The Hamburg Conjecture: A 98:2 Magical Ratio

The Hamburg Conjecture: A 98:2 Magical Ratio

When my father came to visit recently for my birthday, the topic of his AIDS hospice work in the 1980s came up in conversation somehow.

(To be clear, this wasn’t actually at the party because, you know… downer.)

This was the terrifying dark ages of a genuinely horrible disease. A lot of medical professionals wouldn’t even work with AIDS patients.

Of the instances of hospital infection, the majority of cases were straightforward. A transfusion containing HIV infected blood, needle accidents… that sort of thing.

But there were a couple of instances of infection -about two in every hundred- that just… happened. In one case it happened to someone in a neighbouring ward.

Now if you know anything about optimal virulence you know that vector-borne viruses often mutate toward water-borne transmission. We will likely ultimately live in a world where AIDS becomes airborne. Dad was speculating that rare infections could have been instances of genetic mutation that jumped HIV from vector to water-borne but was caught before horizontal transmission because of hospital best practice around sanitisation and quarantine.

Two percent you say?

As you probably know by now, the Rune Soup Operating Definition of Practical Magic (patent pending) is that practical magic is best understood as probability enhancement. It’s worth revisiting PJC’s words in this matter that were first shared in the Octavo review:

“Thus we arrive at the sobering conclusion that although this universe contains enough Chaos to allow magic it doesn’t contain enough to permit gross miracles in a hurry.

The magician will need to target events which depend on very small energy or entropy changes and the results won’t often look much like spectacular parapsychology, they will look more like a series of events going somewhat improbably in the desired direction.”

The Rune Soup Operating Explanation of Practical Magic (patent pending) is that it’s all in your head… except when it isn’t.

“Except when it isn’t.”

That’s the tantalising bit, yeah? Because Gross Magical Effects (GME) definitely happen. We sometimes get the erroneous impression that they happen more often than they really do. And that’s largely down to the fact that the incidence of non-miracles is impossible to tell apart from everyday life. It may occasionally rain rose petals but mostly it just rains. Remember that when doing you’re doing your rain dance.

Seth Godin mentions this anecdote in Linchpin, as I recall: Planes returning to Britain from bombing raids over Europe during the war were assessed for anti-aircraft damage. Based on this assessment, the wings and fuselage received extra armour-plating which made the planes heavier and less maneuverable. This led to even more planes being shot down.

Why did so-called improvements lead to reduced efficiency? Because the planes they should have been assessing were the ones that had been shot down, not the ones that had returned. By definition the returning planes were the ones that received non-critical damage. (Sidebar: armour-plating belongs around the cockpit. Shooting the pilot brings down a plane.)

Gross Magical Effects are returning planes.

This is a graph that the amazing Taleb dislikes immensely. It’s classic Gaussian Distribution. It describes likely outcomes in what he calls Mediocristan. However there are two types of probabilities, two types of randomness, two types of chaos. From the book:

Assume that you round up a thousand people randomly selected from the general population and have them stand next to one another in a stadium… Imagine the heaviest person you can think of and add him to that sample. Assuming he weighs three times the average, between four and five hundred pounds, he will rarely represent more than a very small fraction of the weight of the entire population (in this case, about half a percent).

You can even get more aggressive. If you picked the heaviest biologically possible human on the planet he would not represent more than, say 0.6 percent of the total, a very negligible increase. And if you had ten thousand persons, his contribution would be vanishingly small.

In the utopian province of Mediocristan, particular events don’t contribute individually – only collectively. I can state the supreme law of Mediocristan as follows: When your sample size is large, no single instance will significantly change the aggregate or total. The largest observations will remain impressive, but eventually insignificant, to the sum.

Hamburg swans are the wrong colour.

Consider by comparison the net worth of the people you lined up in the stadium.

Add to them the wealthiest person that can be found on the planet -say Bill Gates, the founder of Microsoft. Assume his net worth to be close to $80 billion- with the total capital of the others around a few million.

How much of the total wealth would he represent? 99.9 percent? Indeed, all the others would represent no more than a rounding error for his net worth, the variation in his portfolio over the past second. For someone’s weight to represent that share, he would need to weigh fifty million pounds!

Try it with academic citations… media references, income, company size, and so on. Let us call these social matters, as they are man-made, as opposed to physical ones, like the size of waistlines. In Extremistan, inequalities are such that one single observation can disproportionately impact the aggregate, or the total.

So while weight, height and calorie consumption are from Mediocristan, wealth is not. Almost all social matters are from Extremistan. Another way to say it is that social quantities are informational, not physical: you cannot touch them. Money in a bank account is something important, but certainly not physical.

Look at the implication for the Black Swan. Extremistan can produce Black Swans, and does, since a few occurrences have had huge impact on history.

Both types of chaos work for magic because, in order to improve at sorcery, we have to separate out the likelihood of GME (Mediocristan) from our ability to make them happen and the impact that they have. (Extremistan.)

The Gaussian curve measures the likelihood of GME. It does not measure the likelihood of successful enchantment. It serves only to highlight that ‘spectacular’, showy results happen comparatively rarely. Consider this story of the exorcist and how all but five percent of cases are referred to mental health professionals. (Magic is all in your head… except when it isn’t.)

Does that mean the magical goal; “get better in the head”; didn’t work in the other 95 cases? Fuck no! It simply means those cases didn’t involve green vomit and crawling backwards up a wall. In most cases of sorcery, anything on the right hand side of the graph (in this case) is a successful result (“probability enhancement”).

Hence we arrive at:

The Hamburg Conjecture

Magical results increase in spectacularity as the probability of their occurrence as preferred outcome decreases. Spectacularity variance is independent of the sorcerer’s ability to achieve a successful probabilistic outcome.

We seek magical results at the pointy end of the bell curve because that’s how magic is supposed to go. Fire and dragons and towers and orcs. But the Hamburg Conjecture states that, oddly enough, your ability to summon dragons cannot be measured in how often they visibly appear. Reality seems to fray at the edges, whatever you do. (“Rules change in the Reaches.”)

The implications of the Hamburg Conjecture?

  • Don’t rely on GME. I know it’s tempting because dragons are awesome but don’t.
  • If you have to rely on GME, get as far as you can toward the ‘edge’ of the bell curve as possible. Put yourself in the lowest probability environment you can. (If you need a miracle cure then get yourself to the Amazon and start chewing, for instance.) It’s easier to magically jump yourself one standard deviation rather than two.

Why is it the Hamburg Conjecture?

Well, because I’m not smart enough to un-ironically invent ‘laws’. Conjecture makes more sense. Also because there’s a grand tradition of naming conjectures and theories after Central European cities.

But also because it was pieced together on my second-to-last trip to Hamburg. (Sidebar: I accidentally walked into Facebook because they’re the floor below us and the offices all look the same. You have to sign a frikking NDA just to get through the door in London. Working with Germans is so much more fun.)

We had spent the day working with huge numbers that happen to have vanishing small successful outcomes; banner ads. (10% of the internet is responsible for 80% of all clicked ads. And yet that’s what everyone measures. Ridiculous. Have you ever clicked on a banner ad? Exactly.) Moving one of the ad units above the map on certain pages results in literally thousands of additional euros on the bottom line each month. But then you get a higher bounce rate on those pages so total traffic drops which reduces the overall clicks.

So, once again drunk on a plane on a work trip, I’m thinking about all these levers you can use to manipulate the probability of preferred Mediocristani outcomes. Which sounds like a not unreasonable definition of practical enchantment. And then -because I’m slow- the significance of the universality of normal distribution occurs to me.

What if, instead of there being magical numbers per se, numbers actually had magical shapes. Normal distribution, fractals, the Fibonacci Sequence and so on. This appeals to me right now because -for my current ‘science thought game’- I’m temporarily entertaining the vague suspicion that DNA is the only ‘real’ species on planet Earth and we’re all just its side effect on the way to wherever it’s going. LUCA was definitely a virus. So it’s where we all started. A shape rather than a thing. DNA is just a set of rules. (Miraculous, extra-terrestrial rules of such elegance and scale that they can’t not have some form of intentionality.)

But who cares? The only question is… Is there any real-world upside to thinking about magic this way? Does it change the map you use to get to your magical destination? Does it improve your outcomes? Because that’s really what it comes down to in the end, isn’t it?

“It is no secret. All power is one in source and end, I think. Years and distances, stars and candles, water and wind and wizardry, the craft in a man’s hand and the wisdom in a tree’s root: they all arise together. My name, and yours, and the true name of the sun, or a spring of water, or an unborn child, all are syllables of the great word that is very slowly spoken by the shining of the stars. There is no other power. No other name.”

- A Wizard of Earthsea



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  1. 3

    Awesome post! I like the idea of going for broke if you want flashy results. It seems fitting. To me, most practical magic is grounded in the art of small changes, with the option of creating long-term change through accretion or slightly larger immediate changes through aggregation.

    On a side note, it seems that there is another idea ripe for contemplation in the quote that you provide from Taleb: the effects of physicality of target phenomenon on the possible magnitude of magical effectiveness. It would seem that, under the assumption of magic as probability enhancement and Taleb’s dichotomy of probabilities, it would be much easier to create large effects (spectacular results) by applying small changes to social/informational matters than it would be to physical matters. Thus it would follow that some targets are more easily affected than others. In this vein, it would be easier to obtain spectacular results in financial magic (largely a social/informational matter) than it would to physical transform water into wine. Of course, this also assumes that you don’t view the entirety of reality as nothing but information…

  2. 4

    “What if, instead of there being magical numbers per se, numbers actually had magical shapes. Normal distribution, fractals, the Fibonacci Sequence and so on.”

    Bit of a shot in the dark after a couple of pints, but…what if numbers DID have magical shapes, and it turned out that in higher dimensions (fourth, fifth, sixth) they turned out to BE shapes? If numbers had physical form, how would that appear to us in higher dimensions?

    When one has got a fair idea of what a human looks like from a fourth-dimensional perspective—which might perhaps be a bit like what you see in this TED talk at about the 3:17 mark—

    It becomes much easier to visualize numbers that have a magical shape. In fact, it starts to really call into question the limitations of our perception of ourselves as solid objects. What we experience ourselves as is simply a section of a 4-dimensional solid. In much the way a circle is a section of a 3-dimensional cylinder…..

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