properties of some or all of the numbers within the set. For instance, 2 is “interesting” in that it’s a prime number, and not only that, but it is the smallest prime number.

So the question is, is there any number which is not “interesting” in that particular sense: that its existence implies anything further about some set of numbers of which it is a member?

Of course, I will admit that even mathematicians have (believe it or not) humanness and that therefore a given mathematician will find one number or one mathematical fact or conjecture more interesting — more engaging to him personally — than another, in the everyday sense of the word.

Mathematics is a fascinating field. :>)))

Mr. Ed, I’m glad I’ve finished my coffee–else my Mac would at a minimum require a long session under the hairdryer! LOLOL

111,777

One hundred eleven thousand seven hundred seventy-seven:

One hun-dred e-lev-en thous-and sev-en hun-dred sev-en-ty sev-en

…1….2…….3…4..5….6……7…..8……9….10..11…12….13..14.15.16..17 syllables

So, 17 = 19? As in my example of mathematical non-existence above, I’d have thought it pretty easy to show that 17≠19. For suppose 17=19. Then 0=2, whereby, for instance, no Russells equal two Russells. Even with a Whitehead thrown in, and P. 64 or no P. 64.

Of course, you can get around this by gratuitously sticking a couple of “ands” into the number when you speak it aloud. But you can’t write it on paper using only digits: 111&7&77 ??? It would have to be understood that the second “&” stands for “hundred and.”

Besides, back about 2nd grade when we learned about large numbers we were taught that it’s not good usage to say “seven hundred and seventy-seven”; always say “seven hundred seventy-seven.” Similarly with 111-thousand stuck on the front.

Russell’s problem is that he never went to school, or else that he can’t count. (No shame in that–neither can I, unless I take my socks off, and sometimes not even then .)

God, I wish I understood this stuff. What’s GR?

More importantly, that “paradox” is no such thing, because the line of argument calls for a switch in the understanding of what is meant by the word “names.”

It is true that the REFERENT of the number-name 111,777 and the REFERENT of some particular description of it are one and the same. But so what? A name and a description are two different things; to lump them together by arbitrarily lumping a description and a name together and then referring to them both as a “name” is a category error.

Furthermore, I’m sure there are other ways of uniquely describing that number. Heck, if you don’t mind sticking in those superfluous and’s, you have a “name” that is still uniquely descriptive but that has neither 17 nor 18 but rather 19 syllables. So what.

(Of course, there’s another category altogether which contains both the category “Names” and the category “Descriptions,” and that is the category “Designators.” But that’s beside the point.)

. . .

Now, there’s another way to look at the issue of the “names” of numbers (and although nearly everything has already been invented, including I am sure this idea, I still also invented it myself in the course of thinking about teaching regular introductory high-school algebra). *pats self on head approvingly*

A thing can, of course, have more than one name. For instance, you might call me Julie or you might call me Mrs. Krauss, but either way you are using the name to refer to ME. (Of course that won’t do if there is another Mrs. Julie Krauss loitering somewhere about.)

When you solve an equation, say x+79 = 81-x, you’ve already specified or described x; x, the number satisfying the equation, is unique.

The point of “solving the equation” or “solving for x” is, specifically, to learn theNUMBER-NAME (as I call it)of x,which is 1.I wish somebody had put it to me that way when I was taking freshman algebra. It would have helped to have known what was the idea. :>(

So, you might give something or other one of its names (or descriptors), and try to figure out from that, and from other background knowledge you might have, another of its names. As when solving an equation.

But you might also have two designators, and be interested in the relationship between their referents. (This is quite often the task in mathematics.) Interestingly, sometimes it turns out that they both refer to the same thing. “Bok choy” = “Chinese cabbage.” But what is the relationship between Santa Claus and Christmas? Or between 111,777 and “one hundred eleven thousand and seven hundred and seventy-seven?”

Andrew — I fancy the gentleman means General Relativity. I could, of course, be wrong.

What I want to know is, what’s TARDIS?

Also, what’s a “spacka”? A spectator, or is it specific to Whovians, or what?

And Nick, interesting posting, interesting comment.

Nick — without expanding on his idea in any way, one guy in a comment on some board said that the reason for the “uncertainty” in QM is that the phenomena occur below the “noise floor.” I assume he means that the signal-to-noise ratio isn’t fixed and that the signal that would tell us where the quantum is, is less than some percentage of the noise.

It sounds good, but me no do QM and me have no idea if the contents are as pretty as the package.

Of course lots of people say Copenhagen is nonsense on stilts. Even if you throw out the Hidden-Variable idea, there would seem to be contenders left standing, like the one above.

Can I go home now? *waves goodby*

General Relativity. The theory of gravity.

The point about uninteresting numbers is mathematical induction really… 1 is the unit so obviously interesting, 2 is the only even prime yadda, yadda. Now at some point you get to the first boring number but in and off itself isn’t that interesting? My point about Pauli was not that he or He created the Universe but that due to our complete lack of understanding of what QMech actually means the discover/invent thing is somewhat moot. And trust me I have spent many hours pondering that one. I suspect David Deutsch and/or John Wheeler might have got closest but the alternatives are not good. Copenhagen is a bloody nightmare and most other interpretations are essentially statistical or even just come down to, “Well it seems to work so…”

It never helped that the likes of Bohr and Heisenberg were cryptic to the point of gnomic.

Now, for something completely different. Hold on to your hat Paul! RIP The Reinterpretation Principle. This is what Feynman got his PhD for. Antimatter is mathematically identical to matter travelling backwards in time. That was supervised by John Wheeler. And there are some bizarre paradoxes even in Newtonian mechanics. And then there is logic and transfinite numbers. Oh, there is some stock of weirdness there. The truth is rarely pure and never simple. Example. Once in Leeds I walked home after a day at the math-face and there was a patch of grass which had been mown by the council. All apart from one little bit. How do you explain that? I could because I’d walked past it in the morning. And I saw the council fella with his ride-on mower and a drunk utterly zonked with an empty bottle by him. The council fella had clearly mowed around him. Makes sense. Who wants to rouse a potentially truculent drunk? But if I hadn’t seen that in the morning it would have been an MH370 of a mystery would it not?

Julie ‘One hun-dred e-lev-en thous-and sev-en hun-dred sev-en-ty sev-en

…1….2…….3…4..5….6……7…..8……9….10..11…12….13..14.15.16..17 syllables’

In England, we would add an ‘and’ in thus:

‘One hun-dred AND e-lev-en thous-and sev-en hun-dred AND sev-en-ty sev-en

…1….2…….3…4..5….6……7…..8……9….10..11…12….13..14.15.16..17 syllables’ +2

It also strikes me as irrelevant that a language may tend to have longer words for bigger numbers, it ain’t necessarily so in all languages, and the argument somewhat discounts scope for neologisms or new numbering conventions, and indeed is more about nuances of a particular language than about mathematics.

As for 2 being an interesting prime as an even number, that is not a function of 2 but rather of the real integers less than 2 only consisting of 1, it is no glory to 2 that there is no real integer less than 2 bar 1, it is just that the scarcity of integers less than 2 makes 2 a prime. 2 is just a beneficiary of 1′s oneness, a freerider even.

As for the fallacy of proving a negative, I was looking for a mathematical proof that there are no interesting numbers, which sounds rather like a Monty Python sketch.

…Let ‘Z’ be the set of interesting numbers, let z be the set of uninteresting numbers… Then let the product of the set of interesting numbers times 4 be Zzzzz …

Mr. Ed,

1. Russell. OK, understand. Yes, he can count; just that he can’t speak English cause he didn’t go to 2nd grade with me. Check. *g*

1.b. Russell again, this time seriously: You’re absolutely right. In fact, there are obviously at least two different number-names for 111,777: The American one I learned and the English one you folks use. And that’s before we ever get to more exotic tongues, like Ancient Greek.

2. I reiterate: in the mathematical sense, 2 IS “interesting” in that it’s a prime, and in fact the first prime. It has other qualities that make it interesting too, but I grant that to Mom in the grocery store, what’s interesting about “2″ is that it’s the number of extra people she has to feed tonight, and she hopes there’s something edible that she can afford that will serve 6 instead of the usual 4 starving teenagers.

Nick’s comment right before yours–using induction to prove that every integer is interesting–rests on precisely the specialized meaning that mathematicians give to the word ‘interesting,’ in a technical context.

3. I see I forgot to say so, but the business about “you can’t prove a negative” came up over at Samizdata right around Christmas last year, so that was my reference. I hear amazingly many people make that statement, and it’s like nails on the blackboard to me, hence the disquisition. I apologize if I mistook you. :>(

4. LOL

Surely everyone here has heard of the “argument by contradiction” or the reductio ad absurdum, to give it its Latin name.I didn’t think they were the same thing, though. I always thought “reduce it to the absurd” was a handy way (taught to me by my physics teacher at school) to see whether a relationship exists or if you have it pointed in the right direction. For example, if somebody claims a minimum wage has no effect on employment, you can suggest a minimum wage of £1,000 per hour to see that the original statement is bollocks. It doesn’t prove anything about the current level of minimum wage, but it highlights that there is a relationship there of some sort.

I’m with you AndrewWS, I think we should both tip-toe away now and leave them to it. I was taught Maths by a tribe of Borneo Headhunters by the way. A devistatingly simple system, but a tad limited… 1, 2, 3, 4, 5,… then Lots!

But let’s not despair of the younger generation, some of them are well up to the mark…

http://www.dailymail.co.uk/news/article-2584808/Move-Einstein-JANE-FRYER-meets-13-year-old-successfully-built-nuclear-reactor-disused-classroom-school.html

Tim,

Context is all. :>)

Wikipedia, boldface by me:

RAB, I think the solution to that particular one of society’s problems is simple, no?

We simply ban being 13.

PS. Are you sure you learned to count correctly? I thought it goes, “1, 2, 3, many.” What is this “4, 5″ supposed to mean?

This bringing in of extraneous (and doubtless untrue, intended to deceive the enemy) material from what are undoubtedly

fauxheadhunters as if it were actual fact has got to stop.I think they’d been Missionary influenced Julie, corollary Headhunters if you will. They taught them to count to five, but then got bored and ate them.

Ah, I see. Well, that might account for it. I hope they didn’t get to my toes. I’d like to count them to see how many I have today, but then I’d have to take my socks off….

Mr. Ed,

Gosh, I learn something new every day. Two things today! RAB has just informed me as to what happened to 4 and 5, and you have added yet another point to the interestingness of 2. Because it had never occurred to me to think of 2 as a free-rider —

andfree-riding on the oneness of One, yet. Amazing, the chutzpah some numbers’ descendants (ascendants?) have!Four is the first real square and if you look at the spots on a D6 five is a pyramid. life Google mit uns is quite bizarre. The Google calculater doesn’t calculate but does weird things. I once tested it. I typed in “what is the volume of the observable universe in US standard teaspoons”

Well, if I had enough teaspoons and enough “stuff” I could be God. It is that spooky. It knew.

It is quite a lot. But then look-up the number of thermodynamic microstates of a mug of tea… Now that is a big number. Oddly enough Ludwig Boltzmann topped himself. But he did provide basically the only definition of entropy. It is on his tombstone. Like Maxwell’s equations (so gorgeous God Himself couldn’t have grokked them – I did in an attic in Nottingham and it was emotional – I felt like Nikola Tesla – then I went back to playing Civ on my 386).

Entropy is this…

S=k.ln(W)

W or also Omega is the ways. It is the number of ways to arrange all the atoms in a system (such as a cup of tea) so S (entropy) is the same. ln is the natural log (to the base

e. There are vastly fewer stars in the Universe than that. And that is a cup of tea.I meant temperature.

A few years back one of our lovely tabloids caused a peadostyria panic. Some fella in the SW was almost lynched by an angry mob because he was a paediatrician. You see the angry mob couldn’t clock the difference between that and paedophile… Sanity eventually prevailed. But was it depressing? It remined me of a NE local legend that during the Napoleanic Wars a French warship was wrecked off the coast of Hartlepool and the patriotic citizens of that town hung the sole survivor – a monkey because they thought the poor little bugger was a French spy and his monkey-talk was seen as French. Now he was the ship’s mascot and one of the sailors had made him a little sailor suit in French colours. Fast forward nigh on two centuries and the Hartlepudlians regenerate their harbour as a tourist trap and this includes a bronze statue of a monkey hanging from a gibbet. Hartlepool is well known in the NE as a chav town. I mean Newcastle has much to commend it, Sunderland isn’t as bad as you might think*, Durham’s centre is a World heritage site and it boasts a magnificent Cathedral and a fine university. My grandmother (from near Hartlepool) stated that it (Hartlepool) was only famous for the quantity of tripe consumed. And she was very sniffy about it. Rightly so. It makes Blyth look like Monaco. Mind, nowhere comes close to the utter shit-hole that is Siloth in Cumbria. That is another story mind.

Although right next to my bro’s girlf’s flat is abandoned the World’s largest largest collection of placka White Lightning wrecking juice bottles. Actually it is grim. The only fuckers who ever missed Sunderland were the Luftwaffe. I feel ashamed everytime I am back-up in my home territory because Bro’s girlf is from Tokyo – one of the great cities of the planet. As the Yorkshire saying goes, “Hell, Hull and Huddersfield”. Peterlee – dear sweet Jesus of Nazareth – that is an epic crapulation. It is a 1960s new town built around… a Stalinesque brutalist ASDA and a shopping precinct full mof pound stores. And it that stenches of urine.

Point of information, the Luftwaffe did not miss Sunderland, they even machine-gunned the street an acquaintance of mine was walking down aged around 6. The Chester Road and Tunstall Park area of Sunderland is perfectly respectable.

Peterlee, Cumbernauld-on-sea, but just far enough away from the coast to not have the benefit of the sea.