Jul 14
martial arts There's been an “elephant in the room” on my blog for quite a while now, and it has prevented me completing a number of articles that I have had in draft for some time.

A bit over a year ago, my friend and mentor, Alan Ruddock died. I've been trying to articulate what that meant for me, and what I thought about Alan, but I have repeatedly failed. This doesn't fully resolve that issue, but at least I can put down some thoughts about Alan here now, or at least about Aikido

Disclaimer: this post probably badly needs some photos, and I'll try to retro-fit that at some point.

I was kindly asked to present an hour at this year's Galway Aikido Summer School, where Alan Ruddock and Henry Kono traditionally taught together for many years. This year Henry continued with his excellent classes in the morning and other instructors that knew Alan took an hour each in the afternoon. I confess I was a bit daunted by some of the others teaching in these slots, particularly the inestimable Lorcan Gogan of PSAC, with whom I shared a session. When I said to him I would have to follow that, he simply replied "Hey, I had to follow Henry!". A fair point. But I did find myself more reticent than usual in my teaching style.

I chose to try and present some thoughts that have arisen from Alan talking about his “dead straight line”. That is that Aikido is often thought of as being circular in nature but Alan was keen to stress it was not at its heart.

In Aikido, we often see uke (the attacker) whirled around nage (the defender) in circles. There are beautiful diagrams about this, and allusion to circles everywhere. Our own club is called the “Belfast Aikido Circle”. So it's impossible to deny circles don't appear. Indeed, there are semi-physical, semi-mystical links to squares and triangles too.

But what Alan meant, in my opinion, (all disclaimers apply) is that you always behaved as if you were operating in a dead straight line.

Aristotle believed that objects, in a perfect (celestial) environment travel in perfect circles, but many centuries later, Newton thought otherwise.

“A body will continue in its state of rest, or uniform motion in a straight line, unless acted upon by a resultant force.”

is better known as Newton's First Law of Motion. In Aikido terms its consequences are simple, if an attacker comes along a straight line, and is subsequently diverted off that straight line, Force, and Energy has been added by someone. Not in some kind of mystical sense of the use of these words you might see in other places, but in their elementary definitions in Physics. So the Force has been added, the big question then is by whom, followed up by why, and an analysis of the consequences.

Let's look at the question of “whom” first. In a previous article, I wrote at some length about the spectator problem in Aikido. Sitting at the side lines you can never know for sure just who is doing what to whom. You can see the nage's hands rise, move or turn, but you cannot know, from outside, whether this is nage initiating these things, or a reaction to uke's movements and attack.

In fact, we can take it a step further than this and say that at best only the two involved can fully know, since it is entirely possible that neither of them will fully know either. In other words, the problem of “whom” is a really knotty one – it's altogether possible that no-one knows.

In theory, at the beginning of a “technique” the nage first moves to a position of safety from the immediate attack and then “blends” with the attack. Even this is an over simplification since nage can be more proactive, but let's set that side for a moment. This moment of initial blending is pivotal. Alan used to tell a story about O-Sensei coming to watch a class of aikido at the Hombu dojo, and after watching, smiling, for some time, he announced “you are all doing a wonderful job, after having your heads cut off.” The analysis of this could be that, especially when facing an armed attack, even if the blend if a “bit out”, there may be more than a “bit” of you missing by the time you start your technique.

Aiki means the harmony of ki, or “energy”, so your blend is the moment where you, and your attacked end in a position of aiki, where both your energies are pointed in the same direction. If the uke's energy was directed at you in a dead straight line, as it often is, then in theory, you should both be pointing in the same dead straight line.

But this is often not the case. You can immediately see deviation from the straight line. Why is this? From Newton, the answer is obvious, one or both person(s) have put extra force into the situation.

This may have been uke, who immediately realising things are not going as planned, starts to react and often turns towards nage to strike them; this being the case nage has to move off the original straight line too to provide space for uke, and to keep the “aiki” principle, continuing to move with the uke. If that's all it is then this is fine. The force and energy being contributed by nage are minimal, it is necessary and sufficient.

But all too often, the honest truth is that as nage, we anticipate the move from uke, or worse don't even think about it, and just start whirling them around us. It may not be immediately clear why this is a Bad Thing. There are two reasons; one is that the aiki principle has been immediately broken, you are no longer in harmony with the attacker but attempting to direct them. The second is why the aiki principle itself matters; when you inject force and energy into the situation a skilled opponent can make use of it. In fact that's practically the central principle of aikido. Probably 90% of the time, particularly in training, your opponent may not even notice, so we all get away with it, and we probably never learn.

So here are some thoughts on training to enforce honesty on this.

Try and do some techniques along a straight line on the mats. You'll need your uke to be initially very well behaved. Don't even think of it as an attack, imagine that you meet a friend at the gates of a park. You see them as they approach and you walk backwards, then sideways, then alongside them as you extend your hand to shake hands with them. They key here is not to make it a conflict. This is astoundingly easy to do when you aren't worrying about having your head punched – just practice the naturalness of this first.

Then, as you walk along your straight line, just allow your hand to rise across the line, the analogy I used as if you are pointing at a squirrel in a tree. It's a simple, gentle irimi-nage that requires a compliant sensible uke who just has to keep walking straight, even into the “throw”.

It's a silly exercise, and you can play with greatly shortening it, but the big deal is, practising doing the throw along a straight line.

The next phase is to allow your uke to, once every so often (and without prior warning), lifting their free hand and turning to – well - lovingly caress your face shall we say? This changes the dynamic, the uke wants to move off the straight line, and so you have to as well. But the key of this exercise is:

  1. do you actually pull them off the line on occasions where they do not turn;
  2. can you really convince yourself you don't move off the line with a little extra force?
It may be a useful exercise.

Another example worthy of note is Shomen Uchi, Ikkyo (tenkan). Or – that when your opponent tries to strike your forehead, you turn, contact their arm and bring it, and the uke to the ground.

Traditionally this is often done by grabbing the arm as it descends and whirling your uke around you. There can be real consequences to this because their other fist is being whirled around you too. There are other problems too – you can have a tendency to pull the arm so closely into your space that uke can merely step behind you and topple you over their leg. It isn't a nice fall. It also provides , ironically, a slow descent of uke into the ground, since you provide them with a lot of implicit support.

So try, from the moment of “Shomen Uchi contact” where your hands meet, to step to the side, and without gripping contact the arm with both hands (the other hand at the elbow). Let your uke continue on their straight line straight forward and downwards. Potentially this is a hard fall, you are providing no force or breaking but just allowing them to sail majestically (potentially teeth first) into the mat. Some care needs be taken with this initially! It is most important that you do not push them down, just act as a ratchet so as they descend they cannot rise.

Again, in real life uke will often start heading towards you early on, trying to recover their balance, and also because in aikido, the tendency for uke and nage to start running around in circles is ever present, and once again, that's fine, the issue is not to interfere with this, but also not to seek to amplify it by hauling them around.

At an early stage you may find it useful not to grab their wrist – this can, in any case, cause all sorts of postural problems – and once you grab something the urge to pull it in is not far behind.

A suitable training for this can be found at your local Supermarket. Find yourself an empty trolley, and as you move it around, you will probably grip it with both hands and pull in one while you push out the other. If you are really mindful to your body you may notice muscles in your abdomen and spine taking the strain. But then fill the trolley to the brim, you will rapidly discover that this trick is not so easy. It's also not so wise, your muscles will shriek in protest at you, and if you do this kind of thing with a large opponent you will likely both be unable to move them, and injure yourself trying.

These are some simple thoughts on the Dead Straight Line that Alan used to talk about. There should always be a delicate positive pressure in that straight line in front of you, so that as things move and the gap appears there you will be immediately slot yourself into it. It is the spike in O-sensei's “Ki” calligraphy; it is the imaginary sword held in front of you that tells you always where you want to go.

Your curved movements are still a succession of Dead Straight Lines.

There is a nice, and relatively elementary parallel from Einstein's General Theory of Relativity. The curved paths that objects like planets make, as commented on by Aristotle appear circular and curved, but actually they are Dead Straight Lines (geodesics) through curved space-time. When the Moon travels around the Earth, it does so in a series of Dead Straight Lines so that it keeps missing the Earth and it perpetually falls towards it. If you do decide to have uke orbit around you, then this is the same principle you need to prevent them spiralling into you, complete with their body weaponry.

But anyway, try playing with Dead Straight Line. I hope you will find it rewarding.

Posted by Colin Turner

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Jun 28
STEM Today, two of my friends independently sent me a story about Tau Day which I had hitherto never heard of. One of them asked for me comment about whether this had any point to it. At first I thought the article was just mathematical trolling, thought about it a bit more, thought there might be a real point to it, thought some more and concluded it seemed rather silly.

The argument is about whether the mathematical constant pi, would be better being replaced throughout mathematics with an alternative tau, which is just twice pi (in other words, replacing pi everywhere with a half of this tau). It's suggested that formulae with tau will be more simple.

Basic Geometry

So this is all about the fact that pi was defined historically as the ratio of the circumference to the diameter of the circle, a very old classical reference stemming back to Greek geometry (incidentally pi is also known as Archimedes' constant since he attempted to calculate an approximation to it). Once upon a time, the formula used in schools would have been:

C = \pi D

related the circumference C to the diameter D. But generally now, we use the radius r rather than the diameter. And so that gives us (for circumference and area):

C = 2 \pi r \quad ; \quad A = \pi r^2

The argument for tau begins by observing the extra 2 in the first formula, and wouldn't be nicer if we just defined tau to be twice pi so that these formula would be so much nicer. Would they?

C = \tau r ; \quad A = \frac{\tau}{2} r^2

Set aside for the moment the fact that pi is probably the most recognisable Greek letter in the world that speaks languages based on the Latin alphabet (aside from those that are, or appear to be the same). Set aside the fact that tau is used for other specific purposes in much of modern Mathematics, and in particular in the discipline of Topology. The first formula might be nicer, but the second one is probably worse, and by enough to make the improvement of the first rather parlous. OK. But the article talks about this being the problem behind radians, so maybe that's where we get the big gain. Let's explore that.

Radians instead of Degrees

There's nothing particularly clever about using degrees. It's an arbitrary choice (360 degrees in a circle) that probably owes a lot to do with historical factors in one civilisation. It is true that when you start to do some significant mathematics with degrees, it starts to look quite unwieldy. The classic two formulae to consider are the length of an arc and area of a sector.

Suppose we have a circle of radius r and we want to work out the length of an arc (a part of the circumference) where the angle subtending this arc is theta degrees (don't panic, no more Greek to come). Then in degrees the formula will be:

s = \frac{\theta}{360} \times 2 \pi r = \frac{2 \pi r \theta}{360}

The reason why is that the fraction on the left is the fraction of the relevant angle out of all the angle available, multiplied by the total arc length available (the whole circumference). The formula is not beautiful, and the similar formula for sector area is also a big ugly.

A = \frac{\theta}{360} \times \pi r^2 = \frac{\pi r^2 \theta}{360}

You will note that in both cases there is a 360 on the bottom of the fraction and a 2 pi on the top. This looks like nature's way of trying to tell us something. What would happen if we used an unit of angle so that, instead of having 360 of them in a circle, we had 2 pi of them in a circle (proponents of tau will just say tau of them in a circle)? The formula, derived using the same logic, become much nicer.

 s = \frac{\theta}{2 \pi} \times 2 \pi r = r \theta
 A = \frac{\theta}{2 \pi} \times \pi r^2 = \frac{1}{2} r^2 \theta

So we get

 s = r \theta \quad ; \quad A = \frac{1}{2} r^2 \theta

Now these are beautiful, elegant formulae, and the underpinning of why radians (the unit of angle we are talking about here) are used instead of degrees in much of higher mathematics, the formula are much simpler (particularly true when using calculus). Also, look at that first formula, it has all the resonance of F = ma. 1 unit of arc length is found in a circle of radius 1 unit with an angle of 1 radian. So beautiful is this that it used as the definition of the radian in many books. So far, so good. Did we really need tau to produce these? Does it matter that it it tau and not pi that cancels out? I can't see why.

Fourier Series

Another example owes to the work of Fourier, who showed that repeating patterns can be broken into sums of the most basic repeating functions, the ones that are most simple are the sine and cosine functions. These are used to model waves of any sort which are of course ubiquitous in nature. It turns out you can build up more odd shapes like triangular and square waves out of these sinusoidal ones. Being able to do this is important in many aspects of Science and Engineering, and eventually this theory leads to all sorts of cool stuff like the way data is compressed in photos and more.

The graphs of Sine and Cosine
The graphs of Sine and Cosine (sin t and cos t)


This graph is labelled in degrees, so you can imagine if we change it to radians as we should then the 360 would become 2 pi. This is where again, proponents of tau will argue that replacing the 360 with a simple tau makes things easier. And it does, if all you want to do is to label that diagram. But the foundation of Fourier theory is building functions up in combinations of these:

 1, \sin t, \cos t, \sin 2t, \cos 2t, \sin 3t, \cos 3t, \ldots

The formulae you need to be able to deal with to do this are (among others):

 a_n = \frac{1}{\pi} \int_{-\pi}^{\pi} f(t) \cos nt dt \quad ; \quad  b_n = \frac{1}{\pi} \int_{-\pi}^{\pi} f(t) \sin nt dt

which I grant, strike fear into the hearts of many. But they don't look nicer with tau (and are a little more awkward):

 a_n = \frac{2}{\tau} \int_{-\frac{\tau}{2}}^{\frac{\tau}{2}} f(t) \cos nt dt \quad ; \quad  b_n = \frac{2}{\tau} \int_{-\frac{\tau}{2}}}^{\frac{\tau}{2}} f(t) \sin nt dt

Remember, the people arguing for tau are claiming it simplifies formulae, not making them look worse.

Euler's Identity

Finally, I cannot leave this without talking about Euler's identity considered by most mathematicians (including myself) to be one of the most beautiful results in Mathematics.

e^{i \pi} + 1 = 0

This result can be written in a few ways, but this way is very commonly used. This is because in this form you can see how this identity connects the five most important numbers of Mathematics: 0, 1, pi, i and e. With tau, it just doesn't have the same beauty:

e^{i \frac{\tau}{2}} + 1 = 0

so I will stick with pi. Thanks all the same.

Posted by Colin Turner

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Nov 15
STEM Last week I wrote a little about the size of black holes, and incidentally discussed very primitive calculations I did on the lifespan of any black hole created by the LHC.

A few days later, this interesting article showed the results of professional physicists on just how little such little black holes could grow, in some cases even if their lifetime was not restricted. Enjoy.

Posted by Colin Turner

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Nov 9
STEM I allowed myself to become rather distracted by my second years last week as the class was finishing. They were talking about an episode of Horizon that discussed General Relativity and theories of Quantum Gravity. What followed was a free ranging discussion on the nature of infinity, mentioned briefly in the program. But we also talked about the nature of a black hole and its size.

It's surprisingly easy to calculate this with reasonably elementary maths and physics. I first did this when I was about 17 (how very sad) using classical physics equations, and was astounded to discover that even so, the answer was correct (I checked it in the Encyclopedia Britannica in the library at the time).

Here is Newton's universal law of gravitation, between two bodies. It describes the force F between two bodies that are r metres apart. Let's take the one with mass M to be the black hole. G is a small (though mysterious) constant.

F = \frac{GMm}{r^2}

You can work out the energy needed to escape the black hole using the old stand by equation that work done is the force times distance traveled against that force, but that only works with a constant force, this force will change as we move, so we need to use the big daddy of multiplication, integration.

 WD = \int_a^b F dr

Specifically, we will work out the energy needed to escape from the event horizon, the surface at which the escape velocity is the speed of light, which is c (299,792,458 m/s). So the energy will be given by moving my little mass m from the radius of the event horizon, let's call is R to infinity, to show we have broken away.

 WD = \int_{R}^{\infty} \frac{GMm}{r^2} dr = \left [ -\frac{GMm}{r} \right ]_{R}^{\infty} = \frac{GMm}{R}

Now, this should just balance the kinetic energy possessed by my little mass m traveling at the speed of light.

 \frac{1}{2} mc^2 = \frac{GMm}{R}

and if we rearrange for R we get that

 R = \frac{2GM}{c^2}

In other words, the radius of the event horizon, the bit we think of as the "hole" is dependent entirely upon the mass of the object. Please note this is based on a very simple model of a non rotating black hole. Nevertheless we can do some nice calculations from this.

The Sun, would have to be compressed from its diameter of about 700 million kilometres into a radius of just under 3 kilometres. The Earth's mass would need to be compressed so much to form a black hole you would need to squeeze its radius of over 6 thousand kilometres into a radius of around 9 millimetres. That's how dense we're talking here.

We can also consider the radius as described by the contained energy of the black hole, since we know that

E=mc^2

and so, replacing our M in our above equation we get

 R = \frac{2GE}{c^4}

Wow. Remember c is a big number, taking it to the power of four is a lot. So why do this? There's been a lot of speculation about the possibility the Large Hadron Collider (LHC) could create a black hole. This has caused a fair degree of panic, and at least one suicide. It's a physicist's dream that a black hole might be created. I just looked up the "high" energies used by the LHC, and high is a relative term. It plans to bash protons together with 7 TeV (Tera electron volts) of energy each, or lead nucleii with 574 TeV each, let's take the latter. Just how much energy is that in a collision? Well, doubling and converting to good old Joules gives 184 micro Joules. That's really not a lot, 184 millionth's of a Joule. A 100W light bulb uses 100 Joules each and every second. How big would the radius of such a black hole that might form be, from that energy? Check the maths, because so far I haven't but I get.

R = 3.040 \times 10^{-48} metres

which is 0.000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,003 metres wide (I hope, I didn't double check the zeros either), which is probably not the planet swallower of people's imagination (but this is fun). But the problem is people think this tiddler will grow very rapidly, but that's because they don't know about Hawking Radiation. This is an interesting quantum effect that means black holes aren't really black, they do emit a little radiation. Large holes would gather surrounding matter faster than their low radiation rate, but small holes have the opposite situation, they radiate more rapidly. The maths for all that is pretty complex, and you need to make lots of assumptions, but the time taken for our little black hole to "evaporate" is (hurriedly calculated by me)

t = 7.21 \times 10^{-79} s

a tiny, tiny fraction of a second. Even allowing for the ambient temperature and some fall in of matter, this little baby is not in equilibrium, it's not getting mass fast enough to accumulate more. It's safe*.


* All disclaimers apply. No liability is assumed for foolish unvalidated experiments done by you or other members of your species. Do not attempt to create black holes in your garage. Any subsequent destruction of your civilization, planet or solar system is at your own risk, and any "EPIC FAIL" signs placed by aliens on the remains is not due to me or my calculation. No calculations have been done on the matter of strange matter either. If you break the planet / system / galaxy or universe you own all the parts.

Posted by Colin Turner

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Oct 4
STEM Derren Brown has been back on our screens recently with a series of big events. It's brought him a lot of publicity, and a lot of the public comment has been amusing to say the least. I've been watching everyone comment on the TV and Radio that he's a trickster, and his explanations of how he does things are often bogus.

Yes.... Yes... That's the point. He's a magician, a showman, he tells you right up front at the start of the show. Misdirection, magic, showmanship and more. It's entertainment. He is the first to make it clear that what he does is a trick. He doesn't claim otherwise. If you can't bring yourself to enjoy that, I humbly suggest you watch something else. And while we are on it, I'm relieved people see it's a trick. I think David Blaine's closeup magic is among the most impressive I have ever seen, and I shudder when those around him don't even seem to consider it's just a trick.

Personally, I love Derren, I love his cheeky smug as hell smile as he gets away with it. I enjoy his faked discomfiture. I enjoy it when he fakes near success in tricks to make them more convincing. I enjoy calling him names as I laugh as he lies through his teeth to the audience. I have casually studied a bit of magic in my time, and he is a fine magician. Many big stage magicians rely on assistants, who actually do all the hard work, but he is clearly the architect of most of his own tricks. I'm reading his book and it is informative and very amusing to me, and I very much respect him as a fellow in fight against (rampant) irrationality (a little bit can be a fine thing).

Sadly I've missed a few of the "events", since it clashes with my Iaido class and I wasn't organised enough to record it. I'm slowly catching up on 4OD. But I did see the program on how he stole the lottery. And I'm a mathematician, and I laughed and laughed at it. I didn't believe a word of it, but even the deceit was cleverly convincing and it's not trivial to say exactly what he really did.

He claims he averaged the results of a crowd of people picking lottery numbers. There's a consequence to this. Consider this: how many ways can 50 people pick a number that averages to 1? How many ways can they pick numbers that average to 30? If you understand this point you'll see the possible "answers" from the crowd have an odd distribution. But the cover story was very amusing in its own right. You don't want to know how he really did it, it'll be shockingly dull.

So yes. We know he didn't show the numbers in advance of the draw. Yes, we know his explanation is nonsense. It's a trick. That's the point. Enjoy it and smile along with his insufferable smugness :-).

Posted by Colin Turner

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Aug 31
STEM The website for Number 10 Downing Street has a new petition calling for an apology for the treatment which led Alan Turing to commit suicide at the age of 41, rather than submit to having his homosexuality "cured" by chemical castration.

Turing was, not only a founding father of Computer Science, but a leading member of the dedicated team at Bletchley Park, who decoded the Nazi Enigma code. This work saved thousands of lives.

As reported on the BBC, the originator of the petition, John Graham-Cumming, is not only suggesting an apology, but a posthumous knighthood for Turing. It would seem the least his country could do for him, after all he did for his country, mathematics and computing.

If you're a UK resident, please consider signing the petition.

Posted by Colin Turner

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Jul 27
STEM New Scientist recently ran an article about steganography. If you don't already know, steganography is essentially encryption with a difference. Specifically, encryption is usually obvious. It may be that the data Alice sends via email to Bob with public key cryptography is entirely secure from eves-dropping by Eve (pun intended, sorry), but Eve will know data is being sent that she might be interested in. Steganography, by contrast, seeks to hide the encrypted data so Eve is not aware of its very existence.

It's a very ancient idea, stretching back to ancient Greece. In modern times a common way to perform the trick is to hide data in an image. One of my more gifted undergraduate students did a final year project on this with me. We used a known password as a seed for a pseudo-random number generator to determine which pixels of the image we would embed the data in. By playing with the least significant bit of one colour in randomly spaced pixels, you can very effectively hide data.

The New Scientist article suggests that if you detect the steganography, and if we obtain the computer of the suspect and if they have carelessly wiped the software, there might be traces that tell you this was done. Now let's remember the whole point of steganography is that the first step is improbable, you most likely won't detect it.

The issue is, in today's geopolitical situation, reasonably serious. It has been suggested (see the wikipedia article I linked above), that such techniques were used to exchange data on site like ebay to plan major terrorist attacks. With lots of analysis software only playing with known algorithms, or relying on comparing modified images with the original (where the original may not be available) what can such a major website do to prevent such abuse? Well, I thought an approach would be to essentially employ the same techniques with random data. That is, randomly poking data into bits in pixels here and there will, up to a certain point, not affect image clarity to the naked eye, but unless the encrypted data is loaded with huge amounts of error correcting code, it will destroy the payload. You could easily automatically run such a filter over uploaded data. I'm sure similar approaches would work for digital sound.

Posted by Colin Turner

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Jul 25
Free Software STEM I hold Richard Feynman in huge regard. He was a fascinating human being, a Nobel laureate physicist, his research in physics was second to none. But he was also a legendary lecturer, in both the fields of physics, and perhaps surprisingly computer science. And even more, he was an exceptionally well rounded person, a gifted artist, an amateur safe cracker and more besides. I own a copy of his lectures on Physics, bought for me by my Mum who felt (probably correctly) that no-one else would buy an item that sounded so boring, though it was on my Amazon wish list. (Incidentally, I think some pages touch on issues like the paradox I presented on crashing cars, I haven't had the leisure to study this more closely).

Recently it was announced (and one of my students kindly wrote to tell me) that Bill Gates had bought up the rights to his lecturers and was making them available. I do praise Bill Gates for his philanthropy, and would have praised him for this, but regrettably, the lectures are only available with Silverlight, and so it's another of a long line of Trojan horses to ensure we buy into a new proprietary standard from Microsoft. A huge shame.

In my last, marathon article, I talked a little about models of reality. A point I didn't make is that we have trouble accepting that; no matter how much we dislike aspects of reality, they remain the same despite that. Feynman encapsulated this beautifully in this YouTube snippet of his QED lectures (which I had showed to my final year students). I have attempted a limited transcript below, but you should hear it in Feynman's excellent good humoured Brooklyn accent for full effect.
And then there's the ... kind of thing which you don't understand. Meaning "I don't believe it, it's crazy, it's the kind of thing I won't accept."

Eh. The other part well... this kind, I hope you'll come along with me and you'll have to accept it because it's the way nature works. If you want to know the way nature works, we looked at it, carefully, [...unsure of this bit...] that's the way it works.

You don't like it..., go somewhere else!

To another universe! Where the rules are simpler, philosophically more pleasing, more psychologically easy. I can't help it! OK! If I'm going to tell you honestly what the world looks like to the... human beings who have struggled as hard as they can to understand it, I can only tell you what it looks like.

And I cannot make it any simpler, I'm not going to do this, I'm not going to simplify it, and I'm not going to fake it. I'm not going to tell you it's something like a ball bearing inside a spring, it isn't.

So I'm going to tell you what it really is like, and if you don't like it, that's too bad.
If you'd like to hear more from this fascinating man, can I suggest more YouTube videos showing an old BBC interview with him:
  1. Part One
  2. Part Two
  3. Part Three
  4. Part Four
  5. Part Five
  6. Part Six

Posted by Colin Turner

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