My essay nigh Cohl Furey together with octonions has been read past times some 6,000 people, higher than the average, but the relative increase of insufferable trolls – together with bans per article – was much higher than the increase of the number of readers.
Many people oft acquaint the medieval Inquisition equally a textbook illustration of an establishment that was preventing the people from researching together with fifty-fifty talking nigh scientific matters. Many Christian readers dearest to defend or lionize the Inquisition or the Catholic Church together with its officially sponsored thinkers – together with they occasionally assail the likes of Galileo Galilei.
Make no error nigh it, I am squarely on Galileo's side together with I would live on on the analogous side fifty-fifty inward disputes where scientific discipline was represented past times a less shining human being than the founder of science.
However, I observe it increasingly obvious that the Inquisition represented the liberty of thought together with the open-minded approach to arguments relatively to the left-wing activists that have got literally contaminated the whole Planet basis past times 2018.
The Inquisition was trying to save some Catholic theses, dogmas, together with "ways of thinking" that it considered vital for the preservation of the "system of the civilized world". They were exactly wrong: this suppression of the liberty of thought wasn't genuinely skillful – or vital – for the preservation of the civilization. But these protected dogmas were rather special – inward some sense, in that location were exactly several risky statements that researchers should have got been careful about.
For example, inward March, I was rather persuaded that Giordano Bruno was burned for his belief inward exoplanets. The thought that other planets are analogous to basis together with they're exactly floating somewhere, independently of ours, was (and is) real clearly unsafe for the perceived centrality of basis together with thence the centrality of the Biblical God, too.
In the Bible, God said that He was focused on the basis inward 1 means or another. If the basis is exactly 1 many planets that have got nil to do amongst each other together with displace inward rather random directions, it was rather stupid for God to focus on Earth, right? The whole thing is rather stupid... together with people may move on on thinking, it's dangerous, together with Giordano Bruno had to live on burned.
There weren't genuinely also many scholars analogous to Giordano Bruno who were burned for heresies related to statements nigh physical sciences. On give of that, Bruno could live on said to live on an ideologue of a sort, non a pure scientist. But I intend that Bruno was a good, scientifically literate scholar together with many of his statements nigh the construction of the Solar System together with the Universe were genuinely (even) to a greater extent than modern than those of Copernicus, Kepler, together with others. Some of the missions searching for exoplanets etc. should live on named afterwards Bruno – that would live on to a greater extent than appropriate e.g. than Kepler.
OK, the Inquisition was genuinely protecting a few theses that were written at a few prominent places of the Bible. Most other things could have got been thought about. If you lot discussed the atomic theory or its details, people wouldn't fifty-fifty have got a clue which of the competing views should live on considered "the persuasion sponsored past times the Catholic Church" together with which of them should live on viewed equally a potential heresy.
Sadly, it seems to me that the contemporary post-truth, generally left-wing, octopus is significantly to a greater extent than far-reaching together with classifies a huge per centum of the possible statements nigh scientific discipline equally heresies – or, inward the modern terms, equally politically wrong propositions. In some corners, including those claiming to live on scholarly ones, people can't enjoin that in that location is acre no threat posed past times the climate change; all predictions of the apocalypse driven past times the population growth or climate alter or other things have got spectacularly failed; that blacks statistically differ from whites, women from men, together with pretty much whatever ii groups defined past times similar criteria differ from each other inward most respects, sometimes dramatically.
People are harassed for maxim anything that could live on potentially interpreted equally the declaration \(X\neq Y\) for whatever \(X,Y\). And in that location are lots of other forbidden ideas. I intend that the per centum of the forbidden statements is higher than it was during the Inquisition because the acquaint replacement of the Inquisition, the laid upwardly of obnoxious left-wing trolls who occasionally plow a academy or a Soros into their key ally, has defined the entirely politically right statements nigh virtually all topics you lot may imagine.
I could encounter that their fanaticism is genuinely extreme because fifty-fifty the next innocent declaration has been treated equally a heresy:
The Standard Model has no octonionic structures inward it together with existing papers claiming to seek out otherwise are wrong.This declaration has apparently nil to do amongst the politically right dogmas that the left-wing trolls defend past times spamming the "mainstream" newspapers together with comment sections on the Internet. What is the human relationship betwixt octonions together with egalitarianism? Well, the work is that:
Everything has something to do amongst the left-wingers' sensitive points.
The snowflakes are troubled past times basically everything you lot may say. In this particular case, the argue why octonions became a politically sensitive number is simple. Influenza A virus subtype H5N1 deceitful article past times Natalie Wolchover connected the success of women inward science amongst the presence of octonions inward the Standard Model.
The twisted logic of the PC assail dogs thence is: If you lot dare to enjoin that octonions inward the Standard Model is pseudoscientific rubbish, you're also against the women inward science, together with thence you're a sexist chauvinist pig! It sounds incredible that some people are then fudged upwardly to politicize all things inward this means but this is where much of the mankind seems to live on evolving.
(Before I banned every troll inward that thread, I have got verified that every unmarried 1 of them was motivated past times identity politics. Cohl Furey is woman individual but a fair individual doesn't attention together with I have got spent much to a greater extent than fourth dimension past times deconstructing pseudoscience written past times male crackpots than female crackpots then delight give me a pause amongst these ludicrous off-topic accusations together with this insane politicization of algebra.)
Even if in that location were octonions inward the Standard Model, it wouldn't do much for (the rational appraisal of the role of) women inward scientific discipline because Ms Cohl Furey exactly copied all these ideas from the likes of Mr M. Günaydin, Mr F. Gürsey, Mr Geoffrey Dixon, together with perhaps a few others together with everything that she has added is exactly irrelevant would-be technical gibberish that changes nil nigh the story whatsoever. So non entirely legitimate physical sciences but fifty-fifty this particular corner of pseudoscience is overwhelmingly dominated past times men.
But the to a greater extent than of import indicate is that the octonions inward the Standard Model are exactly an erroneous idea. There is nil octonionic nigh or within the Standard Model of particle physics. And there's no \(G_2\), the particular Lie algebra that is the automorphism grouping of the octonion algebra, within the Standard Model, either.
95% of the commenters at the Quanta Magazine – who were happily persuaded that in that location were octonions inward the Standard Model – are non entirely scientifically illiterate. They don't genuinely know how to exercise a search engine on the Internet. Or they exactly didn't have got the thought that they could try. (Well, maybe most of them exactly don't desire to acquire the truth – they prefer the lies they are existence served because they decided Ms Furey is slap-up equally a individual – she's impressive, indeed – or equally a political displace together with the truth nigh Nature is secondary.) Just hold back for octonions together with the "Standard Model" on Google Scholar. You volition acquire papers that are decades old.
The most famous paper inward the search ends upwardly to live on 1 past times our (Frank) Tony Smith, a paper amongst twoscore citations. Tony Smith is great, nil against him, together with I have got for certain described him equally a crackpot, together with fifty-fifty if I haven't, I volition do it right now: Tony Smith is a textbook illustration of a crackpot. Still, his papers have got some standards together with you lot would observe reasons to intend that he's a counterpart of the researchers who is working exterior the Academia.
If you lot supercede the octonions e.g. past times \(SO(10)\), you lot acquire a vastly to a greater extent than impressive list of papers. This listing is 500 times longer together with numerous papers on the kickoff page have got over 1,000 citations. That's what it looks similar when scientific discipline has flora some actual testify that in that location could live on a human relationship betwixt the Standard Model together with something else – inward this case, the \(SO(10)\) grand unified guess group.
You wouldn't demand to hold back for Google Scholar. You could read Cohl Furey's CV or anything. You would observe out that she's been writing basically identical papers since 2010. No 1 has ever done followup enquiry on that because the papers clearly don't brand feel according to physicists. Recently, 1 of the copies of these papers penetrated to a magazine – because of a referee's error or his sabotage – which was plenty for her to acquire a PhD together with set down a job. The thirst for woman individual researchers together with the corresponding affirmative activity has move totally extreme, indeed.
But every sane individual could easily figure out that the physicists intend it's no good, they have got no means how to elaborate on these writings, together with nil tin sack realistically alter nigh the condition of these papers, exactly similar nil could alter nigh the crackpot condition of Lisi's papers despite the amazing hype he received from the media.
Alternatively, you lot may know something nigh grouping theory together with particle physics. When you lot have got a Lagrangian or an equivalent facial expression defining the laws of physics, it is genuinely a straightforward exercise to determine the unbroken symmetry group. The Standard Model has the \(SU(3)\times SU(2) \times U(1) / \ZZ_6\) guess group. Sometimes, in that location may live on hidden symmetries that are broken – such equally the grand unified grouping – or hidden symmetries whose activity is nonlocal or otherwise advanced – similar the Yangian or enhanced guess groups inward string theory. The uncovering of such hidden groups requires some ingenious steps. It's manifest that nil similar that is contained inward Furey's together with similar papers. One needs minutes to banking concern check it for a given paper.
Furey's together with similar papers are an algebrology, if I exercise a Mitchell Porter's term – a counterpart of numerology where symbols for algebraic structures, instead of numbers, are religiously worshiped. But exactly similar inward the illustration of numerology, no actual physical role of the worshiped objects is ever found. What she is genuinely doing is exactly counting the number of components together with imagining that the fields of the Standard Model are labeled past times labels that aroma similar directions inward the octonions or an octonion-like algebra. But if you lot rename some fields or components together with give them names of the puppies, it doesn't hateful that you lot have got flora a human relationship betwixt the Standard Model together with dogs. The illustration of octonions is absolutely identical to the illustration of dogs.
The actual characteristic properties of dogs and/or relationships betwixt dogs (with each other or the residual of the world) aren't reflected inward whatever properties or relationships within the Standard Model. And the same is truthful for octonions inward the Standard Model. So in that location are genuinely no dogs together with octonions inward the Standard Model.
There are many concise arguments that instantly seek out that the efforts to combine the Standard Model amongst the octonions are nonsensical. First, the Standard Model is a quantum mechanical theory where all the observables are (and must be) linear maps. And maps are associative. Influenza A virus subtype H5N1 key, pretty much defining, holding of the octonions is that they are non-associative. So the observables cannot live on octonions. They cannot live on functions of octonions, either.
There could hypothetically live on octonions exterior observables, the octonions could play a dissimilar role. But there's genuinely no known argue why physical objects should brand non-associative partitioning algebras useful. There's no known possible physical application of the principal nontrivial performance within octonions, the non-associative product. Something could hypothetically alter nigh this negative declaration inward the time to come but there's a to a greater extent than down-to-Earth declaration nosotros may live on sure about: Furey hasn't changed anything nigh the physical irrelevance of the octonionic production (yet).
So when she uses the tensor products similar \(\HHH\otimes \OO\), the production has no physical implications. The tensor production \(\HHH\otimes \OO\) looks spicy but at the end, it's entirely used equally a generic infinite \(\RR^{32}\). It's exactly some 32 existent components. The tensor production exists but it inherits no interesting properties from the factors. In particular, the tensor production isn't a partitioning algebra. The octonionic production – which is what makes octonions octonionic – is completely forgotten throughout her papers. So the claim that she has used octonions or flora octonions somewhere inward the Standard Model is exactly a sleight-of-hand, an illusion designed to print those who don't hold back carefully at all.
The octonions have got the \(G_2\) automorphism group, a subgroup of \(SO(7)\). Well, \(G_2\) is for certain non a symmetry of the Standard Model. In particular, fermionic fields of the Standard Model don't cast total representations of \(G_2\). There are many reasons why they don't. The proposal that "\(G_2\) is a symmetry of the Standard Model" is then ludicrously wrong that you lot may seek out it wrong immediately, inward many dissimilar ways.
For example, \(G_2\), similar \(E_8\), entirely has existent representations. So when you lot decompose it to representations of \(SU(3)\) etc., you lot volition e'er observe \({\bf 3}\) together with \(\bar{\bf 3}\) inward pairs. For every coloring triplet, for example, in that location volition live on the antitriplet that has the same handedness nether the Lorentz grouping together with the same hypercharge. But the Standard Model is chiral. The left-handed together with right-handed quarks together with antiquarks (and leptons together with antileptons) behave dissimilar hypercharges. The hypercharge of the fields has a sign correlated amongst the field's existence inward \({\bf 3}\) or \(\bar{\bf 3}\), respectively.
The chirality of the weak nuclear forcefulness was discovered inward a sequence of deep insights inward particle physics one-half a century agone or then (the violation of C,P,CP etc.). Mathematically speaking, these discoveries have got also showed that nosotros demand complex – i.e. non-real, non-quaternionic – representations to depict the fermionic fields. (There are no octonionic representations at all because representations are those of associative groups spell octonions violate the associativity.) This was a (moderate) revolution together with in that location can't live on whatever full-blown counterrevolution because the previous, innocent, left-right-symmetric icon of the Universe was falsified together with the falsification is irreversible inward physics.
So obviously, \(G_2\) was never used equally a grand unified group. It's also small, too. It's ludicrously wrong at many levels. The octonions are a rather sophisticated special algebraic construction but that doesn't hateful that they're relevant for the Standard Model – or anything else inward Nature that someone finds important. They're not.
I have got banned roughly 5 obnoxious trolls who were attacking me personally for maxim that the "there aren't octonions inward the Standard Model together with papers claiming otherwise are wrong or pseudoscience". In fact, I noticed something remarkable (the octonion wars weren't the kickoff context inward which I have got noticed that). They observe the absence of octonions inward the Standard Model so incredibly heretical that they are non fifty-fifty able to repeat my elementary statement!
In practice, almost all these trolls have got distorted – together with incredibly softened – my statements because they would in all likelihood drib dead right away if they dared to repeat my elementary statements. So they claimed that I wrote that the octonions weren't "fruitful" inward the Standard Model together with the time to come may exhibit that the papers weren't important, together with then on.
That's non what I wrote together with what I say. I enjoin that the papers are consummate garbage, they are demonstrably wrong now, no human relationship betwixt the Standard Model together with octonions has been flora inward these papers equally they exist, together with because these are mathematical facts, nil tin sack peradventure alter nigh these facts inward the future. You know, that's 1 of the glorious features of mathematics (and mathematical physics) that 1 may unambiguously together with permanently enjoin that some statements are right together with some statements are wrong – instead of the omnipresent would-be diplomatic fog that the folks from the "humanities" prefer at all times. There's exactly null testify of a human relationship inward her papers together with a competent physicist who is asked to observe octonions within the Standard Model volition destination upwardly amongst the respond "there aren't any", whether or non he is allowed to exercise the existing literature on similar questions.
Well, most actual physics researchers volition acquire out some room for a possible novel uncovering inward the future together with they may conduct a welcoming linguistic communication but when they review the existing papers together with sympathize what is existence said, they volition concord that the uncovering hasn't been made yet.
What's going on is that these fanatical, idiotic trolls are – non then subtly – intimidating us all the time. "You can't peradventure enjoin that this paper is wrong," nosotros effectively hear. At most, you lot may enjoin "you are non completely sure whether this bright paper volition live on fruitful inward the yr 2100", together with fifty-fifty that is an unforgivable heresy.
I am sorry, comrades, but your rules don't apply to me. Furey's together with Dixon's papers on octonions are pure crackpottery, they are completely wrong, the jeopardy that something volition alter nigh this fact inward the time to come is zero, people who advise that these papers have got the same condition equally large papers on string theory are exactly psychopaths, together with your fanatical together with unfriendly defence forcefulness of the indefensible together with your efforts to quiet scientists hateful that you lot are a threat for the civilisation together with the civilisation volition either drib dead inward a deadening expiry or it volition have got to hold back for ways to preclude the cloth similar you lot from spreading on the surface of Planet Earth.
And that's the memo.