back to article Boffinry bitchslap brouhaha: Higgs and Hawking head to head

Famous retired physics prof Peter Higgs - of boson renown - has stingingly counter-poohpoohed the theories of his equally well known Nobel Prize rival, Stephen Hawking, who has already poohpoohed Higgs' particle concept. The clash of intellects is expected to be settled by particle-punishment results at the Large Hadron Collider …

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  1. Neil Barnes Silver badge
    Paris Hilton

    the duelling boffinry heavyweights

    Sorry, just wanted to see that phrase again...

    Paris, because she knows what do do with a heavyweight boffin!

  2. Neil Hoskins
    Boffin

    Question...

    I was explaining to the missus that, in a sense, it's more exciting if they *don't* find the Higgs boson, because then they'll have to re-draft the standard model.

    So... she says, does that mean they'll have to spend another fifty billion?

    No, says I, because all those years of data from CERN and Fermilab could be re-examined.

    But hang on. There must have been monstrous amounts of data collected over the years. How much of it has been kept, and how much discarded because it was deemed not to show anything interesting?

  3. Destroy All Monsters Silver badge
    Alien

    What about SUSY, then?

    Vector Bundles at Dawn!

    http://img241.imageshack.us/img241/8962/susyzr5.png

  4. Richard Harris
    Stop

    Huge Assumption

    Of course, there is the possibility that neither of these two "boffins" are correct. Scientists who treat theory like fact are no better than anyone who believes in a religion. It's not a fact if it's based on faith and flimsy rationalisation.

    The last thing science needs is "My God's better than your God" type arguements.

  5. Paul Murphy
    Paris Hilton

    Some of the more interesting things ...

    Have been discovered when people were looking for something else/ accident.

    I'm looking forward to my anti-gravity, zero-point powered, flying car with my sat-nav able to negotiate all 14(?) dimensions.

    Hmm - time for a lie-down now..

    hmm Paris, lie down

    ttfn

  6. Anonymous Coward
    Anonymous Coward

    Boffinry?

    (C'mon Sarah, we know you can't resist a good boffinry every now and again ...).

  7. Mark Vandenbroeck

    If Higgs wins the Nobel prize ...

    ... he'll have to share it with Brout and Englert, 2 Belgian physicists who published their article about a month before Higgs. According to Brout, Higgs even admitted having read their article before he published his.

  8. Matthew

    Hmm

    Hmm, the LHC seems a bloody expensive way of settling a $100 bet.

  9. g00p
    Paris Hilton

    what if..

    ...it is there but they miss the data, or its not even detectable....

    who wins then? hrmmmmmm

    paris, with the quizzical look of nuclear questioning plastered all over her face like concrete...or makeup...I can never tell the difference.

  10. Anonymous Coward
    Boffin

    The answer

    is to not turn on the LHC. Until we do both Hawking AND Higgs are both right. And my cat is both alive and dead.

    Sincerely,

    Schroedinger.

  11. Anonymous Coward
    Anonymous Coward

    Wernstrum!

    That is all.

  12. Liam

    cant we just

    fire them both around and let them collide - the winning scientist is the one that survives?

    exciting times indeed!

  13. Anonymous Coward
    Boffin

    @Neil

    To try and answer your question...

    CERN have a very strange data retention policy. Basically they back up data using in-house software to tape and hope it gets saved. As they collect so much data the loss of one, or more, sample(s) isn't considered significant (unless it's the one with the Higg's Boson in it!!). Recovery is a word and nothing more...

    They try and keep the data for many years so that as new data theories are developed they can re-analyse their data against the new theory.

    One big problem is that tape technology is rapidly changing and they may not have the ability to recover all of the data they want. Also tapes deterioriate and CRC errors can occur effectively destroying a data stream. But, as mentioned, the loss of some data isn't considered significant so they don't really care...

    If only life was so easy in the real world.

  14. apr400
    Boffin

    Answer

    I don't know about elsewhere, but our particle physics group has rooms full of data on film, magnetic spools, dats etc mouldering in the basement.

  15. David Brown

    data storage at CERN

    Surely the data from all past experiments is safe - on 8" floppy disks, in the storage room in the basement.

  16. Damn Yank
    Alert

    Playmobil?

    You're gonna need some more legos...

  17. Britt Johnston
    Joke

    Austrian Rifles

    were reputed to have a 180 degree bend in the barrel: not good for snipers.

    The CERN duelling rules: each professor sits in one of the detection chambers, and fires off a proton shot at his opponent.

  18. Anonymous Coward
    Coat

    "Duelling Boffins"

    Isn't that a piece played on two Theremins?

    *ahem* the one covered in curious particles please....

  19. Graham Dawson

    There's a reason they call it the "god particle"

    The Higgs Boson is supposed to be the "thing" that gives other particles their mass, begging the question... where does it get its mass from? Some other particle?

    The standard model seems flawed to me for this reason alone, the idea that you need some special "particle" to give mass to thing just strikes me as an attempt to fill a hole in the model. A "god particle" of the gaps, you might say.

    You know if they don't find it there'll be about half of them saying the thing is obviously even more elusive than we thought and that they need to build an even bigger accelerator to see it.

  20. Dave
    Alien

    I vote for no Higgso boso

    it seems to me far too trite and trivial that the Grand Theory Of Life The Universe And Everything is all tied up and a done-dusted deal by discovering but 1 particle. What would we do with the hordes of redundant beardie-weirdie particle physicists?? We need two more desktop PC maintenance techs here, but that's about it...

  21. arran
    Pirate

    2 scientists enter

    ONLY ONE CAN LEAVE - LHC TLC SHOWDOWN PPV

    ...

    id pay to watch the two of them beat the snot out of each other... imagine the spectacle of the victor throwing the other into the LHC and...

    wait,

    what would happen if you put someone inside the LHC?

  22. Paul Kinsler

    @Neil Hoskins

    As I recall the torrent of data is so great that the detectors (or ancillary equipment) do event selection in hardware; only the tiny fraction of interesting looking events are logged. Presumably "interesting" is not too closely tied to any particular existing or proposed model, so there'd be a reasonable hope that the recorded data is still useful.

    Disclaimer: I'm not a particle physicist.

  23. Anonymous Coward
    Anonymous Coward

    @ Lewis Page

    Keep up the banter Lewis,

    I always have a good laugh at your pieces.

  24. Mike Sullivan
    Coat

    How do they know what to look for ?

    I mean... some people think it exists... others not. So proton 1 hits proton 2, smaller particles go everywhere... assuming 'new' undiscoverd particle(s) pop up on the scanner... how will they know it is the one their looking for ? Will god vanish in a puff of logic ? will man be able to prove black is indeed white ? Just curious.

    The anti-gravity invisible one...

  25. John A Fotheringham

    Interview from hell

    True story: I once went for an interview (*) where the very first question I was asked was

    "Do you find the Higgs mechanism esthetically pleasing?"

    After a bit of fumbling around I basically said "no", and failed the interview. I've kinda resented it's potential existence ever since So imagine my delight to find that, albeit 20 years late, Prof Hawking has come out in public to back my point of view :-)

    BTW, there is an icon here ( <-- ), it's just that you haven't yet got a monitor big enough to see it.

    (*) The interview was for a a Particle Physics Phd place, so it was probably fair game although most people opened with the more friendly "so you found us alright?" :-)

  26. theotherone
    Boffin

    wot if

    they're both wrong...

  27. Danny

    Taking Bets?

    My money's on Hawking

  28. Simon Painter
    Happy

    Mary Whitehouse

    See that Higgs Boson particle.

    That's *you* that is.

    http://www.youtube.com/watch?v=9UMedd03JCA

  29. Anonymous Coward
    Anonymous Coward

    Big Bang vs Particle Burst

    Before the "big bang" there was nothing, not a single electron. Yesterday, the worlds best super-scientists "pretended" they were looking for a "god-particle". Unfortunately those super-scientists started with matter in this "so-called" experiment. RETARDED! It's ridiculous to think you can duplicate the big bang with matter, when in the beginning, there was no matter; I repeat: "not even a single electron".

    Some scientists have no idea what they are looking for, because they don't know how to ask the 1st question. SAD REALLY!

  30. Anonymous Coward
    Anonymous Coward

    fifty paces

    So how far is a "pace" in a wheelchair?

  31. This post has been deleted by its author

  32. Tim Spence

    Patriotism

    Well I'll be supporting the British entrant, and hoping that the Higgs boson doesn't reveal itself. C'mon Hawking!

  33. DavCrav Silver badge

    @AC

    "Before the "big bang" there was nothing, not a single electron. Yesterday, the worlds best super-scientists "pretended" they were looking for a "god-particle". Unfortunately those super-scientists started with matter in this "so-called" experiment. RETARDED! It's ridiculous to think you can duplicate the big bang with matter, when in the beginning, there was no matter; I repeat: "not even a single electron".

    Some scientists have no idea what they are looking for, because they don't know how to ask the 1st question. SAD REALLY!"

    OK, yeah, whatever. I don't really know where to start...

  34. Sam

    So you can't recreate the big bang with matter because there wasn't any....

    May I be the first to coin the phrase: "'Ere John, it's all gonna bit Heisenberg, innit!"

  35. Marvin the Martian
    Stop

    <The LHC is situated 50 to 175m beneath the surface>?

    I understand the Heisenberg insecurity principle, and I get it that the LHC is stationary. but this is ridiculous.

  36. Jonathan Parkinson
    Pirate

    £10 ON Hawkins

    I have seen his Exoskeleton (And that was in 1997)

    http://www.theonion.com/content/node/39133

  37. Anonymous Coward
    Boffin

    @Marvin the Martian

    It's depth is for shielding purposes, so the results aren't tainted.

  38. Mike
    Go

    Duel in the LHC?

    Reminds me of the joke about the irish firing squad.

  39. Anonymous Coward
    Gates Halo

    Data Retention at CERN

    In the past (when LHC was just LEP), all the data from recorded "events" was backed up on two copies of Cipher tape (3600 bpi). Each truck load of backup sets was stored in two off-site locations, one in the US and one in Gloucestershire, UK.

    With the advent of the LHC plans were afoot to pick a different backup technology, but retain the same off-site storage locations; the chosen backup storage method was Toshiba’s HD-DVD technology and the two-off site storage locations were SecureVault Corp, floor 42 in World Trade Center Building No.2 and the underground storage facility at Tewkesbury.

    These plan are now under revision.

    Bill 'cause his head's so big, the LHC can just about fit on it!

  40. J-Wick
    Thumb Down

    The Standard Model sucks anyway...

    'Empirical' means 'we don't understand it and just keep tweaking the parameters to fit the results as more data comes out'

  41. Peyton
    Happy

    My vote is for Hawking

    He was funny as hell on Futurama... anyone that can laugh at themselves is okay by me - this Higgs fellow sounds like a git

    "Fry: Steven Hawking, aren't you that guy who invented gravity?

    Steven Hawking: Sure, why not."

  42. Anonymous Coward
    Dead Vulture

    @AC 2

    "Before the "big bang" there was nothing, not a single electron. Yesterday, the worlds best super-scientists "pretended" they were looking for a "god-particle". Unfortunately those super-scientists started with matter in this "so-called" experiment. RETARDED! It's ridiculous to think you can duplicate the big bang with matter, when in the beginning, there was no matter; I repeat: "not even a single electron".

    Some scientists have no idea what they are looking for, because they don't know how to ask the 1st question. SAD REALLY!"

    You must have been reading the Vulture Central abridged description of the LHC. I'm pretty sure the unabridged version said the LHC is trying to simulate energy densities a short time AFTER the big bang. I'm no physicist, but I'm pretty sure the term AFTER is significant to the concepts involved.

    Sarcasm warning: Do I need to define "after" verses "before"?

  43. Sam

    So how far is a "pace" in a wheelchair?

    One rotation.

  44. Brian Walshe

    @Marvin the Martian

    The the LHC is big, and the surface above it isn't flat.

  45. Destroy All Monsters Silver badge
    Boffin

    You are off mass shell

    "The Higgs Boson is supposed to be the "thing" that gives other particles their mass, begging the question... where does it get its mass from? Some other particle?"

    Simple:

    http://www.phy.uct.ac.za/courses/phy400w/particle/higgs1.htm

    Complex:

    http://arxiv.org/abs/hep-ph/0703280

    Can't remember whether the neutrino masses are included in there or not. Also, most of the mass of hadrons (protons, neutrons, mesons) comes from their bound energy, namely the supposedly massless gluons gluing the quarks.

  46. Neil Greatorex
    Coat

    @Some of the more interesting things ...

    "Have been discovered when people were looking for something else/ accident."

    Quite right.

    I was looking for my socks this morning, and found a fountain pen!

    Woooaahh, sod Hawkins, Higgs & Heisenberg, that defies explanation.

    OK, I'm gone :-)

  47. Neil Hoskins
    Boffin

    @AC - "before" the big bang?

    Before the big bang there was nothing, not even time. So if there was no time there was no "before". I think you should go off and watch Songs of Praise before you give yourself a headache.

  48. Danny

    In the words of Harry Hill

    There's only one way to settle this...

    FIGHT!!!!!

  49. Gerry

    Creating matter from nothing?

    Ahem, the event under inspection is not big bang but the period shortly after; i.e. fractionally after big bang.

    "The Universe started with a Big Bang – but we don’t fully understand how or why it developed the way it did. The LHC will let us see how matter behaved a tiny fraction of a second after the Big Bang."

    http://www.lhc.ac.uk/

    The distinction matters.

  50. Aodhhan Bronze badge
    Boffin

    Odd bet for Hawkings

    He must be cleaning up his bets a bit. He's been known to bet for a subscription to "Playboy". Even strapped, a man needs porn.

  51. RW
    Joke

    No. 10 Downing just called

    Cabinet has decided that the Higgs boson exists.

    Years ago there used to be a very funny screensaver for Win95 that allowed you to specify different types of "elementary particles"": bosons, tachyons, morons, onions, etc. I wonder what ever became of it?

  52. Sean Nevin

    Re: The Answer

    "is to not turn on the LHC. Until we do both Hawking AND Higgs are both right. And my cat is both alive and dead."

    Yes, but they are also both wrong...

    By the way, I nominate the word "Deiton" to become the official term for it if they do find this so called "lynch-pin" of existence.

  53. john smith

    My Universe

    I say we each created our own Universe 13.7 billion years ago and can probably see our umbilical cord dangling out in space-point of our own big bang Then we are born. And we talk to our neighbours in their Universes. So there are Multiverses alright

  54. Franklin
    Boffin

    Re: data retention . . .

    . . . is not a big deal if they are doing science, since that (ostensibly) requires repeatability, no?

  55. Jerry Bryson

    Particles

    So the Higgs bosun(close). So, if it's Hawking, should it be the Hawking coxswains?

  56. Zack Mollusc

    real crux of the article

    I note that both these very clever chaps showed just how smart they really are by responding to the pooh-poohing promptly.

    "You know, if there's one thing I've learned from being in the army, it's never ignore a pooh-pooh. I knew a major: got pooh-poohed; made the mistake of ignoring the pooh-pooh -- he pooh-poohed it. Fatal error, because it turned out all along that the soldier who pooh-poohed him had been pooh-poohing a lot of other officers, who pooh-poohed their pooh-poohs. In the end, we had to disband the regiment -- morale totally destroyed ... by pooh-pooh!"

  57. amanfromMars Silver badge

    One mans View another man's Vista ..... both Temporal Opinion

    Considering Prof Hawking most unusual Life style, it must be accepted that his own grasp of reality will somewhat unusual and incomplete by virtue of that unique supported existence.

  58. Uncle Slacky Silver badge

    @Danny

    I'm reminded of the Hawking-alike character in "Family Guy".

    "I RULE...I RULE..."

  59. Mr Spoon

    @Richard Harris

    As we're discussing science, I think you meant hypothesis rather than theory. Otherwise you could end up sounding like the ID brigade. We wouldn't want that.

  60. Franklin

    @Richard Harris

    "Of course, there is the possibility that neither of these two "boffins" are correct. Scientists who treat theory like fact are no better than anyone who believes in a religion. It's not a fact if it's based on faith and flimsy rationalisation."

    Which is, of course, why we've built the LHC in the first place--to look for the evidence.

    That's the neat thing about science. We actually look for evidence to support our assertions.

  61. Swee' Pea
    Happy

    God Particle, Weight Loss, Shiney New Toys, and Bets

    I'd LIKE to believe in the mass-donating properties of a particle as an explanation about my own over-mass situation. It seems so elegant compared to the more mundane explanation of too much beer and chip molecules. And I bet there are physically tons of others who want to believe, too. CERN has just turned on the technology to remove the God-particle from protons and they're sitting on a gold-mine.

    Assuming success, it's just a matter of time before late night TV marketers will be offering personal hadron colliders for effortless, in-home use for three easy payments of 29.95 per month (plus postage and handling). Can I order one in advance?

    Oh yeah. The story was about Hawking and Higgs. I guess I just WANT to believe that Higgs finds his particle and proves the God-model and creates a market for in-home hadron colliders so I can have one.

    Of course, if the particle isn't found that won't prove the Atheist-model is correct but it won't create a weight-loss product either.

    Maybe like the SETI project they'll decide that hobbyists could collect and analyze data and they'll* offer in-home colliders to anybody who can cough up 6 easy payments of 39.95.month (plus postage and handling). Then I can have my toy anyway.

    And meanwhile Hawking will have to devise a test device to prove the Atheist-model -- potential for a new toy in 10 - 20 years to replace the worn out the collider.

    Anyway, I'd happily help Higgs and Hawking settle their bet, especially if I could lose a few God-particles in the process.

    *It's hard to say specifically who "they" might be but we see their reps on infomercials.

  62. Anonymous Coward
    Coat

    @marvin the martian

    "Heisenberg insecurity principle"

    i think that's uncertainty principle ..but i'm not sure

    possibly the one on the left

  63. Anonymous Coward
    Anonymous Coward

    Hawking's Nobel.

    Some time in the late 80s the Prof did a series of lectures at Cambridge, called "a short history of the universe". They were popular with the undergrads, and even I managed to attend one or two (unlike the ones that were actually essential to my getting something better than a third). The lecture course, as should be obvious, got turned into a book. The lectures were informal, but the moment the Prof cracked a "joke" about what he was going to do with his Nobel prize money, I thought "he's never going to get one".

  64. Anonymous Coward
    Stop

    Hawking should know...

    ...that you can't prove the non-existence of anything. So there are two possible outcomes: either the Higgs boson exists and Hawking loses his money, or we can't tell and he keeps it (but doesn't win any). So his expected loss is in the region of $50.

    I don't see how someone that smart can be so bad at making bets.

  65. Neoc
    Coat

    Re: What about SUSY, then?

    Ah, if you knew SUSY like I knew SUSY...

    Mine's the HEV with the "Gordon Freeman" nametag.

  66. Scott
    Unhappy

    But absence of proof is not proof...

    What I don't understand is if the LHC *doesn't* find the HB, how does that prove it doesn't exist? It just proves their experiments didn't find it. Finding it is the only sure result, not finding leaves us in exactly the same position.

    Not to mention of course that if they do find it, they will then need to work out what *it* is made of!

  67. Trygve Henriksen
    Thumb Up

    AC@ Hawking KNOWS what he's doing with his bet...

    He knows that if the boson isn't found(and he believes it never will be), he can call or email Higgs as often as he like and ask 'earned that $100 yet?'

  68. Anonymous Coward
    Anonymous Coward

    This big bang thing

    seems like a really convenient explanation for anything that cannot be explained.

    So, how did that happen, well it just sort of blew into existence.

    Yeah, there was nothing and then poof there was something :)

    I have a theory, unfortunately Pratchett came up with it first, but his was a fantasy setting, mine is high tech, the universe didn't start with a bang but a bootstrapping, and the static you hear is just residual noise left over from version 1 drivers.

    I will have my Nobel prize now, no need to wrap it.

  69. amanfromMars Silver badge
    Alien

    Primary Primeviral Infections Pioneering DNA OverActive Malfunction

    "The lectures were informal, but the moment the Prof cracked a "joke" about what he was going to do with his Nobel prize money, I thought "he's never going to get one"." .... By Anonymous Coward Posted Thursday 11th September 2008 22:03 GMT

    AC,

    You wouldn't happen to have a Perfect ReCollection of that Particular "joke" ? In a Quiet Lonely Place is Darkness Oft a Blessing and Mischief an Unnecessary Vice in Sins SuperSubAtomic NEUKlearer EMissions.

    Blame IT on the LHC for the Buzz they have Created for dDelivery of SpinWAIted IntelAIgent Discourse..... Future Matters in the State which Matters ..... Tempestuous Control for FAIR Weather Fare Further Friends.

    If they Deny Responsibility and Accountability, you could always Waste your Time and Everybody's Money Suing. Far better Filling a Fund to Found an Alternate Reality Game Exercising XXXXtraOrdinarily Rendered Control of Multiple Games Scenarios....... 11 Dimensions and Beyond.

  70. Zac Jackson
    Paris Hilton

    @Britt Johnston - Austrian Rifles...

    "... each professor sits in one of the detection chambers, and fires off a proton shot at his opponent."

    Heh! I initially read that as "protein shot". Oh dear lord, the mental images...

    Paris, because... do I really have to explain?

  71. C Ridley

    @Tim Spence

    "Well I'll be supporting the British entrant, and hoping that the Higgs boson doesn't reveal itself. C'mon Hawking!"

    Err... They're, like, both British, innit? (afaik Higgs is a Geordie)

  72. Anonymous Coward
    Thumb Down

    Hawking's gambling problem

    Hawking has already lost one notable bet, over whether black holes destroy information (he had to give the winner an encyclopedia of baseball). Based on his past record, I'd bet against him (although I really don't want an encyclopedia of baseball).

    http://www.newscientist.com/article/dn6193-hawking-concedes-black-hole-bet.html

  73. john smith

    LHC

    I would like to know when LHC is really going to coillide the particles at CERN?

  74. Dave
    Alert

    @Britt Johnston

    I think that you will find most rifle barrels _are_ built on a 180 degree angle, it's angles close to 360 that are the problem.

  75. Anonymous Coward
    Coat

    No mention..

    ..of all this kerfuffle on the BBC Breakfast Show coverage of the turning-on of the LHC.

    I know because I watched it all with the assumption that one of the bemused couch-monkeys hosting the show would be bound to accidentally call it a "Large Hardon Collider" but I was sorely disappointed (and late for work).

    Paris because she certainly understand the turning-on of a large hard..

    ..on second thoughts I'll just get me jacket.

  76. Anonymous Coward
    Anonymous Coward

    @ Tim Spence

    So which one isn't British?

  77. The Inventor

    It will be Hutchins, not Higgs, or Hawking

    They are both wrong. Dr. Tom won't find what his looking for, or evidence thereof. Dynamic Mass is a Hypervector, as is Extension and Time Flow. Each Hypervector works in combination with the others, each Hypervector has available to it 4 degrees of freedom of rotation. This means, in Linear terms, that there is 4 dimensions of Extension, 4 dimensions of Time Flow, and 4 Dimensions of Dynamic Mass, with all four linear dimensions perpendicular to each other. Neutrinos do for Protons, what photons do for electrons, help them change energy levels relative to something larger. As nice and well thought out of a design that the LHC is, it still is configured wrong to 'see' what it is that for which they are looking. They need to be able to determine the angle and momentum induced on a sensor pixel, not just count the particles of a particular energy, they need to include the geometry of the sensor array, 100,000,000 data collectors (if I recall correctly), to see if they get 'bent'. Genertaing an image based on the sensor geometry, and tracking the paths, IMHO, will gain them more and better data with which they would better be able to see what it that for which they are seaching.

  78. Daniel
    Boffin

    God Particle Discovered ...

    ... and says "just bloody leave me alone, will you!"

  79. Anonymous Coward
    Boffin

    @AA Black Holes and Information ...

    Actually, black holes don't destroy information as such, but as they appear to be infinite entropy objects, they simply reduce the data to a very disorganised state (a bit like a Microsoft database product).

    Apparently, if Hawking radiation theory is correct, eventually as they evaporate they will re-emit the data in the form of a collimated stream of radiation — veeeerrrry slowly.

    This way, little problems like conservation of energy and thermodynamics all balance out at the end of time (as soon as that, huh?) and everything will coalesce back to its original state!

  80. Neil Stansbury
    Thumb Up

    @Graham Dawson

    The Higgs particle doesn't have mass per say - it's the Higgs field that particles travel though that coveys mass (allegedly). The standard Model of particle physics says that for every field there must be a commensurate particle - hence the Higgs Boson.

    BTW:

    @ Scott

    In this case the absence of proof is proof. The Standard Model predicts that the LHC should see the reminant particles of the Higgs as it is so short lived. If the predicted particles aren't there the theory is wrong.

    Personally I agree with Hawkins...

    Einstein's Relativity is beautifully elegant, whilst the Standard Model maths runs at 30+ pages of horribly inelegant equations full of kludges fixes & assumptions.

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