IMAGINARY NUMBERS

Next meeting IMAGINARY NUMBERS  on Friday  March 9th
Some  sixteenth century mathematicians found a solution to a problem that had puzzled generations before them: a completely new kind of number. For more than a century this discovery was greeted with such scepticism that the great French thinker Rene Descartes dismissed it as an "imaginary" number.
This name stuck - but so did the numbers. Long dismissed as useless or even fictitious, the imaginary number i and its properties were first explored seriously in the eighteenth century. Today the imaginary numbers are in daily use by engineers, and are vital to our understanding of phenomena including electricity and radio waves We offer part of a recorded discussion on this topic with leading academics in this field….we can then pursue this discussion ourselves.

 

Join us at the, "Salon Meeting Room"

Location: ( map below)

First Floor, 1a Hollybush Place,

Off Bethnal Green Road, E2 9QX
We are across the street from

Bethnal Green Tube Station.

If you are coming from the tube station,

walk under the iron railway bridge.

Hollybush Place is then the FIRST STREET

ON YOUR RIGHT, JUST NEXT TO THE RAILWAY BRIDGE.

The “Globe” Estate agents ( a red painted shop,is right on it’s corner)

You can also take these busses:

8, 106, 254, 309, 388, D3, D6

 

The entrance to the venue is located 10 yards

down Hollybush Place. Go up the stairs to the first floor

and across the roof patio to the Salon room

 

Call if you get lost and we will be happy to direct you :[masked]  4578

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  • Ray W.

    Why don't you post a transcript, or a video of the meeting?

    September 19, 2012

  • Community A.

    Very interesting presentation and lively discussion afterwards.

    March 21, 2012

  • A former member
    A former member

    Dear Peter, this is an open & eclectic discussion group for amateurs as well as corporate professionals as yourself. It is not supposed to be a " rigorous" lesson session which seemed to be what you were trying to offer . Your view that "humans are machines" carried very little weight with the group. All views need to be listened to & are valid since , as we now know, nothing is 100% "provable ?"

    March 14, 2012

  • A former member
    A former member

    A somewhat elementary topic of discussion, and Melvin Bragg (In Our Time) is a totally inadequate introduction to ANY rigorous topic, but it did give rise to a reasonable discussion.... But if the fact that nothing is 100% provable (including the fact that"nothing is 100% provable" lol) means that all views and opinions are equally valid, then indeed all knowledge, and all human endeavor is vain. Sad...

    March 13, 2012

  • Louise

    Really disappointed that I can't make it. Hoping more talks of the same ilk are coming up!

    March 9, 2012

  • lan B.

    Njörl's Saga. (An intermittent, 30-minute long Monty Python sketch. Zeus, l'm too old for this stuff .. )

    March 7, 2012

  • Paul

    This is the longest, most epic thread we have ever had in this group.....

    March 6, 2012

  • lan B.

    Poopa?

    March 6, 2012

  • lan B.

    You want to collate my wisdom, such as it is?

    (What's your name? Boswell?)

    OK will phone you around 8-ish if convenient. lf not ping me back soon and we'll retime it. Apologies for the delay in reply!

    March 6, 2012

  • lan B.

    Right. Well l'm willing to paraphrase and explain and re-explain to anyone should they find my messages or any part thereof confused or confusing.

    (Of course, the complainant will need to tell me WHICH terminology is causing them confusion!)

    Otherwise, l don't think that my GRAMMAR is confusing. Long-winded, maybe, but that's an attempt at precision, if not concision :-)

    March 5, 2012

  • lan B.

    Alas, specialist terminologies abound within any specialist field worth serious consideration, such as knitting for instance. Technical terminology COULD be regarded as a species of data-compression: we don't always have to define everything in terms of logically irreducible primitives every time we ask the baker behind the counter for a doughnut!

    March 3, 2012

  • lan B.

    Logically speaking l guess l'm obliged to agree. However, judgments re general comprehensibility depend of course on prior assessments of the general level of knowledge (or ability) held by the group as a whole -- both of which as you've already pointed out don't necessarily amount to the same thing. ( l could digress enormously discussing the background assumptions implicit even in drawing an over-simplistic dichotomy such as that, but l won't just now. Some other thread, maybe!)

    March 3, 2012

  • lan B.

    (ln answer to your first msge): Yes l agree.

    (ln answer to your second): OK. Enjoy the Tate. What's on? An installation?

    March 2, 2012

  • lan B.

    Apologies that this is going on too much. Someone wandered into the office at the crucial point as l was about to finish the last msge, thus demonstrating the falsity of my claims as to precision! The passage SHOULD have read:

    "and on the whole l like my own approach. Even if such attempts at precision might be perceived by onlookers as unnecessarily pedantic or indeed pompous. (l now await constructive criticism with bated breath.)

    "

    March 2, 2012

  • lan B.

    indeed pompous.

    March 2, 2012

  • lan B.

    it also seems reasonable that an onlooker lacking my own insider knowledge would be best positioned to point out any characteristic STYLE of failure to communicate.

    Sorry. Maybe that's verbose -- windbaggish even. l've grown used to my own habits of written expression and they are as precise as l am able to make them, and on the whole l even if such attempts at precision might be perceived by onlookers as unnecessarily pedantic or (l now await constructive criticism with bated breath.)

    March 2, 2012

  • lan B.

    Otherwise though, if you as a mathematician don't understand my exposition of the derivation of the Minkowski spacetime metric, a reasonable conclusion to draw might be that the fault lies with me. What do you think? Any tweaking of my pedagogical effectiveness (such as it is) would be worth paying attention to, as long as you can be specific about instances in which l've clearly shot myself in the foot in terms of explanatoriness, and if there's some consistent pattern of defectiveness, then

    March 2, 2012

  • lan B.

    .. appropriate. (Beaten by a single WORD. Damn.)

    March 2, 2012

  • lan B.

    buff, lacking any PRIMARY interest in maths, but appreciating its logical perfection and economy of expression. Physics would certainly be unthinkable without it!

    Right. Got THAT off my chest ..

    What should we discuss NEXT by way of considering life, the universe and everything?

    (BTW, l coin a lot of the terminology which l often more typically use within abstract discursive contexts MYSELF. l would be a lexicographer's nightmare. But l think that my coinage is invariably LOGICALLY)

    March 2, 2012

  • lan B.

    .. in the sense that terms need to be precisely defined and used in a tool-like way in order to minimise ambiguity. (The more that philosophers KNOW, the less easy they find it to UNDERSTAND each other!)

    That said, my experience of most professional philosophers during the past 20 years has been that a lot of them are w...ers. (And l seriously don't want to lower the tone as is commonly fojund on perhaps most bulletin boards.)

    lt happens that for most of my life l've been a "pan science"

    March 2, 2012

  • lan B.

    Great! we're getting onto PSYCHOLOGY. (We'll need to open a new thread on the Msge Board.

    l'm bound to agree that as a mathematician you've been dealinmg with what l'd call operational definitions, such that your "doing" and "thinking" actually amount to exactly the same thing. l'm not entirely devoid of such activity myself, because probably my maininterest is what is known in the trade as analytical philosophy. l have a global "take" on "knowledge" which is quite strongly operational

    March 2, 2012

  • lan B.

    ln any case it's now my turn to be genuinely puzzled: you're a mathematician, and in my exchanges with you specifically -- as opposed to during "2 atoms" -- l have only used mathematical terms. (l think!)

    March 2, 2012

  • lan B.

    .. make sense of the physics in a not merely chatty, New Scientist-style, glossy magazine way.

    Once you have the dimensional specification of some measurable and know how to navigate toward some currently unavailable but relevantly connected knowledge, then you have as COMPLETE an understanding as is in principle possible, lMHO.

    (Hope that doesn't sound too pompous.)

    March 2, 2012

  • lan B.

    Well touché then l guess! l felt a bit gormless (as we say oop north) at your patient explanation yesterday concerning your undoubtedly correct mathematical intuition, but the indeed OBVIOUS move which you made:

    "any extension of real arithmetic would have to agree with De Moivre in the integer cases, and with some solution in the non-integer ones"

    ..wasn't at all obvious to ME (because l'm not a mathematician; l just familiarise myself with operations as and when necessary in order to

    March 2, 2012

  • lan B.

    by a light beam -- l don't have to specify "photon" at this juncture since quantum mechanics doesn't enter into the discussion -- in time t must equal c multiplied by that same t. That is, they sum to zero. The taking of the square root of the summed terms gives the expression for the metric and it therefore necessarily involves an imaginary coefficient, as mentioned.

    March 2, 2012

  • lan B.

    Not much for me to say re your own "l've read the 2 atoms thread twice .. " comment, Peter, but as for the Minkowski observation, obviously the complex plane is, well, a plane, but i appears as the coefficient of ct in the metric describing the interval for flat spacetime:

    x + y + z + ict = 0

    because (as you probably appreciate) and as l pointed out to Will, t is treated as a pseudo-spatial scalar along with the straightforward spatial scalars x, y, z, simply because the distance travelled

    March 2, 2012

  • lan B.

    Sorry l've just realised l've been mixing threads. My reply was to something said by Peter about an hour ago in a personal email conversation:

    "The absence of a unique solution for non-integer A is an (important) but ultimately technical detail. The integer case alone is sufficient to establish that no other consistent extension is possible.
    "

    March 1, 2012

  • lan B.

    Thanks Peter

    l'm not man enough to prove the reductio which must precede any conclusion as to the truth of what you say. (No doubt it is true!)

    March 1, 2012

  • lan B.

    [ .. Continued .. ]

    (ln particular, the crucial relevance of complex numbers both to the relativity theories and to quantum mechanics.)

    March 1, 2012

  • lan B.

    .. Yes. The difference lies in the fact that if one gives A a non-integer value then there is no longer a unique solution.

    BTW thanks for your address. Mine is:

    [masked] Have you any preliminary ideas as to how to structure any possible talk? lts content? lts emphasis? Proofs, history, personalities, relevance to physics and technology of calculations employing complex numbers?

    [Continued .. ]

    March 1, 2012

  • lan B.

    Chroist! Wrong tAAA-rget. Oi thote it wuz Paul, but appIRentlt there's another bla-oowk ay-ut there with ENT-ipodean conNICtions.

    ld all ga-oows ter sha-oow that yer shouldn't jamp the gan, igh?

    (Henceforth my msges will revert to containing more sensible content. Apologies for the irrational interlude.)

    March 1, 2012

  • lan B.

    Aa-oow oi forgot! Fair dinkum Abo wavefunction psi symbol you've adopted there, Cobber!

    March 1, 2012

  • lan B.

    Hi Paul

    WlLcome beck! Whoy the SOILence, mite? Help us ay-ut. When the ga-oowen gits raff, the profISSionals cam ay-ud-a the billabong, eh?

    (Apologies.)

    As you know l've always used the msge board but since the exchange started between Peter and myself l've had to use this line instead. Goodbye, lurid italicisations!

    How would you conduct things? lntroduction to the distinction between reals and complex numbers? Leading to a derivation of De Moivre's Theorem?

    Please advise!

    March 1, 2012

  • Oz

    Why not post it on the message board in one post? It's at the top under discussions.

    February 29, 2012

  • lan B.

    EVERYTHING, but it is sufficient unto the predictively accurate purpose at the particular state of scientific knowledge in question.

    Apologies for being unable to be more concise. Apparently it's endemic. l'm an irremediable windbag.

    February 29, 2012

  • lan B.

    .. Which turns out if you suck it and see (as did Minkowski!) to provide exactly the right description of "flat" spacetime at least (as determined empirically!)

    THIS is what l was getting at in the later stages of "2 Atoms" in saying that the maths is obligatorily ALWAYS correct(!), but in "mapping it onto the phenomenology" as l put it we are literally creating a situation analogous to that which holds between an A-Z Street Map and the ACTUAL streets of London. (l.e. the map doesn't capture

    February 29, 2012

  • lan B.

    [Ran out of characters again. This Meetup software is utterly bloody ridiculous]:

    Continuing from immediately previous posting from me: .. And once you've made that move, the expression for the resulting spacetime interval is obliged to sum a negative component, along with each of the 3 x, y, z components. Quite naturally, just as time as an independent parameter is orthogonal to any space axis you like, then so are the imaginary number components ofcomplex numbers orthogonal to the reals

    February 29, 2012

  • lan B.

    Yes l'm in agreement with all you say. (Gratifyingly unusual for most encounters.) l think that the reason for Will's disagreement w. Andrew and l in the 2 Atoms thread stems largely from his seeing the Minkowski metric as totally arbitrary, whereas of course dimensionally speaking multiplication of the time involved in travelling a specific square root of x^2 + y^2 + z^2 as a 4-dimensional extension of Pythagoras' Theorem necessitates multiplying by some v, and the natural choice has to be c.

    February 29, 2012

  • lan B.

    Right. The upcoming one, or later? We clearly have similar views in regard to this particular philosophical position (mathematical platonism) and l take it we agree that mathematical concepts such as "number" are indeed "inventions" but also much more. ln making discveries, mathematicians are exploring the implications of theinterplay of their own axiomatised systems. The situation is exactly analogous to chess, albeit much more universal,and as to WHY the "something else", we could explore.

    February 29, 2012

  • lan B.

    l wholeheartedly endorse your wonderfully accurate appraisal of Melvin Bragg, Peter. :-) (C.P. Snow, roll over!) Regarding future discussions with a little meatier content, yes, that sounds interesting. Maybe we can confer by direct email contact?)

    February 29, 2012

  • A former member
    A former member

    Is this a discussion or a talk?

    February 28, 2012

  • Paul

    A very interesting topic!

    February 23, 2012

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Rafaël

We just grab a coffee and speak French. Some people have been coming every week for months... it creates a kind of warmth to the group.

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