Hermione’s Stone (2)

Minus Signs

Hermione’s Stone (according to my alternative plot) was now, it seemed, firmly stuck in some sort of time loop, being picked up, thrown, picked up and thrown ad infinitum. What struck me by the diagram I had constructed, was that for Hermione (and Harry) to undertake this time trick, the universe would comprise of not just two versions of them, but three – the third being themselves travelling back through time. Hermione & Harry (and stone) in reverse, if you will.

If that were so, surely the Universe would, for a period of time (t3+t2) have extra mass, or indeed energy, apparently from nowhere. Energy would not have been conserved.

Can the ‘extra energy’ be cancelled out ? Does the minus sign in front of the t2 and t3, to denote the direction of time travel, play a part ?


Hold on.

If the mass/energy of the Hermione, Harry and Stone travelling back in time was somehow negative, as well as the direction of time travel, that would cancel out the extra mass/energy of the pair now walking forwards in time. It would get round the conservation of energy problem, at least, and not necessitate the creation of a whole new parallel universe.

Is it possible that the act of travelling back in time would require that the object which is travelling becomes a ‘negative mass’ or have ‘negative energy’ (from the perspective of the Universe).

Note it is postulated (ref) that quantum particles can (sort of) travel back in time, borrowing energy from the future, as long as the Universe ‘doesn’t notice i.e. it is over a very short time. It’s related to the uncertainty principle. This gave me some hope and got me thinking beyond Harry Potter’s Universe.

Brain Storm. Random Questions.

Exploring my ignorance, now the brain starts to whir in all sorts of directions…

So what do we mean by ‘negative mass’.Does it have meaning ?

Is ‘negative mass’ linked to ‘negative time’.

Is ‘negative mass’ or ‘anti-mass’ in this context the same as anti-matter ?

If it’s similar to or the same as anti-matter, is it possible that the ‘missing anti-matter’ supposed to be created at the Big Bang has been sent off in the opposite direction, perhaps into a negative-time, into a ‘Negative Universe’ ? (cue Star Trek flashback)… (2)

Does anti-mass result in anti-gravity ?

Does negative mass (or antimatter ?) flow back in time(1) ? If so, how would we know ? Are negative-particles (or antimatter) subject to the 2nd Law of Thermodynamics ? So far, we’ve only made a few sizeable atoms of antimatter for fractions of a second, right ? How does one test antimatter’s properties ?

Would a ‘Negative Universe’, shooting off along the negative time-axis, possess ‘negative gravity’ and push the ‘Positive Universe’ away from it ? (and vice-versa)… inflation, accelerating universe, dark energy, etc. etc. (3)

The Higgs Boson is supposed to be its own anti-particle – would that make it time-invariant ?

Is gravitation time-invariant ? Is time itself an emergent property of some initial conditions or state ?


Questions, Questions

Am I asking the right sort of questions or have I let my imagination run away with me ? Surely, someone has looked at some of these possibilities before. The answer is pleasingly, yes.

Curiously, ten minutes after the thought on ‘time as an emergent property’, Book of the Week ‘Reality is Not What It Seems’, by Carlo Rovelli, popped up on BBC Radio 4, citing research on this sort of thing and quantum gravity. Book promptly ordered for Christmas !

Update: Fascinating book, worth a read, though still leaves us with more questions (as it’s still an area for speculataion and conjecture)

Maybe I’ll look at these more deeply in another post.

Note: The excitement for me is trying to follow the consequences of a set of conditions (even from the realms of fantasy) and seeing were it takes me. What pops up. That in itself is fun. It sparks the brain. I’m even using maths again. The trick has been to be able to put thoughts to one side and come back to them when time and conditions permit. I use a pencil and paper. It’s also interesting to then see if and how my resultant ‘naive questions’ have played out in research – ‘am I barking up the right tree or just barking’.

Update: April 2017, ‘Scientists create effective negative mass’ e.g. The Guardian  ‘under certain precise conditions, normal particles can be made to behave as though they had negative mass’

Update (01.o5.17) Refs: Wikipedia on Negative Mass

  1. In 1970, Jean-Marie Souriau demonstrated, through the complete Poincaré group of dynamic group theory, that reversing the energy of a particle (hence its mass, if the particle has one) is equal to reversing its arrow of time.[14][15] 
  2. Some bimetric theories of the universe propose that two parallel universes instead of one may exist with an opposite arrow of time, linked together by the Big Bang and interacting only through gravitation.[16][17][18]
  3. The negative matter of the coupled metric, interacting with the matter of the other metric via gravity, could be an alternative candidate for the explanation of dark matter, dark energy, cosmic inflation and accelerating universe.[19][20] 

The upshot of research suggests that negative mass cannot coexist with positive mass as it would violate certain conditions. If this is the case, then it would seem that reverse-time-travel is also impossible in a positive universe, if there is a the necessity to create negative mass to achieve it.

I had also been toying with idea of a ‘negative universe’ and it’s effects on ours e.g. missing antimatter, universal acceleration. Some thoughts on this area were presented in the late 60s. More recent analysis (Petit & Agostini, 2014) of this field suggest that a ‘negative universe’ (at least from our perspective) could exist and also have a repelling effect on our ‘positive universe’ contributing to the recently observed  ‘accelerating universe’ effect (from which the term ‘dark energy’) was derived. They also look at large scale voids possibly having negative matter at their centres, but this seems to contradict.

Let us say the questions remain open.

JAH 01.05.17

P.S. And all this from watching Harry Potter !

Posted in Maths, Physics, Space, Uncategorized | Leave a comment

Hermione’s Stone (1)

Harry Potter and the Prisoner of Azkaban

A couple of weeks ago now my family and I were watching said film. We’ve seen it many times so each viewing is an opportunity to spot something new. It was the scene where the our three heroes are in Robbie Coltrane’s cottage and a stone smashes a nearby pot. Hermione picks it up. It is notable by the fossilised ammonite it has. Knowing the story by now, I thought to myself, “I wonder if Hermione puts the stone in her pocket then, later (or earlier), having travelled back in time, she throws it back at herself”.

When we finally reached the scene of throwing, it was clear that Hermione had actually picked up the stone atop a giant pumpkin. OK, problem solved, mischief managed.

But, hey. What if she HAD pulled the stone from her pocket, thrown it through the window, smashed the pot and then her past-self picked it up ?

This raises an interesting question, amongst many:

If this did happen, where did Hermione’s Stone come from ?

[in principle it didn’t need to be the stone, it could have been a clod of earth, or something smaller like a molecule, picked up on her shoe, deposited at the scene, then picked up on her shoe again]


Hermione and the Fossilised Stone

To try to understand this more clearly I drew some sketches on paper, then eventually diagrams in Powerpoint so I could illustrate it here.


You’ll note that I’ve tried to simplify the process’s characteristics, so H is Hermione, s is the stone, ti are time intervals and the arrows represent the apparent flow of events or causality.  By doing this we not only start to understand what might be going on with Hermione’s Stone, s, but also other features. The time t1 is somewhat trivial, but at this point serves to illustrate that stuff went on before the ‘stone incident’.The time represented by t2 is that between picking up the stone and the point at which Hermione spins the ‘Time Turner’ in the infirmary, with Harry. Now, at this point in events the two go back in time ‘rapidly’ to a time t3 before the ‘stone incident’ to allow them enough time to reach the cottage. You’ll note that I’ve initially characterised this as -t2 and -t3, the minus-sign representing the direction of time-travel i.e. backwards. So, now the two have stopped travelling back, they join the ‘normal flow of time’ (or at least that local to Hogwart’s). Time flows forward t3 until the ‘stone incident’ at which point our time-travelling Hermione has released the stone (to be picked up by her former self) and carries on her way with Harry, under the normal flow of time, by t2 then t4. t4 represents an arbitrary length of time after the infirmary, let’s say until the end of the film.

This is the final iteration of the diagram, in which H walks off into the future (and the next film) after time t4, but not necessarily in line with where she came in. Could this be the ‘new universal line’ ?

Stone Circle ?

So what did happen to the stone ?

Well, it would appear that the stone is stuck in some sort of ‘time loop’ or ‘stone cycle’, constantly cycling around between ‘just before the stone incident’, at (t1-t3), and the ‘infirmary time-turning event’ at time (t1+t2), then back again.

Did the stone exist before this point ?

If not, has it been spontaneously created ? (remember we’re in a magical world)

If so, was there an initial cycle, where Hermione picked up the stone, then subsequently recycles the stone, or indeed does she end the cycle in some future iteration, by not putting it in her pocket. Then it gets really confusing. Unless, perhaps at each cycle a new universe is created. Does that work ?

Worse still, in such nonsense, has causality been broken, do paradoxes ensue, are multiple universes created ? In an ammonite’s shell, does it suggest that TIME TRAVEL IS NOT POSSIBLE  ?

(or not in this sense, at least)

That’s ruined the film and Doctor Who for me in one go !


OK, now we’re left with more questions than we started with. But hey.

Conserving the Illusion

For the sake of Doctor Who, let’s assume time travel i.e. going back in time, is possible in some form.

Looking at the diagrams again, what struck me was that during the the period (t1-t3) to (t1+t2) there are more than one Hermiones in the universe (whatever universe that happens to be). There are not only the two Hermiones (and Harrys) walking through the film in ‘the normal flow of time’ but also the Hermione and Harry travelling back in time. There, but in reverse, if you will.

Three Hermiones, three Harrys and up to three Stones !

Hold on. Wouldn’t that break the ‘Law of Conservation of Energy’ ?

(if it exists in the magical universe)


Next on Hermione’s Stone: Minus Signs

Posted in Maths, Physics, Problem Solving, Science, Space, Uncategorized | 1 Comment

MathsJam Show-and-Tell: The Bridges of Cardiff County

The Seven Bridges of Cardiff ?

This is a straight copy of the initial questions I posed at Cardiff #MathJam on Tuesday 20th October 2015, at the ‘Grape and Olive’ pub.

Königsberg: Seven Bridges for Seven Brothers

In 1736 Leonhard Euler was in desperate need of a new idea for that year’s Math Jam Pub Crawl. He happened to be in Königsberg (now Kaliningrad, an exclave of Russia) and wondered if they could visit the inns of the city by only crossing each of its bridges once (no swimming or using boats). However, they could start or finish where they liked.

To simplify things, it didn’t matter what they did on each of the ‘land masses’ they entered (presumably finding the quickest way round their respective hostelries, but that’s another story), so they could be represented by a single point, vertex or node. Indeed once he took this line of thought, each bridge could be represented by a connection or edge (see below).

7BofK7BofK Graph a





“Now we’re getting somewhere. This looks like maths to me!”, he thought. “I shall call this structure a graph”, and Graph Theory was born. Now, on a ‘dry run’ (lemonade only) Euler observed that except at the start and end vertices, for each transitional vertex he could only enter by one connection and leave by another, or, the number of times he entered the transitional vertex equalled the number of times he left i.e. the number of bridges (or edges) must be even for a vertex one doesn’t start or finish on.

“Duh, obvious !”, said his fellow Math Jammer, Dan Bernoulli.

The trouble with Königsberg was that each land mass had an odd number of bridges attached, so no matter which way he looked at it no-one could complete a ‘Eulerian Pub Crawl’. “Hopefully everyone will be so drunk after the first few pubs, my six Maths Jam comrades won’t notice”, he considered.

Given a some wood, paint, a little ingenuity and a bit of DIY, how could this problem have been solved ? 

NB: 100 years later William Hamilton (founder of ’Physics Chutney’) turned the problem on its head. “What about if each vertex only once?”, and the Hamiltonian Pub Crawl was invented. Not that difficult for Königsberg, but more tricky for other graphs.

The Bridges of Cardiff County

It’s long been a contention of mine that Cardiff doesn’t have enough bridges across the Taff.  I thought at the time that there were only 7 bridges, so I enlisted Leonhard Euler to help. Let’s start by looking at a map. There are 3 main rivers slicing through area of Cardiff County: Rhymney, Taff and Ely, giving us 4 land masses, or vertices.

Map cdf

Now the M4 poses a problem. If we cross the Taff from Vertex 2 using the M4, we can only re-enter the city at Culverhouse Cross. This is at Vertex 4, so connection or edge should be drawn from 2 to 4, although the actual bridge crosses from 2 to 3.

River Bridges cdf

P.S. There are in fact 9 bridges across the Taff.

Using this information, can you create an Eulerian Pub Crawl (or Path) across the city?

Answers to come…

There’s a more interesting practical problem. The city not only has river bridges but many railway bridges. If we’ve got enough time the evening I’ll take you through. It creates up to 13 vertices !

Post to come JAH 23.10.15

Posted in Maps, Maths | Tagged , , | Leave a comment

Steel Report: Lecture by New Tata Steel Strip UK Director, Stuart Wilkie (Part 1)

The Newport & District Metallurgical Society held its AGM and new Presidential address last night (24th Sep 2015) at Cardiff University. Stuart Wilkie has held many posts in Tata Steel, the last one of which was a short stint as MD of Cogent Power (my old company). Since the start of the year he has been given the task of running the Tata Steel Strip UK Hub in South Wales, namely Port Talbot and Llanwern steelworks, with approximately 4500 people.

The theme for his address was ‘Transformation & Tata Steel Strip UK’, showing with some detail, the process of business transformation they are currently undertaking and proposing for the next 10 years.

The primary purpose of this post is to get SOME of the observations, thoughts and ideas down while they’re still relatively fresh in my head. There are many more items that could be discussed.

The opening challenge showed us a graph illustrating the relative EBITDA (Earning Before Income Tax Depreciation and Amortisation) of competitors within Europe. Voestalpine (VA) were consistently at the top and positive (‘price high, sell well) and after a dip Tata sister plant in The Netherlands, Ijmuiden (IJ), had also reached similar levels. Strip UK had hit rock bottom in 2011 and remained there since. The question was how had IJ managed to climb back, and how could Strip UK learn from this.

There is a more cutting question of course: Why did a sister plant go through this process of fundamental improvement without it’s UK sibling noticing (or not doing anything about it), but we won’t dwell on that here.

It sounds like IJ had in fact gone through a fairly classic, logical consultant initiated, transformation programme, something British Steel, Corus and now Tata had already gone through on a number of occasions (remember T-Map ?), so what was different ? My impression was that this time the consultants had majored on significant behavioural and organisational change at grass roots and leadership level, hand-in-hand with all the ‘normal’ business improvement activity identified (from voice of the customer analysis to process improvement), in order to make the improvements and improvement culture stick or ‘sustain’. Importantly, a concentration of higher-value products was mooted.

Back to the Future ?

So what have Strip UK done ? Well, they’ve followed the same tack, admittedly (SW) ‘3 years after they should have done’ and got Stuart in to make it happen. The package is called ‘Delivering Our Future’. We were presented with the dense 110 page document of transformation information (fairly typical of McKinsey) with LOTS of great-looking analysis (I suspect at some expense !). It concentrates on: Cost of Liquid Steel, Maintenance, Customer Value, Operations Spend and Other (incl. Energy), in 41 projects, with £1.9Bn of investment (in kit) over 9 years.

The size of the prize ? Well the aim is to increase the EBITDA margin from 0 (zero, at best) to around £70-75/tonne. Supporting this was a re-concentration on and re-organisation around the ‘Trio’ of agents: Production, Technical and Maintenance – very much back to the future – and work on changing mindset (throughout the workforce). For instance, shift managers would be allowed to manage operations, and not spend half their time reporting to the senior managers in order to wait for permission. This leaves the senior mgrs to concentrate on the tactical aspects.

 I’m in favour of this depth of analysis (I’ve been involved before, on a number of occasions and in different environments), but Strip UK have done this many times before, so it comes with the risk of ‘change fatigue’. There also the danger of ‘analysis paralysis’ and overloading the workforce with a raft of detailed information (hopefully story-telling) and initiatives. It sounds like it’s ‘being done to them’ not initiated by them. So much for ownership. All that info was difficult enough for me to take in (and I knew where they were coming from).

Thoughts & Questions

Has the ‘Tonnes Culture’ of UK Strip (particularly Port Talbot in my experience) really disappeared or is it likely to ? A behavioural move from ‘cost cutting’ to genuine ‘value generation’ would help.

Are people at the coal face, where the value is created (or can easily be destroyed) really valued themselves ? Again, deliberate mention by SW of ‘minimum wage guys’ in packing.

Is just canvassing 1600 middle-managers (yes 1600 !) viewpoints on the proposals indicative of the remaining hierarchical nature of this business ?

What happened to the OGSM projects from 2011 I wonder ? I suspect many of the process improvements suggested (or follow-ons) ended up in this document, so maybe just regurgitating well worn benefits.

In part 2 (not published yet):

Customer Value (for Valued Customers ?): Too little, too late ?

UK Steel – SW quotes ‘A Perfect Storm’; Tata pulls the plug on the project.

Not a great place to end the lecture.

JAH 25.09.15

16th October: With ex-Tata Steel facilities at Redcar closing and now, today, 1200 jobs likely to go at Scunthorpe, Dalzell and Clydebridge it looks like the ‘Perfect Storm’ has hit.

Will Port Talbot be allowed to ‘Weather the Storm’ this time round ?

18th January 2016: It appears that the perfect storm has made landfall in South Wales – at least 750 jobs expected to go in Port Talbot and another 3oo around the plot: Trostre in Llanelli, Llanwern in Newport, Orb ? From what I’ve heard this morning, this might just be the opening salvo, a warning shot, if you will, from Tata HQ.

That’s it for now. I’ll try to post part 2 when the dust has settled.

Posted in Business, Business Improvement, Human Behaviour, Leadership, Steel Industry | Tagged , , , , , | Leave a comment

Pythonomics (2): What did the Euro ever do for us ?

Originally written in June 2012. Anything changed ?


Revolution !

Rex is addressing a room of masked Greek MEPs beneath the European Parliament in 2015 …

Rex: We get in through the underground heating system here … up through to the main audience chamber here … and the President’s wife’s bedroom is here. Having grabbed his wife, we inform him that she is in our custody and forthwith issue our demands. Any questions?

Georgios : What exactly are the demands?

Rex : We’re giving him two days to dismantle the entire apparatus of the Eurozone Imperialist State and if he doesn’t agree immediately we will send her to Coventry …   No, Walsall ! [cut to a misplaced scene of the 70s Bull Ring in Birmingham]

Rex: They’ve bled us white, the bastards. They’ve taken everything we had, not just from us, from our fathers and from our fathers’ fathers.

Philip : And from our fathers’ fathers’ fathers.

Rex: Yes.

George: And from our fathers’ fathers’ fathers’ fathers.

Rex: All…

View original post 351 more words

Posted in Uncategorized | Leave a comment

A Blog a Day Keeps the Doctor Awake (030115)

3rd January 2015

I think it’s time to try to redevelop some writing ability beyond that of a somewhat constrained 140 character tweet, so I’m going to use my underutilised blog site to help.

I’ve just started reading Prof. Alice Roberts’ new book ‘The Incredible Unlikeliness of Being: Evolution and the Making of Us’. Even early on, as I am, there are many fascinating insights about the development of various species’ characteristics, and ultimately our own, through an exploration of paleo-embryology and genomics, illustrated by Alice herself. I’ll pluck some snippets out in subsequent blogs, but so far I would say it is a book definitely worth having in your science collection. Tip: Best read in a mild Bristolian accent. Book details here

Interestingly, (for me at least) when Alice popped up on the BBC programme ‘Coast’, I was sure I’d seen her somewhere before. On checking, I found she’d studied medicine and anatomy at Cardiff back in the 90s. I studied my postgraduate degrees here at the time and had remembered her from the throng of student life, particularly the walk to college up and down Penylan Hill, distinctive by her gait and hair colour. Indeed, it turns out she studied in the medical year below my wife’s.

2015 brings the UK General Election to us. There should be plenty to comment on over the next few months.

I may add to the day’s blog as I think of things during the day, but now for breakfast.

Blimey, that’s 250 words, already.


Posted in Blog A Day, Science | Leave a comment

Term & Short Termism

Originally posted a year ago. Anything changed ? #ukmfg


Prompted by the sale of several apparently successful UK engineering and manufacturing firms this year e.g. Invensys to Schneider Electric in August,  I feel that this grow-and-sell behaviour is reinforced, if not driven, by the short-term mindset, still common in British commercial culture and finance.

It is characterised, for example, by:

– An inability to think beyond the next financial or political period – at best 5 years, normally 1 year.

– Consequently little business ‘generational thinking’ is evident

– Re-inventing the wheel (and re-branding it)

– Selling off the foundational elements of what could be robust businesses or indeed sectors or economies, before allowing for them to develop.

– Selling off to outside interests transfers power, decision-making and the future into other’s hands, not necessarily to your own interests.

– Home-grown long-term-thinking manufacturing leaders are few and far between.

– UK Financial leaders & thinkers continue to undermine any greater future for a self-determining UK manufacturing sector.

– Low levels of investment in both the…

View original post 196 more words

Posted in Uncategorized | Leave a comment